Introduction to Biophysical Methods for Protein and Nucleic Acid Research
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Edited by
Jay A. Glasel Murray P. Deutscher Department of Biochemistry University of ConnecticutHealth Center Farmington,Connecticut
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Cover photo: The 13 subunit of the E. coli replicase, DNA polymerase III holoenzyme, encircles DNA acting as a sliding clamp to tether the rest of the replicase machinery to the chromosome. The two subunits of the holoenzyme are shown in red and yellow. The commercial molecular modeling program "Quanta" (Molecular Simulations, Inc., Burlington, MA) operating on a Silicon Graphics, Inc., Indigo computer was used to produce the Postscript output. For other views of the same structure see Kong, X.P., Onrust, R., O'Donnell, M., and Kuriyan, J. (1992), Cell 69 425-437. Courtesy ofDrs. X. P. Kong and J. Kuriyan, Laboratory of Molecular Biophysics, The Rockefeller University, New York, N.Y., and Drs. R. Onrust and M. O'Donnell, Microbiology Department, Cornell University Medical College, New York, N.Y.
This book is printed on acid-free paper. Copyright 9 1995 by ACADEMIC PRESS, INC. All Rights Reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher.
Academic Press, Inc. A Division of Harcourt Brace & Company 525 B Street, Suite 1900, San Diego, California 92101-4495
United Kingdom Edition published by Academic Press Limited 24-28 Oval Road, London NW1 7DX Library of Congress Cataloging-in-Publication Data Introduction to biophysical methods for protein and nucleic acid research / edited by Jay A. Glasel, Murray P. Deutscher. p. cm. Includes bibliographical references and index. ISBN 0-12-286230-9 1. Proteins--Research--Methodology. 2. Nucleic acids--Research-Methodology. 3. Amino acid sequence. 4. Nucleotide sequence. I. Glasel, Jay A. II. Deutscher, Murray P. QP551.I63 1995 574.19'245--dc20 95-8162 CIP PRINTED IN THE UNITED STATES OF AMERICA 95 96 97 98 99 00 QW 9 8 7 6 5
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Contents
Contributors Preface xi
ix
Chapter I Basic Physical Properties of Proteins and Nucleic Acids Jay A. Glasel
Glossary 1 I. Introduction 10 II. A History of the Concept That Molecules Can Be Very Large III. Basic Properties of Macromolecules 12 IV. Fourier Transforms 48 V. Summary 51 References 51
Chapter 2 Electrophoretic Methods David E. Garfin
Glossary 53 Symbols 55 I. Introduction 56 II. Gel Electrophoresis 57 III. Isoelectric Focusing 86 IV. Immunoelectrophoresis 92 V. Blotting 94 VI. Pulsed-Field Gel Electrophoresis VII. Capillary Electrophoresis 100 References 103
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Contents Chapter 3 Hydrodynamic Methods Walter F. Stafford and Todd M. Schuster
Glossary 111 Symbols 115 I. Introduction 118 II. Analytical Ultracentrifugation 119 III. Sucrose Density Gradient Sedimentation 132 IV. Diffusion 133 134 V. Sedimentation-Diffusion Equilibrium VI. ViscosityMeasurements 140 VII. Resources 143 References 143
Chapter 4 Mass Spectrometry Richard M. Caprioli and Marc J.-F. Suter
Glossary 147 I. Introduction 152 II. Instrumentation 153 172 III. Combined Techniques IV. Applications 174 V. Conclusions 201 References 201
Chapter 5 Electron Microscopy Arthur R. Hand
Glossary 205 I. Introduction 208 II. Principles of Electron Optics 209 III. Design and Operation of Electron Microscopes IV. Methods of Sample Preparation 222 V. Applications of Electron Microscopy in Cell and Molecular Biology 244 References 258
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vii Chapter 6 Optical and Vibrational Spectroscopic Methods Takashi Miura and George J. Thomas, Jr.
Glossary 261 Symbols 266 I. Introduction 267 II. Electronic Spectroscopy 269 III. Vibrational Spectroscopy 286 Appendix 310 References 313
Chapter 7 Nuclear Magnetic Resonance B. W. Bangerter
Glossary 317 I. Introduction 328 II. Basic Principles of Nuclear Magnetic Resonance Spectroscopy III. Experimental Methods for Structure Determination 348 IV. Nuclear Magnetic Resonance of Proteins 359 V. Nuclear Magnetic Resonance of Nucleic Acids 369 VI. Conclusion 376 References 377
Chapter 8 Diffraction Methods Norma M. Allewell and Jaishree Trikha
Glossary 381 Symbols 388 I. Introduction 388 II. Crystals 391 III. Collecting Diffraction Data 400 IV. Calculating Electron Density and Patterson Maps V. Obtaining Phases 415 VI. Building Models 422 VII. Refinement 423 VIII. Evaluating the Model 425 IX. Analyzing the Model 426
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Contents X. Neutron Diffraction 426 XI. Fiber Diffraction 428 XII. Databases 430 XIII. New Directions 430 References 431
Chapter 9 Computational Techniques in Macromolecular Structural Analysis Michael B. Bolger
Glossary 433 Acronyms 438 I. Introduction 439 II. Sequence Homology 439 III. Secondary Structure Predictions of Proteins 451 IV. Computers and Graphical Representations 461 V. Calculation of Structural, Thermodynamic, and Catalytic Properties 471 References 487
Index 491 Computer Program Supplement 507 Instructions for Using the Disk Supplements
508
Contributors Numbers in parentheses indicate the pages on which the authors' contributions begin.
Norma M. Allewell (381) Department of Biochemistry, College of Biological Sciences, University of Minnesota, St. Paul, Minnesota 55108 B. W. Bangerter (317) Department of Chemistry, Yale University, New Haven, Connecticut 06520 Michael B. Bolger (433) University of Southern California School of Pharmacy, Los Angeles, California 90033 Richard M. Caprioli (147) The Analytical Chemistry Center and Department of Biochemistry and Molecular Biology, The University of Texas Medical School, Houston, Texas 77030 David E. Garfin (53) Life Science Group, Bio-Rad Laboratories, Inc., Hercules, California 94547
Jay A. Glasel (1) Department of Biochemistry, University of Connecticut Health Center, Farmington, Connecticut 06032 Arthur R. Hand (205) Department of Pediatric Dentistry, School of Dental Medicine, and Central Electron Microscope Facility, University of Connecticut Health Center, Farmington, Connecticut 06030 Takashi Miura (261) Pharmaceutical Institute, Tohoku University, Aoboyama, Sendai 980, Japan Todd M. Schuster (111) Department of Molecular and Cell Biology, University of Connecticut, Storrs, Connecticut 06268
Walter F. Stafford (111) Boston Biomedical Research Institute, Boston, Massachusetts 02114 Marc J.-F. Suter (147) Chemistry Department, Swiss Federal Institute for Environmental Science and Technology (EAWAG), 8600 Duebendorf, Switzerland
George J. Thomas, Jr. (261) School of Biological Sciences, University of MissourimKansas City, Kansas City, Missouri 64110 Jaishree Trikha (381) Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, Boston, Massachusetts 02115
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Preface
Driven by developments in precision instrumentation, in electronics miniaturization, and in computer hardware and software, and by the growing interest in understanding structures of biomolecules, biophysical methods have entered the working lives of molecular biologists and biochemists in a forceful way. To do state-of-the-art research in many areas of biological science, a student or senior scientist must be aware of what instruments are available, what information can be obtained, what alternatives exist, etc. As an example of just how important such methods can be, most of us routinely use gel filtration chromatography to obtain molecular masses of proteins and nucleic acids with accuracies approaching + 10% (neglecting effects of shape). However, mass spectrometric methods have now been developed that can yield molecular masses of macromolecules to + 0.001%, and in less time. Yet, many graduate students and researchers in the biological sciences lack the mathematical and physical backgrounds necessary to use biophysical procedures fruitfully, and, often, they are even unaware of biophysical tools that they might effectively employ in their research. While many advanced monographs and textbooks that deal with biophysical methods are available, they generally do not serve the needs of those requiring an introduction to the field. This book is meant to occupy niches both as a textbook and as an initial reference source. Not only will it serve the needs of advanced undergraduates and graduate students learning biophysical techniques for the first time, but it also has been designed to provide experienced investigators with enough information about biophysical procedures to enable them to carry out a method on their own or to collaborate with an expert in the field. In neither case do we assume a working knowledge of the mathematics of physical chemistry. The subject areas have been chosen to cover a wide range of the methods most frequently needed to answer current biological problems. Each chapter presents a description of the physical basis of the method, the type of information that may be obtained with the method, how data should be analyzed and interpreted, and, where appropriate, practical tips about equipment and procedures. Mathematics is included at a level to make the methods understandable and useful without being necessarily complete and rigorous. Thus, we hope to provide the basic understanding that will enable a nonphysically oriented rexi
xii
Preface
searcher to begin to speak in a common language with an experienced practitioner. It is our goal to open the field of biophysical methodology to those who might otherwise not appreciate the importance and usefulness of this area for their own biological training or research problems. Biophysical methods are now so numerous that this book makes no pretense of being all-inclusive. We have attempted to include those methods that are in wide use and whose understanding is fundamental to learning about new developments. Other methods are not discussed although they are widely used and were once at the forefront of experimental biophysics. For example, molecular biology could not have advanced to its present stage without the widespread use of radioactive tracers. However, molecular biologists rarely consider the detailed physics behind their use. Furthermore, we are entering an era in which the use of newer nonradioactive methods is rapidly replacing beta and gamma counters. Thus, we have not included a chapter on biophysical applications of radioactivity. On the other hand, some techniques as old as the modern era of physical chemistry are currently undergoing revivals because of advances in instrumentation, and for such methods we have included discussion. In contrast to most biophysical methods, there is one that does not even involve direct measurements on molecules. That tool is computer molecular modeling and graphics. It was not long ago that in some universities computergenerated images of objects were under the administration of art departments. While that era may not be distant in terms of years, in technical terms it is as far away as the middle ages. Tremendous desktop computing power is now available in thousands of laboratories, and computer molecular modeling has emerged as a valuable tool for both research and teaching. The sophistication of modern software coupled with advances in every aspect of computer hardware has brought this about. In addition, many laboratories have physical links between their desktop and remote computers that can serve and receive data and programs. That is, most of us are connected to "the network." Because of the importance and increasing use of the methodologies, a chapter describing computer applications has been included. Inasmuch as a scientific language barrier often exists that prevents many students and working scientists from appreciating what biophysical specialists are talking about, each chapter includes a glossary of terms and concepts. The glossaries contain definitions and sometimes extensive discussion. They are meant for readers who are unfamiliar with the concepts of physical biochemistry. Depending on the subject, more advanced readers may want to read through a chapter with little, or only occasional, reference to the Glossary for that chapter. Glossary items are indicated in boldface type the first time they appear in each chapter. The first, introductory, chapter summarizes the basic properties of macromolecules. It discusses the mass, shape, electrical, and magnetic properties of proteins, nucleic acids, and their components. In particular, this chapter provides the reader with the scientific vocabulary used throughout the book. In addition, it indicates to the reader what aspects of macroscopic behavior are complex and what aspects are simple. The next two chapters concentrate on descriptions of modern versions of venerable techniques used to determine molecular masses, shapes, and interac-
Preface
xiii
tions. Thus, the second chapter, "Electrophoretic Methods," presents a discussion of the modern manifestation of electrophoresis. While almost all biochemists now do some type of electrophoretic measurement in their laboratories, they may not be aware of the breadth of electrophoretic methods and available detection methods. In this chapter, the poorly understood theory of electrophoresis is overshadowed by the empirical methods developed to do electrophoretic experiments. Consequently, this chapter is much more of a "how-to" discussion than any other in the book. The third chapter deals with analytical ultracentrifugation and viscosimetry. Other than in mass spectrometry, nowhere are the new technical developments more evident than in ultracentrifugation. Those of us familiar with the Beckman "Model E" ultracentrifuge, and its bulk and instrumental complexity, marvel at developments that have shrunk the size of the ultracentrifuge to that of a 3' • 3' • 3' preparative ultracentrifuge. Moreover, the new instrument is vastly more "user-friendly," and so is the associated computer analysis of the data. On the other hand, the basic explanations of the behavior of macromolecules in an analytical ultracentrifuge have not changed over the years. In Chapter 3, the description of ultracentrifugation is brought out in a simple way, and is followed by current applications of the method. Viscosimetry is also included because it is an often-neglected, simple technique that can give quick results on certain overall macromolecular properties (e.g., deviations from spherical shape). Chapter 4 describes the theory and instrumentation underlying the exciting developments that have taken place in mass spectrometry within the past ten years. While the theory of mass spectrometry is quite simple, the basis for the production of ionized macromolecules in a vapor phase is certainly neither simple nor completely understood. Consequently, ionization techniques and their respective applications to biophysical measurements are described rather than theoretically analyzed. This chapter presents an extensive discussion of applications of modern mass spectrometry that are of interest to biochemists and molecular biologists. These include protein molecular mass measurements, determination of posttranslational modifications, and the rapidly developing strategies for peptide sequencing. Chapter 5 describes the application of electron microscopic methods to the determination of macromolecular shapes. Electron microscopy has historically been of great use in visualizing overall macromolecular shapes, particularly those of nucleic acids. More recently, electron micrographic images of protein assemblies have been used, via Fourier transform techniques, to obtain macromolecular structures. The fact that this mathematical technique is brought up in two other chapters (Chapters 7 and 8) underscores the necessity for beginners to learn something about fundamental, important, theoretical concepts that can be applied to a variety of measurements. Chapter 6 is the first of two chapters devoted to spectroscopic methods. The basic aspects underlying all spectroscopy are dealt with in Chapter 1. However, Chapter 6 focuses on the application of the theory to electronic and vibrational spectroscopy. The section on electronic spectroscopy deals with measurements that are done regularly in many laboratories, for example, concentration determination of proteins and nucleic acids. However, it also deals with the resurgence in a technique m circular dichroismmthat fell from favor so completely
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Preface
that many younger workers may not know about it, but which now can be very important for assessing protein secondary structure. The discussion also includes applications of fluorescence spectroscopy to biophysical problems. The chapter then goes on to discuss vibrational spectroscopic techniques (Raman scattering, infrared absorption) that can provide information on intramolecular structural details in proteins and nucleic acids as well as information on kinetics of isotopic exchange. This section includes a discussion of the newly emerging field of ultraviolet resonance Raman spectroscopy and its application to proteins and nucleic acids. Chapter 7, the second of the spectroscopic chapters, discusses applications of nuclear magnetic resonance (NMR) techniques to biochemistry and molecular biology. This chapter forms a bridge between low and medium resolution techniques for determining molecular structure (as discussed in previous chapters) and high resolution ones such as X-ray and neutron diffraction measurements (discussed in Chapter 8). Thus, low resolution techniques such as electron microscopic methods can yield some structural information at resolutions of several angstroms. A medium resolution technique such as NMR can be used at present to determine families of structures of macromolecules in solution with molecular masses less than ~ 25,000 daltons. However, X-ray and neutron diffraction can give atomic positions for carbon and higher atomic number atoms to a few tenths of an angstrom in very large, crystallized macromolecules. NMR theory is presented at a beginning level in Chapter 7 with the object of providing the reader with both scientific concepts and vocabulary. The basic NMR experiment can be understood without a detailed knowledge of quantum mechanics. Thus, this chapter places emphasis on giving the reader a basic outline of what different parameters are derived from NMR data and how they are interpreted in terms of molecular structure. In the current era, multidimensional NMR measurements occupy a central role in macromolecular structure determination. The author of this chapter has tried to present a description of multidimensional NMR in a way that a beginner can get a physical picture of what the experiment involves. He then presents typical examples of successful applications of the technique, with particular attention to the magnitude of a project of structural determination. Chapter 8 presents the theory of X-ray and neutron diffraction with as little dependence on mathematics as we thought possible for the chapter to be useful. Furthermore, at least two mathematical concepts, the Fourier transform and phase differences in electromagnetic waves, are discussed in other contexts elsewhere in the book. Therefore, the reader should already be comfortable with the concept. The appearance of this mathematical operation in several chapters of the book emphasizes our basic pedagogical philosophy that physical methods should be approached from a unified fundamental background. For example, all forms of spectroscopy have much in common, and X-ray and neutron diffraction phenomena have much in common with their analogous optical effects. As the database of successfully solved macromolecular structures becomes larger, comparative methods of getting starting structures for new X-ray data are becoming more important, and one such method is emphasized in Chapter 8. The chapter also concentrates on explaining aspects of diffraction theory and experiments that most puzzle beginners in the field. For example, the authors have worked hard at explaining the concepts of the reciprocal lattice and the meaning of resolution in a structural determination.
Preface
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The final chapter of the book concentrates on two separate aspects of using computers, particularly desktop computers, in protein and nucleic acid research. One aspect is obtaining and interpreting structural information. The other is the current state of predicting macromolecular structure. The former is of great interest because of hardware and software advances that have made it possible to access large structural and sequence databases. With such access, it is possible for workers to compare their own structural information with that of previous structures. The author of this chapter has concentrated on how the database information is obtained over the network and how the data so obtained are analyzed. Theory and practice in prediction of aspects of macromolecular structure are also discussed at a beginning level in this chapter. Many of these methods are being used in ways that may seem insidious to a beginner. For example, as discussed in Chapter 8, after a structure has been "solved" using all available X-ray data, it has become customary to subject the structure to energy minimization on a computer to "anneal" the structure into a more physically realistic one. In some cases, this may move many atomic centers by angstrom distances. The same methods are being used to determine model conformations of, for example, antigen-antibody interactions. In this case both components are annealed using a theoretical treatment and then molecular modeling is used to fit the two structures together. A special feature of the book is the inclusion of supplementary Macintosh and MS-DOS/Windows disks. These disks contain the molecular modeling programs MAGE and RasMol along with sample data files used to obtain some of the figures in Chapter 9. These programs can be used to build and display new structures or display structural data obtained from databases such as the Protein Data Bank. Therefore, the programs pertain to data obtained by X-ray diffraction, neutron diffraction, and NMR spectroscopy. In addition, several journals now store structural information from published articles in their own databases. These may be obtained via the Internet and displayed using MAGE and RasMol. We have found that contemporary students adapt rapidly to the use of these programs and gain valuable structural insights from the calculations, such as intermolecular distances and angles, available within the programs. It is hoped that this volume will prove useful to both students and established investigators, and that it will foster greater interaction between the biochemical/molecular biological and the biophysical communities. We thank the class of 1994, "Biophysical Methods 366, University of Connecticut Health Center," Yingqun Huang, Steve Wiltshire, and Debbie Sardinha for their critiques and suggestions for selected chapters.
Jay A. Glasel Murray P. Deutscher
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GLOSSARY Absolute temperature
Absolute zero is the temperature at which atomic and molecular translational motion ceases. Temperatures above this are given in degrees Kelvin (K). The absolute zero is 273.15 K below the freezing point of pure water at 1 arm pressure, i.e., 0~ is 273.15 K.
Activity coefficient
Activity coefficients are parameters that relate the thermodynamic activities of dissolved molecules to their physical concentrations. When molecules or ions in solution are far enough apart so that no mutual forces are exerted on one another, they follow the thermodynamic laws of ideal solutions. In a solution, the chemical potential of species i,/~i, is given by [d,i =
(3G/3ni),
where ni is the n u m b e r of moles of molecular species i and G is the total free energy of the solution. That is,/~i is the partial molal free energy. In an ideal Introduction to Biophysical Methods for Protein and Nucleic Acid Research
1
Copyright 9 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.
Jay A. Glasel solution jU, i =
jU, i, 0 -4-
R T In
x i,
where xi is the mole fraction of the species i, R is the universal gas constant (see
physical constants), and T is the absolute temperature. The term/zi, 0 is the chemical potential of the species under a defined standard condition. In a nonideal solution (e.g., a concentrated electrolytic solution), a function, the activity, must be introduced in place of xi to account for deviations from ideality. The activity, ai, is defined by a i = fixi~
where fi is the activity coefficient. Then, jU, i =
/d,i, 0 -}-
R T In x i
-4-
R T In fi = [d,i,o q- R T In a i.
The activity coefficient is, in general, a function of the composition of the solution. Theoretical treatments of nonideal solutions, such as the Debye-Hiickel theory, attempt to predict experimentally determined activity coefficients.
Boltzmann's distribution law This distribution law stems from statistical mechanics (i.e., the theory of the behavior of large numbers of mass-particles in gas, liquid, or solid phases). It describes the population distribution of allowed energy states for the mass-particles. As derived by Ludwig Boltzmann in 1886, the law states that if No is the number of molecules in any given state, the number N in a state whose potential energy is AE above that of the given state is N = No e x p ( - A E / k T ) , where k is Boltzmann's constant (k = R / N , where N is Avogadro's number). Although derived without regard to quantum mechanics (which had not been discovered in 1886; see Quantum mechanics: electrons and photons), the law applies to populations of molecules with quantized energy states.
Brownian motion This term refers to random motion of small particles suspended in a fluid. The motions are caused by statistical fluctuations in the net m o m e n t u m exchange between the molecules of the fluid and the suspended particles when they collide with each other. Another term used to describe a r a n d o m process such as Brownian motion is "stochastic." Chirality If a molecule cannot be superimposed on its mirror image it is said to be chiral, a word that is derived from the Greek word for hand. Hands are chiral objects because right and left hands have a nonsuperimposable mirror image relationship. Molecules that have the same molecular bonding skeleton, but differ in the absolute arrangement of atoms in space, are called stereoisomers. Stereoisomers that are related as object and nonsuperimposable mirror image are termed enantiomers. The fact that an enantiomeric stereoisomer can exist in a variety of conformations (three-dimensional geometries) does not destroy the enantiomeric relationship. That is, it is not possible to interconvert distinct enantiomeric isomers by free rotations about single bonds. A fundamental principle of organic chemistry is that a tetrahedral carbon atom with four chemically distinct substituents (an "asymmetric" carbon atom) within a molecule will result in enantiomeric forms. Each such carbon atom
Chapter I Basic Physical Properties of Proteins and Nucleic Acids forms a separate chiral center within the whole molecule. A section of a macromolecule, or a whole macromolecule, can have chirality in the same sense that right-handed and left-handed screw threads have overall chirality. The basis of the contribution of optical rotation and circular dichroism phenomena to biophysical measurements lies in the chirality of macromolecules in different conformations. Debye-Hiickel theory This widely accepted theory predicts the thermodynamic properties (i.e., parameters such as activity coefficients) of d i l u t e electrolytic solutions. The theory begins with recognition that Coulomb's law gives the electrostatic force acting between individual pairs of electrically charged particles suspended in a medium as F = ele2/if.Y2 t where el and e2 are their respective electric charges, E is the dielectric constant of the medium, and r is the distance between the charges. This force is called a long-range force because it decreases only as 1/r 2 (a very short-range force would decrease, for example, as 1//.6 t o 1//'12). In an electrolytic solution containing highly dissociated salts, even though the ions are well separated, the total effect of all the other ions present on the potential energy of a given individual ion is large because of the long range of coulombic forces. The influence may be calculated for very dilute solutions of simple electrolytes by an approximation developed by P. Debye and E. Hfckel in 1923. The central result of the approximation is that the electrostatic energy is a simple addition to the free energy of the collection of ions. If we consider various kinds of positive and negative ions of charge z i e (where z i = q- 1, + 2, etc., depending on the charge on the ion) at concentrations ni and e is the electrical charge of the electron in coulombs (C), the approximation predicts that the electrostatic energy per mole of ions is
1
E = --~ z 2 e2KN/E,
where N is Avogadro's number and K is given by 1
K =
8r
~ l'liz2
]1/2
.
In this expression for K, the term 89 ~ Ciz2 is known as the ionic strength and is usually given the symbol L and ci is expressed in molarity of ions of a given species. Using this additional electrostatic energy formulation, various thermodynamic relations can be derived. For example, an important thermodynamic parameter is the activity coefficient fi for an electrolytic solution. The natural logarithm of the activity coefficient of an ion in a d i l u t e s o l u t i o n , on the basis of Debye-H6ckel, is given by In fi = - z a e 2 K N / 2 E R T .
Jay A. Glasel
Thus, In fi is proportional to the square root of the ionic strength. It is customary to define an activity coefficient of a salt in terms of the separate activity coefficients of its constituent ions. According to this convention, for a uni-univalent electrolyte (where both positive and negative charges are univalent) the activity coefficient takes the form f+ = (f+ f_)1/2. For a uni-univalent electrolyte, the logarithm of the mean activity coefficient is, numerically, - In f§ = 0.51(I) 1/2,
and for the more general case, - In f_+ = 0.51z+z_(I) 1/2. These results are collectively called the Debye-H6ckel limiting law for the activity coefficients in dilute solutions. Deviations from the limiting law are small below ionic strengths of approximately 0.01 M. Dielectric constant Basically, this constant is used to derive the change in coulombic force between two charged bodies when they are separated by substances instead of by a vacuum. In electrical theory, the dielectric constant is defined as the ratio of the capacitance of an electrical capacitor (e.g., two parallel conducting plates separated by a small space), when the space between its plates is filled with a substance, to the capacitance when the space is a vacuum. The capacitance is the number of charges per unit area the plates can store. When the electrostatic force between the plates is high, the capacitance is high. The dielectric constant of a substance is related, at the microscopic level, to the polarizability (how easily the electronic charge cloud surrounding the nuclei can be distorted by an electric field) and the molecular dipole moments (see Moments: Electrical and magnetic) of its molecular constituents. Dielectric constants are large for liquids made up of polar molecules and, conversely, are small for nonpolar ones. Dielectric constants are relatively easy to determine experimentally. Isoelectric point The isoelectric point for a macromolecule is the pH at which its formal net charge is zero. At its isoelectric pH a macromolecule will undergo no net motion toward either pole when subjected to an electric field (as in an electrophoresis experiment). If the isoelectric point of the macromolecule lies between pH 4 and pH 10, and the macromolecule combines only with hydrogen and hydroxyl ions, its isoionic point and its isoelectric point may be very close. The isoelectric point may be found experimentally from a titration experiment, which consists of measuring the number of hydrogen ions (H +) dissociated per macromolecule as a function of pH. Isoionic point The isoionic point for a macromolecule is the pH of a macromolecular solution when the solution contains only the macromolecule and ions arising from the dissociation of the solvent. For example, a solution of a macromolecule in deionized water can be made isoionic by exhaustive dialysis against deionized water. The isoionic pH may be found experimentally by per-
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
5
forming the dialysis and measuring the pH of the resulting solution.
Magnetization Starting at the subatomic level, magnetization is the production of macroscopic magnetism by bringing about alignment of a large number of nuclear a n d / o r electron magnetic dipole moments. Sometimes this is spontaneous. For example, electrons in certain types of iron crystals will spontaneously align with their electron magnetic dipole moments parallel to each other. The total macroscopic magnetic moment is the vector sum of the individual electron magnetic dipole moments. This is ferromagnetism, and its macroscopic manifestation is a magnet. In other cases the submicroscopic permanent magnetic dipoles require external magnetic fields to bring about their parallel alignment of the dipoles. The alignment is called paramagnetism and the vector sum is called the induced macroscopic paramagnetic moment; the alignment is lost when the external field is removed. Later in this chapter a second type of external field-induced macroscopic magnetism is discussed. This is called induced macroscopic diamagnetism. Diamagnetism is a property of all atoms or groups of atoms. It results in antiparallel alignment of the induced moment with the external field and is lost when the external magnetic field is removed. Because nuclear and electron magnetic dipole moments are associated with properties of the particles called intrinsic spin, they behave dynamically like magnetic tops (i.e., like bar magnets spinning around their long axes). Moment of inertia Moments of inertia are dynamical parameters that relate to the forces necessary to accelerate a three-dimensional body in radial directions. Moments of inertia are therefore involved in the analysis of rotational motions of molecules. The moments of inertia are defined for a rigid body made up of point masses mi at coordinates xi, yi, zi (in a cartesian coordinate system) that are rigidly joined together. For example, the quantity, Ix, where Ix = E mi(y 2 + Z2)
(the symbol ~ denotes a summation over all the particles of the system), is called the moment of inertia of the body about the axis 0x. For a spherical body there are three moments of inertia (one about each axis) and they are equal. In a general x, y, z coordinate system undergoing rotation and translation with the body, the moment of inertia for an irregularly shaped, rigid body is expressed by a mathematical function with nine parameters, as opposed to the three for a spherical body. Fortunately, however, a rotation of the coordinate system can always be found (called the principal axis transformation) in which only three moments of inertia are required to describe rotational motion about the center of mass (taken as the origin of the coordinate system) for even an irregular shape. The description of rotational motion about these axes is important for understanding rotational Brownian motion (also called rotational diffusion), which is at the heart of interpretation of nuclear magnetic resonance relaxation times and the Overhauser effect described in Chapter 7.
Moments: Electrical and magnetic Electrical moments are defined by spatial arrangements of positive and negative electrical charges. Contrary to magnetic moments (see below), isolated positive or negative electrical charges can exist. The electrostatic fields surrounding isolated electrical charges are spherically symmetrical, and are given mathematically by Coulomb's law.
Jay A. Glasel
Technically, an isolated charge is called an "electrical monopole." An electrical
dipole exists whenever there are two equal charges of opposite sign separated by
a distance d. The electrostatic field surrounding an electrical dipole is highly directional in space but can be expressed in simple mathematical form at distances that are large compared to d. A molecular dipole moment, P, can be defined for this case as P = 2qd, and the electrostatic field around the dipole is described using P as a parameter. Molecular electric dipole moments arise, for instance, when two atoms of different electronegativity are covalently bound. For symmetric but nonspherical monopolar charge distributions (as might result, for example, from a football-shaped distribution of positive charge), the resulting symmetric electrostatic field, at distances that are large compared to the size of the charge distribution, is mathematically described as a monopole contribution (Coulomb's law), to which are added a series of other contributions that give the corrections from sphericity. Each succeeding term is of lesser importance. The electrostatic field correction of the first of these terms gives a nonspherical electrostatic field using a parameter called the quadrupole moment. The importance of this parameter in biophysical chemistry is that the positive charges of several atomic nuclei of biophysical interest behave as oblate or prolate ellipsoid-shaped positive electrical charge distributions that coexist with nuclear magnetic dipole moments. That is, the surrounding electrostatic field has an electrical quadrupole moment contribution. These nuclei (for example, 14N and 170) have special properties in nuclear magnetic resonance (NMR) experiments. Magnetic moments are formed by spatial arrangements of magnets, each with two poles, commonly designated "north" and "south" poles. One of the fundamental properties of all electromagnetic theory, embodied in the classical equations of Maxwell, is that although monopoles exist for electrical charge (so there can be isolated positive or negative charges), there are no magnetic monopoles in our universe. Consequently, there are no isolated north and south poles. However, unpaired electrons, certain atomic nuclei, and certain other fundamental particles can act like intrinsic magnetic dipoles. That is, they behave in an external magnetic field as if they were subatomic bar magnets. The magnitude of nuclear and electron magnetic moments is expressed in units of magnetons. Phase of a periodic wave The phase of a wave defines when any designated portion of the wave arrives at a selected point along its path. For a sinusoidally varying wave, F = F0 sin(cot + ~b),where F0 is the maximum value achieved by the wave F during a cycle, co is the angular frequency of the wave in radians/ second (the period of the wave is 1/co), t is time, and ~bis called the phase angle. Two waves are in phase when q~ = n(2cr) = 2nlr, where n is an integer (including 0). Two waves are completely out of phase when q~ = (2n + 1)~r. Physical constants Physical constants are numerical values characterizing certain physical processes (such as how rapidly light is propagated, i.e., the speed of light). Modern science postulates that these constants are fixed by the nature of the universe. They are believed to be time-invariant and the same throughout the universe. As measurement methods have become better and better over the years, the accepted values of the constants have tended to converge toward narrower and narrower limits of uncertainty. The following tab-
Chapter I Basic Physical Properties of Proteins and Nucleic Acids ulation lists the physical constants of most use to biophysical chemists. They are given in both the International System (SI) of units and the c e n t i m e t e r / g r a m / second (CGS) system of units.
Quantity
Symbol
Avogadro's number Electron charge Light speed in v a c u o Planck's constant Bohr magneton Electron rest mass Gas constant Electron magnetic dipole moment Proton magnetic dipole moment
N e c
h jU,B
me R /d,e /d,p
Value 6.0221367 1.60217733 299792458 6.6260755 9.2740154 0.91093897 1.9858866 9.2847701 1.41060761
SI
CGS
10 23 m o 1 - 1
10 23 mo1-1
10 -19 C
10-20 emu 102 cm sec-1 10- 27erg Hz- 1 10-21 erg G -~ 10-27 g cal mol- 1 K - 1 10-21 erg G10-23 erg G -1
m sec-1 10- 34j Hz- 1 10 -24 J T -1 10 -30 kg
cal mol- ~K- ~ 10-24 j T-1 10 -26 J T -1
Polyelectrolytes Polyelectrolytes generally are long-chain molecules carrying a large n u m b e r of ionizable sites. These long-chain molecules m a y exist in solution in either linear open conformation, as do m a n y small nucleic acid fragments, or they m a y be folded into regular three-dimensional structures, as are most native proteins. RNA and long-chain D N A (for example, in chromosomes) have three-dimensional structural characteristics, but, compared to proteins, less is k n o w n of the rigidity and distribution of these structures. In all cases, solutions of the polyelectrolytes are electrically neutral: for every charged group fixed to the macromolecule there must exist, s o m e w h e r e in the vicinity, a counterion of opposite charge. Physical biochemists have studied the cases wherein the counterions are small, mobile ones, such as alkali metal and halide ions. Much less is k n o w n theoretically about biologically important counterions, such as the polyamines, that interact with RNA and DNA. Physical biochemistry is often concerned with the ways the electrical charges influence the physicochemical behavior of polyelectrolyte solutions. Although the total charge on a polyelectrolyte m a y be a constant u n d e r fixed conditions, it is actually an average total charge because of the dynamic equilibrium taking place at each ionizable group between charged and uncharged forms. At a p H near where the formal charge is zero (the isoelectric point), the effects of these flickering charges become important in determining polyelectrolyte-polyelectrolyte interactions. The formal charge is the s u m m a tion of all the positive and negative charges on the polyelectrolyte u n d e r given conditions. The s u m m a t i o n does not take into account the dynamic equilibrium going on as, for example, conjugate acids and bases associate and dissociate. Quantum mechanics: Electrons and photons D e p e n d i n g on the experiment, electrons m a y behave as mass-particles or as packets of electromagnetic radiation. This is the w a v e - p a r t i c l e duality that is incorporated into the basic theorems of q u a n t u m mechanics. If a beam of electrons is projected onto a crystal surface at a suitable angle of incidence, the distribution of intensities of the reflected electrons is not at all w h a t w o u l d be expected for particles reb o u n d i n g from a surface. Instead, the intensities are represented by a pattern with maxima and minima just like interference patterns that occur w h e n light is
Jay A. Glasel diffracted. Hence, the experiment with electrons is called electron diffraction. Experiments with electron beams accelerated by known voltages established the relation A = h/meV,
where A is the wavelength of the electron wave, h is Planck's constant, me is the mass of the electron (defined as its mass when its velocity is very small compared to the speed of light, and called its rest m a s s ) , and V is its particle velocity. This equation is one of the results that forms the basis of quantum mechanics. In some experiments described in this volume, e.g., electron microscopy (Chapter 5), the wave character of electrons is all-important. A particle moving with the velocity of light, c, is called a photon. If the above equation is applied to a photon, = h/mc.
However, for any wave, ~ , equals the velocity of the wave. In this case Av = c. Combining these two expressions, mc 2 = h v
Because the mass is moving at the speed of light it has energy, according to Einstein's famous equation, E = m c 2 = h v,
which is a fundamental equation of quantum mechanics that gives the energy of a photon of electromagnetic radiation. A photon has an equivalent rest mass of h v/c a and a momentum of h ~,/c.
Radius of gyration At the macromolecular level, the radius of gyration is the effective equivalent radius that a distribution of atoms making up the macromolecule would have if it were behaving as a sphere. The term originally referred to the classical mechanics of rigid bodies. In classical mechanics, the radius of gyration, R0, of a solid spherical body is defined by the equation I = M R 2, where I is the moment of inertia and M is the mass. Note that the requirement is for a rigid body, not necessarily a spherical one. The concept enters into macromolecular chemistry when interpreting physical measurements related to the rotational properties of a macromolecule. For example, the intrinsic viscosity of a solution containing macromolecules is related to the radii of gyration of the molecules. Random coil In polymer chemistry a random coil refers to an array of configurations differing by alternative rotational conformations about the covalent bonds making up the polymer. Differences in the energies of alternative conformations about a given bond are on the order of R T (where R is the universal gas constant and T is the absolute temperature). In a true random coil, configuration of the macromolecule in a dilute solution is devoid of discernible geometric form, and will not bear an obvious resemblance to the ordered conformation. The array of configurations may be treated statistically; in particular, we can find the average physical properties of the array of configurations. These average properties then describe the behavior of the whole system of random coils under consideration.
ChapterI BasicPhysical Propertiesof Proteins and Nucleic Acids Strictly speaking, molecular shape is the three-dimenShape, molecular sional distributions of atoms making up a molecule. However, as ordinarily used, description of molecular shapes depends on context. For example, a protein may be described as globular if its behavior in a particular experiment is approximately that of a spherical solid body. That is, if the three-dimensional distribution of atoms was tightly w r a p p e d in plastic film and the result was roughly a sphere, it would be described as globular. In another description, the same protein, in the same conformation, might be described as consisting of a relatively open series of helices, sheets, and bends. In Chapter 9 different molecular shapes are illustrated. Included with this volume, the computer programs RasMol and Kinemage allow different representations of any macromolecule.
Supercoiling: Linking number, writhing number, and twist Linking number, L, writhing number, W, and twist, T, are related parameters that are used to describe supercoiled, circular, double-stranded DNA. Consider first the most common form of double-stranded, helical, linear DNA. The two antiparallel strands form a helix with 10.4 base pairs per turn. An integral number, the linking number, L, is defined for helical double-stranded DNA as the number of times one strand of DNA twists around the other in the right-handed direction. The quantity T is the number of hydrogen-bonded (Watson-Crick) base pairs in the helix divided by 10.4. Therefore, in the linear molecule just defined, L = T. This must be true for linear DNA, but it is not necessarily true for circularized DNA. Thus, if this same molecule is circularized (like strands being attached to like), the result is a circular, unstrained, helical structure that is called "relaxed." In solution, hydrogen bonds between opposite-strand bases are continuously breaking and reforming due to thermal agitation. Even so, the relaxed structure is the stable one. However, we now consider another possible molecule of linear double-stranded, helical DNA with exactly the same composition and number of bases. If turns are physically u n w o u n d (breaking the hydrogen bonds holding them in place), both L and T decrease by the number of turns that have been unwound. However, if this molecule is then circularized before the helix winds up again, there is built-in topological strain in the resulting molecule. The circularization prevents the molecule from reforming the relaxed conformation without distorting the molecule. The strain can be partly relieved by an energetically favorable conformational change in the whole circularized molecule that reforms b a s e - b a s e hydrogen bonds so that the whole molecule tends to maximize the number of helical turns (i.e., T becomes greater than L). The only way to do this is to form a tertiary structure that is supercoiled. That is, the double helix winds around itself to relieve the strain. The mathematical relation between L, the degree of supercoiling W (defined as the number of turns that the double helical axis makes about the superhelical axis), and T, the final structure is W=L-T.
Here L is a constant for a particular structure and, as just mentioned, is an integer. Neither W nor T need be an integer. In fact, in solution neither W nor T need be a constant. For a particular nonrelaxed circular structure characterized by a certain L, structures with different combinations of W and T will be in dynamic thermal equilibrium with each other, subject to the condition that each structure satisfies the equation given above. As noted later in this chapter, the
10
Jay A. Glasel importance of supercoiling in biophysical chemistry is that supercoiled DNA is more compact than a relaxed molecule of the same length. We are all familiar with an analogous phenomenon: the behavior of the helical cord found on most telephones. We tend to introduce strains in the cord by repeatedly picking up the receiver and putting it back in different directions on the body of the instrument. Supercoils form to relieve the strain and appear as the cord twisting around itself. If we want to relieve the built-up strain we can hold the instrument up with the receiver dangling down. The receiver will then spin around the cord powered by the strain energy until it dissipates. The cord is then in its relaxed form, with no supercoils, when the receiver is placed back on the instrument.
System of units Over the years many systems of units of measurement have been used. Currently, the International System (SI, or Syst6me International d'Unit6s) is considered the world standard. It is based on the meter, kilogram, second, ampere, Kelvin, and mole (for length, mass, time, electrical current, absolute temperature, and amount, respectively). The CGS system, which may be more familiar to some readers, is based on the centimeter, gram, second, abampere, Kelvin, and mole for the corresponding SI measurements. Converting measurements using one system to units of another system is often troublesome and leads to numerical errors. However, the "Merck Index," which is readily available, contains useful conversion tables.
I. Introduction This introductory chapter deals with the basic definitions and concepts involved in the study of macromolecular chemistry. It concentrates on the physical foundations of experiments that are described in this volume. The intention is to present a largely nonmathematical picture of the physical chemistry of macromolecules as a preparation for higher level treatments in the other chapters. Readers with a good understanding of undergraduate physical chemistry may wish to go directly to the later chapters.
II. A History of the Concept That Molecules Can Be Very Large Our present concept of the existence of macromolecules began with Raoult's discovery of the ideal solution law in 1887. An ideal solution is described in thermodynamic terms, and has the following properties: (1) there is no change in volume on mixing the pure components of the solution, (2) there is no heat evolved on mixing the pure components of the solution, and (3) the change in entropy caused by mixing the pure components is governed strictly by a simple probability expression. Almost immediately after Raoult discovered the ideal solution law that now bears his name, it was found that most solutions are not ideal. However, a large majority of solutions have properties that thermodynamicists call "regular," and for this class of solutions, deviations from ideality are very small. Prior to Raoult there was no way of determining molecular masses of compounds in solution. As a result of his discovery, it was realized that molecular masses of solutes could be measured by the cryoscopic method (the freezing point de-
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
11
pression that, for example, takes place when salts are dissolved in water). According to Raoult's law, low molecular masses for solutes correspond to large freezing point depressions. This method was applied to various materials dissolved in a wide variety of different solvents. Generally, organic molecules dissolved in organic solvents, and salts dissolved in water, all resulted in large freezing point depressions. However, in other cases, for example, rubber or starch dissolved in organic solvents and water, respectively, freezing point depressions were found to be small. Thus, using Raoult's laws, the molecular masses derived for rubber and starch, 18,000 and i2,000 Da, respectively, were much larger than those being observed by chemists of the time for other pure compounds. In fact, the established way of looking at things at that time, based on Graham's work in 1861, was to regard some matter as having a colloidal (gluelike) state. The word colloid comes from the Greek word for glue. This name was used because gelatin showed the typical behavior of this class of substances. The Brownian motion of colloidal particles had been discovered in 1827; the colloidal concept was developed for 60 years up to Raoult's time. According to this idea most matter in solution existed as colloidal particles. It was common not to distinguish between a colloidal particle composed of many molecules of ordinary size, held together by secondary forces, and a large molecule held together by covalent bonds. There was no reason to do so; the energies of bonds were unknown. For those familiar with the dynamics of scientific opinion, the result was predictable. Raoult's law was new and had experienced failures (almost all small) for electrolytic solutions. To reconcile the experiments on rubber and starch with what was already known, it was simply assumed that Raoult's law was inapplicable to colloidal solutions. Therefore, most interested scientists believed that the solution behaviors of compounds such as rubber and starch were manifestations of molecular association. The word macromolecule was coined by Staudinger in the 1920s to emphasize the molecular, rather than the associational nature, of what we now call polymers. Tremendous polemical battles ensued that centered around the truth or falsity of this concept. Indeed, it was not until the 1930s, largely as a result of direct chemical synthesis of polymers such as nylon, that the existence of high molecular mass substances was widely accepted. The acceptance of the macromolecular concept was also helped by the development of instruments for performing light-scattering, electrophoretic, and centrifugal sedimentation experiments during this period. The development of nonthermodynamic instrumental techniques provided the means to prove the correctness of Staudinger's viewpoint. In particular, a cornerstone of the colloidal idea was the observation from the newly developed technique of X-ray diffraction that indicated that the unit cells (the concept of unit cell is discussed in Chapter 8) for crystalline rubber and cellulose were similar in size to those of simple molecules. In 1926 it was shown that the X-ray diffraction by cellulose fibers is consistent with a chain length composed of an indefinitely large number of units (Flory, 1953). This interpretation made unnecessary the assumption that a molecule could not be larger than the unit cell. Because the first proteins were being crystallized at roughly the same time, the interpretation opened the way for acceptance of proteins as macromolecules. Developments in instrumental and theoretical techniques applied to biochemistry took place at an accelerating rate during the era from 1930 to 1950.
12
Jay A. Glasel Consequently, when the classic paper by Avery, MacLeod, and McCarty (1944) establishing the informational properties of deoxyribonucleic acid appeared, the paper contained ultracentrifugal information on the molecular mass of the DNA. The macromolecular nature of DNA was accepted much more easily because the controversy over proteins had been settled by this time. It is possible that the acceptance of both was eased by the fact that all of the methods available erred on the side of low molecular masses. Thus, the Avery group found a molecular mass of 500,000 Da (a value we know now is much too low for pneumococcal DNA) for their DNA, and early polymer chemists, using faulty theoretical analysis of physical experiments, consistently found molecular masses of macromolecules to be too low by an order of magnitude.
III. Basic Properties of Macromolecules The intrinsic properties of macromolecules that are important for the purposes of this volume include (1) mass, (2) shape and structure, (3) electrical charge, (4) electrical and magnetic moments, (5)kinetic properties (rotational and translational motions, internal motions), and (6) color (interactions with electromagnetic radiation), including (a) molecular electrical dipole, and multipole, moment interactions with radiation, (b) molecular magnetic dipole moment interactions with radiation, (c) interactions of nuclei of atoms with electromagnetic radiation, and (d ) interactions of unpaired electrons in molecules with electromagnetic radiation. Physical methods are presently available that involve using all of these properties. Sometimes many different methods employ similar properties in different ways. These redundant methods may, however, differ greatly in ease of performance and interpretation, accuracy, and expense. For example, optical rotatory dispersion (ORD) and circular dichroism (CD) have their basis in similar molecular properties, but differ very much in ease of interpretation of data. In the succeeding chapters of this volume many of the available methods are discussed. The purpose of this chapter is to discuss the fundamentals of the properties being measured. In particular, we want to highlight differences in the properties of small molecules and macromolecules. A. M a s s With the advent of highly accurate methods for measuring macromolecular masses (see Chapter 4), an accurate usage of the term mass has become necessary in biophysical chemistry. Unfortunately, some biochemistry textbooks either ignore the problem or confuse weight with mass. The weight of an object is defined as the force of the object against the earth. Thus, weight is measured in newtons (N) or dynes (kg m/sec 2 in SI units, gm cm/sec 2 in the CGS system; i.e., 1 N = 10s dynes; see System of units). Weight is not expressed in grams. The mass unit as originally defined in the metric system is that amount of mass contained in 1 c m 3 of water at a specified temperature and pressure. This amount of mass is called the gram. It was Newton who found that in any
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
13
geographical locality the masses, or amounts of inertia, of bodies are proportional to their weights. Thus, in that locality the masses of two bodies are compared by putting them on a balance and comparing their weights. A mass spectrometer is an instrument that measures inertial properties of atoms and molecules (specifically mass/charge; see Chapter 4). Because charges are integral numbers, the mass spectrometer can give the masses of individual isotopes of elements. Notwithstanding the physical difference between mass and weight, many still refer to "atomic weight" or "molecular weight" when they mean "atomic mass" or "molecular mass." Before 1960 there was a difference between chemical and physical atomic mass units for historical reasons. The chemical definition of 1 atomic weight unit was 1/16 of the average isotopic mass of atomic oxygen derived from oxygen gas as it exists in nature. This base was used for many years as the chemical atomic weight. The physical definition of I atomic mass unit was 1 / 16 of the mass of the neutral atom of the isotope 160. This base was used for decades for determining nuclidic masses. Consequently, the chemical atomic weight unit was 1.000274 times the physical atomic mass unit. The distinction between chemical and physical scales becomes important for macromolecules because they contain many atoms, and therefore the existence of even lowabundance stable isotopes can contribute measurably to their molecular mass. This confusing situation of having two different scales was resolved by international agreement whereby both scales are based on the nuclidic mass of 12C. The accepted unit of mass for nuclides, atoms, and molecules was the dalton, originally symbolized by the lowercase letter d. The dalton is defined as exactly 1 / 12 of the mass of the neutral atom 12C; the dalton is thus approximately 1.6605655 • 10-27 kg (to 6 parts per million). The symbol for the dalton (but not the definition) was changed in the 1980s to Da, which will be used in this volume when referring to molecular and atomic masses. The archaic and inaccurate terms, atomic weight and molecular weight, will not be used.
B. S h a p e and Structure The premise behind much of modern biophysical work is that the threedimensional structure of proteins determines their function. That is, the information content stored in DNA appears ultimately in functional form as threedimensional distributions of mass and charge, namely, proteins. The proteins have specific functions determined by these distributions. Much of this volume is therefore concerned with methods for determining structures of proteins. One of the important functions of some proteins is their specific interactions with nucleic acids. Consequently, there is increasing interest in the origin of the forces between these two types of molecules. We will discuss the problem in a later section of this chapter. Bloomfield, Crothers, and Tinoco (1974) have written a one-volume monograph on the detailed physical biochemistry of nucleic acids. Monographs on proteins tend to specialize in one or another aspect, such as structure or interactions. Two starting points for further reading might be a more recent monograph on structural methods (Branden and Tooze, 1991) and a classic monograph stressing thermodynamic and electrolytic analysis of mac-
14
Jay A. Glasel Table I The Genetic Dictionary a
Amino acid
Tripletb
Aminoacid
Triplet
Glutamicacid Asparticacid Glutamine Asparagine
GAPy GAPu AAPy CAPu
Lysine
AAPu
Phenylalanine Tyrosine
GGX GCX GUX CUX UUPu AUPy AUA UUPy UAPy
Histidine Arginine
Tryptophan
UGG
Serine
Cysteine Proline
UGPy CCX
Threonine Methionine
CAPy CGX AGPu AGPy UCX ACX AUG
Glycine Alanine Valine Leucine Isoleucine
a From Bloomfield et al. (1974). Exceptions to the correspondences in this dictionary exist in certain organisms and organelles. bAbbreviations: X, any base; Pu, purine; Py, pyrimidine.
romolecular properties (Tanford, 1961). Table I summarizes the informational properties of nucleic acids by showing the relation between the genetic code and the encoded amino acid residues. At present, it is not understood w h y macromolecules have different sizes; we just know that they do. In certain cases we can rationalize their size. For example, for a transmembrane protein, such as a receptor, to function, it clearly must be larger than the thickness of the plasma membrane. However, it is certainly not clear w h y two enzymes with approximately the same size can differ in catalytic efficiency by orders of magnitude. Figure I shows a variety of proteins displayed on the same scale. In an inset the sizes of a cross-section of a membrane bilayer, of transfer RNA, and of a DNA double helix are shown on the same scale as the proteins. Clearly, future theoreticians have their work cut out for them, if we are ever to understand structure-function relations in a logical and quantitative way. Although powerful methods such as X-ray diffraction and NMR have been applied to characterize macromolecular structures, the number of hours required to gather the data and solve a given structure makes these techniques prohibitive in most cases. Additionally, X-ray diffraction requires good macromolecular crystals and NMR requires large amounts of very pure material. In most cases a protein chemist would like to know some minimal information about a newly obtained protein. This information would probably include the mass of the protein, whether it is a homo- or heteromultimer, its amino acid composition, and its overall shape. With the exception of methods for determining amino acid composition, modern methods for obtaining experimental values for all of these parameters are discussed in this book. In Chapter 9 there is further discussion of analyzing the intramolecular structure of proteins and
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
15
nucleic acids by computer methods. The purpose of this section of the introductory chapter is to introduce some fundamental concepts known to underlie all macromolecular structures. As we will see below, the quantitative descriptions of the three-dimensional structures of proteins are based on recognizing various different structural motifs whose particular arrangements define each particular protein. For nucleic acids, the overall three-dimensional structural motifs are fewer in number, but within each polydeoxyribonucleotide or polyribonucleotide structure there are subtle structural variants that may have biological importance. An understanding of macromolecular structure is therefore based on understanding the descriptions of the structural motifs. These motifs, we shall see, are groups of residues in individual conformations that confer a distinct overall shape to the group. The individual conformation of a residue is described by a set of torsional angles, that is, the angle of rotation about each covalent bond in the molecule (except bonds between heavier atoms and hydrogen atoms). Proteins and nucleic acids have allowed, but sterically constrained, rotations about certain covalent bonds. The definitions of the angles have been fixed by international convention (Nomenclature, 1970, 1983). However, this has been done relatively recently. Literature previous to (and sometimes after) these agreements sometimes contains definitions of angles that are different from those currently in use. We will discuss the current definitions for proteins, because almost all available structural information uses these definitions. However, in some cases there is not complete agreement with a single convention for nucleic acids. Where appropriate, alternate conventions are pointed out for nucleic acids.
1. Description of Primary Structures of Peptides and Proteins Bonds between atoms are denoted A i ~ B j , with the bond lengths written b(A~, Bj). The symbol for the bond angle included between three atoms, Ai, Bj, Ck is written ~-(Ai, Bj, Ck). The symbols used to describe the various torsion angles important in polypeptides are q~, 6, o~,/~, and X. Torsion angles refer to a system of four atoms. A
\
B~C
/
D
If this system is projected onto a plane normal to bond B m C , the angle between the projection of A r a B and the projection of C ~ D is described as the torsion angle (also sometimes called the dihedral angle and internal rotation angle) of A and D about the bond BmC. The torsion angle is written fully as 4 (ai, Bj, Ck, DI). In the eclipsed conformation, in which the projections of A - - B and C ~ D coincide, the torsion angle is given the value 0 ~ A torsion angle is considered positive (+) or negative ( - ) as follows: when the system is viewed along the central bond in the direction B ---* C (or C ~ B), the bond to the front atom A (or D) requires rotation to the right or to the left, respectively, in order that it may eclipse the bond to the rear atom D (or A). Torsion angles are measured in the range - 1 8 0 ~ angle-< + 180 ~ It does not matter whether the system is
16
Jay A. Glasel
Fig. 1 Comparison of the sizes and shapes of some soluble proteins drawn to the same scale. The inset shows the sizes of tRNA, of a segment of double-stranded DNA, and of bilayer membranes at the same scale. From Goodsell and Olson (1993). v i e w e d from one end or the other. These relationships are s h o w n in Fig. 2, w h e r e a generic torsion angle, 0, is shown. The three torsion angles, ~b, 6, and oJ, that define the c o n f o r m a t i o n of an a m i n o acid residue in the m a i n chain of a p o l y p e p t i d e are s h o w n in Fig. 3. Table II gives the main-chain torsion angles for various conformations of peptides of L a m i n o acids. Based only on steric factors, certain torsion angles in peptides
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
17
Fig. 1 (Continued)
and proteins are more probable than others. These lead to so-called regular structures that form the basis of the motifs discussed below. Table III gives approximate torsion angles for some of these regular structures. It should be noted that a general feature of these regular structures, and indeed a major factor in protein three-dimensional structure, is the fact that ~ois almost always found to be within a few degrees of either 0 ~ or 180 ~ The physical origin of this
18
Jay A. Glasel e
D
A o.~
A
D
o
B) J
"~
e_.positlve
D-O
A
(m
oo0o r
0 negativ__.s
Fig. 2 Newman and perspective projections illustrating definitions of positive and negative torsion angles in a general system of four atoms, A, B, C, and D, joined by covalent bonds. Note that a right-handed turn of the bond to the front atom about the central bond gives a positive value of 0 from whichever end of the system is viewed. From Nomenclature (1970).
is that the peptide bond has a significant electron delocalization that forces the four a t o m s (HmNamide--Ccarbonyl--O) into a plane. When a~ is + 180 ~ the conformation of the amide hydrogen and the carbonyl oxygen is termed trans. When a~ is 0 ~ the conformation is cis. In most natural polypeptides, the trans conformation is highly favored energetically. The definition of a conformation of an amino acid residue is completed by specifying the orientation of the side-chain groups to each other. The specifica-
ACi.I \\x 0i ~
W
G! i i
+I "
Hi +
~ \\x
~r C~-
Hi ~' "" "~ ~ ~ "~ .~.
~
~'i-1
Fig. 3 Perspective drawing of a section of a polypeptide chain consisting of two residues. The limits of a residue are indicated by dashed lines and notations for atoms and the different mainchain torsional angles are indicated. The chain is shown in a fully extended conformation with ~bi = ~/i = O9i = 180~ The residues are in the L configuration. From Nomenclature (1970).
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
19
Table II Main-Chain Torsion Angles for Various Conformations in Peptides of L-Amino Acids a 4) (deg)
Rotation about N - C a b
6 (deg)
Rotation about C4-C
0
C~-C trans (all referred to N - H ) C 4- H cis C~-R trans C4-C cis C 4- H trans C 4- R cis
0
C~-N trans (all referred to C - O ) C ~- R cis C 4 - H trans C 4 - N cis C 4- R trans C 4- H cis
+ + + -
60 120 180 120 60
+ + + -
60 120 180 120 60
a From Nomenclature (1970). b Note: trans to Ni-H; is the same as cis to Ni-Ci_l; trans to C;-O; is the same as Ci-Ni+ 1 . For a description of D amino acids, interchange C 4 - H and C4-R in the table.
t i o n s t a r t s a t t h e a l p h a (or) c a r b o n a t o m . F i r s t , t h e s i d e - c h a i n a t o m s a r e l e t t e r e d , or lettered and numbered,
from the Ca atom working
chain. The torsion angles are given the common two (or three) superscripts.
outward
from the main
symbol X and are specified by
I n t h e s i t u a t i o n g i v e n b e l o w , w h e r e A is t h e a l p h a
carbonation,
A~B
D / m C--E \ F
the first (or second) superscript would
indicate the bond B--C
a n g l e is m e a s u r e d ,
indicate whether
and the last would
about which the
t h e a n g l e is m e a s u r e d
Table III Approximate Torsion Angles for Some Regular Structures in Peptides of L-Amino Acids a Structure b
4) (deg)
6 (deg)
to (deg)
Right-handed ce helix [a-poly(L-alanine)] Left-handed c~ helix Parallel-chain pleated sheet Antiparallel-chain pleated sheet [fl-poly(L-alanine)] Polyglycine II Collagen Poly(L-proline) I Poly(L-proline) II
- 57 + 57 - 119
- 47 + 47 + 113
+ 180 + 180 + 180
- 139 - 80 -51, -76, -45 -83 -78
From Nomenclature (1970). b Note: For a fully extended chain ~b = 4t = to = + 180 ~
a
+ + + 153, + + +
135 150 127, + 148 158 149
- 178 + 180 + 180 0 + 180
20
Jay A. Glasel
relative to D, E, or F. For example, in leucine, ,u Xi3,1,2, Xi3,1,3 refer to the torsion angles specifying the three hydrogen atoms attached to C ~1. In valine, Xi 2'1 and Xi 2"2 refer to the torsion angles specifying atoms Ci ~/1 as Ci ~/2. One of the problems afflicting even experts in protein structure is building molecular models (including computer models) with amino acid residues in their correct r configurations about their alpha, asymmetric carbon atoms. Normally, of course, this means all the residues should be in their L configurations. Checking for this configuration step by step in building or examining a portion of a peptide is always wise and fortunately very easy. The CORN mnemonic is useful for this purpose. Looking at the Ca atom from its H atom, the other substituents should read CO-R-N. in the clockwise direction. CO, R, and N represent the carbonyl group, side-chain group, and main-chain nitrogen atoms, respectively.
2. Description
of the
Primary Structures
of Nucleic
Acids
Compared to polypeptides, relatively little is taught about the configurations of polynucleotides. However, as more interest centers on protein-nucleic acid interactions, it becomes more important to understand the structures of nucleic acids. In this section we will discuss the configurations and nomenclature of nucleosides and nucleotides (a description of planar nucleic acid bases can usually be found in most biochemistry textbooks). The rules for configuration nomenclature have been set out by international agreement as in the case of polypeptides (Nomenclature, 1983). Exactly specifying the structures for the nucleosides can become very complicated because the ring atoms of the sugar are not planar and the out-of-plane atoms depend on the compound. There are also five torsion angles not in the sugar ring, about which rotation can take place: C l ' ~ b a s e , C 2 ' ~ O 2 ' , C 3 ' ~ O 3 ' , C 4 ' ~ C 5 ' , and C 5 ' ~ O 5 ' . Figure 4 shows the general structure of ribonucleosides and deoxyribonucleosides. From studies on a large number of nucleosides, four of the sugar ring atoms form a plane to within a small fraction of an angstrom, but the fifth atom in the ring is significantly displaced. The four nearly planar atoms are C1 ', C4', O1 ', and either C2' or C3'. If the out-of-plane ring atom is on the same side of the plane as the 5' carbon, the conformation is designated endo. The conformation is exo if the out-of-plane ring atom is on the side opposite the 5' carbon. C2' endo and C3' endo are the most commonly found configurations. Their corresponding exo configurations are rare. The general conclusion is that either C2' or C3' will be out of the plane determined by C1', C4', and O1 '. The ribose pucker is important to the function of nucleic acids. For example, unless the sugars are either C2' or C3' endo, a double helix conformation for DNA is very strained. The orientation of the base relative to the sugar in a nucleoside is labeled with the symbol X. Eventually, this nomenclature will be a problem when more structures of nucleic acid-protein complexes are known in detail, because the same symbol is used for protein side-chain torsion angles (see above). Relative to the sugar, the base can have two main orientations about the C I ' ~ N link. These are called syn and anti and are shown in Fig. 5. Unfortunately, other definitions for X have been used in the past. Table IV gives conversions from other definitions to the present one. In nucleic acids, rotation about the C 4 ' ~ C 5 ' bond allows 0 5 ' to assume different positions relative to the sugar ring. Three main configurations with
Chapter I Basic Physical Properties of Proteins and Nucleic Acids H5'
21
H5"
~
/
1'
base
~O
C1' 1' IC2' 02'
03'
\.
\H
ribonucleoside
(ribose derivative)
C5'
base
OH
OH
ribose
C5'
OH
OH
arabinose
base
I~
C5'
base
C5'
OH OH
base
1
OH xylose
lyxose
Fig. 4 The configuration of the ribonucleosides found in RNA. The deoxyribonucleosides found in DNA are identical except that they lack 02'. The configuration of other possible pentoses is also shown. From Bloomfield et al., (1974).
all substituents in staggered positions are possible, as shown in Fig. 6. Normally, the three configurations are described by the two torsion angles q ~ o o ( O 5 ' m C 5 ' m C 4 ' m O 4 ') and q ~ o c ( O 5 ' m C 5 ' ~ C 4 ' m C 3 ' ) or by use of the angular ranges, (+) or ( - ) gauche or trans. However, according to the I U P A C IUB convention, it is necessary only to state the torsion angle 7 (= q~oc) in order to define the orientation about the C4' ~ C 5 ' bond. Table V gives the different definitions for %
3. Shapes of Disordered Proteins and Nucleic Acids A disordered macromolecule is one wherein distances between units on the covalent chain forming the polymer are not time invariant. That is, for an array of macromolecules we can only specify statistical distributions giving probabilities that the units will be found at given distances from one another at any given instant. Very few biological macromolecules carry out their in vivo functions in a disordered state. Indeed, most of them lose biological function when they are disordered (disordered is a term that biophysicists have come to prefer to denatured). However, order-disorder transitions caused by treatment of functional proteins with heat, solvent changes, pH changes, etc. can tell us something about what forces hold proteins in their ordered state, and in certain cases reveal what amino acid residues reside in the interior of a protein. Therefore, we need a description of the disordered state of macromolecules. A great deal of information and theoretical analyses are available for disordered proteins and nucleic acids because of the industrial uses of polymers. In biophysi-
22
Jay A. Glasel
Fig. 5 (Top) Diagram illustrating how the overall geometry of a nucleoside changes if bases are in syn or in anti orientation. Adenosine and uridine are shown in their anti orientations. 8-Bromoguanosine and 6-methyluridine are in syn orientations due to steric hindrance caused by their substituents ortho to the glycosyl link. In 8-bromoguanosine an intramolecular hydrogen bond (broken line) stabilizes the syn conformation. Note sugar puckerings, with C3'-endo preferred for anti orientation but C2'-endo preferred for syn orientation. (Bottom) Definition of anti and syn
orientation ranges (Nomenclature, 1983) shown for a pyrimidine nucleoside. X is defined as the torsion angle O4'-C1'-N1-C2. The pyrimidine base is coming out of the paper. From Saenger (1984).
cal chemistry, one often refers to d i s o r d e r e d b i o p o l y m e r s as being in a r a n d o m coil. Technically speaking, the s t u d y of the d i s o r d e r e d states of p o l y m e r s in solution is referred to as the statistical mechanics of chain molecules (Flory, 1969). A freely jointed chain, or " b e a d s on a string" model, is the starting point for analysis of d i s o r d e r e d structures. A p p l i e d to proteins a n d nucleic acids, the b e a d s c o r r e s p o n d to units, such as a m i n o acid residues or nucleotides, w h i c h are joined by m a i n - c h a i n covalent b o n d s about w h i c h free rotation is possible.
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
23
Table IV Conversion of Different Definitions for Torsion Angle about the Glycosol CI'-N Linkage a Difference between Nucleic acid
Present X b
Other definition
Purine
--
O4'-C1
Pyrimidine
p
O 4 ' - C1 ' - N 1 - C 6
'-N9-C8
present and other + 180 ~
Purine
O4'-C1'-N9-C4
O2'-C1'-N9-C8
Pyrimidine
O4'-C1'-N1-C2
O2'-C1'-N1-C6
- 62.5 ~ + 116.5 ~
Purine
p
O2'-C1
'-N9-C4
Pyrimidine
--
02' -C1 '- N 1 -C2
- 62.5 ~
+ 116.5 ~
a F r o m S a e n g e r (1984). b Xp. . . . . t = Xother q- d i f f e r e n c e .
Thus, the simplest model does not consider side-chain torsional angles. If we superimposed images of all the possible configurations for a chain of this type, we would see a picture that looked like a fuzzy sphere. Theoretical analysis bears this out and shows that the mean-square radius of gyration for an unperturbed, freely jointed chain with a large number of beads is ~$2~0 =
nl 2/6,
where n is the number of beads and l is the distance between the beads (assumed here to be equal). The subscript on ~s2~0 indicates that this is the base mean-square radius of gyration for comparison with further analysis. For example, if we had 600 beads separated from each other by bonds totaling 20 nm, the root-mean-square (rms) radius of gyration would be 200 nm. This is a very large structure with a density of only 0.000018 beads / nm 3. What happens when restrictions are applied to this freely jointed model to make it more realistic? For example, suppose that the bond angles between contiguous bonds are restricted to tetrahedral angles (i.e., the chain is composed of beads joined by carbon-carbon single bonds? In this case, theory shows that for this perturbed chain, ~$2~ ' = 2~$2~0, where the prime superscript o n ~$2~' serves to indicate that this mean-square radius of gyration includes the first restriction. With double the rms radius of gyration the volume increases by a factor of 8, and the density of beads falls by the same factor. Suppose we then introduce the additional restriction that rotation about each bond is restricted to a normal distribution about a certain average angle? If this average angle is 45 ~ ~$2~ ' ' = 11.7{s2~0 for this doubly perturbed chain. Introducing these restrictions has a very large effect in the direction of increasing the dimensions of the random coil. In Chapter 3 we will see how experimental measurements on macromolecules can be related to the radii of gyration and can be used to characterize deviations from an idealized random coil. The point is that the proportionality of ~s2} to n is preserved even on introduction of various restrictions on complete flexibility. We have just seen that the general form of ~$2~ is onl 2, where ~r is a factor that reflects restrictions on free rotations about bonds. This form suggests that an actual chain can be replaced by a statistically equivalent one that contains
24
Jay A. Glasel H5'2
,04 ,
H5,1~'~05'/ C 3'
+SO
(gauche, gauche)
C2'
0 5,
SE I
C3'
(•
~
C2'
/
| BASE
C3'
ap
( gauche,trans )
-SC
( trans, gauche )
C2'
Fig. 6 Definition of torsion angle ranges about the C 4 ' - C 5 ' bond, looking in the direction C5' ~ C4'. From Saenger (1984).
fewer segments than n, each with a longer effective bond length. Then, ($2) '' = ne 12/6,
where n e and le are the effective units and effective bond lengths, respectively, subject to the condition that nl = nel e. The double prime in {s2}'' indicates that this includes both restrictions discussed above. This concept will be used shortly in describing DNA molecules in solution. Many cases are known of cyclical macromolecules (e.g., plasmid DNA). For the case of a cyclic random coil, statistical theory gives the following simple relation, <S2>0, cyclic = ($2>0, linear/2"
Table V Different Definitions for Torsion Angle ~/ about the Exocyclic C4'-C5' Bond ~ Present 7
Other definitions for orientation about the C 4 ' - C 5 ' bond
+ sc -sc ap
gauche, gauche; (+)gauche; gg; ( +)g trans, gauche; trans; tg; t gauche, trans; (-)gauche; gt; (-)g
" From Saenger (1984).
,,
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
25
Applied to a real polypeptide chain, we can see that the values of bond angles are determined by covalent forces. For example, we know that a peptide bond is planar due to delocalization of the carbonyl bond electrons, whereas the Namide~C~mCcarbonyl angle is nearly tetrahedral. On the other hand, the restrictions on rotations about bonds are determined largely by intramolecular and solvent-macromolecular forces. It is this fact that theoreticians attempt to deal with in trying to predict how a given sequence of primary structure may fold up into its "ordered" or "preferred" conformation. In the early 1950s, Pauling and Cory started working with models of polypeptides and realized that a combination of torsional angles q~ and qJ could be chosen so that all the C = O and N - - H groups could form linear intramolecular hydrogen bonds with optimal acceptor-donor distances. Thus began the study of secondary structures of polypeptides and proteins: the beads of the restricted flexible chain are allowed to interact not only with their nearest neighbors, but also with nonadjacent beads. Not too long after, Watson and Crick, using analogous reasoning applied to DNA, realized that intermolecular hydrogen bonds could stabilize two chains of DNA in certain preferred conformations.
4. Descriptions of the Secondary Structures of Proteins and Nucleic Acids Polypeptides and polynucleotides have one class of secondary structure in common: the helix. Definitions of the general parameters describing a helix are given in Fig. 7. The pitch of a helix is the distance traveled along the helical axis for complete 360 ~ rotation. The pitch height P relates the number n of units (amino acid residues or nucleotides) in one turn and the unit height h, defining the translation per residue along the helical axis by P = nh. The unit twist is t = 360~ and is the rotation between one unit and its nearest neighbor. Helices are described as right-handed if they follow the rule: they show clockwise rotation when viewed along their axes and moving from front to rear. That is, for a polypeptide or polynucleotide, looking from either end of the helix, the main chain spirals in a clockwise direction for a right-handed helix. We note two things about helices. First, because of its handedness, a helix has chirality (Testa, 1979). The uses of this property are expanded in Chapter 6, where the optical activities of helices are discussed. Second, L-polyamino acids can be part of either right- or left-handed helices. The only conclusion that can be drawn from the stereochemistry of the amino acids is that if an L-polyamino acid forms a right-handed helix, its D-polyamino acid counterpart must form a left-handed helix. A popular notation for polypeptide helices is to give the number of residues in a turn and the number of atoms forming one hydrogen-bonded unit in a single compound number. Thus a 3.613 helix is one with 3.6 residues per turn, and 13 atoms per hydrogen-bonded structure. The most frequently encountered polypeptide helices are 3.613 (an cr helix), 310 , 4.416 (a "rr helix), and the 27 ribbon (a ribbon is just a special case of a helix). Table VI shows parameters for some common polypeptide helices. For polypeptides, certain sterically favorable combinations of the torsion angles 4~ and q~exist. A two-dimensional plot of 4~ vs 6 with energy contours
26
Jay A. Glasel
b& .p. O
Fig. 7 Definitionof helical parameters. Pitch P, axial rise per residue h, and unit twist t, shown for a right-hand helix with n = 5 residues per turn. From Saenger (1984).
indicating these favorable combinations is called a q~-6 m a p or, alternately, a R a m a c h a n d r a n plot. Figure 8 s h o w s a R a m a c h a n d r a n plot, indicating regions of greatest stability a n d o b s e r v e d points for proteins (Richardson, 1981). In describing helical s y m m e t r i e s of nucleic acids the s y m b o l N m is used, w i t h no differentiation b e t w e e n p u r i n e s a n d pyrimidines. That is, there are just nucleotides. In this notation, the s y m b o l 111 w o u l d indicate 11 nucleotides in one t u r n of the helix (this is the A form of DNA). S o m e t i m e s n o n i n t e g r a l helices such as 9.331 are n o r m a l i z e d to exact repeats. That is, 3 • 9.33 = 28 a n d so this structure m a y be conveniently d e s i g n a t e d 283 . Some helical p a r a m e t e r s for each s t r a n d of D N A d o u b l e helices are given in Table VI. Nucleic acid helices h a v e chirality, just as do p o l y p e p t i d e helices. It h a p p e n s that the n a t u r a l D N A helices are m a i n l y r i g h t - h a n d e d . H o w e v e r , synthetic sequences such as p o l y ( d G - d C ) a n d regions of natural D N A form a left-handed d o u b l e helix
Table VI Structure Types and Helical Parameters for Polypeptides a Structure type helix 310 helix 27 ribbon
Polyproline helix Antiparallel fl-pleated sheet
Pitch (A)
Designation b
Axial rise (A)
Turn angle per residue (deg)
5.41 6.00 5.60 9.36 6.95
3.613
1.50 2.00 2.80 3.12 3.47
99.7 120 180 - 120c 180
310 27
Polyproline helix Antiparallel ~pleated sheet
a From Dickerson and Geis (1969). b The numbered designation format is (residues/turn)atoms per H-bondring" c The polyproline helix is left-handed.
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
27
Fig. 8
(a) Ramachandran plot showing allowed combinations of the 4~ and X angles in a polypeptide. Shaded areas show sterically allowed regions; the labels a,/3, and L correspond approximately to conformational angles found for the usual right-hand a helices,/3 strands, and left-hand a helices, respectively. (b) Observed values for all residue types except glycine. Each point represents ~b-X combinations for an amino acid residue in a high-resolution X-ray structure. From Branden and Tooze (1991); adapted from Richardson (1981).
called Z-DNA, which apparently has biological significance (Saenger and Heinemann, 1989). Table VII gives helical parameters for some DNA structures.
5. Tertiary Structures of Proteins and Nucleic Acids Ramachandran plots are useful summaries of secondary structural data for a given protein. They tell at a glance the relative abundances of helical, sheet, and irregular structures for the protein. However, they cannot give an idea of the three-dimensional runs of secondary structures that determine the overall shape of a protein. Consequently, it is currently more popular to present structural data in the form of topological diagrams (Branden and Tooze, 1991). The basis for this is that simple combinations of a few secondary structure elements with specific geometric arrangements have been found to occur frequently in protein structures. These are called structural motifs. Examples of the common motifs are shown in Fig. 9. Several motifs usually combine to form domains. The domain is the fundamental unit of tertiary structure of a protein and is defined as a polypeptide chain, or part of a chain, that can independently fold into a stable tertiary structure. For example, the extremely efficient enzyme triosephosphate isomerase has a tertiary structure that is a combination of just four motifs, as shown in Fig. 10. Chapter 9 discusses the graphical presentation of tertiary structures of proteins as well as the present status of attempts to predict theoretically the arrangement of motifs from their primary structures. Nucleic acids can form strands of very high molecular masses, extending to
28
Jay A. Glasel Table VII Structure Types and Helical Parameters Derived from X-Ray Diffraction Measurements for Natural D N A s a
Structure type
Pitch(/k)
A B C Z
28.2 33.8 31.0 45.6
Helical Symmetry 111 101 9.331(283) 121
Axialrise (/~)
Turn angle per residue (deg)
2.56 3.38 3.32 3.80
32.7 36.0 38.6 - 30
a Adapted from Leslie et al. (1980). a range > 1012 Da. Beyond the formation of d o u b l e helices, w e can ask a b o u t the shapes a s s u m e d by very high molecular mass nucleic acids. In C h a p t e r 3, hyd r o d y n a m i c m e t h o d s for s t u d y i n g the p r o b l e m experimentally are discussed. F r o m the h y d r o g e n - b o n d e d structure of d o u b l e - s t r a n d e d DNA, it is easy to see that unless considerable energy is e x p e n d e d in breaking h y d r o g e n - b o n d s , it is v e r y difficult to m a k e an acute b e n d in the double helix, a l t h o u g h regions with gentle b e n d s are k n o w n . Macromolecules that can b e n d only g r a d u a l l y a n d s m o o t h l y in solution are given by p o l y m e r chemists the descriptive n a m e " w o r m l i k e chains." The shape of this type of m a c r o m o l e c u l e requires a treatm e n t slightly different from that required by r a n d o m coils. In order to characterize the stiffness of a nucleic acid chain, w e a s s u m e the chain starts at an origin and w e follow it along the positive z-axis. We then w a n t to k n o w the average projection (z) at the end of the chain (after n units that are s e p a r a t e d from each other by distances l). If the chain w e r e a completely stiff rod, (z) w o u l d have its m a x i m u m value at a distance nl. The q u a n t i t y nl is called the contour length of the chain. The theoretical t r e a t m e n t of a w o r m l i k e chain further assumes that the b e n d i n g takes place g r a d u a l l y t h r o u g h small angles, 0. That is, w e replace the freely jointed chain discussed above by a semirigid string w i t h a c o n t i n u o u s curvature. We w a n t to k n o w w h a t average quantities, such as radii of gyration, will be in this case. The result is, for angles very close to zero, a = 2l/02.
The q u a n t i t y a is called a p p r o p r i a t e l y the "persistence length." It is the average
Fig. 9 (A) An example of the helix-loop-helix motif. Two a helices connected by a short loop region constitute this motif. (B) An example of the hairpin motif. The hairpin is built up from two adjacent/3 strands that are joined by a loop region. (C) The "Greek key" motif. Four adjacent antiparallel/3 strands arranged in a pattern similar to the repeating unit of one of the ornamental patterns used in ancient Greece. An example of the structure in Staphylococcus nuclease is shown. (D) The/3- cr-/3 motif. Two adjacent parallel/3 strands connected by an a helix from the C terminus of strand 1 to the N terminus of strand 2 constitute this motif. From Branden and Tooze (1991). Fig. 10 A combination of a - / 3 - a motifs make up the three-dimensional structure of the highly efficient enzyme triose phosphate isomerase. From Branden and Tooze (1991); adapted from Richardson (1981).
Chapter 1 Basic Physical Properties of Proteins and Nucleic Acids
29
extension along the z-axis of a very long chain. If 0 is very small, as we have assumed, a can become much larger than l. If a is very large, the polymer has very long projections along the z-axis--it does not bend very much and is a rigid chain. A further result of a rigorous analysis of a wormlike chain gives a little more physical insight into the meaning of persistence length. In the discussion of random coils we introduced the concept of the effective length of bonds l e . This effective bond length was larger than the real bond length. In a wormlike chain we find that le = 2a. Thus, the effective bond length separating two units in a wormlike chain is twice its persistence length. Because a can be very much larger than l, so can the effective bond length. The result of a more complete treatment is that for wormlike chains, (z) = a(1 - exp{-nl/a}). Suppose the chain is very short so that nl > a,
le =
- exp{-lene})].
2a, for wormlike chains of large contour length, so (S2)worm, nl>>a ~- 1 / 6 n e 12.
This coincides with the expression for the mean square radius of gyration previously given for a random coil. In contrast, for wormlike chains with nl _; -
\~_
@j/
| |
|
|
|
Fig. 12 Model of a wormlike negatively charged polyelectrolyte in solution. From Morawetz (1975).
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
33
stranded DNA is considered, the helical conformation will make the macromolecule even more resistant to bending. The shapes of nucleic acids were discussed above in terms of the wormlike character of these macromolecules. Several theories applicable to polynucleotides have been developed. A useful short summary of more advanced aspects of polyelectrolyte solutions than discussed here is given in a monograph by Eisenberg (1976). All the theories developed so far predict the same type of behavior. However, our discussion is based on a review by Manning (1972). Theoreticians have treated the polyelectrolytic properties of nucleic acids on the basis of a worm standing at attention: i.e., nucleic acids are modeled as long rigid rods with charge densities determined by the regularly spaced phosphate groups. Nucleic acids are associated with a counterion phenomenon that is different than that associated with proteins. This is because of the high charge density existing in a nucleic acid chain at neutral pH. For DNA, the charge spacing is about 1.7 A. For globular proteins with much lower charge densities, the Linderstrom-Lang/Debye-Hfickel theory predicts a potential distribution around the macromolecule that varies continuously as a function of counterion concentration (Fig. 11). For rodlike nucleic acids with high charge densities, theoretical studies show an important difference in the behavior of counterions and the behavior of the electrical double layer around globular proteins. The difference is that, for nucleic acids, as the ionic strength is increased from zero by addition of salts, a critical concentration is reached above which counterions are suddenly attracted to the surface of the rod. The effect is called "counterion condensation." In slightly more quantitative terms, it is found theoretically that a critical charge density, ~crit, exists on the surface of a rodlike molecule; at this critical charge density counterions associate with the surface of the rod so that the net charge density in dilute solutions is maintained at the critical value. Several features of the phenomenon of counterion condensation must be noted. For water solutions, ~crit corresponds to a charge spacing of 7.14 A. Therefore, for DNA (and other single- and double-stranded nucleic acids) counterion condensation always occurs. That is, counterions condense so as to reduce the effective charge density to the critical value. Because of the properties of water, this charge density is independent of temperature, ionic strength, or the nature of the nucleic acid. The condensation takes place to the same extent no matter how much the solution is diluted. That is, the tendency of the condensed counterions to escape into the surrounding solution (and increase their entropy) is always overcome by the strong electrostatic attraction that the nucleic acid has for them. The theory of counterion condensation has been worked out approximately for solutions with salts of different valencies. The important qualitative conclusion from these studies is that ions of higher valency condense preferentially. This is probably the reason small concentrations of divalent cations have such pronounced effects on the properties of nucleic acids, and not that the ions are bound in some more specific way. The polyelectrolytic character of proteins and DNA affects their behavior in a variety of laboratory procedures. Some of these processes are discussed in other chapters of this volume, including electrophoresis (Chapter 2), viscosity (Chapter 3), and sedimentation (Chapter 3). To complete our introduction to polyelectrolytes, we now discuss their
34
Jay A. Glasel conformational changes due to intra- and intermolecular charge interactions. In a highly charged macromolecule, various charged groups will repel one another if they have charges of the same sign. If the conformation of the macromolecule can change in a way that increases the distance between the charged groups, the electrostatic energy of the molecule will decrease. From what has been previously discussed here, the magnitude of this decrease will be reduced if high concentrations of salt are present. In this case the charged groups will be shielded by the electrical double layer effect. It is for this reason that globular proteins tend to become disordered when they are highly charged at pH values far from their isoelectric point, and that double helical structures such as that of DNA tend to revert to random coils in low ionic strength solutions. Conversely, both effects can be counteracted to some extent by additional salt, increasing the ionic strength. The charge effects in helix-coil transitions of polynucleotides are dominated by the counterion condensation effect. A crucial point here is that the linear charge density on a single-stranded polynucleotide is different than that for a double helix. The values of the parameter ~crit are different for the helical and coiled forms. If ~rit,h and ~crit,c are the helical and coil values of this parameter, respectively, theory predicts 0= 1
-
(1/~crit, c -- 1/~crit, h) =
1 - 77,
where 0 is the number of counterions condensed onto each one of the fixed charges. It turns out that for DNA, rl = 0.32. It can be seen that the number of condensed counterions per charge group decreases by rl when the helix reverts to a random coil form. Most important effects accompanying this change (release of ~/counterions into the solution) are an increase in the entropy of the solution and a change in the energy of interaction of the charged groups with their ionic atmospheres. In fact, theory predicts that the change in energy of interaction, AE, when the helix reverts to a coil, is AE
oc
-
rlkT
ln(c) 1/2,
where c is the concentration of added salt. Because ~/is positive, an increase in salt concentration stabilizes the helix form. We must be concerned with another phenomenon related to disordered proteins and nucleic acids: how the dimensions of a polyion depend on the mutual repulsion of fixed charges, and how this will affect the properties of the solution. The basic phenomenon is called polyelectrolyte expansion. Clearly, any physical measurement that is dependent on the radius of gyration of a macromolecule will be sensitive to conditions that change the magnitude of polyelectrolyte expansion. The polyelectrolyte properties of polynucleotide chains are particularly pronounced and closely related to the properties of synthetic coiling polyelectrolytes, such as polyacrylic and polymethacrylic acids. The characterization of DNA as a wormlike macromolecule in solution (see the discussion of DNA shapes, Section III,B,5) has led to the use of DNA as a model for testing polyelectrolyte solutions. On the other hand, the interest in proteins is in their native structures and in the effects of their polyelectrolytic properties on maintaining those structures, in the functions of the structures, and in the purification techniques to isolate proteins.
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
35
Polyelectrolyte expansion is caused by charge repulsion of like fixed charges on a disordered macromolecule. The tendency is opposed by electrical double layers and counterion condensation around charged groups in proteins and nucleic acids, respectively. As an extension of the discussion presented above, it is clear that adding exogenous salt to solutions of disordered proteins or nucleic acids will tend to oppose their expansion by shielding charges from one another. The only exception to this might be a thermally disordered protein in a pH range wherein the protein contains regions of positive and negative charges that attract one another. In this case the formation of electrical double layers around the charges at high ionic strengths could cause expansion of the chain. However, the main effects on chain expansion are with nucleic acids. Counterion condensation reduces coulombic repulsion among the backbone charges, and therefore reduces the expansion. The effects of changing ionic strength on measurements involving the radius of gyration of nucleic acid chains are very large. Consequently, ionic strengths must be precisely specified for these experiments. The physical and chemical properties of water play important roles in determining the properties of polyelectrolytes, such as proteins, in solution. In particular, two properties of liquid water are mentioned now and will be discussed in more detail later in the chapter. The first is that liquid water at any temperature has lower entropy than one might predict by analogy to other chemically similar liquids (such as its electronic congeners H2S or H2Se). Physical chemists have attempted for years to produce a theoretical description of the dynamic structuring of water that leads to this property. The picture that is widely accepted at present is based on liquid water being described as a mixture of nonbonded individual molecules and transient defective ice structures. In ice, each water molecule is hydrogen-bonded to four other water molecules. For any water molecule in ice, two hydrogen bonds result from partial donations of protons to two adjacent oxygen lone electron pairs and the remaining two bonds result from partial acceptance of protons from adjacent molecules onto the two oxygen lone pairs. The result is a very open but rigid structure for crystalline ice. The picture of liquid water is that of partial continuation of some of this structure when ice melts. It is supposed that small regular icelike structures form and break apart constantly throughout the liquid. The interval between bond formation and breakage is thought to average around 10 - 1 1 10 -12 s e c (Eisenberg and Kauzmann, 1969). A second property of water is also very important to its characteristics as a solvent. This is its high dielectric constant. As in the Debye-H~ickel theory we can generalize the electrostatic (coulombic) force between two charges i and j separated by distance rij in a vacuum as F ~ 1 / Er2j, where E is the dielectric constant of the medium between the charges. The dielectric constant is a dimensionless number. It is always greater than unity, with values of about 1.001 for gases, 2 to 10 for solid insulators such as glass, and from about 87 (0~ to 55 (100~ for liquid water. Thus, the force between two charges is much less in liquid water than when the charges are the same distance apart in a vacuum. This is the reason solid NaC1 dissolves easily in w a t e r m t h e coulombic forces between the sodium and chloride ion pairs are
36
Jay A. Glasel decreased by a factor of up to 87 when liquid water comes between them. However, the dependence of electrostatic forces on the reciprocal square of the distance means that the forces are effective over relatively long distances. Thus, all the ions in a salt solution continue to influence each other even when the solution is very dilute. Physical chemists refer to these as long-range forces. In contrast, many other forces discussed in this chapter depend on intermolecular distances, with powers as high as 1 / r 12. Finally, the dielectric constant of the solvent is of great importance for theoretical studies of protein and nucleic acid conformations in solution. The problem is that Coulomb's law as stated previously is accurate only for a continuous medium. In a polyelectrolyte such as a protein, the charges may only be separated by a few nanometers. Consequently, the m e d i u m between them is not bulk water. There may be room for only a few solvent molecules. What, then, is the dielectric constant of this medium? In many cases theoretical predictions of structure are done on the basis of a fixed dielectric constant with a value between unity and that of bulk water. If the dielectric constant used is unity, the calculation is called a "vacuum" one (Chapter 9). The equilibrium binding of hydrogen ions, metal ions, and other species to proteins and nucleic acids has a marked effect on their macromolecular structures. We first consider hydrogen ion binding by noting that the dissociation of a molecule into its anion and a proton, MH ~.-~-A- + H +, is characterized by a temperature-dependent, ionic strength-dependent, equilibrium constant K. The negative base-10 logarithm of the equilibrium constant is called the pK. The pK value is used to express the acid-base properties of individual ionizable groups on proteins and nucleic acids. For proteins, the important ionizable groups are the N- and C-terminal amino and carboxyl groups, respectively (if they are not "blocked" by chemical substitutions that prevent their ionization), and ionizable side chains of their constituent amino acids. The ranges of pK values for the groups most commonly found in proteins are given in Table VIII. Different proteins contain different mixtures of side-chain residues. They are classified according to whether the ratio, (Arginate + Lysinate) / ~ (Glutamate + Aspartate), is greater or less than one. The sum is taken over all the Arg, Lys, Glu, and Asp residues in the protein. If the ratio is less than one, the protein is called acidic. If the ratio is greater than one, it is a basic protein. Acidic and basic proteins will migrate in opposite directions in an electrophoretic experiment. In a polyacrylamide gel electrophoretic experiment to determine protein molecular mass (Chapter 2), the protein is disordered so that it assumes a flexible form whose radius of gyration is proportional to its macromolecular length and therefore to its molecular mass. It is then usual to cause the disordering with an amphoteric detergent such as sodium lauryl sulfate (also called sodium dodecyl sulfate, SDS) that has a negative charge over a wide pH range and a hydrophobic group
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
37
Table VIII pK Values for Common Acidic and Basic Groups in Proteins Group or residue
Approximate pK range in proteins
Unblocked amino-terminal residue Unblocked carboxy-terminal residue Arginine Lysine Cysteine Histidine Aspartic and glutamic acids Tyrosine
7.6-10.6 3.0-5.5 11.5-12.5 9.8-10.4 8.0-9.0 6.0- 7.0 4.0-4.8 9.5-10.5
that binds strongly to all disordered proteins. This coats the protein molecules with large numbers of negative charges so that regardless of whether their native forms are acidic or basic, the disordered, SDS-treated proteins always migrate as a polyanions. At some pH, whether they are initially acidic or basic, native proteins will assume a formal net charge of zero. That is, the total average charge is zero at this pH, even though they may have large (but equal) numbers of positive and negative charges. This point on the pH scale is called the isoelectric point (the pH at that point is usually designated the P/e)- Given the amino acid composition of a protein, an approximate pie can be calculated theoretically. The calculations are easily done on a computer and several computer programs exist to do this, and to plot out the resulting predicted titration curve. For example, the popular GCG molecular biology program has such a subprogram. These theoretical isoelectric points are approximate because the effects of the array of fixed charges in a polyelectrolyte on each pK value cannot be taken into account accurately for reasons given above. However, it is true that isoelectric points for a protein can be measured accurately (Chapter 2), and can be used to help characterize a protein. The measurement is sensitive enough to detect a change of one formal charge difference between two proteins. This means that mutations or substitutions involving an ionizable residue can be detected this way. Preparative isoelectric focusing is also possible as a method of purifying proteins. At the isoelectric point, while the net average charge on the protein, (Zp), is zero, molecules in solution will carry different electric charges at any given instant. Thus molecules with charges of 0, + 1, + 2, . . . , - 1, - 2, . . . will be present. For example, Fig. 13 shows the fractions of different charge forms for hemoglobin at its isoelectric point. Figure 13 shows that there are significant numbers of molecules with net charges between + 4 and - 4 at any instant. Because of this, the mean square charge (Zp) is not zero. This phenomenon has important consequences for the electrostatic properties of proteins because it results in a large effect on the activity coefficient of the protein. In particular, theoretical treatment (Timasheff, 1970) shows that the charge fluctuations re-
38
Jay A. Glasel 0.25
I
i
I
i
I
I
i
2
4
6
0.20 L'XI
N
(D
"~ 0.15 O3 C C
o
0.10
_
0 t-,
LL 0.05
.
I
-6
-4
-2
0
Z2 Fig. 13 Distribution of forms with net charge (Z) for isoelectric hemoglobin. Reprinted from Timasheff (1970), p. 9, by courtesy of Marcel Dekker, Inc.
sult in a significant attractive force between protein molecules at their isoionic point if the ionic strength of the solution is low. In the limit of low concentration, the net attraction is proportional to the square root of the protein concentration. As a practical matter, the effect is of interest because protein molecules held at their isoelectric points tend to precipitate due to the attraction between them. Another effect the charges on proteins have at pH values different from their isoelectric values is important in crystallizing the proteins. Both the anions and cations in a salt solution are highly hydrated. That is, the ions are quite tightly bound to water molecules, which surround them in at least one layer. At very high salt concentrations, possible with salts such as ammonium sulfate (which is saturated at 4.1 M at 25~ so little water may be available to solvate the protein that the protein molecules are driven to polymerize. The polymerized proteins may then come out of solution in some disordered polymeric form. This is called salting out a protein. The effect can be used as a crude form of purification because different proteins will salt out at different salt concentrations. However, of equal or greater importance, if the salt concentration is increased slowly under controlled temperature conditions, many pure proteins crystallize out of solution. This is the basis of many efforts to crystallize proteins for use in X-ray and neutron diffraction studies (Chapter 8).
D. Magnetic Properties One can build an intuitive picture of certain atomic properties by using a picture of an atom that disregards the wave-mechanical picture of electron proba-
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
39
bility clouds around nuclei and pictures instead electrons in orbits circling atomic nuclei. When a steady external magnetic field is applied to such an atom, the motions of the atom's electrons are altered. The alteration produces an induced electrical current within each atom. Electrical currents always have magnetic fields associated with them, and for the orbital electrons just mentioned, the directions of the induced magnetic fields are always opposed to the direction of the steady applied field. These induced magnetic fields have effects within each atom, most importantly on their own nuclei, and on other atoms and nuclei that may happen to be in the same molecule. The production of these induced fields is just an extension of Lenz's law, a law discovered in the nineteenth century. According to Lenz's law, the current induced in a circular loop of wire by an applied magnetic field corresponds to a magnetization in the direction opposing the field. Because all molecules have electrons, they all respond to externally applied magnetic fields by tending to oppose them. This behavior is called diamagnetism. Note that an electrical field always induces an electrical dipole moment (electrical polarization) in the direction of the field. There is no electric analog of diamagnetism. The amount of diamagnetism a molecule exhibits, the diamagnetic susceptibility, can be measured. The diamagnetic susceptibility of even a macromolecule may be calculated to a good approximation by adding up the tabulated susceptibilities of groups of atoms within the whole molecule. In certain cases, the diamagnetic susceptibility of a group of atoms depends importantly on the spatial direction of the external field with respect to the group of atoms. The case of most importance to biophysical chemistry is that of aromatic rings. In aromatic rings the ~r electrons are, of course, delocalized. But they are delocalized in a highly directional way. For instance, when the plane of a benzene ring is perpendicular to the external field, maximum diamagnetic susceptibility is exhibited by the benzene molecule because the delocalized electrons can travel easily around the track formed by the ring. When the ring plane is parallel to the applied field, the diamagnetic susceptibility is minimized because the direction of the driving force is across the plane of the ring and therefore not part of the normal track of the electrons. Why is this effect of importance for macromolecules? The answer is that for certain macromolecules, particularly proteins and nucleic acids, aromatic rings are in fixed orientation with respect to other nonaromatic groups. Magnetic fields are characterized by "lines of force." For a steady applied homogeneous magnetic field, the external field's lines of force are parallel and evenly spaced. At the molecular level, the presence of intramolecular centers of high diamagnetism, such as caused by an aromatic ring, distort the lines of force away from homogeneity. This distortion can extend to the total (applied plus induced) field seen by neighboring atoms or groups of atoms. Certain techniques, particularly NMR (see Chapter 7), can detect the effect on these atoms in a way that is useful for identification of atoms near aromatic groups. Furthermore, the basic diamagnetic effect just outlined is the physical basis for the NMR phenomenon called the chemical shift. Thus, the position of the spectral features of aromatic amino acids in an NMR experiment is determined by their rings' extremely large diamagnetic susceptibility. In 1845, while investigating the effect of a magnetic field on the optical properties of substances, Michael Faraday discovered that magnetic properties
40
Jay A. Glasel are not confined to a few substances, but that all substances are magnetic (i.e., they interact with an external magnetic field). He discovered that all substances can be divided into two classes, diamagnetic substances and paramagnetic substances; those in the first class, we have already discussed m they are repelled from an applied magnetic field. Those in the second class are attracted into a magnetic field even though they also have a repelling component (their essential diamagnetism). Many biologically important macromolecules have paramagnetic moments associated with them. Usually, this comes about when there is an ionic or covalent bond between the macromolecule and a molecule or ion that has an unpaired electron associated with it. An example of the former is molecular oxygen, and examples of the latter are transition metal ions. The origin of molecular paramagnetism is the interaction of unpaired electron magnetic dipole moments with an externally applied magnetic field. Molecular paramagnetism is the magnetic analog of dielectric polarization. On the other hand, in Chapter 7 the interaction of certain nuclei with magnetic fields is described in terms of nuclear paramagnetism, which is the basis of NMR experiments. Electron paramagnetism arises because electrons have the physical properties of not only mass and negative charge, but also have the property that they are intrinsic magnetic dipoles. According to the Pauli principle, in most cases electrons in molecules are paired in such a way that their magnetic dipoles cancel out. The presence of an unpaired electron within the framework of a macromolecule confers to the macromolecule a measurable p r o p e r t y m overall paramagnetism. Overall paramagnetism is usually much larger, and in the opposite direction from the ubiquitous diamagnetic moment. Its magnitude is also temperature dependent, in contrast to diamagnetism. Additionally, the paramagnetic ions or molecules are often located at the site in proteins associated with the biological function of the macromolecule. For example, the oxygen molecule in oxyhemoglobin is closely associated with the iron atom of the heme group. Also, transition metal ions are often located at the active sites of enzymes, where they are required for activity. Thus, the paramagnetic moment of the macromolecule may be affected by reactions that change the valence state of their paramagnetic moieties. In this book we have not included a discussion of this type of measurement, termed electron spin resonance (ESR). However, there is another effect of paramagnetic molecules and ions. Because the unpaired electron magnetic moment is almost 2000 times larger than the nuclear magnetic moment, the presence of materials with unpaired electrons anywhere in a macromolecule (or even in a solution containing the macromolecule, such as dissolved oxygen) has an enormous effect on nuclear magnetic resonance measurements of all kinds. These effects are mentioned in Chapter 7.
E. Kinetic Properties In solution, molecules undergo translational diffusion (with components in the x, y, z directions in a Cartesian coordinate system) and rotational diffusion (specified by angles 0 and q~ in a spherical coordinate system). It is normally assumed that these processes are independent of one another and that both take place due to random collisions of molecules. Strictly speaking, translational
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
41
diffusion is characterized by three translational diffusion coefficients. However, translational diffusion is almost always assumed to be isotropic (meaning movement in any direction is equally probable) as opposed to anisotropic (where there are favored directions) and therefore can be characterized by one diffusion coefficient. As an intuitive approximation we can picture translational diffusion as taking place by discontinuous jumps of a molecule from one position to another. In a liquid the number of collisions that a given molecule undergoes per second is very large, abut 1015/sec. If the mean value of the square of the displacement is ~$2~ (this quantity is normally called the net mean-squared displacement) in any direction after time t, the translational diffusion coefficient is Dtran s =
~/~5~2/t.
D usually has units of cm2/sec. A more rigorous classical treatment for translational diffusion of a sphere was given by Stokes: Dtran s =
kT/6yr,/a,
where ~/is the viscosity of the liquid and a is the radius of the sphere, k is Boltzmann's constant, and T is the absolute temperature. Physical chemists are often interested in diffusion in pure liquids. For this case the diffusion coefficient is referred to as the self-diffusion coefficient. Here, we are interested in diffusion coefficients for macromolecules in aqueous solutions. Thus, for equally hydrated spherical molecules of molecular mass M, classical theory predicts that the diffusion coefficients should vary as 1 / M 1/3. This is approximately true. For example, ribonuclease (M = 13,683 Da) and urease (M = 480,000 Da) have translational diffusion coefficients of 11.9 x 10 -7 and 3.46 • 10 -7 cm 2 sec -1, respectively, at 20~ In contrast, water molecules have a selfdiffusion coefficient of about 10 -5 cm 2 sec -1 at the same temperature. Translational diffusion coefficients are of importance in understanding biomolecular interactions, especially the type of reaction involving a small molecule binding to an active site on a macromolecule (e.g., enzyme-substrate, receptor-drug, antibody-hapten binding). However, experimentally, translational diffusion coefficients are difficult to measure directly. The most convenient methods are probably intrinsic viscosity and sedimentation equilibrium experiments (Chapter 3). Rotational diffusion is a more complex subject to discuss theoretically, compared to translational diffusion. The reason is that most molecules, especially macromolecules, do not have overall spherical shapes. That is, they would be expected to undergo anisotropic rotational motions. Classical theory shows that the random rotational path of an irregular body dissolved in a liquid is described by a mathematical function (called a "tensor") with nine components. When interpreting data that depend on rotational diffusion (e.g., nuclear magnetic resonance relaxation times; Chapter 7), it is almost always assumed that anisotropic rotational diffusion can be described by, at most, three components. This assumption is based on the intuitive idea that rotational diffusion takes place around the same principal axes of the moment of inertia of the
42
Jay A. Glasel molecule. Strangely enough, although various sophisticated theories have been developed to describe rotational diffusion for molecules in solution, it is described very well in most cases by a simple equation developed by Einstein early in his career. This equation gives the rotational diffusion coefficient for a sphere: Dro t =
kT/8,rr,oa 3,
where a is the radius of the sphere and the other symbols have their previous meanings. Note that the units for Dro t (radians sec -1) are different from the units for translational diffusion. Rotational diffusion describes the path a point on the sphere takes as a function of time due to random rotational reorientations. Figure 14 shows what the path might look like. Consequently, if (/~-~2) is the net mean-squared angular rotation of the sphere in radians in time t, Drot ~_~ ~/~-~2) /
t,
in analogy to the similar expression for translational diffusion. The predicted rotational diffusion coefficient for a macromolecule of mass 50,000 Da in water is about 4 • 10 6 sec -1, whereas that for a water molecule is about 5 • 101~s e c -1. These values are very close experimentally to measured ones. The molecular mass dependence of Dro t f r o m this picture is much larger than for Dtran s. The rotational diffusion coefficient depends on 1 / M . Provided rotational diffusion is assumed to be isotropic, parameters derived from several different measurements can give experimental values for Dro t . In particular, NMR relaxation measurements are used (Chapter 7). Conversely, isotropic rotational diffusion has to be assumed to interpret data in terms of macromolecular structures derived from NMR measurements. In NMR relaxation experiments, the quantity being sought is the "correlation time." The correlation time can be explained as follows. At an initial time, t = 0, we assume each atom in a rigid
zl Aj
I I
Fig. 14 An example of a rotational random walk from point A to point B on a sphere. From Carrington and McLachlan (1967).
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
43
molecule has some starting x, y, z coordinates with respect to axes fixed in space (these axes are often referred to as "the laboratory frame of reference"). At succeeding times, as the molecule undergoes random angular jumps, its alignment (that is, its atomic coordinates in the fixed axis system) begins to lose any deterministic relation to its alignment at t = 0. There is only a probability that it was aligned in the initial direction. This is expressed by a function called a correlation function that expresses the loss of statistical correlation between initial atomic coordinates and those at any later time. The rate at which this correlation is lost is exponential and is characterized for each spherical molecule, by a time called the correlation time, rc, that is related to the rotational diffusion coefficient by the simple equation, rc = 1 /
6Dro t .
For the macromolecule mentioned above with mass 50,000 Da, the correlation time is about 4 • 10 -8 sec. In one correlation time (0.04 ~sec) the net angle tuned will be about 33 ~ (31/2 radians) from any initial alignment. For anisotropic rotational diffusion the situation is more complex, but can be solved analytically provided it is assumed that rotational diffusion can be described by three rotational correlation times and that rotational motions take place around the moments of inertia principal axes, as described above. A more difficult situation is when there is intramolecular rotational diffusion. Simple examples are methyl group rotation and aromatic ring flips in proteins and nucleic acids. These motions are superposed onto the overall macromolecular motions. In general, there are different correlation times associated with each of the different motions. An analytical solution for the case of a methyl group freely rotating in a macromolecule has been found. However, this is the only such solution for this type of problem. F. Color In this section we are concerned with the basic concepts of spectroscopymthat is, how electromagnetic waves of different wavelengths interact with matter. At the heart of this discussion are the basic principles of quantum mechanics. If we generalize our common knowledge of color to include the results of interaction of electromagnetic radiation, irrespective of wavelength, with matter, then we can unify all the forms of interaction into one general physical picture. That is, the elements of spectroscopy that are discussed below are basic to all particle, atomic, and molecular systems. For our purposes, matter has the following properties that interact with electromagnetic radiation: 1. Permanent or induced molecular electrical dipole, and multipole, moments 2. Permanent atomic magnetic dipole moments 3. Electron and nuclear magnetic dipole moments One of the greatest examples of the unification of ideas in the short history of science took place in the 1860s and 1870s when Maxwell was able to combine the physical description of electromagnetic radiation with that of electricity and magnetism. Thus, he considered an electrical dipole moment held apart by some means, and asked, in effect, what the physical result is of two charges
44
Jay A. Glasel oscillating in simple harmonic motion with respect to one another. The equations he developed permitted a solution to this problem. The result can be described by saying that the oscillating dipole emits (loses) energy into its surroundings in the form of an electromagnetic wave. Electromagnetic radiation is made up of electric and magnetic field vectors whose magnitudes oscillate with time at a frequency v = ro/2~r radians sec-1 [09 is in units of hertz (Hz)] and propagate with the speed of light c (see physical constants). Figure 15 shows the space variations of the electric and magnetic field vectors (with magnitudes E0 and H0, respectively) in a plane-polarized wave propagating along the x axis in a Cartesian coordinate system. For this wave, Ey = E0 sin ro(t + x / c ) , G = H0 sin ro(t + x / c ) . The wavelength of the wave is ,~ = c l ~,.
In the past, the phase of a wave was defined as rot + ro x / c
and therefore the phase changed with time. At present, the time-invariant constant, rox/c, is sometimes called the phase, and sometimes the phase angle or phase shift. We will call q~ the phase angle of a wave. The point is, different q~ values correspond to motions in different phases of each wave. in the wave drawn in Fig. 15, consider a fixed plane at x = constant, transverse to the direction of propagation. At all points of this plane, the electric field intensity Ey oscillates in simple harmonic motion with angular frequency ro and amplitude E0. We describe all these motions as being in phase with each other. Thus, at any fixed point in space the electric vector performs simple harmonic motion along a fixed direction (the y axis), and the magnetic vector performs a similar vibration in a direction normal to this (the z axis). This wave is called a linearly polarized wave because the electric field vector at any point is directed along a
Y
,~'" J
Fig. 15 The space variations of the magnitudes of the electric (E0)and magnetic (H0)field vectors in a traveling sinusoidal plane wave that is linearly polarized.
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
45
fixed line at all instants of time. A more general case, for a given frequency, is that there are both x and z components for both electric and magnetic fields. The resultant vectors, at a fixed point in space, will sweep out ellipses in the y - z plane. Such a wave is called elliptically polarized. A circularly polarized wave is the special case of the ellipse; that is, the two simple harmonic motions are of equal amplitude and have a 90 ~ phase difference. Finally, in an electromagnetic wave the electric and magnetic field vectors are not independent. In fact, the magnetic vector oscillates in phase with the electric vector. If the radiation were due to many dipoles vibrating in random directions with no phase relation to each other, then there would be (1) no plane of polarization and (2) no phase coherency for the emitted radiation. Radiation without phase coherency is called incoherent. It will turn out that all natural radiation (e.g., radiation from the sun) and some man-made radiation (e.g., a light bulb) are incoherent. On the other hand, some man-made radiation is coherent (e.g., laser light). Natural radiation and sources such as light bulbs produce radiation with no preferred plane of polarization. However, using filters that specifically absorb light from all planes of polarization except one, these sources can be made to yield planepolarized, incoherent radiation. The way that this light interacts with macromolecules forms the basis of the optical rotatory dispersion and circular dichroism experiments described in Chapter 6. The brief picture outlined above is the classical description of the production of electromagnetic radiation and of its interaction with electrical and magnetic dipoles. The meaning of the word classical, as used in the physical sciences, is that the phenomenon being described is nonatomic, and nonrelativistic. That is, classical physics involves descriptions and interactions of large bodies moving slowly compared with the speed of light. The classical description suffices to explain some phenomena in everyday lifemfor example, how radio waves are produced and received. However, when applied directly to atomic phenomena the classical picture fails. For example, it predicts that within a chamber made up of material consisting of large numbers of our atomic oscillators there would be an infinite electromagnetic radiation density. The reason is that classically, some of the oscillators can be oscillating at infinitely high frequency. This would produce light of ultrashort wavelength. This prediction of classical physics was called the "ultraviolet catastrophe" when its implications were understood at the beginning of the twentieth century. Reportedly, Lord Kelvin, one of the best classical physicists of the time, said words to the effect that all of physics was known except for two clouds hanging over its head. One cloud was the ultraviolet catastrophe, the other was the failure of the Michelson-Morley experiment (the failure to detect the ether that was thought to be the medium through which electromagnetic radiation traveled). The resolution of the first cloud led to the discovery of quantum mechanics and the resolution of the second led to the discovery of special relativity. This was cloud-choosing at a high level. In an intellectual event of enormous practical importance, Max Planck was able to unify the classical and atomic pictures before atomic structure was known. He did so by assuming that the classical picture of radiation emanating from oscillating dipoles was fundamentally correct. However, in a complete break from classical thinking, he assumed two things:
46
Jay A. Glasel 1. The atomic oscillators vibrate at discrete frequencies characterized by energy levels En =
nhv,
where n is an integer, h is what Planck defined as a new fundamental constant of nature (now called Planck's constant; see Glossary, physical constants), and v is the frequency of the oscillators. 2. The probability W(n) of an oscillator existing in an energy state E n is given by the Boltzmann distribution law, W(n) ~ e x p ( - E n / k T ) = e x p ( - n h v / k T ) ,
where k is the Boltzmann constant and T is the absolute temperature. From these two assumptions and the results of Maxwellian classical theory, Planck derived the equation describing the distribution of radiation frequencies within the chamber described above, held at a certain temperature, and from which radiation cannot escape. Such chamber is called a black box. Planck's equation described the distribution of frequencies found experimentally in black boxes. This was the origin of quantum mechanics. The basic concepts of quantum mechanics, discrete energy levels for the oscillators and the level populations, are all we really need to know to develop a physical understanding of all forms of interaction of electromagnetic radiation with matter. Einstein used the Planck discovery to derive some of what we need to understand. His reasoning was as follows. Assume that a dipole does have discrete energy levels, and consider two of them: the mth and the nth. Einstein assumed that when light of the right frequency falls on such a dipole, the dipole can absorb that photon of light and make a transition from state n to state m. The probability that this occurs each second depends on which starting level we are considering, but for all levels Einstein assumed that the probability is also proportional to the intensity of the light. He called this absorption probability, Bnm. He also assumed that light is emitted by the oscillating dipole and that emission can take place in two ways. One way is spontaneous emission with probability a m n . In this process the dipole in excited state m loses radiation independent of any light falling on it. Another emission process he assumed is again under the influence of the light falling on the excited oscillating dipole-stimulated emission. The rate for this he again assumed is proportional to the intensity of light and has a probability Bran. With these assumptions, Planck's black box law, and the laws of thermodynamics, Einstein deduced the following: Bnm = Bmn ,
Amn = KB,nn,
where K is a constant made up of other fundamental physical constants (such as the speed of light). Stated in plain language, Einstein's results are that the probability of absorption is equal to the probability of stimulated emission, and if we know the probability of absorption (or induced emission) we can calculate the probability of spontaneous emission. Note that no assumption as to the nature of the dipoles has been made. They can be atomic dipoles due to the separation of nuclei from their surround-
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
47
ing electrons, they can be nuclear magnetic dipoles, they can be permanent molecular electric dipoles due to a molecule being made up of atoms of different electronegativity, etc. They are all subject to the same phenomena of induced absorption and emission and spontaneous absorption and the mathematical relation between these. Once we understand the implications of Einstein's and Planck's results, the way is open to exploiting them to understand all forms of spectroscopy applied to biomolecular systems. It is also useful to have an idea of the magnitudes of the probabilities just mentioned and how they affect spectral results. For a strong electric dipole transition in molecules, iron is on the order of 108 sec-1, and for magnetic dipole transitions, Am,, is on the order of 10 -3 sec -1. The quantum mechanical uncertainty principle relates the spectral width, &v, of an absorption band to the lifetime of the excited state by the simple equation A ~ = Am n
where v is in units of radians per second. Thus, a strong electric dipole transition (e.g., ultraviolet absorption) can be expected to have a spectral line width of 108/2~r Hz, whereas a magnetic dipole transition (e.g., an NMR absorption band) can be expected to have a spectral width of 10-3/2"rr H z - - t h a t is, 1011 times narrower. We also note that if the probability of spontaneous emission is low, as it is for magnetic dipole transitions, then the only path for loss of excitation energy is induced emission and that requires radiation of the same frequency as for excitation. In fact, if the radiation continuously falls on a transition with low probability of spontaneous emission, the upper and lower states rapidly become equal in population. The result is no net absorption of energy from the incident radiation. The low probabilities for spontaneous emission and consequent possibility of equalizing populations of upper and lower energy states are associated with nuclear magnetic resonance and form the basis for understanding the "relaxation" and "saturation" phenomena that are discussed in Chapter 7. Continuing our applications of Einstein's results we can easily understand the principle behind lasers. The acronym "laser" is very descriptive: light amplification by stimulated emission of radiation. In the simplest example of a laser, we have brought about an atomic or molecular system consisting of three energy levels. Conditions are arranged so.that the highest energy level has a very high probability of spontaneous emission to a middle state characterized by a low probability of spontaneous emission. Therefore, when light whose energy corresponds to the transition from the ground (lowest energy) level to the highest level falls on the system, we will pump atoms or molecules from the ground state to the highest energy state. However, as we are pumping them, they are continuously dropping to the middle state and giving off radiation with energy corresponding to the difference between upper and middle levels. This energy is lost to us but, if we pump enough, we will have succeeded in producing a middle energy level that is very highly populated. Now, if just a little light of energy, corresponding to the difference between the highly populated middle level and the ground level, falls on the system, Einstein's result says that it will stimulate emission of radiation of that energy. This will stimulate more emission, etc., until the populations of upper and lower energy levels regain their Boltzmann distributions. Thus, this is a way to stimulate large
48
Jay A. Glasel Molecular energy
Frequency
Region
Wavelength
1019 _ u Electronic
(inner
shells)
I0 m i0 rt _ 1016
Electronic (valence
shells)
Vibrational
_
iOts _ i014 _ i013 _ i012 _
Rotational
i 0 II _
i0 jo _ I09
t 108 X-ray
_ _ 10-8
1--I07
_ _ 10-7
I 106 Vacuum U V i- lOS Ultraviolet (U V) J 104 Visible
_ _ 10-6
1_103 Infrared (IR) 1 i02
~
For IR
110 Millimeter
crn-~
Microwave
IO-S _ _10 -4 -
-10-3
_ _ 10-2
10-1
m
--1 --I0
-
-
-10
2
I0 e - Nuclear orientation
(high
fields)
107--
Rodiofrequency
_ _ 10 4
106 - _
_ _ i0 5
IOs - _ 104-103 - _ Nuclear orientation (zero
field)
102 - _
_ _ 10 3
_ _ 10 6
Audiofrequency
_ _ i0 ? _ _
cm
108
I0-cycles/seconds
Fig. 16 Nomenclature of various frequency and wavelength regions and the types of spectroscopy with which they are associated. From Whiffen (1966).
amplifications of light. What has just been described is the principle underlying a pulsed laser. When the pumping is continuous, stimulated emission is continuous and we have a continuous laser. In summary, the vibrating dipole picture as modified by quantum mechanics may be used to visualize phenomena in all of spectroscopy. It does not matter whether we are talking about a nuclear magnetic dipole or a molecular electric dipole. The principles are the same. For electronic spectroscopy the vibrating dipoles correspond to electronic motions with respect to the nuclei of atoms and molecules. For vibrational spectroscopy the dipoles correspond to permanent or induced molecular electric dipole moments. For magnetic resonance spectroscopy the dipoles correspond to the motions of the nuclear (or electron) magnetic moments. Figure 16 shows the energies, frequencies, and descriptions of various parts of the electromagnetic spectrum used for different spectroscopy experiments on molecules.
IV. Fourier Transforms The readers of this volume will find the process called the Fourier transform used in several chapters (in different guises). This is a case in which a funda-
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
49
mental physical principle assumes different manifestations. The Fourier transform is, in fact, a pervasive and useful tool in the physical sciences. Fortunately, Fourier transforms are familiar to almost all of us, not as abstract mathematical operations, but as definite physical operations. We will first describe the fundamental principle for periodic time-varying quantities, i.e., waves. However, as we will later point out, the same principle holds for any periodically varying quantity. Imagine two sine waves (as a physical example, violin strings vibrating at the same time but at different frequencies) added together. Figure 17 shows the individual frequencies and the resultant total waveform that results from the linear superposition of the two frequencies. Even with two sine waves, Fig. 17 shows a fairly complicated curve. Clearly, this could be extended to a large number of different waves, giving a very complex total waveform. It is also true that almost any curve can be obtained by adding together infinite numbers of sine waves of different frequencies. If we know each of their amplitudes, we can produce the total curve. This method of analyzing a periodic function is called the method of Fourier transforms or, occasionally, Fourier analysis. How is it done? The answer is that it can be done both mechanically and mathematically. Indeed, each of us does Fourier transformation almost continuously. If our sense of hearing could not sort out the different waveforms we could never pick out speech or musical tones amid superimposed noisemsomething we are normally very good at. In fact, our ears take in sounds (mixtures of time-varying amplitudes of acoustical waves) and convert them to spectra (time-varying amplitudes of different frequencies). Our ears do this by having groups of specialized detectors in the inner ear. Each group responds with high sensitivity to only a narrow range of the many frequencies that we just saw can be contained in the incoming waveform. The ear therefore reacts to sound by breaking down the incoming waveform into different frequency components. Each group of frequency-specific cells has an output signal that is proportional to the amplitude (intensity) of the sine wave component at that frequency. In short, the output of the assembly of groups is a Fourier transform of the incoming total wave. By mechanisms we are still discovering, the brain decides to interpret frequency components whose amplitudes vary regularly, such
Fig. 17 A complex waveform resulting from linear superposition of two sine wave functions F a and F b .
50
Jay A. Glasel as speech and music, and rejects as noise those whose amplitudes are randomly varying. To do this, the brain must obviously use the information that the amplitudes at the different frequencies vary in time. In an almost exact analogy, when we want to convert an electromagnetic waveform into its components, we can pass the wave through an electronic device that has groups of elements that each respond only to a narrow frequency range. This device is called a spectrum analyzer. When attached to an oscilloscope, it enables us visually to see the amplitudes of the different frequency components making up the wave and how the amplitudes vary in time. That is, we can continuously view the Fourier transform of the incoming wave. An optical mechanism for doing the same thing is a prism or optical diffraction grating. The incoming waveform of light is broken up into its component frequencies by the action of the dispersive element (i.e., the prism or grating). We call the result a spectrum. Thus, a waveform, whether optical, electrical, or acoustical, and its spectrum are physically equivalent representations of the same thing. Mathematically, we call the two representations "Fourier transform pairs." From the above information, we know that physical (or physiological) devices can analyze complex curves into sums of sine waves of different amplitudes. Can this be put into a mathematical form so that, given the equation for the curve to be analyzed, we can get the amplitudes of the waves making up the curve? The answer is, of course, yes. The mathematical forms for a continuous Fourier transform pair are
1 L F(co)ei~ dco,
f(t) = ~ F(co) =
f
--
oo
f(t) exp -i~t dt, oo
where F(co) and f(t) are the Fourier transform pair in the frequency and time domains, respectively, and i is the complex number symbol. The function F(co) is commonly called a spectrum. For those readers not used to seeing complex numbers in integrals, more understandable forms of these general equations are produced when the relation, e +-i~~
=
c o s ( c o t ) -4-
/sin(cot),
is substituted into the above equations. Thus, F(co) becomes
F(co)=Lf(t)cos(cot)dt+iLf(t)sin(cot)dt. In many cases in physics, a mathematical equation is known for f(t) and therefore the integrals can be solved exactly. However, for our present purposes a detailed mathematical discussion is not very useful, because in the experiments described in this volume, the curves are complicated and no simple equation describes them. In some experiments, what is done with these complicated curves is to mathematically approximate their Fourier transform. For example, if the curve is a time-varying waveform, such as described above, we can make the following change. Instead of the spectrum analyzer device, we substitute a computer that samples the waveform's total amplitude as a function of time. The computer puts each sample into a different memory location along with a digital representation of its amplitude at the time the sample was made. Thus,
Chapter I Basic Physical Properties of Proteins and Nucleic Acids
51
amplitude vs time has been stored in the computer's memory. In contrast to the case in which time is continuous, the time elements here are discrete. Consequently, the approximate Fourier transform is called a discrete Fourier transformation. In even the most perfect experiment with the largest computer, we can study f(t) for only a finite amount of time; we cannot ask the computer to do the integration required in the continuous form of the Fourier transform. Instead we ask the computer to approximate the integration by a summation over the time elements for which it has amplitude information. This is called a discrete Fourier transform (DFT). The development in the 1960s of the fast Fourier transform (FFT) computer algorithms to evaluate DFTs provided means of rapidly calculating spectra of time-varying signals. We can easily see that this is much better than a physical device such as a spectrum analyzer. In an electronic analyzer only a relatively few filter elements can be present, because they are bulky. However, a modern computer's memory can contain a staggering number of memory elements. Obviously, the more samples that are taken, and smaller the sampling time, the better the approximation to the spectrum the DFT is going to be. We have described what Fourier transforms are and how they apply to time-varying waveforms. In this volume this is applied to modern NMR spectroscopy (Chapter 8). However, at the start of our discussion we mentioned that Fourier transform techniques also apply to any periodic functions. Another way a function can be periodic is to have a spatially periodic value. An example of this is atoms arranged periodically in space. In the chapter on X-ray and neutron diffraction (Chapter 7) we will see Fourier analysis applied to analysis of the diffraction pattern resulting from X-rays or neutrons falling on a crystal. A good monograph on Fourier transforms and analysis exists (Bracewell, 1986).
V. Summary The biophysical principles discussed in this chapter are the basis for methods discussed in succeeding chapters in this book. In the effort to obtain biophysical knowledge of proteins and nucleic acids, students and investigators must keep in mind the basic purpose of the knowledge. That basic purpose is to relate biophysical properties to biological function. Thus, for example, it is wonderful to be able to sequence a gene, predict the sequence of the protein it encodes, isolate the protein, and then perhaps determine its three-dimensional structure. However, even at this advanced stage of knowledge of a particular system, we still have a long way to go toward relating it to the functioning of a living system. This presents a challenge, because the basis for all our work is the hypothesis that life--that is, the integrated functions of small molecules, proteins, and nucleic acids m i s based on known rules of physical chemistry. Meeting this challenge will be a major task for twenty-first century biological science.
References Avery, O. T., MacLoed, C. M., and McCarty, M. (1944). Studies on the chemical nature of the substance inducing transformation of pneumococcal types. I. Induction of transformation by a desoxynucleic acid fraction isolated from pneumococcus type III. J. Exp. Med., 79, 137-158.
52
Jay A. Glasel Bloomfield, V. A., Crothers, D. M., and Tinoco, I., Jr. (1974). "Physical Chemistry of Nucleic Acids." Harper & Row, New York. Bracewell, R. (1986). "The Fourier Transform and Its Applications" 2nd ed. McGraw-Hill, New York. Branden, C., and Tooze, J. (1991). "Introduction to Protein Structure" Garland Publishing, New York and London. Carrington, A., and McLachlan, A. D. (1967). "Introduction to Magnetic Resonance." Harper & Row, New York. Dickerson, R. E., and Geis, I. (1969). "The Structure and Action of Proteins." Harper & Row, New York. Eisenberg, D., and Kauzmann, W. (1969). "The Structure and Properties of Water." Oxford University Press, New York. Eisenberg, H. (1976). "Biological Macromolecules and Polyelectrolytes in Solution." Oxford University Press (Clarendon), Oxford. Flory, P. J. (1953). "Principles of Polymer Chemistry." Cornell University Press, Ithaca, NY. Flory, P. J. (1969). "Statistical Mechanics of Chain Molecules." Wiley (Interscience), New York. Goodsell, D. S., and Olson, A. J. (1993). Soluble proteins: Size, shape and function. Trends Biochem. Sci. 18(3), 65-68. Leslie, A. G. W., Arnott, S., Chadrasekaran, R., and Ratliff, R. L. (1980). Polymorphism of DNA double helices. J. Mol. Biol. 143, 49-72. Manning, G. S. (1972). Polyelectrolytes. Annu. Rev. Phys. Chem., 23, 117-140. Morawetz, H. (1975). "Macromolecules in Solution," 2nd ed. Wiley, New York. Nomenclature (1970). Commission on Biochemical Nomenclature. Abbreviations and symbols for the description of the conformation of polypeptide chains. J. Biol. Chem. 245, 6489-6497. Nomenclature (1983). Commission on Biochemical Nomenclature. Abbreviations and symbols for the description of conformations of polynucleotide chains. Eur. J. Biochem. 131, 9-15. Richards, E. G. (1980). "An Introduction to the Physical Properties of Large Molecules in Solution." Cambridge University Press, Cambridge, UK. Richardson, J. S. (1981). The anatomy and taxonomy of protein structure. Adv. Protein Chem. 34, 167-339. Saenger, W. (1984). "Principles of Nucleic Acid Structure." Springer-Verlag, New York. Saenger, W., and Heinemann, U., eds. (1989). "Protein-Nucleic Acid Interaction." CRC Press, Boca Raton, FL. Tanford, C. (1961). "Physical Chemistry of Macromolecules." Wiley, New York. Testa, B. (1979). "Principles of Organic Stereochemistry." Dekker, New York. Timasheff, S. N. (1970). Polyelectrolyte properties of globular proteins. In "Biological Polyelectrolytes" (A. Veis, ed.), pp. 1-64. Dekker, New York. Whiffen, D. H. (1966). "Spectroscopy." Wiley, New York.
GLOSSARY Ampholytes Amphoteric electrolytes. Small multicharged organic buffers used to establish pH gradients in isoelectric focusing. Amphoterir Referring to molecules, such as proteins, capable of positive, negative, or zero net charges. Anolyte
The electrolyte at the anode of an electrophoresis cell.
Blotting Any of several methods in which sample molecules are probed while on the surfaces of synthetic membranes. Capillary electrophoresis ( C E ) Electrophoresis carried out in capillary tubes, with migration of the sample down the axis of the tube. Capillary gel electrophoresis (CGE) in gel-filled capillaries.
Capillary electrophoresis carried out
Capillary zone electrophoresis (CZE) The simplest form of capillary electrophoresis in which a homogeneous buffer is used throughout the system. Introduction to Biophysical Methods for Protein and Nucleic Acid Research
53
Copyright 9 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.
54
David E. Garfin The electrolyte at the cathode of an electrophoresis cell. Catholyte Clamped homogeneous electric field (CHEF) pulsed gel electrophoresis An electrode arrangement for generating homogeneous alternating electric fields oriented 120 ~ from one another.
Continuous buffer system buffer is used throughout.
Electrophoresis system in which the same
Discontinuous buffer system Electrophoresis system in which different buffer ions are present in the different parts of the system. Also sometimes called multiphasic systems. Electroosmotic flow (EOF) Fluid flow in an electrophoresis system resulting from charged groups on the chamber walls of the apparatus. Electrophoresis The motion of charged particles in an electric field. The motion is brought about by the coulombic forces acting between the particles and the field. Field-inversion gel electrophoresis (FIGE) A form of pulsed-field gel electrophoresis with alternating electric fields oriented 180 ~ from one another.
Immunoelectrophoresis (IEP) Any of several methods in which antigens are detected with antibodies following gel electrophoresis. Isoelectric focusing (IEF) An electrophoretic method for separating amphoteric molecules in pH gradients. Isoelectric point (pI)
The pH at which an amphoteric molecule carries no
net charge.
Joule heating
The heating of an electrical conductor when an electrical current flows through it. Joule heating is sometimes referred to as ohmic heating.
Micellar electrokinetic chromatography (MEKC)
A form of capillary electrophoresis in which uncharged analytes become separable on becoming trapped in micelles of an ionic detergent. Mixed-bed ion-exchange resin A special form of ion exchange chromatographic resin that is used to eliminate both anions and cations from solutions. The resin contains equivalent amounts of groups in the H + and O H - forms. Mobility The electrophoretic steady-state velocity of a charged particle per unit of electric field./~ = v/E = q/f, in cm2/V-sec, where q is the charge and f is the frictional coefficient. Poisson distribution A probability density function that is an approximation to the binomial distribution. It has the characteristic that its mean is equal to its variance. Stars in space, bacteria plated in a petri dish, radioactive disintegrations per unit time, and sizes of pores in gels are all distributed in accordance with the Poisson distribution. Poisson equation The differential equation that relates the electrostatic potential at any point in space to an electric charge distribution. The fundamental problem in electrostatics is to determine solutions to the Poisson equation appropriate to a given charge distribution in order to find out the resulting electrostatic potential.
55
Chapter2 Electr0phoreticMethods Polyacrylamide gel electrophoresis (PAGE)
An electrophoretic method in which molecules migrate through a molecular lattice (the gel) created by polymerized, cross-linked polyacrylamide.
Programmable autonomously controlled electrode (PACE) pulsed-field gel electrophoresis A computer-controlled electrode arrangement for generating alternating fields of variable magnitude and orientation.
Pulsed-field gel electrophoresis (PFGE) Methods for separating very large DNA molecules using electric fields whose directions alternate. Resolution In chromatography resolution is defined as (distance between two band centers)/(sum of the bandwidths). See Separation; see also the text for a discussion of the distinction between resolution and separation. Resolving gel
A gel in which the lattice pores are small enough to have a molecular sieving action, which serves to separate sample molecules.
Separation In chromatography, the distance between band centers is referred to as their separation. Stack The region in discontinuous electrophoresis in which sample ions are electrochemically concentrated between the leading and trailing buffer ion fronts. "Stack" is also used as a verb. Stacking gel A gel in which the lattice pores are very large and serve mainly as an anticonvective medium in the initial phase of discontinuous electrophoresis during the process of stack formation.
SYMBOLS bp
Number of nucleic acid base pairs.
%C
Proportion of cross-linker in a polyacrylamide gel, expressed as a weight percentage. %C = (grams cross-linker)/(grams acrylamide + grams cross-linker).
kb
Number of nucleic acid base pairs expressed in units of 1000 base pairs.
kDa
Units of molecular mass in increments of 1000 Daltons.
M
Relative molecular mass.
Rf
Relative mobility.
SDS
Sodium dodecyl sulfate (sodium lauryl sulfate).
%T
Percentage of total monomer in a polyacrylamide gel, expressed as a w e i g h t / v o l u m e percentage. %T = (grams acrylamide + grams crosslinker) / 100 ml.
TAE
Tris-acetate-EDTA electrophoresis buffer solution: 40 mM Trisacetate, 1 mM EDTA, pH 8.
TBE
Tris-borate-EDTA electrophoresis buffer solution: 89 mM Tris, 89 mM boric acid, 2 mM EDTA, pH 8.3.
Tris
Tris(hydroxymethyl)aminomethane; a buffer component (molecular mass 121.1 Da, pK a 8.3).
56
David E. Garfin
I. Introduction Biochemists and biophysicists devote much effort to the separation of proteins and nucleic acids for identification and characterization (Bollag and Edelstein, 1991; Deutscher, 1990; Janson and Ryden, 1989; Sambrook et al., 1989). There are many different techniques for separating proteins and nucleic acids based on their chemical and physical properties. In particular, the intrinsic charges of proteins and nucleic acids are much exploited in biochemistry. Electrophoresis, isoelectric focusing, ion-exchange chromatography, and mass spectrometry, in one way or another, use the characteristic charges of molecules to separate them. The motion of charged particles in externally applied electric fields is called electrophoresis. Several highly popular electrophoretic methods for manipulating protein or nucleic acid mixtures have been developed. This chapter consists of capsule descriptions of the types of methods most likely to be encountered. It emphasizes gel electrophoresis, because this is by far the most used electrophoretic technique. Electrophoresis is the highest resolution method available for the separation of proteins and nucleic acids and most biochemical laboratories have some capabilities for the electrophoretic analyses of their samples. In addition, the available preparative electrophoresis methods achieve levels of purity that are unattainable by other means. Electrophoresis evolved from Tiselius' fundamentally simple movingboundary technique in free solution to one- and two-dimensional gel systems capable of exquisite resolution of highly complex mixtures (Vesterberg, 1989, 1993). Sophisticated capillary instruments with on-line detection bring automation to the analytical processes. Most kinds of electrophoresis are relatively inexpensive and easy to perform, and results are easy to interpret. Despite its popularity as an analytical technique, the detailed theoretical understanding of electrophoresis is incomplete. Although it is not possible to obtain quantitative structural data from electrophoresis, valuable qualitative information about the relative charges and sizes of macromolecules can be acquired from it. The most common use of electrophoresis is the qualitative analysis of mixtures of proteins or nucleic acids.
A. Basic Concepts The fundamental concepts of electrophoresis are relatively straightforward. In fact, electrophoresis gives the impression of being very simple. It is a transport process in which externally applied electric fields drive charged molecules through various media. A molecule of charge q in an electric field E experiences a force F = qE.
Frictional, viscous drag opposes the electrical force. In free solution, the frictional force is linearly proportional to the velocity, v, of the molecule. The magnitude of viscous drag is fv, in which f, the frictional coefficient, reflects the size and shape of the macromolecule. Under the two opposing forces, mole-
57
Chapter 2 ElectrophoreticMethods
cules rapidly reach steady-state, terminal velocities, with the two forces equal
qE =fv. The electrophoretic mobility of the molecule, tt, defined as the steady-state velocity per unit field, or/z = v/E = q/f, is a characteristic property describing the response of the molecule to electric fields. The units of mobility are cm 2/ V-sec. This highly simplified calculation illustrates the basic idea, common to all theories of electrophoresis, that the electrophoretic mobility of a macromolecule is proportional to the ratio of its net charge to its frictional coefficient (Compton and O'Grady, 1991). However, a number of complicating factors are hidden in the apparent simplicity of the definition of mobility. Both the charges and frictional coefficients of proteins and nucleic acids are established by their compositions and by the nature of the solvent. Charge and shape are influenced by factors such as pH, by the types and amounts of ions in the solution, and by denaturants such as detergents, reducing agents, and urea. It is not possible to account for solvent effects on the properties of macromolecules without making major approximations. For example, the counterions surrounding a molecule shield it from the external field. The only mathematical treatment possible for this important aspect of electrophoresis is for the unrealistic case in which the macromolecule is considered to be a uniformly charged sphere, and even then simplifying assumptions must be made in order to solve the relevant Poisson equation (Mosher et al., 1992; Overbeek and Bijsterbosch, 1979; Tanford, 1961). Regardless of the mathematical difficulties in interpreting electrophoretic mobilities, they can be reproducibly determined. For any given set of electrophoresis conditions, the mobilities of individual molecules are invariant. Proper conditions for a particular separation are easily chosen with a bit of experimentation, and once identified will continue to provide reliable information about the molecules being studied. It is common and accepted practice to infer the charges and shapes of molecules by comparing their mobilities to those of similar molecules with known characteristics. A general goal of electrophoresis is to maximize differences in mobilities and thus maximize the separations of molecules in the region of interest. The most common means for altering electrophoretic mobilities is to force sample molecules to migrate through gels in order to take advantage of molecular sieving. The interactions between migrating molecules and gel structures are poorly understood, and this adds yet another element of uncertainty to theories of gel electrophoresis. Nevertheless, there is much practical knowledge about the electrophoresis of proteins and nucleic acids in different gel systems, so that one can draw on collective experience to select the appropriate procedure for any particular application.
II. Gel Electrophoresis Gel electrophoresis is by far the most popular type of electrophoresis. Equipment and reagents for gel electrophoresis are readily available and familiar to laboratory workers. The technique is easy to perform and reliable results can be expected with a minimum of practice. Although gel electrophoresis is a rela-
58
David E. Garfin
tively simple technique, it is not a trivial procedure. On the contrary, gel electrophoresis may be the most useful analytical method available in biochemical work. A. G e l s
Gels are an interesting state of matter. Structurally, they are intermediate between solids and liquids (Tanaka, 1981). Details of the structures of gels or of the interactions between macromolecules and gels are poorly understood. Models of gel structure are inadequate for full theoretical treatments of gel electrophoresis. In addition, it is difficult to cast gels of precisely controlled structure and shape. Gel electrophoresis, thus, remains a semiempirical method. Conclusions drawn about a molecule must be based on comparison of its electrophoretic mobility with those of known standards run in the same gel. Of the various support matrices that have been used for electrophoresis, only agarose and polyacrylamide gels are of any real importance (Righetti, 1989). From a practical point of view, the structural features of the two types of gels are very similar. Three-dimensional networks of the constituent polymers form when gelation takes place. As gels form, individual agarose or polyacrylamide polymers combine into fibers that then aggregate into larger bundles joined in random meshworks. Agarose gels are held together by hydrogen bond formation between components whereas covalent cross links join the fibers and bundles of polyacrylamide gels. Both types of gels exist as random distributions of solid material and open spaces, or "pores," apportioned in Poisson distributions of sizes (Rodbard and Chrambach, 1970). The concept of gel pores is imprecise. The term pore refers to no particular geometric structure. Operationally, the pores of a gel are defined by the resistance the gel imparts to the motion of charged particles. This resistance varies with the sizes and shapes of macromolecules. Gels can be thought of as three-dimensional sieves that limit the motion of migrating molecules. During electrophoresis, molecules move between the buffer-filled pores of the gel. The dense regions of the gel act as barriers to translation. The ability of proteins or nucleic acids to squeeze through the small-pore regions of the gel depends on the structures of the molecules. The greatest numbers of configurations, and thus the greatest entropy, are available to the macromolecules in the large-pore regions of the gel. To move between open regions, molecules must force their way through small-pore regions of the gel, where entropy is lower (Smisek and Hoagland, 1990). From a macroscopic point of view, migrating molecules segregate into discrete zones corresponding to their mobilities. When the electric field is turned off, migrating molecular zones cease moving. The gel matrix limits diffusion, constraining individual types of molecules in distinct bands at their final positions. In order to analyze the band pattern of a gel, separated molecules are treated to fix their positions in the gel and then are stained to make the bands visible (Fig. 1).
1. Agarose Gels The pores of agarose gels are larger than those of polyacrylamide gels. Proteins larger than about 500 kDa in size and DNA larger than about 2000 base pairs
59
Chapter 2 Electrophoretic Methods
Fig. 1 A typical sodium dodecyl sulfate-polyacrylamide gel electrophoresis band pattern. Soluble proteins extracted directly from fish meat with denaturing sample buffer were compared by electrophoresis in a commercial precast 15%T, 2.7%C resolving gel run under standard (Laemmli) conditions. The overall dimensions of the gel were 7 • 9 • 0.1 cm (h • w • t). Each of 10 sample wells was 1.25 cm high by 0.5 cm wide. There was 1 cm of 4%T, 2.7%C stacking gel between the bottoms of the sample wells and the beginning of the 15%T resolving gel (4.75 cm in height). Electrophoresis at 200 V was continued for 35 min until the bromophenol blue tracking dye reached the bottom of the gel. Starting current was 52 mA and final current was 26 mA. The gel was stained with Coomassie Brilliant Blue R-250. Only 6 of the 10 wells were used. The outer two calibrator lanes contain standard proteins with molecular masses of 6.5,14.4, 21.5, 31, 45, 66.2, 97.4,116.25, and 200 kDa, respectively, from bottom to top. The central four lanes contain muscle extracts from (left to right) salmon, catfish, shark, and sea bass. The polypeptides obtained from the different fish species are clearly distinguishable from one another.
can be separated in agarose gels. Polyacrylamide should be used for smaller molecules. Agarose is a natural polysaccharide isolated from certain agar-bearing seaweeds (FMC BioProducts, 1988; Sambrook et al., 1989). Suppliers provide several different types of agarose, qualified for particular electrophoretic purposes. Agarose varieties differ in their physical and chemical properties, such as gelling temperature, gel strength, porosity, and electroosmosis. It is important to select the appropriate agarose for each particular purpose. Agarose is usually supplied as a dry powder. For casting gels, agarose is first dispersed in water or buffer, then boiled or heated in a microwave oven until completely melted. After a short period of cooling (to about 50~ the molten agarose is poured into an electrophoresis cassette or mold, in which gelation takes place.
2. Polyacrylamide Gels Polyacrylamide gels (CH 2~ C H - - C O - - N H
are formed by copolymerization of acrylamide 2) and a cross-linking comonomer, usually N,N'-meth-
60
David E. Garfin
ylenebisacrylamide (bisacrylamide) ( C H 2 - - C H - - C O m N H - - C H 2 m N H m C O m C H - - C H 2 ) . Cross-linkers are bifunctional acrylic agents that covalently link adjacent linear polyacrylamide chains (Righetti, 1989). Cross-linkers other than bisacrylamide are available for specialized purposes. For example, piperazinediacrylamide (PDA) allows low-background silver staining, important for critical two-dimensional gel electrophoresis (Hochstrasser et al., 1988a). The gel-forming reaction is a vinyl addition polymerization initiated by a free radical-generating system (Flory, 1953). For most gels in common use, polymerization is initiated by the addition of ammonium persulfate (the initiator) and an accelerator, tetramethylethylenediamine (TEMED) (Bio-Rad Laboratories, 1993a; Crambach and Rodbard, 1971). In this system, TEMED accelerates decomposition of persulfate molecules into (two each) sulfate free radicals and these in turn initiate polymerization. The free base of TEMED is required for this reaction. Polymerization efficiency falls rapidly at pH values below about pH 6 (Caglio and Righetti, 1993). Photopolymerization, with riboflavin as the accelerator, is used for low-pH gels (see Section III,A). A three-dimensional network is formed when the bifunctional bisacrylamide molecules cross link adjacent polyacrylamide chains. The rate of polymerization is dependent on (1) the net concentration of monomers and free radicals, (2) the temperature, and (3) the purity of the reagents. All of these parameters need to be controlled for reproducible gels. Because the reaction is dependent on free radicals, any compound that can act as a free radical trap will act as a polymerization inhibitor. Because oxygen is the most abundant radical trap, proper degassing to remove dissolved oxygen from acrylamide solutions is critical for absolute reproducibility (Chrambach, 1985). Nevertheless, completely acceptable gels can be obtained without degassing. By convention, polyacrylamide gels are characterized by a pair of values, %T and %C, where %T is the weight percentage of total monomer, including cross-linker (in g/100 ml), and %C is the proportion of cross-linker as a percentage of total monomer. The effective pore size of a polyacrylamide gel is an inverse function of the total monomer concentration (%T). For any given total monomer concentration, the effective pore size also varies with the proportion of cross-linker in the reaction mixture (%C). When %T is increased at a fixed, low-cross-linker concentration, the number of chains increases and pore size decreases. On the other hand, pore size is a biphasic function of %C. As %C is varied at constant %T, pore size decreases to a minimum at about 5%C. It then increases with further increases in %C, presumably because of the formation of shorter and thicker bundles of linear chains of polymer (Chrambach, 1985; Richards and Lecanidou, 1971, 1974). The use of high-quality reagents is a prerequisite for reproducible, highresolution gels. This is particularly true for acrylamide, which constitutes the most abundant component in the gel monomer mixture. Residual acrylic acid, linear polyacrylamide, and ionic impurities are the major contaminants of lowgrade acrylamide preparations. 1. Acrylic acid will copolymerize with acrylamide and bisacrylamide, thereby conferring ion-exchange properties to the resultant gel. 2. Linear polyacrylamide, by providing a nucleus for uncontrolled polymerization, can lead to irreproducibilities in gels.
Chapter2 ElectrophoreticMethods
61
3. Ionic contaminants can include both inhibitors and accelerators of polymerization. In particular, metals such as copper can inhibit gel polymerization. Buffer components should be of reagent grade and only thoroughly deionized water should be used for all phases of gel electrophoresis. High-quality electrophoresis chemicals are available from many sources. a. Polymerization Reactions Monomer solutions are commonly made as concentrated stock solutions. For protein gels, 30%T, 2.7%C monomer stock is preferred; it is made by dissolving 29.2 g of acrylamide and 0.8 g of bisacrylamide in 72.5 ml of completely deionized water (final volume 100 ml; specific gravity 1.025). The monomer solution should be filtered--disposable vacuum filtration units are convenient m and stored in the refrigerator, preferably in amber glass bottles. For nucleic acid gels, 30%T, 3.3%C stock is used, prepared as above from 29 g acrylamide and 1 g bisacrylamide. [Note: Acrylamide monomer is toxic. Direct exposure to it should be avoided.] Initiator concentrations are determined empirically to give visible polymerization in 15-20 min after addition. Under these conditions, gelation is essentially complete in 90 min. Final ammonium persulfate and TEMED concentrations of 0.05%, each, are usually sufficient for polymerization of resolving gels (see Section II,B,l,a). When stacking gels are used (see below), all that is required of them is that they have large pore structures. Because of this, stacking gels can be set to polymerize rapidly, in 8-10 min, with final concentrations of 0.05% ammonium persulfate and 0.1% TEMED. Monomer stock and buffer are combined at the desired concentrations and deaerated under moderate vacuum for about 15 min. Initiators are then added and the gel is poured into the casting apparatus. When a stacking gel is to be used (see below), the resolving gel mixture is poured first. It is overlaid with water-saturated isobutanol to exclude air from the top of the gel and aid in forming a sharp intergel boundary. After approximately 1 hr, the alcohol layer is thoroughly rinsed from the top of the gel and the stacking gel mixture is poured directly on top of the resolving gel. A sample well-forming "comb" is introduced at this time to form spaces in the gel for sample application. The gel is ready to run when the stacking gel has polymerized. Polyacrylamide gels are inherently unstable outside the pH 4 - 6 range. After storage at 4~ for about 4 months in the usual electrophoresis buffers, deterioration of the sharpness of the band patterns will sometimes be noticeable. Thus, for very high-resolution work, only fresh gels should be used. The breakdown of polyacrylamide is a slow hydrolysis of the pendant carboxamide groups (-- CO - - NH2) of the acrylamide monomers that occurs in basic buffers (Boschetti, 1989). Hydrolysis leaves behind ionized carboxyl groups (--COO-). Old gels swell, their pore structures change, and they take on ion-exchange characteristics because of this hydrolysis. The aging of polyacrylamide has commercial significance because it places limitations on the shelf-life of precast polyacrylamide gels.
B. Buffer Systems Although knowledge regarding the properties of gels is sparse, much is known about the behavior of buffer ions in electric fields. Many interesting and useful
62
David E. Garfin buffer systems have been devised, so that there is a great deal of flexibility in the choice of buffer system (Chrambach, 1985; Chrambach and Jovin, 1983; Hames, 1990; Laas, 1989a; Mosher et al., 1992). The electrolyte buffer obviously has a profound effect on the electrophoretic run. The buffer determines power conditions and affects separation and resolution. Proteins differ widely in their sensitivity to ionic strength, ionic species, pH, and cofactor requirements. The buffer chosen for the electrophoresis of native (nondenatured) proteins often depends more on the proteins under study than on the demands of electrophoresis. With nucleic acids and proteins at concentrations of about 1 m g / m l or greater, a continuous buffer system can be used. The same buffer, at constant pH, is used in the gel and electrode reservoirs of a continuous system. Also, the sample is loaded directly on the gel in which separation will occur. As molecules migrate through the pores of the gel, they are fractionated according to mobility. Bandwidths are determined mainly by the height of the applied sample volume, and this limits the resolution attainable with continuous systems. Dilute samples require large volumes to supply detectable amounts of material, and relatively wide bands are obtained. With gels of constant pore size, continuous systems are restricted to high-concentration samples for best results. Discontinuous (or multiphasic) buffer systems use different buffer ions in the gel and in the electrode solutions. These systems are designed to sharpen sample zones for high-resolution separations. In multiphasic, discontinuous zone electrophoresis, samples are applied to a large-pore stacking gel that serves as an anticonvective medium. All ionic species, including the sample molecules, form moving fronts. Buffer ions in the gel form an ion front that moves ahead of the sample molecules. Electrode buffer ions form a front that trails behind the sample. The sample ions between the buffer fronts concentrate into extremely narrow zones arranged in order of decreasing mobilities. The sample molecules rapidly "stack" into a very narrow region, no more than a few hundred micrometers thick, containing on the order of 100 m g / m l of protein (Chen et al., 1978a). Stacked samples move through the large-pore stacking gel as very narrow individual zones, regardless of the initial sample volume, and enter a resolving (or separating) gel of restrictive pore size as a series of very thin, closely spaced bands. Once in the resolving gel, sieving becomes predominant and the sample molecules "unstack" and separate on the basis of size and charge. Early studies with RNA questioned the need for stacking gels for the electrophoresis of nucleic acids (Richards and Lecanidou, 1971). As a consequence, nearly all electrophoresis of nucleic acids is done with continuous systems.
1. Discontinuous Buffer Systems Ornstein (1964) and Davis (1964) developed the first high-resolution polyacrylamide gel electrophoresis (PAGE) system for native proteins. Their popular system is still in widespread use. It was designed for the analysis of serum proteins, but works well for a broad range of protein types. The OrnsteinDavis buffer system is the first technique to try when working with a new, native protein sample. Ornstein recognized that high resolution is achieved when the starting zone of the sample proteins is as narrow as possible. He devised an electropho-
Chapter 2 Electrophoretic Methods
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retic method that sharpens protein zones well beyond the limits attainable by mechanical means. His formulation is based on the equations describing current flow in ionic solutions and the properties of buffers. A mathematical discussion of electromigration processes is beyond the scope of this chapter. An easy-to-follow derivation of the essential equations is given by Foret and Bocek (1989) and Kleparnik and Bocek (1991). Ornstein's idea was to sandwich sample proteins between two closely spaced moving fronts of electrolyte ions. Under the influence of the electric field, sample proteins become compressed between the leading and trailing ion fronts and segregate into contiguous zones in the order of their relative mobilities. This process takes place in the region provided by the large-pore stacking gel. Sample proteins arrive at the resolving gel in a very thin starting band. Once proteins are in the resolving gel, sieving predominates to effect the separation. The Ornstein-Davis system uses chloride as the leading ion, glycinate as the trailing ion, and Tris as the common ion. Of the possible components available at the time the system was developed, the properties of these buffers were best suited to the requirements of the electrophoresis. Similar electrochemical analyses have yielded a very great many electrophoresis buffer systems. Jovin (1973a), in fact, proposed some 4269 theoretically possible buffer systems covering the pH range from 2.5 to 11 in 0.5 pH units. Very few of these buffer systems have actually been tried, probably as a consequence of the unwieldy and confusing nomenclature and the lack of clear directions on how to choose the correct system for a given application (Chrambach and Rodbard, 1981). Chrambach and Jovin (1983) simplified the nomenclature and reduced the number of buffer systems to a manageable 19. The treatment of discontinuous electrophoresis by Jovin (1973b,c,d) and those of Everaerts et al. (1976) and Schafer-Nielsen and Svendsen (1981) are more comprehensive and correct than that of Ornstein. Allen (1974) devised alternative discontinuous buffer systems that make use of conductivity differences to achieve zone sharpening at constant pH (Allen et al., 1984; Allen and Budowle, 1994). By far the most popular gel system is that of sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) as devised by Laemmli (1970). In Laemmli's system, SDS is incorporated into the original Ornstein-Davis buffers. a. O r n s t e i n - D a v i s Gels: Discontinuous and Nondenaturing It is instructive to consider the ionic events that take place during discontinuous electrophoresis. The Ornstein-Davis system is convenient for this purpose, especially considering its popularity. Other discontinuous systems function by analogous mechanisms. The Ornstein-Davis system uses two different buffers containing different anions and a common cation to separate proteins. Chloride, present in the gel when it is cast, becomes the leading-front ion and glycinate ion in the electrode buffer forms the trailing front. Tris, the common ion, maintains electroneutrality. Most serum proteins carry net negative charges in this system and migrate toward the anode. The Ornstein-Davis system consists of four interrelated parts: (1) a stacking gel, (2) a resolving gel, (3) an electrode buffer, and (4) the sample (Fig. 2). The successive stages in a separation are as follows.
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Fig. 2 Stages in the separation of a protein mixture with the Ornstein-Davis discontinuous buffer system (see the text for details). (A) The gel is formed in two sections. A large-pore stacking gel is cast on top of a restrictive resolving gel. Each gel section contains Tris-C1 buffer, but the concentrations and pHs of the buffers in the two sections are different. The stacking-gel buffer is indicated by light shading and the resolving-gel buffer is shown with dark shading. Sample proteins, dissolved in diluted stacking-gel buffer, are placed in wells formed in the stacking gel (dark horizontal lines). Tris-glycine electrode buffer (clear) is in contact with the top of the gel, the top of the sample, and the bottom of the gel. The anode is below the gel and the cathode is above it (not shown). Serum proteins have net negative charges in this system and move downward toward the anode. Tris ions are distributed throughout the system and serve to maintain electroneutrality. The electric field intensity, E, shortly after application of voltage, is represented in the graph at the right of the gel picture. The E field in the gel is relatively low as a consequence of the relatively high conductivity imparted by the mobile chloride ions. (B) When voltage is applied, the anionic constituents of the system become aligned in the order of their electrophoretic mobilities. The magnitude of the mobility of the chloride ion (C1) in the gel buffer is greater than the mobility of the glycinate ion (Gly) in the electrode buffer. Sample proteins, with intermediate mobilities, are sandwiched (in order of mobility) between the chloride and glycinate ion fronts. The proteins in the sample become "stacked" in the very narrow region between the two moving fronts of buffer ions and form a spatially thin starting zone. Electric field intensity is influenced by the local distribution of charge carriers, which are proteins in the sample zone. The E field in the differing ion-containing zones becomes adjusted so that all ionic boundaries migrate at the same speed. (C) Shortly after stacking is completed, sample proteins enter the small-pore resolving gel, where they are slowed by sieving. In the resolving gel, the glycinate ions overtake the sample proteins and run just behind the chloride ions. During the resolving stage, proteins respond to a relatively high electric field determined by the concentration of glycinate ions in the gel. Electrophoresis continues with the sample proteins in Tris-glycine buffer until power is switched off.
i. Gel composition T h e gel is f o r m e d in t w o sections (Fig. 2A). A l a r g e - p o r e s t a c k i n g gel (4%T) is cast o n t o p of a restrictive r e s o l v i n g gel ( 5 - 3 0 % T ) (Bollag a n d Edelstein, 1991). T h e s t a c k i n g gel c o n t a i n s 0.125 M Tris-C1, p H 6.8, a n d the r e s o l v i n g gel c o n t a i n s 0.375 M Tris-C1, p H 8.8. T h e p H d i s c o n t i n u i t y b e t w e e n t h e t w o sections of the gel w a s d e s i g n e d to r e g u l a t e the effective m o b i l i t y of the g l y c i n a t e ions f r o m the c a t h o d e c h a m b e r . T h e c o n c e n t r a t i o n s of Tris-C1 in the t w o gels w e r e d e r i v e d f r o m e l e c t r o c h e m i c a l c o n s i d e r a t i o n s . T h e p o r o s i t y of the s t a c k i n g gel is large e n o u g h to n o t i m p e d e m o v e m e n t of p r o t e i n s a n d f u n c t i o n s m a i n l y as a n a n t i c o n v e c t i v e s u p p o r t m e d i u m d u r i n g f o r m a t i o n of t h i n s t a r t i n g z o n e s . P r o t e i n s e p a r a t i o n takes place in the l o w e r , r e s o l v i n g gel. T h e p o r o s i t y of this s e c o n d gel is e m p i r i c a l l y d e t e r m i n e d to m a t c h the mobilities of the p r o t e i n s in t h e s a m p l e . T h e r e is n o reliable w a y to p r e d i c t the correct gel c o n c e n t r a t i o n for a n u n t e s t e d p r o t e i n m i x t u r e w i t h o u t a n a l y z i n g it in gels. T h e choice is m a d e s u c h t h a t the p r o t e i n s of i n t e r e s t in the s a m p l e m i x t u r e are r e s o l v e d in the gel. It
Chapter 2 Electrophoretic Methods
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is common to begin with a 7.5%T gel for the initial electrophoresis of a sample of unknown mobilities (Hames, 1990). ii. Sample composition The sample buffer is 0.0625 M Tris-C1, pH 6.8. The sample is loaded into the system by placing it between the (0.125 M) Tris-C1 in the stacker gel and the Tris-glycine in the electrode buffer (0.025 M Tris, 0.192 M glycine, pH 8.3). The ionic strength of the sample solution is lower than those of the buffers above and below it. As a consequence, when power is applied, a voltage drop develops across the sample to help drive it into the gel. iii. Stack formation When voltage is applied, and current begins to flow, chloride ions in the gel sections, anionic proteins in the sample, and glycinate ions in the electrode buffer begin to move toward the anode (Fig. 2B). Tris (a base) and any cationic proteins in the sample migrate toward the cathode. As chloride ions move out of the sample, a localized, low-conductivity, high-field region is created behind them. The increased field behind the chloride ion front accelerates the proteins in the sample and the glycinate ions from the electrode buffer to the same velocity as the chloride (E/z = constant). The degree of ionization of glycine at the pH of the electrode buffer (pH 8.3) is such that the effective mobility of glycinate ions is less than those of chloride and the proteins in the sample. (The effective mobility of a weak electrolyte is the average mobility of the ionized form;/d, e f f = /d,X,where x is the fraction of molecules ionized at a particular pH and/z is their mobility. Each molecule can be thought of as being ionized x% of the time and uncharged the rest of the time. The pK a of glycine is pH 9.8. At pH 8.3, glycine molecules are 1/30 dissociated to glycinate ions.) A moving-boundary region is rapidly formed, with the chloride ions in the front, the glycinate ions in the rear, and the sample proteins compressed between them. The proteins form into individual thin zones, stacked like coins, in order of decreasing mobility between the leading chloride and trailing glycinate ions. The pH of the stacking gel becomes pH 8.3 as the glycinate ions move through it. In the stack, a low electric field moves in front of each protein zone and a high electric field moves behind each of them. Any protein molecule moving ahead of its zone is met with a lowered electric field and is slowed down until its zone overtakes it. Conversely, a protein molecule that gets behind its zone is speeded up by the increased electric field there. In the steady state, each protein is concentrated into a thin, high-density zone determined solely by the mobility of the protein under the electrophoretic conditions. iv. Separation When the moving boundary region reaches the interface of the stacking and resolving gels, the proteins experience a sharp increase in retardation due to the restrictive pore size of the resolving gel. At the same time, the pH is sharply increased to pH 8.8 and rapidly increases to pH 9.5 as the Tris-C1 is replaced by Tris-glycinate. The effective mobility of glycinate ions at pH 9.5 is high enough that they overtake the slowed proteins in the sample and move past them to run just behind the chloride front (x = 1/3). The protein zones become unstacked, and begin to separate into macroscopic bands by molecular sieving (Fig. 2C). In the resolving gel, proteins move at pH 9.5 for the remainder of the run. The operating pH of the separating gel, pH 9.5, was included in the design specifications of the Ornstein-Davis system to arrange for an effective mobility of glycinate greater than that of the fastest serum
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David E. Garfin
protein (prealbumin) in 7.5%T gels (Jovin, 1973d; Ornstein, 1964). As the run progresses, the initially very thin protein bands spread to thicknesses of the order of millimeters as a consequence of diffusion and dilution. b. Laemmli Gels: Discontinuous and Denaturing Laemmli modified the Ornstein-Davis system to allow molecular weight determinations to be made. The Laemmli (1970) system incorporates 0.1% SDS (an anionic detergent) in the Ornstein-Davis buffers and employs a denaturing step in sample treatment (Bollag and Edelstein, 1991; Garfin, 1990a; Hames, 1990). The treatment is designed to denature completely sample proteins to their constituent polypeptide chains prior to electrophoresis. When a mixture of proteins is heated in buffer containing SDS (2%) and a thiol reducing agent such as 2-mercaptoethanol (5%), the proteins are completely denatured and the resultant polypeptides take on a uniform charge-tomass ratio imparted by the SDS. The reducing agent breaks the disulfide bonds between segments of the native proteins, while the SDS, a well-known denaturant, coats most polypeptides with a uniform 1.4 g of SDS per gram of polypeptide (Reynolds and Tanford, 1970). The properties of the detergent overwhelm those of the polypeptides. All SDS-coated polypeptides take on similar extended, rodlike shapes with dimensions proportional to their molecular weights. In addition, the charge density of SDS-polypeptides is independent of pH in the range from 7 to 10. Fractionation in the gel is governed strictly by molecular sieving, so that separation of polypeptides in this system can be used to estimate their molecular weights. The characteristic features of a SDS-PAGE gel during an electrophoretic separation are shown in Fig. 3. Several types of proteins do not behave as expected during SDS-PAGE (Andrews, 1986; Hames, 1990; See and Jackowski, 1989). Incompletely reduced proteins, with some intra- or intermolecular disulfide bonds intact, are not saturated with SDS, because some of their SDS-binding domains are unavailable to the detergent. Glycoproteins and lipoproteins are also not saturated with SDS, because their nonproteinaceous components do not interact with the detergent. Proteins with unusual amino acid sequences, especially those with high lysine or proline content, very basic proteins, and very acidic proteins behave anomalously in SDS-PAGE, presumably because the charge-to-mass ratios of the SDS-polypeptide complexes are different than those that would be expected from size alone. Similarly, very large SDS-proteins, with molecular masses in the hundreds of kilodaltons, may have abnormal conformations. Polypeptides smaller than about 12,000 Da are not resolved well in most SDSPAGE systems. Small SDS-polypeptide complexes either have the same, roughly spherical, conformations or they do not separate from the band of SDS micelles that forms behind the leading ion front. Because the properties of SDS dominate the system, Laemmli buffers, as usually described, are somewhat more elaborate than strictly necessary. In particular, it is not necessary to cast stacking gels and resolving gels at a different pH (Wyckoff et al., 1977). Whether the stacking gel is cast at pH 6.8 or pH 8.8, SDS-polypeptides stack as a unit behind the leading chloride ion front. (This is strikingly demonstrated with prestained protein standards, which are mixtures of proteins derivatized with reactive dyes.) Stacking gels are still needed for best results, but they need not be at separate pH or ionic strengths. They can be
Chapter 2 Electrophoretic Methods
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Fig. 3 Characteristics of SDS-PAGE. The naturally colored subunits of chromatographically pure phycocyanin are seen as they separate in a preparative SDS-PAGE resolving gel (14%T, 2.7%C). Chromophores covalently bound to two of the subunits of phycocyanin make them visible throughout the electrophoresis run. The two dark annular bands in the middle of the gel are, respectively, an 18.5-kDa subunit (lower) and a 21-kDa subunit (upper). An uncolored 23-kDa subunit migrates behind the two colored bands. Because the protein was colored, tracking dye was not needed in the sample buffer. This made the features of the gel visible. The top of the stacking gel (4%T) is visible below the raft of bubbles on top of the buffer surrounding the glass gel tube. Below the top of the stacking gel is the junction between the stacking gel and the resolving gel. The resolving gel extends to the bottom of the tube. Small air pockets between the resolving gel and the glass tube can be seen at the left. These air pockets are magnified by the curvature of the glass and did not affect the separation of the bands. The chloride- glycine moving-ion front and a zone of SDS micelles can be seen below the 18.5-kDa band. They are visible because their refractive indexes differ from their surroundings. The ion front appears as the sharp boundary beneath the broad micelle band. A cooling core is in the center of the cylindrical gel.
cast in t h e s a m e b u f f e r as t h e r e s o l v i n g gel. Also, gels d o n o t n e e d to be cast w i t h SDS in t h e m . T h e SDS in t h e s a m p l e b u f f e r is sufficient to s a t u r a t e the p r o t e i n s w i t h t h e d e t e r g e n t a n d 0.1% SDS in t h e c a t h o d e b u f f e r is sufficient for m a i n taining protein saturation during electrophoresis. T h e L a e m m l i a n d O r n s t e i n - D a v i s gel s y s t e m s can b e u s e d w i t h nucleic acids as w e l l as w i t h p r o t e i n s (Tas, 1990). T h e L a e m m l i s y s t e m is p r e f e r r e d , b e c a u s e the SDS d e n a t u r e s c o n t a m i n a n t n u c l e a s e s .
2. Continuous Buffer Systems W i t h r e g a r d to c o n t i n u o u s b u f f e r s y s t e m s , a l m o s t a n y b u f f e r b e t w e e n p H 3 a n d 10 m a y be u s e d for e l e c t r o p h o r e s i s . M c L e l l a n (1982) c o m p i l e d a p a r t i c u l a r l y
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useful list of buffers for continuous electrophoresis. Solutions of relatively low ionic strength are best suited for electrophoresis, because these keep heat production to a minimum. On the other hand, protein aggregation may occur if the ionic strength is too low. The choice will depend on the proteins under study, but in general the concentration limits for electrophoresis buffer ions are from 0.01 to 0.1 M. Typical continuous buffer systems that have been used are Trisglycine (pH range 8.3-9.5) (Chen et al., 1978b), Tris-borate (pH range 8.3-9.3) (Margolis and Kenrick, 1968), and Tris-acetate (pH range 7.2-8.5) (Fairbanks et al., 1971). Borate ions can form complexes with some sugars and can therefore influence resolution of some glycoproteins. Very basic proteins, such as histones, are separated in acetic acid-urea gels (Spiker, 1980). Weber and Osborn's (1969) continuous SDS-PAGE system uses sodium phosphate buffer (pH 7). Omission of a stacking gel limits this popular system to high-concentration samples for best resolution.
3. O t h e r Buffer S y s t e m s As already noted, a multitude of discontinuous systems has been described (at least theoretically) (Jovin, 1973a). For basic proteins, the low-pH alanineacetate system of Reisfeld et al. (1962) is often chosen (Hames, 1990). Allen (1974; Allen et al., 1984, 1989, 1993) advocates Tris-sulfate/Tris-borate, Trisformate/Tris-borate, and Tris- citrate/Tris-borate for electrophoresis of both proteins and nucleic acids (stacking also improves the resolution of nucleic acid gels). Neville (1971) developed a useful procedure for SDS-PAGE using a Tris-sulfate/Tris-borate buffer system. (This system was actually one of those calculated by Jovin's theoretical treatment. The chloride ion included in the lower gel buffer and the operational pH shift do not play roles in the electrochemistry of this SDS-PAGE technique and are unnecessary.) The Neville system was developed to stack and fractionate SDS-saturated proteins in the 2 to 300-kDa range. It has not gained much popularity. Another system for SDSPAGE is similar to that of Laemmli but with Tris replaced by its analog ammediol (2-amino-2-methyl-l,3-propanediol) (Wyckoff et al., 1977). This system reportedly gives better resolution than either the Laemmli or Neville systems, especially in the I to 10-kDa range (Bury, 1981). Replacement of glycine with Tricine in the Laemmli electrode buffer provides excellent separation of small polypeptides (Schagger and van Jagow, 1987). At the pH values used, Tricine migrates faster than glycine in the stacking gel. This has the benefit that small SDS-polypeptide complexes separate from the broad band of SDS micelles that forms behind the leading-ion front. In particular, 16.5%T, 3%C separating gels are useful for separations in the range from 1 to 70 kDa. Stacking gels in this system are 4%T, 3%C. Resolution is sometimes enhanced by inclusion of a 10%T, 3%C spacer gel between the resolving and stacking gels. Tricine-SDS resolving gels contain 1 M Tris-C1, pH 8.45, and 13% (w/v) glycerol. Stacking and spacer gels contain the same buffer without glycerol. It is not necessary to include SDS in the gel buffer. Electrode buffer is 0.1 M Tris, 0.1 M Tricine, 0.1% SDS, pH 8.25. Sample buffer is 0.1 M Tris-C1, pH 6.8, 2% (v/v) 2-mercaptoethanol, 20% (w/v) glycerol, 0.025% bromophenol blue. Sample buffer should contain no more than 1%SDS for best resolution of the small proteins (1-5 kDa). Proteins of very low molec-
Chapter 2 ElectrophoreticMethods
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ular mass are not completely fixed and may diffuse from the gels during staining. This system is becoming very popular for polypeptide analyses.
C. Choice of System 1. Native Proteins The choice of electrophoresis system for proteins depends on the particular proteins of interest. There is no universal buffer system ideal for the electrophoresis of all native proteins. Both protein stability and resolution are important considerations in buffer selection. The Ornstein-Davis buffers are a recommended first choice (Ornstein, 1964; Davis, 1964). The 19 discontinuous buffers selected by Chrambach and Jovin (1983) and the list of continuous buffers provided by McLellan (1982) are also recommended. Some native proteins may aggregate and precipitate at the very high protein concentrations reached during stacking in discontinuous electrophoresis. Consequently, either they might not enter the resolving gel or they might cause streaking as accumulated protein slowly dissolves during electrophoresis. If the proteins of interest behave in this manner, it is probably best to use some form of continuous-buffer electrophoresis. The pH chosen must be in the range over which the proteins of interest are stable. The pH should also be far enough from the isoelectric points (see the discussion of isoelectric focusing in Section III) of the proteins of interest that they carry enough net charge to migrate through the gel in a reasonable time. On the other hand, separation of two proteins at a given gel concentration is best near one of their isoelectric points, because the isoelectric protein will barely move in that pH range. The choice of pH is usually a compromise between considerations of resolution and stability. For best results with continuous systems, the concentrations of the proteins of interest should be at least 1 m g / m l to keep sample volume at a minimum. The sample should be loaded in a buffer with an ionic strength about 1/2 to 1/5 that of the gel and electrode buffers (dialysis may be required) so that a voltage drop can develop across the applied sample to drive the proteins into the gel. The choice of proper gel concentration is, of course, critical to the success of the separation. The separation of proteins is heavily influenced by the concentration (%T) of the gel. Too high %T can lead to exclusion of proteins from the gel and too low %T can decrease sieving. One approach, useful with the McLellan continuous buffers, is to use relatively large-pore gels (5%T to 7%T) and to alter mobilities with pH. An approach for discontinuous systems is to start with a 7.5%T gel, then, if that is not satisfactory, to try a number of gel concentrations between 5%T and 15%T. Pore-gradient gels can also be tried (Hames, 1990).
2. Denatured Proteins and Nucleic Acids It is easier to choose suitable concentrations for SDS-PAGE and DNA gels than for native protein gels because separations of SDS-polypeptides and polynucleotides are dependent mainly on chain length. Laemmli gels with 7.5%T resolve proteins in the 40- to 200-kDa range, those with 10%T resolve 20- to 200-kDa proteins, 12%T gels separate proteins in the 15- to 100-kDa range, and 15%T gels separate 6- to 90-kDa proteins.
70
David E. Garfin Electrophoresis of nucleic acids is done almost exclusively with continuous-buffer systems. TBE and TAE are used for DNA and RNA in both polyacrylamide and agarose gels. Allen's discontinuous buffers may improve resolution (Allen et al., 1989, 1993). Agarose gels (1%, w / v ) separate linear DNA molecules in the 500- to 7000-bp size range and 0.5% agarose gels separate DNAs in the 2000 to 20,000-bp range. With polyacrylamide, 5%T and 10%T gels are used for separation of linear DNA molecules of 200-2000 and 50-1500 bp, respectively.
D. Detergents and Denaturants Detergents are employed in electrophoresis when it is necessary to disrupt protein-lipid and protein-protein interactions. A variety of detergents has been used for this purpose. SDS is the most common detergent used in PAGE analyses. The basic concepts of protein-detergent interactions have been reviewed and discussed, both in general terms (Helenius and Simons, 1975; Neugebauer, 1990) and as related to electrophoresis (Hjelmeland and Chrambach, 1981). Most proteins are readily soluble in SDS, making SDS-PAGE a generally applicable method. In SDS-PAGE, the quality of the SDS is of prime importance (Brown, 1988; Margulies and Tiffany, 1984). The effects of impurities in SDS are unpredictable. Of the contaminants, the worst offenders are probably the alkyl sulfates other than dodecyl sulfate (C,2); especially decyl sulfate (C 10), tetradecyl sulfate (C14), and hexadecyl sulfate (C16). These bind to proteins with different affinities, thereby affecting mobilities. Lipophilic contaminants in SDS preparations, including dodecanol, can be trapped in SDS-protein complexes and SDS micelles, leading to loss of resolution. Only purified SDS should be used for electrophoresis, but even with pure SDS, various glycoproteins, lipoproteins, and nucleoproteins tend to bind the detergent irregularly. The resultant SDS-polypeptides then migrate "anomalously" with respect to their molecular masses. Lithium dodecyl sulfate (LDS) has been substituted for SDS in PAGE analyses (Kubo and Takagi, 1986) as has cetyltrimethylammonium bromide (CTAB) (Akins et al., 1992). LDS is more soluble than SDS at low temperatures, which allows gels to be run at 4~ CTAB is a milder denaturant than SDS and preserves certain biological activities that are destroyed by SDS. Urea is used very often as a dissociating agent in gel electrophoresis (Grierson, 1990; Sealey and Southern, 1990). Urea, which disrupts hydrogen bonds, is used in situations wherein hydrogen bonding can cause unwanted aggregation or formation of secondary structures that affect mobilities. It is well suited as a denaturant for nucleic acids. Urea is an essential component of gels in which it is necessary to maintain DNA or RNA in single-stranded configurations, such as when accurate molecular mass determinations are desired. Dissociation of hydrogen bonds requires high urea concentrations (7-8 M). Maintenance of nucleic acids as single strands requires that electrophoresis be run at elevated temperatures (60~ Complete denaturation of proteins requires also that samples be treated with a thiol-reducing agent to break disulfide bridges (Hames, 1990). High concentrations of urea increase the sieving properties of polyacrylamide gels, either because of viscosity effects or by reducing the effective size of
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water channels (pores). Urea disrupts the hydrogen bonds holding agarose gels together as well as those in the samples, so that urea cannot be used in agarose gels. Urea must be present during electrophoresis, but, unlike SDS, urea does not affect the intrinsic charge of the sample polypeptides. In urea gels, separation of proteins is on the basis of both net charge and size, so that accurate molecular mass determinations are difficult. Urea solutions should be deionized by treatment with a mixed-bed ion-exchange resin before use. (Mixed-bed ion-exchange resins, such as Bio-Rex 501-X8, contain strong anionic and cationic functional groups on inert matrices, such as styrene divinylbenzene. They are used for removing positively and negatively charged contaminants from nonionic solutions. Deionization is most easily achieved by percolating urea solutions though a resin bed in a chromatography column or Buchner funnel.) Formamide (---98%) is sometimes used as a denaturant for RNA and DNA gels (Grierson, 1990; Sealey and Southern, 1990). Like urea, it disrupts hydrogen bonding. Formamide should also be deionized with a mixed-bed resin before use.
E. Sample Preparation Samples for SDS-PAGE by the Laemmli procedure are prepared in 0.0625 M Tris, pH 6.8, 2% SDS, 5% 2-mercaptoethanol, 10% glycerol, and about 0.025% (w/v) bromophenol blue tracking dye (Bollag and Edelstein, 1991; Garfin, 1990a; Haines, 1990). It is best to prepare a stock sample buffer containing everything but 2-mercaptoethanol and to add this reagent right before use. The glycerol provides density for underlaying the sample on the stacking gel below the electrode buffer. The tracking dye allows both sample application and the electrophoretic run to be monitored (it migrates with the ion front). There is sufficient SDS present in the sample buffer to ensure saturation of most protein mixtures. Except in the rare instances when the sample is in a very high-ionicstrength solution (>0.2 M), it can be dissolved 1:1 (v/v) in stock sample buffer. It is much better, though, to dilute the sample at least 1:4 (v/v) with the stock sample buffer. The amount of sample protein to load on a gel depends on the detection method to be used. Enough of the protein of interest must be loaded on the gel for it to be subsequently located (see Section II, H). Detection in gels requires on the order of 1 ~g of protein for easy visibility of bands stained with anionic dyes such as Coomassie Brilliant Blue R-250 or 0.1 ~g of protein with silver staining (Bio-Rad Laboratories, 1993b). Complete dissociation of most proteins is achieved by heating diluted samples to 95-100~ for 2 - 5 min. For native, discontinuous gels, upper gel buffer diluted twofold to fivefold for sample application is commonly used. Tracking dye and glycerol (or sucrose) are added to these samples also, and protein concentrations should fall within the same limits as for SDS-PAGE. With discontinuous systems, the volume of sample is not very important as long as the height of the stacking gel is at least twice the height of the sample volume loaded on the gel (Chrambach, 1985; Jovin, 1973d). Continuous systems require minimal sample volumes for best resolution. Careful sample handling is important when sensitive detection methods are employed. Silver-stained SDS-PAGE gels sometimes show artifact bands
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in the 50- to 70-kDa molecular mass region and irregular but distinctive vertical streaking parallel to the direction of migration. The appearance of these artifacts has been attributed to the reduction of contaminant skin keratin inadvertently introduced into the samples (Ochs, 1983). The best remedy for these artifacts is to avoid introducing keratin into the sample in the first place. Monomer solution, stock sample buffer, gel buffers, and upper electrode buffer should all be filtered through nitrocellulose and stored in well-cleaned containers. It also helps to clean the gel apparatus thoroughly with detergent and to wear gloves while assembling the equipment. Nucleic acid samples should be freed of proteins by protease treatment and (or) phenol extraction (Sambrook et al., 1989) before electrophoresis, because residual protein can cause aggregation of the sample in the well. Nuclease treatments can be used to remove either DNA from RNA samples or vice versa. Desalting is also recommended, but this is usually accomplished by ethanol precipitation after deproteinization. Samples can be dissolved in 1:2 or 1:10 (v/v) dilutions of electrophoresis buffer for loading on gels. Denaturation is accomplished by dissolving samples in loading buffer containing 7 M urea or 50% formamide and heating them at 75~ for a few minutes. Glycerol (10%) or 10% sucrose in the sample buffer provides density for underlaying samples below electrophoresis buffer. With nucleic acids, tracking dye consists of a combination of 0.025% each of bromophenol blue and xylene cyanol FF. The bromophenol blue migrates about twice as fast as xylene cyanol FF. Bands are identified by their positions relative to the two tracking dyes (Sambrook et al., 1989). Prepared samples are placed in sample wells of gels, either in the vertical or horizontal configuration, by underlaying from a microliter syringe or micropipette. Both types of device provide good control of sample volume. Syringes must be thoroughly rinsed between applications to avoid cross contamination of different samples. Standard pipette tips are too wide to fit into narrow sample wells, but several thin tips, specifically designed for sample application, are available. The choice of sample-loading device is one of personal preference. F. A p p a r a t u s
Apparatuses for gel electrophoresis are relatively simple. Electrophoresis cells are essentially plastic boxes with anode and cathode buffer compartments, electrodes (usually platinum wire), and jacks for making electrical contact with the electrodes. Some sort of device seals the gel chamber during gel formation. Gels are held either vertically or horizontally between the electrode chambers during the run. High-voltage direct current supplies provide electrical power for electrophoresis. Gel-forming reagents and buffers able to sustain electrical currents form the basis of the systems. Micropipettes, test tubes, and heating blocks are sample-handling necessities. Many suitable devices are available from a number of suppliers. Most polyacrylamide gel electrophoresis is done in vertical chambers, but some is done in horizontal, flat-bed electrophoresis devices. Gels are cast as rectangular slabs. The slab format provides uniformity, so that different samples can be compared in the same gel. In a small number of applications, gels
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are cast in cylindrical glass tubes. For comparative purposes, slab gels are far superior to tube gels. The vertical cells currently used are variants of Studier's design in which the gel slab is formed between two glass plates (Andrews, 1986; Bollag and Edelstein, 1991; Grierson, 1990; Hames, 1990; Sealey and Southern, 1990). Polyacrylamide gels adhere to glass sufficiently to be held vertically during electrophoresis. Conventional gels are of the order of 16 or 20 cm long and can accommodate up to about 25 samples. Longer gels give better separation in SDSPAGE and are used for complex samples. A typical run takes 4 - 5 hr. Plastic spacers establish gel thicknesses and sample wells are formed in the tops of the gels using plastic comb-shaped inserts during polymerization. Deep wells accommodate larger sample volumes than can be loaded on horizontal gels. Gel thicknesses of 0.75 or 1 m m give adequate loads for good sensitivity, while at the same time allowing relatively high voltages to be applied to the cell without excessive heating. Gel cassettes are positioned between separate anode and cathode compartments. (Both electrode compartments usually contain the same buffer solution.) Samples are underlaid beneath buffer in the wells. The better cells provide means for heat dissipation, because uneven heat distribution on the gel slab can cause band distortions. The so-called minicells allow rapid analysis and are often adequate for relatively uncomplicated samples. The design of these cells allows analyses to be completed two to three times faster than is possible with conventional cells. Minigels are about 7 cm long by 8 cm wide and are very easy to handle. Each gel can hold up to 15 samples and a typical two-gel run (up to 30 samples) can be completed in less than 1 hr (not counting setup and polymerization time). Agarose gels are generally run submerged under buffer in horizontal chambers, often called "subcells" (Grierson, 1990; Sealey and Southern, 1990). Molten agarose is poured into trays for gel formation. Gel thicknesses are determined by the volumes of agarose poured into the trays. Sample wells are formed in the bodies of the gels by suspending combs in the molten agarose. Gel trays are placed on the beds of the horizontal cells. The gels are covered with buffer and samples are underlaid in the wells. Vertical configurations are also possible. Frosted glass must be used when agarose gels are run in vertical chambers to keep the gels from sliding out of the cassettes.
G. Power C o n d i t i o n s Regulated direct current (dc) power supplies, designed for electrophoresis, allow control of every electrophoretic mode. Constant voltage, constant current, or constant power conditions can be selected. If desired, free-running, unregulated electrophoresis can be carried out. Many power supplies have timers and some have integrators, allowing runs to be automatically terminated after a set number of accumulated volt-hours (Allen et al., 1984). All modes of operation can produce satisfactory results, but for best results and good reproducibility, some form of electrical control is important. The choice of which electrical parameter to control is almost a matter of preference. The major limitation is the ability of the chamber to dissipate the heat generated by the electrical current (Woolley, 1987). During an electrophoretic run, electrical energy is
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David E. Garfin converted into heat. This Joule heating can have many deleterious consequences, such as band distortion, increased diffusion, enzyme inactivation, and protein denaturation. All good electrophoresis chambers have provision for transferring heat from the gels to the outside environment. In general, electrophoresis should be carried out at voltage and current settings at which the run proceeds as rapidly as the ability of the chamber to draw off heat allows. That is, the run should be as fast as possible without exceeding desired resolution and distortion limits--and these can only be determined empirically for any given system. Each experiment will impose its own criteria on cooling efficiency. Sometimes it is sufficient to carry out electrophoresis on the lab bench. Other situations might require that the apparatus be moved into the cold room. Occasionally, it will be necessary to employ recirculated coolant. Electrical quantities are interrelated by fundamental laws. Each gel has an intrinsic (sometimes time-varying) resistance, R, determined by the ionic strength of its buffer. When a voltage V is impressed across the gel, a current I flows through the gel and the external circuitry. These three quantities are related by Ohm's law: V = IR, where V is expressed in volts, I in amperes, and R in ohms. In addition, power P, in watts, is given by P = IV. Joule heating, H, is related to power by the mechanical equivalent of heat, 4.18 J/cal, or H = P/4.18 cal/sec. With the Ornstein-Davis and Laemmli buffers, R increases during the course of electrophoresis. Thus, for runs at constant current in these gels, the voltage, power (I2R), and consequently the heat of the gel chamber increase during the run. Under constant voltage conditions, current, power (V2/R), and heat decrease during electrophoresis as R increases. Vertical cells are run at electric field strengths of 10-20 V / c m or currents in the range of 15-25 m A / m m of gel thickness. Horizontal cells are run at lower voltages, with fields in the range of 1 - 10 V / cm. Constant current conditions, as a rule, result in shorter but hotter runs than do constant voltage runs. The increased run times of constant voltage conditions give increased time for the proteins to diffuse, but this appears to be offset by the temperature-dependent increase in diffusion rate of the constant current mode. Probably the best way to regulate Joule heating while maintaining optimum resolution is to carry out electrophoresis in the constant power mode. In this mode, voltage and current are automatically adjusted to maintain their product constant at the dissipation limit of the chamber. With continuous buffers, it is sometimes possible to shorten run times by diluting the buffer to decrease its ionic strength. Because P = V 2 / R , every twofold lowering of ionic strength allows voltage to be increased by a factor of 1.4 without an increase in heating. Not all buffer systems can tolerate dilution, however.
H. Detection Detection of proteins in gels is accomplished by staining them with dyes or metals (Bio-Rad Laboratories, 1993b; Bollag and Edelstein, 1991; Garfin, 1990a). Coomassie Brilliant Blue R-250 is the most common protein stain and is recommended for routine work. Coomassie Brilliant Blue G-250 should be used for staining gels containing low molecular mass polypeptides (Schagger and van Jagow, 1987). Silver staining (Rabilloud, 1990) is the most sensitive method for
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staining proteins and nucleic acids in gels and should be employed when electrophoresis is used to assess the purity of a preparation, e.g., an antigen preparation. Copper staining allows rapid and sensitive detection of protein bands in SDS-PAGE gels without fixing proteins irrecoverably in gels. Discussions of various detection methods, including radiolabeling, and means for quantitating proteins in gels can be found in Allen et al. (1984), Allen and Budowle (1994), Andrews (1986), Hames (1990), Merril (1990), and Syrovy and Hodny (1991). All of the steps in gel staining are done at room temperature with gentle agitation (e.g., on an orbital shaker platform) in any convenient container, such as a glass casserole or a photography tray. Always wear gloves when staining gels, because fingerprints will stain. Permanent records of stained gels can be obtained by photographing them or by drying them on filter paper or between sheets of cellophane using commercially available drying apparatus.
1. Proteins a. Dye Staining Coomassie Brilliant Blue R-250 is the standard stain for protein detection in polyacrylamide gels (Wilson, 1983). Easy visibility requires on the order of 0.1-1/xg of protein per band. The staining solution consists of 0.1% Coomassie Brilliant Blue R-250 (w/v) in 40% methanol (v/v), 10% acetic acid (v/v), which also fixes most proteins in gels. Gels are first removed from the electrophoresis cell, then soaked in an excess of staining solution for 3060 min. Background stain is removed (destaining) by soaking the gel in a large excess of 40 methanol, 10% acetic acid, with several changes. Gels containing low molecular mass polypeptides are fixed in 50% methanol, 10% acetic acid for a maximum of 1 hr. They are stained with 0.025% Coomassie Brilliant Blue G-250 (w/v) in 10% acetic acid for 1-2 hr and are destained with 10% acetic acid. b. Silver Staining The method developed by Merril and co-workers can be as much as 100 times more sensitive than dye staining (Merril, 1990). Bands containing 10-100 ng of protein or nucleic acid can be easily seen. The reagents are available in kit form for use with polyacrylamide gels. Fixation of proteins in gels is with 40% methanol, 10% acetic acid (v/v). Methanol is removed by washing gels in 10% ethanol, 5% acetic acid (v/v). Proteins are then oxidized in a solution of potassium dichromate in dilute nitric acid. Excess oxidizer is washed out of the gels with water and the gels are treated with silver nitrate solution. Silver ions bind to the oxidized proteins and are subsequently reduced to metallic silver by treatment with alkaline formaldehyde. Color development is stopped with 5% acetic acid. Another method that requires only one simultaneous staining and development step is that of Gottlieb and Chavko (1987). It can be used to silver stain proteins and nucleic acids in polyacrylamide or agarose gels and is available in kit form. Following fixation in 50% methanol, 10% acetic acid, and 5% glycerol and washing with water, gels are soaked with a solution containing a silverammine complex bound to tungstosilicic acid. Silver ions transfer from the tungstosilicic acid to the proteins or nucleic acids in the gel by an ion-exchange or an electrophilic process. Formaldehyde in the alkaline solution reduces the silver ions to metallic silver to produce the images of the bands of macromole-
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cules. Because silver ions do not accumulate in the bodies of gels, background staining is very light.
c. Copper Staining Rapid, single-step staining of SDS-PAGE gels is achieved by incubating gels in 0.3 M copper chloride for 5 min, then washing them with water (Lee et al., 1987). Proteins are not permanently fixed by this method and can be quantitatively eluted after chelating the copper. Blue-green precipitates of copper hydroxide form in the bodies of the gels except where there are high concentrations of SDS, such as that bound to the proteins. Clear protein bands can be easily seen against the blue-green backgrounds and photographed with the gels on black surfaces. The resultant, negatively stained images of the electrophoresis patterns are intermediate in sensitivity between Coomassie blue and silver staining. The electrophoretic pattern is lost when copper-stained gels are dried, so they must be photographed, restained with Coomassie blue, or stored in water. 2. N u c l e i c A c i d s Nucleic acids in either polyacrylamide or agarose gels are most easily stained with ethidium bromide (Grierson, 1990; Sambrook et al., 1989; Sealey and Southern, 1990). This fluorescent dye intercalates between stacked bases of DNA and RNA. The resultant nucleic acid-dye complex has an increased fluorescence yield compared to the dye free in solution. After electrophoresis, gels are immersed for 30-60 min in buffer or water containing 0.5 ~ g / m l of ethidium bromide (5 /~g/ml for RNA), then washed with water. When viewed under short-wavelength ultraviolet illumination (302 nm), nucleic acid bands in gels appear bright orange against clear or pale orange backgrounds. Permanent records of gels stained with ethidium bromide can only be obtained by photographing the gels. Transilluminators and camera stands are commercially available for this purpose. [Note: ethidium bromide is a mutagen. Direct exposure to it should be avoided.] Methylene blue stains RNA and DNA in polyacrylamide gels (Peacock and Dingman, 1967). Following electrophoresis, gels are immersed in 1 M acetic acid for about 30 min to drop the pH of the gel for staining. Then, the nucleic acids in the gels are stained with 0.2% methylene blue in 0.2 M acetate buffer, pH 4.7. Destaining is accomplished by many successive water washes. The gels can be dried on filter paper or between cellophane sheets or photographed for permanent records. DNA and RNA can also be stained with one of the two silver stains discussed above. I. M o l e c u l a r M a s s E s t i m a t i o n
Sample treatment during SDS-PAGE by the Laemmli procedure breaks proteins down to their constituent subunits and leaves the subunits coated with the anionic detergent. The electrophoretic mobilities of the resultant SDSpolypeptide complexes all assume the same functional relationship to their molecular mass. To a first approximation, migration rates of SDS derivatives are inversely proportional to the logarithms of their molecular masses. SDSpolypeptides, thus, move through gels in a predictable manner, with low mo-
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lecular mass complexes migrating faster than larger ones. This means that the molecular mass of a protein can be estimated from the relative mobilities of its subunits in a calibrated SDS-PAGE gel. Molecular mass estimations are among the most often used applications of gel electrophoresis and account in part for the popularity of the Laemmli SDS-PAGE method. Molecular masses are determined in SDS-PAGE by comparing the mobilities of test proteins to the mobilities of known protein markers. The relevant parameter is the relative mobility, Rf, defined as the mobility of a protein divided by the mobility of the ion front. This parameter normalizes mobilities to a significant and characteristic measurable quantity. Rather than determine mobilities, it is sufficient to calculate Rf as the quotient of the distance traveled by a protein from the top of the resolving gel divided by the distance migrated by the ion front. Because the ion front is difficult to locate, in practice, mobilities are normalized to the tracking dye that migrates only slightly behind the ion front: Rf = (distance to band)/(distance to dye). The dye front can be marked by a notch in the edge of the gel or by inserting a needle soaked in india ink into the gel before the gel is stained (the dye front is not visible after staining). It is also acceptable to normalize mobilities to that of one of the protein bands in the gel. Plots of the logarithm of protein molecular mass (log M) versus the relative mobility, Rf, fit reasonably straight lines. In each gel, a lane of standard proteins of known molecular masses is run in parallel with the test proteins. Plots of log M vs. Rf constructed from the distances migrated by the standards calibrate the gel. The Rf values of the test proteins are compared with those of the standards. Interpolation of the Rf values of test proteins into the standard curve gives their approximate molecular masses. Standard curves are actually sigmoid in shape (Hames, 1990; See and Jackowski, 1989). The apparent linearity of a standard curve may not cover the full range of molecular masses for a given protein mixture in a particular gel. However, log M is sufficiently slow, in a mathematical sense, to allow fairly accurate molecular mass estimates to be made by interpolation, and even extrapolation, over relatively wide ranges. The approximate useful ranges of single-percentage SDS-PAGE gels for molecular mass estimations is as follows: 40,000 to 200,000 Da, 7.5%T; 30,000 to 100,000, 10%T; 15,000 to 90,000 Da, 12%T; 10,000 to 70,000 Da, 15%T. Mixtures of standard proteins with known molecular masses are available commercially for calibrating electrophoresis gels. It is important to bear in mind that the molecular masses obtained using Laemmli SDS-PAGE are those of the polypeptide subunits and not those of native, oligometric proteins. Moreover, proteins that are incompletely saturated with SDS, very small polypeptides, very large proteins, and proteins conjugated with sugars or lipids behave anomalously in SDS-PAGE, as mentioned in Section II,B,l,b. Nevertheless, SDS-PAGE provides reasonable molecular mass estimates for most proteins. Similar standard curves can be constructed for nucleic acids. For reliable size estimates, DNA and RNA molecules must be in configurations in which their mobilities depend only on chain length. DNA molecules must be either linear and double stranded, without any partially single-stranded regions, or completely denatured to single strands. RNA samples must be free of aggregates and hydrogen-bonded structures. Urea is usually included in gels intended for molecular mass determinations of single-stranded nucleic acids
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David E. Garfin (Grierson, 1990; Sealey and Southern, 1990). Nucleic acid size standards are available from a number of suppliers.
J. Special-Purpose Gels This section presents four of the many variations of gel electrophoresis that have been developed to provide more information about macromolecules than furnished by the basic methods. Procedures are described for separating extended size ranges of molecules, for studying the conformations of proteins and nucleic acids, for resolving very large numbers of proteins, and for sequencing nucleic acids. Details of the procedures can be found in the references cited.
1. Pore-Size Gradient Gels Gradient gels, that is, gels with continuously changing pore sizes in the direction of migration, are popular for analyses of complex mixtures spanning wide molecular mass ranges (Allen et al., 1984; Allen and Budowle, 1994; Andrews, 1986; Hames, 1990; See and Jackowski, 1989). They consist of gradients of polyacrylamide concentration (%T). In a gel in which the pores become continuously smaller in the direction of motion, there is an apparent band sharpening as molecules migrate to the limits of porosity and essentially stop moving (Margolis and Kenrick, 1968; Rodbard et al., 1971). This can be advantageous in a number of cases. For example, anomalous behavior of glycoproteins in SDSPAGE, thought to be due to variable SDS binding, can be overcome in gradient gels in which molecular sieving predominates over charge effects. The main advantage of pore gradient gels is that both large and small molecules can be run in the same gel. Gradient gels, however, cannot match the resolution of two molecules obtainable with a properly chosen single concentration of acrylamide. A good approach is to use gradient gels for estimates of the complexities of mixtures. This may be sufficient for some purposes. However, best resolution requires the appropriate uniform concentration gel. Various devices are commercially available for producing polyacrylamide gradients of almost any desired shape. These devices range in complexity from programmable pumps to simple cylinder pairs that form gradients hydrostatically. Precast gradient gels are also available commercially. Discontinuous buffer systems give best resolution in gradient gels: 4-15% gradient minigels, based on the Laemmli buffers, resolve SDS-polypeptides in the 40 to 200-kDa size range, 4-20%T gels separate 10 to 100-kDa SDSproteins, and 10-20%T gradients are useful in the 10 to 100-kDa range. 2. Transverse Gradient Gel E l e c t r o p h o r e s i s The unfolding of proteins and the melting of DNAs can be studied by examining their electrophoretic mobilities in continuously varying concentrations of denaturant (DeWachter et al., 1990; Goldenberg, 1989; Goldenberg and Creighton, 1984; Myers et al., 1987). In a similar way, titration curves for proteins can be determined electrophoretically in gels containing pH gradients (Rosengren et al., 1977; Righetti, 1983). Protein or DNA molecules at any point along the sample application band migrate through the gel at constant denaturant concentration or constant pH. The effect of local conditions of denaturation or pH on any particular molecule in the gel is reflected in its mobility. Unfold-
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ing of proteins and melting of DNA result in decreases in the mobilities of the affected molecules. The direction moved by a protein during electrophoresis (whether toward the cathode or anode) depends on whether its pH is above or below its isoelectric point. By applying samples as long bands extending across gels containing horizontal gradients of denaturant or pH, denaturing curves or titration curves can be directly obtained. The relevant gradients are incorporated into gels so that they are situated perpendicularly to the direction of electrophoretic migration. The shapes of the resultant bands give information on the stabilities of proteins and DNAs or on the pI values of proteins. The usual configuration of denaturing gradient gels is the vertical polyacrylamide slab. Urea is the denaturant most commonly employed. The effect of urea on DNA molecules is to denature them with the strands separating (melting). Melting is a function of urea concentration and begins at domains rich in A + T base pairs. Urea also causes proteins to unfold as hydrogen bonding is disrupted. The extent of unfolding is dependent on the concentration of urea. Separate domains of proteins can undergo distinct unfolding transitions. Modifications to the gel casting procedure are needed to incorporate urea gradients into gels. The cassettes used for this technique are rigged so that after gels containing urea gradients are cast, they can be rotated 90 ~ for electrophoresis. The two sides of the gel end up with either 0 or 8 M urea. Any point between the two sides contains urea at some linearly proportioned concentration between the two extremes. Continuous buffer systems are used. The choice of buffer for protein denaturation curves depends on the particular protein being studied. Gels for studies of protein unfolding are run at room temperature. DNA melting curves are generally run in TBE buffer at an elevated temperature of about 60~ Samples are loaded across the tops of the gels. Following electrophoresis, the gels are stained and the bands obtained are analyzed. Horizontal slab gels are used for generating pH titration curves. In these gels, pH gradients are generated by means of the same ampholytes as used in isoelectric focusing (Section III). For the initial analysis of a new protein sample, the pH range spanned should be pH 3-10. Thereafter, if warranted, other pH gradients can be used. Polyacrylamide gels are cast with narrow troughs extending across their middles. Electrofocusing is carried out with the fields parallel to the troughs for a time sufficient for the ampholytes to form stable pH gradients. The gels are then rotated 90 ~ so that the pH gradients are perpendicular to the second direction of motion. Samples are loaded into the troughs and the fields are applied. In any particular gel, each sample protein in the trough is in a fixed pH environment. Those proteins at pH below their pI move toward the cathode. Those at pH above their pI move toward the anode. Proteins at their pI do not move. Those proteins far away from their pI move with higher mobility than those close to their pI. The pI of a protein is the point in the pH gradient where the S-shaped band crosses the trough.
3. Two-Dimensional Gel Electrophoresis The resolution of gel electrophoresis can be increased by combining two different techniques to produce a two-dimensional separation of the components in a sample. One approach is to incorporate a sample treatment step, such as denaturation or enzymatic modification, between first and second electrophoresis steps run at right angles to one another. Molecules altered by the treatment
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migrate to definitive positions in the second gel. Unaltered molecules migrate along the diagonal of the second dimension. With RNA molecules, it is sometimes sufficient simply to use two different gel concentrations in two gels run at right angles to one another (DeWachter et al., 1990). The best approach is to use two different physical principles for the two different gel directions. The most common two-dimensional technique is O'Farrell's method for proteins (Dunbar, 1987; Dunbar et al., 1990; Dunn, 1987; Harrington et al., 1991). Protein samples are first subjected to isoelectric focusing (IEF; see Section III) then to SDS-PAGE in a perpendicular direction. It is this procedure that is usually referred to in discussions of high-resolution two-dimensional gel electrophoresis (2DGE). The first dimension of 2DGE, IEF, separates proteins according to their isoelectric points. The second fractionation, by SDS-PAGE, further separates the same proteins by molecular mass. Very high-resolution two-dimensional methods have been developed, allowing thousands of polypeptides to be resolved in a single slab gel. The technique works best with soluble proteins, such as those from serum or cytoplasm. It is relatively labor intensive for an electrophoresis technique, requiring a relatively high skill level for best results. Hochstrasser's modification of the original method gives very high resolution 2DGE of serum proteins (Hochstrasser et al., 1988b). In this method, the IEF gel is 5%T, 2.6%C, containing 2% (w/v) ampholytes, 9 M urea, 30% CHAPS (detergent), and 10% Nonidet P-40 (NP-40) (detergent). Gels are cast in 1.5 to 2.5-mm (i.d.) glass capillary tubes. (Some practice may be required before bubble-free gels can be repeatedly cast.) First-dimension runs are done in tanks using 6 mM phosphoric acid as the anolyte and 20 mM sodium hydroxide as the catholyte. First-dimension IEF capillary gels are extruded from their glass tubes and placed on the tops of SDS-PAGE gels, which are run with Laemmli buffers. For serum proteins, 13.3%T, 2.6%C gels, cast without SDS, are recommended. Irreproducibility in 2DGE arises from the variability in pH gradients inherent in the use of carrier ampholytes in the IEF dimension and from the difficulty in positioning the IEF capillary on the SDS-PAGE gels. Immobilized pH gradients and mechanical positioning devices may change this and allow for reproducible two-dimensional gels suitable even for clinical work. 4. N u c l e i c A c i d Sequencing Gels Gel electrophoresis is at the heart of nucleic acid sequencing methodology. Molecular biologists routinely read nucleic acid sequences from electrophoresis patterns obtained with thin, denaturing polyacrylamide gels (Andrews, 1986). When coupled with chemical or enzymatic techniques for generating defined fragments of DNA or RNA, gel electrophoresis provides records of nucleotide sequences that are easily deciphered (D'Alessio, 1982; Davies, 1982; Deininger, 1983; Maxam and Gilbert, 1980; Smith, 1980). In nucleic acid sequence analysis, a purified piece of DNA or RNA containing the sequence of interest is isolated (e.g., a DNA fragment produced by digestion with restriction endonucleases). It is used to generate arrays of partial sequences differing in length by one nucleotide and spanning the entire sequence to be determined. Specific treatments produce separate arrays of partial sequences terminating in one of the four nucleotides (Ausubel et al., 1987). For a
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given molecule, chemical or enzymatic sequencing reactions yield mixtures of progressively larger polynucleotides that are of random length, start at a common, labeled origin, and terminate with specific, known nucleotides. Four separate chemical or enzymatic reactions are used to generate radioactively labeled oligonucleotides covering the sequence of interest. Radiolabeling allows detection of submicrogram quantities of oligonucleotides. Sequence information is obtained, one nucleotide at a time, by identifying the next longest chain among the four arrays. Chemical sequencing methods are degradative. Starting material is a fragment of DNA or RNA that is labeled at one end. The end-labeled fragment is subjected to four separate chemical treatments, each of which preferentially breaks the polynucleotide backbone adjacent to one particular base. Reaction conditions are adjusted to ensure only partial chain cleavages. The enzymatic method for sequencing RNA is also degradative. Partial sequences are generated by limited digestions with base-specific ribonucleases. In contrast, the enzymatic sequencing methods for DNA are synthetic. They depend on the primed synthesis of complementary copies of a single-strand DNA template by DNA polymerase. Because DNA polymerase cannot initiate DNA chains, the enzyme is used to elongate a primer chain annealed to a specific site on the template DNA. The nucleotide added to the growing end of the elongating primer chain is selected by base-pair matching to the template DNA. Chains are terminated by incorporating 2',3'-dideoxynucleotides into the newly synthesized DNA. The dideoxynucleotides lack the 3'-hydroxyl group necessary for the incorporation of the next nucleotide into the chain. Whenever a dideoxynucleotide is incorporated at the 3' end of the growing primer chain, elongation is selectively stopped. Reaction conditions are set to produce the requisite arrays of partial sequences. Enzymatic sequencing has become more popular than chemical methods, possibly because of the availability of several commercial kits for the purpose. Gel electrophoresis is used to order the partial nucleotide sequences according to size, keeping the products of each nucleotide-specific treatment in a separate lane. Each successive partial sequence in the ladder of gel bands contains one nucleotide more than its predecessor, and the identity of this nucleotide is known from the ordering of the gel lanes. The complete sequence is read from an autoradiograph of the gel by noting the terminal nucleotide of each successively longer partial sequence. Standard sequencing gels are thinner than most other kinds of gels (0.4 m m or thinner). They are run in TBE buffer containing 7 M urea. It is important that the polynucleotide fragments be single stranded for accurate chain length separations. Thus, relatively dilute solutions are loaded on the gels to minimize reannealing of separated strands, and gels are run at elevated temperatures. Power conditions are chosen for each particular sequencing cell so that electrophoresis takes place at temperatures of 50-70~ Sequencing gels can distinguish polynucleotides containing n nucleotides from those containing (n - 1) nucleotides, where n can range up to hundreds of nucleotides. A 5%T, 5%C sequencing gel 50 cm long, run for about 2.5 hr, can be used to determine sequences about 300 nucleotides long. After electrophoresis, gels are covered with plastic wrap and exposed to X-ray film to produce the autoradiographs from which sequences are read.
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David E. Garfin The reading of sequencing gels is the most time consuming part of a sequencing project. After a bit of experience, it is possible to quickly and reliably read sequences from the radioautographs and to identify and correct for artifacts in the gels. When many gels must be analyzed, though, the process becomes tedious and error-prone. Several types of computer-based instruments simplify the task of sequence reading and computer programs automate data manipulation and comparisons of different sequences. Fully or partially automated film readers are available that enter sequence information directly into computers for storage and manipulation (Eby, 1990). In addition, instruments can be purchased that incorporate storage phosphor screens to capture the energy from radioactive emissions for later electronic data acquisition (Johnston et al., 1990). These instruments allow imaging and quantifying sequencing-gel band patterns without the need for X-ray film. Fully automated sequence analyzers make use of laser-induced fluorescence to collect sequence data (Smith et al., 1986). Sequences are analyzed directly as chains of fluorescently labeled oligonucleotides migrate past a detector. Some of the instruments for sequence analysis are relatively expensive, but they are becoming increasingly popular because of the advantages of automated data collection (Barrell, 1991).
K. Preparative Gel Electrophoresis Proteins and nucleic acids can be purified for further study by gel electrophoresis in one of two ways. In the band-elution method, proteins or nucleic acids are first separated in a slab gel, then extracted from bands excised from the gel (Grierson, 1990; Hames, 1990; Sealey and Southern, 1990). With continuouselution electrophoresis, bands of separated macromolecules are run off the bottom of the gel and swept away to a fraction collector, as is done in column chromatography. Both methods retain the high resolution of gel electrophoresis. Elution from gel slices can be done by either passive diffusion or electrophoresis. The purity of the recovered molecules depends on how well the bands of interest can be identified and how cleanly the bands can be cut out of the gel slab. With a continuous elution device, the final purity of the recovered proteins or nucleic acids depends mainly on the correct choice of gel and buffer.
1. Extraction from Gel Slices Gels intended for protein or nucleic acid extraction are cast thicker than analytical gels (1.5-3 ram). Sample wells spanning the widths of the gels accommodate as much sample as possible. The maximum amount of sample that can be loaded on a gel depends on how well the molecules of interest are separated from their neighbors in the sample mixture. Because bands become wider as the amount of material increases, as sample loads are raised, the corresponding loss of resolution will eventually become unacceptable. Loads are easily tolerated that are 10- to 50-fold greater per unit of gel cross-section than are usually run in analytical gels. Thus, with some large slab gels, proteins can be recovered in tens-of-milligram amounts. Copper staining is advisable for visualization of protein bands in preparative SDS-PAGE, because this stain does not employ fixative solvents. Desired bands are located and cut from the stained gel. Excess copper is removed by
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incubating gel slices in three changes (for 10 min each) of 0.25 M EDTA, 0.25 M Tris-C1, pH 9 (Lee et al., 1987), or in Tris-glycine electrophoresis buffer. Gel slices are then incubated in the appropriate elution buffer. With native gels, a separate marker lane for each gel is cut off the gel and stained with Coomassie blue. After destaining, the marker lane, shrunk by methanol, is swollen back to its original size by soaking it in water. The marker lane can be aligned with the preparative section of its parent gel to locate the protein bands of interest. Nucleic acid bands are located for excision by staining with ethidium bromide.
a. Passive Diffusion Proteins and nucleic acids are often extracted from macerated gel slices by simple diffusion (Sambrook et al., 1989). Pieces of gel containing the molecules of interest are crushed with a mortar and pestle and are left covered with buffer until the molecules diffuse into the supernatant fluid. Nucleic acids are recoverable from gels cast with low-melting-temperature agarose. This agarose melts at about 65~ and gels at approximately 30~ The melting temperature of this agarose is low enough that the double-strand structure of DNA is retained when it is melted. Excised gel slices are covered with buffer and warmed to 65~ until the agarose melts. Phenol extraction and ethanol precipitation are then used to recover the DNA or RNA. An alternative procedure for recovering DNA from low-melting-temperature agarose makes use of an enzyme, called agarase, that digests the molten agarose (Burmeister and Lehrach, 1989). Agarase treatment is recommended for recovery of large DNA fragments. For liquefying polyacrylamide gels, alternative cross-linkers, other than bisacrylamide, have been developed. Appropriate treatment of gels made from these alternative comonomers causes labile bonds in the crosslinkers to break so that the gels liquefy. The alternative cross-linkers are not completely satisfactory, partly because the molecules of interest must be separated from residual polyacrylamide strands. b. Electroelution Electrophoretic elution is an efficient method for recovering proteins and nucleic acids from gel slices. In the simplest versions of this method, proteins and nucleic acids are electrophoretically driven out of gel pieces into dialysis sacks in the type of apparatus used for running cylindrical gel rods (Sambrook et al., 1989). More sophisticated commercial devices are available for the rapid recovery of proteins and nucleic acids in small volumes, with expected yields of greater than 70% (Harrington, 1990). Elution takes about 3 hr and is done in any suitable buffer. In the absence of SDS, nucleic acids often become bound to the membranes used in some of these devices, limiting the yields obtainable. Andrews (1986) describes several variations of electrophoretic elution. 2. C o n t i n u o u s E l u t i o n E l e c t r o p h o r e s i s In continuous elution electrophoresis, separated bands migrate off the bottom of a gel and into an elution chamber. A flow of buffer washes material out of the elution chamber and sweeps it away to a fraction collector. Purified molecules are recovered in test tubes ready for analysis (Andrews, 1986; Chrambach, 1985; Chrambach and Nguyen, 1979; Hediger, 1984; Koziarz et al., 1978). The gels in the preparative gel electrophoresis device shown in Fig. 3 (Chen, 1989) are formed between a cylindrical outer tube and a cylindrical core.
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They can be thought of as either hollow cylinders or slab gels folded around so that their two lateral edges join. The device can hold gels that are 9 or 13 m m thick and up to 12 cm long. The elution chamber consists of a thin polyethylene frit. A dialysis membrane, directly beneath the elution frit, prevents macromolecules from being drawn out of the chamber by the electric field. Elution buffer enters the chamber around the perimeter of a specially designed gasket and is drawn out of the apparatus by a peristaltic pump. The p u m p forces eluate through a UV monitor and onto a fraction collector. Special precautions are taken during polymerization of polyacrylamide to ensure a uniform pore structure in the gel. To assure that separated molecules migrate in compact, parallel bands, temperature gradients across the gel must be minimized. The temperatures of the internal and external surfaces of the gel are equalized by continuously pumping lower electrophoresis buffer through the central cooling core. The most important parameter in preparative SDS-PAGE is the pore size of the gel. The monomer concentration that best resolves two molecules varies with their molecular weights. Changing the gel composition from the optimal concentration by increasing or decreasing the monomer concentration ultimately decreases resolution. It is important to note that the appropriate monomer concentration for preparative electrophoresis is not necessarily the same as that used for analytical work. For reasons that are not entirely clear, optimum separation of two molecules occurs when the relative mobility of the protein of interest is around 0.55. Thus, the monomer concentration that provides sharp, well-resolved bands in the middle of an analytical gel will generally be the correct monomer concentration to use in a preparative gel. Molecules running with the ion front of an analytical gel will be best separated preparatively by a gel monomer concentration greater than that used in the analytical gel. Similarly, for preparative fractionation, molecules remaining near the top of an analytical gel will require a lower %T than that of the analytical gel. A series of analytical gels should always be run to ascertain the correct preparative gel concentration for SDS-PAGE. The purification illustrated in Fig. 4 was obtained by SDS-PAGE from a properly optimized preparative gel. Elution profiles such as shown in Fig. 4A are not always attainable. Not all UV monitors can discriminate closely spaced peaks. The three components of phycocyanin shown in the figure were well resolved in this run. They were thus recovered at high purity. As shown in Fig. 4B, there was little mixing of the component polypeptides in the recovered fractions. An important technical distinction in preparative electrophoresis is that between "separation" and "resolution" (Giddings, 1969; Lunney et al., 1971; Marker et al., 1977). Separation of bands refers to the distance between band centers, whereas resolution refers to separation relative to bandwidths. Optimal purity in preparative work requires minimized bandwidths as well as wide separation of bands. Note that the bands of phycocyanin in Fig. 4B overlap very little. They are, thus, both well separated and well resolved. For analytical gels, the distinction between separation and resolution is usually not made and the two terms are used interchangeably. Preparative native-PAGE is a technique for high-yield purification of biologically active proteins. In contrast to SDS-PAGE where detergentpolypeptide complexes migrate according to size only, the mobilities of pro-
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Fig. 4 Elution profile and SDS-PAGE analysis of electrophoretically purified phycocyanin subunits. The electrophoresis run shown in Fig. 3 was continued until the bands had migrated off the bottom of the gel. A flow of buffer sweeping across the bottom of the gel drew eluted material out of the gel chamber. (A) The eluate was pumped through a UV monitor to a fraction collector. The UV absorbance of the eluate is shown. The ion front and micelleband are labeled as ionic contaminants. The three subunits were well resolved in fractions 9-32. (B) Individual fractions were analyzed by (silver-stained) SDS-PAGE using 14%T resolving minigels. Starting material for the preparative run is shown in the extreme left and right lanes. The 18.5-kDa subunit eluted in fractions 9-17, the 21-kDa subunit in fractions 18-29, and the 23-kDa subunit eluted in fractions 29-32. The single bands seen in the lanes are criteria of purity.
teins in native-PAGE systems d e p e n d on both their charges and their sizes. There is no single electrophoresis buffer system that will optimally purify all native proteins. W h e n selecting conditions for the purification of a native protein, the pI of the protein u n d e r investigation and the p H of the electrophoresis system m u s t both be considered. In preparative native-PAGE of proteins, the most i m p o r t a n t consideration is the p H of the electrophoresis buffer. The p H of the electrophoresis buffer system m u s t be within the p H range over which the protein u n d e r s t u d y is stable and retains its biological activity. In addition, the p H of the chosen buffer system m u s t leave the protein with sufficient charge for it to m o v e through the gel at a reasonable rate. Changes in p H alter the charges (and shapes) of proteins. The net charge on a protein is d e t e r m i n e d by the difference between the p H of the solvent and the isoelectric point of the protein. A buffer with an alkaline p H value relative to the pI of a particular protein imparts net negative charge to the protein. In such a buffer system, the protein migrates t o w a r d the anode. Electrophoresis buffers with acidic p H values relative to the pI of a protein impart net positive charge to it so that it migrates t o w a r d the cathode. A buffer with a p H value identical to the pI of a protein results in zero net charge and the protein will not m o v e at all in an electric field.
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In native-PAGE, protein mobilities are best modified by the pH of the buffer. Electrophoresis buffers with pH values close to the pI of the protein of interest will theoretically provide the best resolution. However, the resultant migration rate may be too slow for elution from the preparative gel column. Conversely, buffers with pH values far away from the pI of the protein of interest result in fast migration rates, but, with a loss of resolution. The choice of pH becomes a compromise between separation and speed (in the pH range of protein stability). The discontinuous buffer system of Ornstein (1964) and Davis (1964) should be the first nondenaturing gel system tried. The resolving gel of the Ornstein-Davis system becomes pH 9.5 once the glycinate ions displace the chloride in the gel. This pH may be outside the range of stability for some proteins. Alternative discontinuous buffer systems devised for preparative work, spanning the pH range from 3 to 10, can be found in the article by Chrambach and Jovin (1983). Protocols for using the Jovin discontinuous buffers are analogous to those for the Ornstein-Davis buffer system. An advantage of discontinuous systems for dilute protein solutions is the use of stacking gels to concentrate the sample. However, the stacking phenomenon can cause aggregation or coacervation of some proteins and this can severely interfere with resolution. If discontinuous systems cannot be used because of stacking-induced aggregation, a continuous buffer system will be required. McLellan's (1982) continuous buffers, from pH 3.8 to 10.2, are particularly well suited to preparative work. Conditions for purification of native proteins should first be optimized on a small scale using minislab gels. The sample should be partially purified before gel electrophoresis. A method for identifying the protein of interest, such as by immunoblotting or enzyme activity, is essential. It is difficult to predict the migration rate of proteins in native buffer systems without preliminary analysis. It is helpful to know the pI of the protein of interest. With discontinuous systems, the mobilities of native proteins can be modified by changing the pore size of the gel. This is accomplished by changing the amount of acrylamide monomer in the gel. However, the mobilities of proteins in continuous systems are best altered by pH. DNA molecules, such as restriction fragments, can also be separated by continuous-elution electrophoresis. TAE or TBE buffers are recommended. The uniform charge distribution of nucleic acid molecules makes them similar to SDS-protein complexes as far as electrophoresis is concerned. Optimization for nucleic acid purifications should follow the same procedures as for SDSPAGE. Test gels and gels used to analyze fractions from preparative electrophoresis should always be silver stained to allow detection of trace contaminants that might not be visible after dye staining.
III. Isoelectric Focusing Isoelectric focusing (IEF) (Allen et al., 1984; Allen and Budowle, 1994; Andrews, 1986; Chrambach, 1985; Righetti, 1983; Righetti et al., 1990) is an electrophoretic method for separating amphoteric molecules in pH gradients. The net charge
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on an a m p h o t e r i c molecule is determined by the p H of its local environment. Proteins, the best-known examples of amphoteric molecules, carry positive, negative, or zero net formal electrical charge, d e p e n d i n g on the p H of their surroundings. W h e n proteins move through a m e d i u m with varying pH, their net charges change in response to the p H they encounter. Under the influence of an electric field, a protein in a p H gradient will migrate until it focuses at the position in the gradient where its net charge is zero. The net charge of any particular protein is the sum of all of its positive and negative charges. These are determined by the ionizable basic and acidic side chains of the constituent amino acids and prosthetic groups of the protein. For every protein there is a specific p H at which the net charge it carries is zero. This isoelectric p H value, termed pL is a characteristic physicochemical property of every protein. If the n u m b e r of acidic groups in a protein exceeds the n u m b e r of basic groups, the pI of that protein will be at a low p H value. Conversely, if the basic groups o u t n u m b e r the acidic groups, the pI will be high. Proteins show considerable variation in isoelectric points, but pI values usually fall in the range of p H 3-10. Proteins are positively charged in solutions at p H values below their pI and negatively charged above their isoelectric points. Thus, at p H values below the pI of a particular protein, it will migrate toward the cathode during electrophoresis. At p H values above its pL a protein will move toward the anode. A protein at its isoelectric point will not move in an electric field. W h e n a protein is placed in a m e d i u m with varying p H and subjected to an electric field, it will initially move toward the electrode with the opposite charge (Fig. 5). During migration through the p H gradient, the protein will either pick up or lose protons. As it does, its net charge and mobility will decrease and the protein will slow down. Eventually, the protein will arrive at the point in the p H gradient equaling its pI. There, being uncharged, it will stop migrating. If a protein at its pI should h a p p e n to diffuse to a region of lower pH,
Fig. 5 Isoelectricfocusing. A protein is depicted in a pH gradient in an electric field. A pH gradient formed by ampholyte molecules under the influence of an electric field is indicated. The gradient increases from acidic (pH 3) at the anode to basic (pH 10) at the cathode. The hypothetical protein in the drawing bears a net charge of + 2, 0, or - 2, at the three positions in the pH gradient shown. The electric field drives the protein toward the cathode when it is positively charged and toward the anode when it is negatively charged, as shown by the arrows. At the pI, the net charge on the protein is zero, so that it does not move in the field. The protein loses protons as it moves toward the cathode and becomes progressively less positively charged. Conversely, the protein gains protons as it moves toward the anode and also becomes less negatively charged. When the protein becomes uncharged (pI) it ceases to move in the field and becomes focused.
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it will become protonated and be forced toward the cathode by the electric field. If, on the other hand, it diffuses into a pH higher than its pL the protein will become negatively charged and will be driven toward the anode. In this way, proteins condense, or focus, into sharp bands in the pH gradient at their individual, characteristic pI values. Focusing is a steady-state mechanism with regard to pH. Proteins approach their respective pI values at differing rates but remain relatively fixed at those pH values for extended periods. This type of motion is in contrast to conventional electrophoresis in which proteins continue to move through the medium until the electric field is removed. Moreover, in IEF, proteins migrate to their steady-state positions from anywhere in the system. Thus, the sample application point is arbitrary. In fact, the sample can be initially distributed throughout the entire separation system. Stable, linear pH gradients are the keys to successful IEF. Establishment of such gradients is accomplished with synthetic carrier ampholytes (Just, 1983). Ampholytes (amphoteric electrolytes) are mixtures of polyamino-polycarboxylate compounds. They are small (about 300-1000 Da in size), multicharged, organic buffer molecules with closely spaced pI values and high conductivity. Ampholytes are included with the monomer solution used to cast analytical gels and with the sample in preparative IEF chambers. When a voltage is applied across a solution of ampholytes, they partition into a smooth pH gradient, increasing monotonically from the anode to the cathode (Laas, 1989b; Mosher et al., 1992). The slope of the pH gradient is determined by the pH interval covered by the carrier ampholyte mixture and the distance between the electrodes. The proper choice of ampholyte range is very important to the success of a fractionation. Ideally, the pH range covered by the focused carrier ampholytes should be centered on the pI of the proteins of interest. This ensures that the proteins of interest focus in the linear part of the gradient, with many extraneous proteins excluded from the separation zone. Carrier ampholyte concentrations of about 2% (w/v) are best. Concentrations of ampholytes below 1% (w/v) often result in unstable pH gradients. Ampholytes at concentrations above 3% (w/v) are difficult to remove from gels and can interfere with protein staining. IEF is a high-resolution technique that can resolve proteins differing in pI by less than 0.05 pH unit. The technique is rapid and nondenaturing and can be run preparatively as well as analytically. Typical analytical gels take 90 min to run and preparative runs are over in 4 hr. Antibodies, antigens, and enzymes usually retain their activities during IEF. However, IEF does require careful sample preparation and the use of relatively expensive ampholytes. Ampholytes sometimes form complexes with proteins, which may necessitate steps for their removal. In addition, some proteins precipitate near their pI values. For best results, low-ionic-strength sample buffers are necessary and nonionic detergents or urea are often included in IEF runs to minimize protein precipitation. Some proteins, especially membrane proteins, require detergent solubilization during isolation. Ionic detergents, such as SDS, are not compatible with IEF, although nonionic detergents, such as octylglucoside, and zwitterionic detergents, such as 3-[(3-cholamidopropyl)dimethylammonio]-l-propane sulfonate and its hydroxyl analog (CHAPS and CHAPSO), can be used (Hjelmeland
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and Chrambach, 1981). Triton X-100 and NP-40 may be less satisfactory due to the slight charge content of some commercial preparations.
A. Analytical Isoelectric Focusing As an analytical tool, IEF is carried out in large-pore polyacrylamide (5%T, 3%C) or agarose gels (1%), which serve mainly as anticonvective matrices (Garfin, 1990b). Polyacrylamide IEF gels are polymerized with an initiator system, including riboflavin for photopolymerization. Photochemical initiation of polymerization with all three compounds, riboflavin, ammonium persulfate, and TEMED, results in more complete polymerization of IEF gels than does chemical polymerization alone in gels containing low-pH ampholytes. Suitable initiator concentrations are 0.015% ammonium persulfate, 0.05% TEMED, and 5/~g/ml riboflavin. Photochemical polymerization is allowed to continue for 2 hr, with the second hour under direct lighting from a nearby fluorescent lamp. The most common configuration for analytical IEF is the horizontal polyacrylamide slab gel. Gels are cast on glass plates or specially treated plastic sheets with one exposed face. They are placed on cooling platforms and run with the exposed face upward. Electrolyte strips, saturated with 0.1-1 M phosphoric acid at the anode and 0.1-1 M sodium hydroxide at the cathode, are placed directly on the exposed surface of the IEF gel. Contact between the electrical power supply and the electrolyte strips is maintained by electrodes of platinum wire. In another possible configuration, the gel and its backing plate are inverted and suspended between two carbon rod electrodes without the use of electrolyte strips (Awdeh et al., 1968). Ultrathin gels ( < 0.4 mm) allow the highest field strengths and, therefore, the highest resolution of the analytical methods. Electrofocusing can also be done in tubes, and this configuration constitutes the first dimension of two-dimensional gel electrophoresis (Dunbar, 1987; Dunbar et al., 1990). The pH gradient and the applied electric field determine the resolution of an IEF run. According to both theory (Giddings and Dahlgren, 1971) and experiment, the difference in pI between two resolved adjacent protein IEF bands (&pI) is directly proportional to the square root of the pH gradient and inversely proportional to the square root of the voltage gradient (field strength) at the position of the bands): ApI ~ [(pH gradient)/(voltage gradient)] 1/2. Thus, narrow pH ranges and high applied voltages give high resolution (small &pI) in IEF. In addition to the effect on resolution, high electric fields also result in shortened run times. However, high voltages in electrophoresis are accompanied by large amounts of generated heat (Joule heating). Thus, there are limitations on the magnitudes of the electric fields that can be applied. This is partly because resolution decreases with increasing temperature (because diffusion coefficients increase with temperature) and partly because gels can actually get hot enough to burn. Because of their higher surface-to-volume ratio, thin gels are better able to dissipate heat then thick ones and are therefore capable of higher resolution. Electric fields used in IEF are generally of the order of 100 V/cm. Urea is a common solubilizing agent, especially for those proteins that
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David E. Garfin precipitate at their isoelectric points. For maintaining protein solubility, 3 M urea is often satisfactory, but concentrations up to 8 M urea have been used. Only fresh solutions of urea, treated with a mixed-bed ion-exchange resin, should be used. Many protein samples require the use of detergents for their solubilization. For IEF work, the zwitterionic detergents CHAPS and CHAPSO, or the nonionic detergent octylglucoside, at concentrations of 1-2% in the gel, are recommended. Even in the presence of detergents, some samples may have stringent salt requirements. Salt should be present in a sample only if it is an absolute requirement. Carrier ampholytes contribute to the ionic strength of the solution and can help to counteract a lack of salts in a sample. Small samples (1 to 10 ~1) in typical biochemical buffers are usua.lly tolerated, but better results can be obtained with solutions in deionized water, 2% ampholytes, or 1% glycine. Suitable samples can be prepared by dialysis or gel filtration. Good visualization of focused lanes generally requires a minimum of 0.5/~g of protein with dye staining or 50 ng of protein per band with silver staining. One of the simplest methods for applying samples to thin polyacrylamide gels is to place filter paper strips impregnated with sample directly on the gel surface. Up to 25 ~1 of sample solution can be conveniently applied after absorption into 1-cm squares of filter paper. A convenient size for applicator papers is 0.2 • 1 cm, holding 5/~1 of sample solution. Alternatively, 1- to 2-~1 samples can be placed directly on the surface of the gel. There are no fixed rules regarding the positioning of the sample on the gel. In general, samples should not be applied to areas where they are expected to focus. To protect the proteins from exposure to extreme pH, the samples should not be applied closer than 1 cm from either electrode. Preforming the pH gradient before sample application will also limit the exposure of proteins to pH extremes.
1. Detection of Proteins Staining solution for proteins in IEF gels consists of 0.04% Coomassie Brilliant Blue R-250, 0.05% Crocein Scarlet in 27% ethanol, 10% acetic acid. Gels are soaked in staining solution for at least 1 hr. Destaining is done with several changes of a large excess of 40% ethanol, 10% acetic acid until a clear background is obtained. IEF gels can also be silver stained for increased detection sensitivity.
B. Preparative Isoelectric Focusing Laboratory-scale preparative electrofocusing (Garfin, 1990b) is accomplished in devices such as the Rotofor cell (Bier, 1986; Egen et al., 1984; A.-C. Hochstrasser et al., 1991). Preparative fractionations on the scale of from hundreds of milligrams to grams of protein, with recoveries of greater than 90%, are possible. Purifications of 10- to 100-fold place IEF procedures intermediate between ionexchange and ligand-binding chromatographies as preparative methods. IEF is well suited for use at any stage of a preparative scheme, and is particularly effective in the early stages of purification. In many cases, simple sequential fractionation and refractionation on the same device provide the desired purity.
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It is not necessary to attain steady-state focusing in preparative IEF, because adequate separations m a y be achieved before then. The Rotofor cell separates proteins by IEF in free solution (Fig. 6). Zone stabilization in the cell is achieved by rotating the sample chamber about a horizontal axis. The separation column is divided into compartments by means of screens of w o v e n polyester. The screens offer resistance to fluid convection, but do not hinder the flow of current or the transport of proteins. Proteins, which are initially dispersed uniformly t h r o u g h o u t the chamber, migrate to the one or more compartments that are at p H values nearest to their isoelectric points. The combined effect of compartmentalization and rotation is superior to either m e t h o d alone in maintaining the stability of focused zones. The segmentation of the column also facilitates fraction collection. The focusing chamber, capable of holding up to 55 ml of sample, is divided into 20 compartments by a core m a d e up of 19 disks of polyester screen (6-~m pores). A ceramic cooling finger runs t h r o u g h the center of the focusing chamber to dissipate the heat generated during the run. Two electrode assemblies hold the anolyte (0.1 M H3PO 4) and catholyte (0.1 M N a O H ) solutions.
Fig. 6 Preparative isoelectric focusing. A mixture of naturally colored proteins consisting of phycocyanin (pI 4.6), myoglobin (pI 7.0), hemoglobin A (pI 7.1), hemoglobin C (pI 7.5), and cytochrome c (pI 9.6) were combined in water containing 1% ampholytes (pH 3-10). The mixture was loaded directly into a Rotofor cell and was focused for I hr at 12 W constant power, as described in the text. Bands of focused proteins can be seen in the segmented focusing chamber. The anode (pH 3) is at the left and the cathode (pH 10) is at the right of the chamber (cf. Fig. 5).
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Appropriate ion-exchange membranes and gaskets isolate the electrolytes from the sample in the focusing chamber while allowing electrical contact with the material in the chamber. Vent caps provide pressure relief from the gases that build up in the electrode chambers by electrolysis during the run. Rotation inhibits convection, maintains even cooling and efficient electrical contact, and prevents the screens from becoming clogged by precipitated protein. Runs are done at 4~ at constant power (12 W) for 4 hr or less. Samples are collected by aspiration through tubing lines connecting the 20 individual compartments with corresponding test tubes in a vacuum chamber. The individual test tube fractions are easily sampled for assay or measured for pH with standard electrodes. Samples for the Rotofor need not be completely desalted before fractionation. Ions in the sample solution will be electrophoresed into the two end compartments in the early stages of the run. Carrier ampholyte (2%, w/v) in the initial sample solution supplies enough ampholyte for refractionation of pooled material. After the tubes containing the protein of interest have been identified, they can be pooled for a second run. The pH range covered on refractionation is centered on the pI of the protein of interest and generally covers a total pH range of less than 1 pH unit. Thousandfold purification by refractionation has been achieved. The ideal sample run on the Rotofor cell would contain only the protein mixture, water, and ampholytes. However, pI precipitation may require that 3 M urea be included for solubility. When higher urea concentrations are needed, the Rotofor cell is run at 12~ Detergents (1-2%, w/v) may also be added to samples. Zwitterionic detergents, such as CHAPS, CHAPSO, and nonionic octylglucoside, are satisfactory.
1. Removal of Ampholytes from Proteins There are a number of ways to separate ampholytes from proteins. Electrophoresis, ammonium sulfate precipitation, gel filtration, ion-exchange, and hydroxylapatite chromatographies have all been used. Dialysis is a simple and effective method for removing ampholytes from solutions of proteins. Pooled fractions are first adjusted t(~ 1 M NaC1 to disrupt weak electrostatic complexes between ampholytes and proteins, then are dialyzed against appropriate buffers. Extensive dialysis is required for thorough removal of ampholytes. There is no good way to demonstrate complete absence of ampholytes in a protein solution, but for many applications they need not be entirely removed.
IV. Immun0electr0ph0resis Immunoelectrophoresis (IEP) is a technique for studying antigens and antibodies (Axelsen, 1983; Garvey et al., 1977; Lizana, 1989; Marchalonis and Warr, 1982). Antigen samples are first separated into their component parts by electrophoresis in agarose gels. They are then probed with antibodies while still in the gels. Because the technique is based on the diffusion of large molecules, the open pore structure of agarose gels is required for the electrophoresis step. This limits the electrophoretic resolution that can be obtained. Nevertheless, the
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high specificity of antibodies allows many antigens in a given sample to be identified. In the simplest version of the method, antigen samples are placed in small (2-4 mm), circular wells punched in thin (1-2 mm), 1% agarose gels. Gels are cast on glass plates or treated plastic sheets and placed between electrode chambers in horizontal electrophoresis cells. Electrophoresis cells for IEP tend to be simple plastic boxes with separated electrode chambers. Contact between electrophoresis buffers and IEP gels is usually made with buffer-saturated filter paper wicks. A suitable IEP buffer is 0.08 M Tris, 0.02 M Tricine, 0.3 mM calcium lactate, pH 8.6. Electric fields for IEP are of the order of 5 V/cm. When electrophoresis is completed, antisera are placed into longitudinal troughs cut into the gels parallel to the migration path. Troughs, 1-2 mm wide, are placed about 0.5 cm from the sample wells. One trough is cut on each side of the sample lane. Different antisera can be placed in the two troughs. The gels are incubated overnight and the antigens and antibodies diffuse toward each other in the gel. Sweeping arcs of precipitated proteins (precipitin) form in the gels where antigens and antibodies meet at appropriate concentrations (equivalence). Major precipitin arcs are visible directly in the gels and minor ones can be visualized by staining. The presence of a precipitin arc is evidence for both antigen in the electrophoresis sample and antibody in the antiserum. The complexity of the pattern of precipitin arcs depends on both the number and types of antigens in the sample and the number and types of antibodies in the antiserum. Two major variations of immunoelectrophoresis are the so-called one- and two-dimensional rocket immunoelectrophoresis techniques. The name "rocket" is derived from the rocket-shaped precipitin peaks that form following the antigen-antibody reaction. The heights of precipitation peaks in rocket immunoelectrophoresis are roughly proportional to the concentrations of antigens in the samples, so that these two methods are semiquantitative. In rocket immunoelectrophoresis, antigens are subjected to electrophoresis in agarose gels in which antibodies are embedded. The pH of the electrophoresis buffer is near the pI of the antibody molecules, so that the antibodies do not migrate in the gel during electrophoresis. For one-dimensional rocket IEP, antigen samples are placed in wells punched out of the antibody-containing gels prior to electrophoresis. Rockets form during electrophoresis where the antigen and antibody meet at equivalence. By comparing rocket heights of test samples with those formed by known standards, concentrations of specific antigens can be determined. Identification and measurement of multiple antigens are possible with two-dimensional (or cross) rocket immunoelectrophoresis. The first step in this method is a regular agarose gel electrophoresis to separate the antigens in the sample. Next the electrophoresis lane is cut from its gel and fused to an agarose gel containing embedded antibodies. A second electrophoresis at right angles to the first direction is run. During the second electrophoresis step, antigens migrate through the antibodies in the second gel. Precipitin arcs form along the equivalence regions of the antigen-antibody pairs in the reactants. The multiplicity of precipitin arcs depends on the complexities of the antigen sample and the antiserum in the second gel.
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David E. Garfin Immunoelectrophoresis methods have been largely replaced by immunoblotting (see below) as research tools. IEP is more commonly used in clinical applications. At one time IEP methods formed the basis of serological analyses. A skilled technician can make a detailed serological diagnosis, including fairly accurate estimates of antigen concentrations, from a set of immunoelectrophoresis patterns.
V. Blotting Several types of synthetic membranes bind proteins and nucleic acids tightly enough that they can be used as supports for solid-phase immunoassays. Membrane-bound molecules are readily accessible to antibody or nucleic acid probes. This has led to the development of a variety of highly specific and sensitive procedures collectively known as blotting (Baldo and Tovey, 1989; Bers and Garfin, 1985; Bjerrum and Heegaard, 1988; Gershoni, 1987). The most informative blots are those in which proteins or nucleic acids are transferred from an electrophoresis gel to a support membrane and then probed. The most common support membrane is nitrocellulose. Proteins bind to it under conditions of low ionic strength and can be transferred from gels to membranes by electrophoresis. In contrast, high ionic strength is needed for nucleic acids to bind to nitrocellulose. Because high ionic strength is incompatible with electrophoresis, absorptive methods (from which the term "blots" is derived) were developed for transfers of nucleic acids from gels to membranes. Because this chapter is devoted to electrophoresis, only electrophoretic protein transfer is discussed. Probing of membrane-bound proteins is generally done immunologically with antibodies. For historical reasons, immunoblotting is also called Western blotting. It combines the selectivity of gel electrophoresis with the specificity of immunoassays, allowing individual proteins in complex mixtures to be detected and analyzed. Immunoblotting was developed because of the desire to probe for proteins that otherwise are inaccessible to antibodies while in highresolution polyacrylamide gels. The selectivity and specificity of immunoblotting are being utilized in clinical diagnostics. Prepared membrane strips are becoming available to clinics for testing sera for the presence of antibodies to various infectious organisms.
A. Principles of lmmunoblotting A typical immunoblotting experiment consists of six interrelated steps (Bio-Rad Laboratories, 1991; Garfin, 1992; Garfin and Bers, 1989; Timmons and Dunbar, 1990). (1) Proteins are first fractionated by electrophoresis in a polyacrylamide gel. (2) The proteins are then transferred from the gel to a membrane where they become immobilized as a replica of the band pattern of the gel. (3) Next, unoccupied protein-binding sites on the membrane are saturated to prevent nonspecific binding of antibodies. (4) The blot is then probed for the proteins of interest with specific, primary antibodies. (5) Secondary antibodies, specific for the primary antibody type and conjugated to detectable reporter groups, such
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as enzymes or radioactive isotopes, are then used to label the primary antibodies. (6) Finally, the labeled protein bands are made visible by the bound reporter groups, which in the case of enzymes convert appropriate substrates into insoluble, colored products. As might be expected, many variations in methodology have been devised.
1. Electrotransfer Nitrocellulose membrane is the best known blotting membrane. Protein binding to nitrocellulose, which is thought to be due to hydrophobic forces, is instantaneous, nearly irreversible, and quantitative over a wide range of protein concentrations (up to about 80-100 /~g/cm2). Polyvinylidene difluoride (PVDF) membranes also bind proteins tightly (170-200 ~ g / c m 2) and are stable in the chemicals used for protein sequence determination. Individual bands cut from PVDF blots can be inserted directly into solid-phase sequenators (Matsudaira, 1990). Electrophoresis is used to transfer proteins from gels to membranes. Electroblotting produces a faithful replica on the membrane, retaining the full resolution of the gel. There are currently two main types of electroblotting apparatus: tanks of buffer with appropriately placed electrodes, and flat-plate electrode arrangements for so-called semidry transfers. Blotting apparatuses are available to accommodate gels of all sizes. Transfer tanks are made of plastic with electrodes mounted at or near the walls of the tanks. Nonconductive cassettes hold the membranes in close contact with the gels. The cassette assemblies are placed in the tanks transverse to the electric fields and submerged under conducting buffer. Large volumes of buffer in the tanks dissipate the heat generated during transfer. In semidry blotting, the gel and membrane are sandwiched horizontally between two stacks of buffer-wetted filter papers in direct contact with two closely spaced, solid-plate electrodes. The term "semidry" refers to the limited amount of buffer that is confined to the stacks of filter paper. Of the two blotting systems, tanks are recommended for most routine work. With tanks, temperatures can be regulated during blotting and transfers are somewhat more efficient than with semidry systems. Under semidry blotting conditions, some small proteins are driven through the membranes, and because low buffer capacity limits run times, some large proteins are poorly transferred. Nevertheless, because semidry transfers require considerably less buffer and are easier to set up than the tank method, they are often favored by laboratories performing large numbers of blots. The buffer usually used to transfer proteins from one- or two-dimensional SDS-PAGE gels to nitrocellulose membranes is electrophoresis electrode buffer without SDS, but containing methanol. For most purposes, 25 mM Tris, 192 mM glycine, 20% (v/v) methanol, pH 8.3, will give good transfers. With semidry blotters, transfer of SDS-PAGE proteins can be accomplished with 48 mM Tris, 39 mM glycine, 20% methanol, pH 9. Methanol in blotting buffers removes SDS from protein-detergent complexes and increases the affinity between proteins and nitrocellulose. However, methanol causes a general reduction in gel pore size, restricting transfer of some proteins. It may also cause some proteins to precipitate and transfer inefficiently. Lengthy equilibration of
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the gel in the buffer should be avoided; simple washing of the gel in transfer buffer gives best results. Methanol is not required in the transfer buffer when proteins are electroblotted from gels not containing SDS.
2. Processing of Blots Regardless of the transfer method, the processing of blots involves essentially the same set of steps. The recommended buffer for all processing steps of immunoblotting is 0.02 M Tris-C1, 0.5 M NaC1, pH 7.5. Following transfers, unoccupied binding sites on the membranes must be saturated to prevent the nonspecific binding of antibody probes. Failure to block membranes adequately results in unacceptably high backgrounds. Effective blocking of nitrocellulose blots is achieved with 3% nonfat dry milk for 30-60 min, followed by washes with 0.05% Tween 20 (a nonionic detergent). Prior to probing, dried, blocked blots can be stored for months at room temperature or longer in the refrigerator or freezer. High-avidity, high-purity antibodies make the best primary and secondary probes. Tween 20 (0.05%) and a ballast of heterologous protein (e.g., 1% nonfat dry milk) should be included in the dilution buffers to minimize adsorption of probes to membranes. The ultimate sensitivity of a blot is determined by the enzyme that labels the probe. Chromogenic enzyme substrates for blotting applications allow protein bands to be directly visualized. They are converted into insoluble, colored products that precipitate and bind to membranes at the sites of the enzymes. Depending on the enzyme and substrate, sensitivities range from the low tens of picograms to the low hundreds of picograms of detected protein. Alkaline phosphatase (from calf intestines) and horseradish peroxidase (HRP) are the most commonly used labels. Alkaline phosphatase (AP) is the label of choice for sensitive chromogenic detection of immunoblots. The preferred substrate for AP blots is a mixture of 5-bromo-4-chloro-3-indolyl phosphate (BCIP) aKd nitro blue tetrazolium (NBT). The substrate BCIP is dephosphorylated by the AP, then oxidized in a reaction coupled to reduction of NBT. The resultant highly visible, purple-colored product is deposited only on the labeled bands. Sensitivities in the range 10-100 pg of detected protein can be expected. Chemiluminescent substrates are at least 10-fold more sensitive than BCIP-NBT. The disadvantage in their use is that detection requires the use of photographic (or X-ray) film. Exposures must be optimized by trial and error and the films must be developed. Storage-phosphor imaging-screen instruments can also be used for detection of chemiluminescence (Nguyen et al., 1993). In comparison, color development of BCIP-NBT can be directly observed on the blot as substrate is converted to product by the enzyme. Chemiluminescent substrates appear to be favored in laboratories doing autoradiography, because film development equipment is readily available. Luminol is an appropriate chemiluminescent substrate for HRP (Durrant, 1990) and certain dioxetane compounds are suitable for use with AP (Bronstein et al., 1992). The luminol signal fades with time, so that exposures must be set up shortly after addition of substrate to the blot, whereas the dioxetanes produce a more longlived signal. In order to identify particular protein bands, they must be compared to all of the proteins in the sample and to known standards. This requires the indis-
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criminate staining of all the proteins on the blot. It is possible to stain a duplicate gel for comparison purposes, but because the fixing and staining of gels causes them to shrink and distort, correlation of gel and blot patterns is difficult. It is more desirable to stain a lane, a section, or a duplicate blot for the total protein pattern. Amido black is the most commonly used dye for total protein staining of blots. Other dyes have been used as well, but the best current total protein stain is probably colloidal gold. Colloidal gold total protein stain, which is available as a stabilized sol, is quite sensitive. Detection limits are in the low hundreds of picrogram range of target protein and can be enhanced by an order of magnitude by subsequent treatment with silver (using kits designed for this purpose).
VI. Pulsed-Field Gel Electrophoresis Conventional agarose gel electrophoresis cannot resolve DNA molecules larger than about 20 kilobase (kb) pairs. Under special conditions (very low agarose concentration and low ionic strength), DNAs up to about 50 kb in length can be resolved, but under ordinary conditions, these large molecules do not separate from one another in the agarose matrix (Fangman, 1978). The explanation for this limitation obviously has to do with the mechanisms by which DNA molecules move through gels. The theoretical understanding of the process is being spurred on by intense interest in the structures of genomes. The dynamics of DNA molecules, with their uniform, linear charge distributions (one negative charge per nucleotide under electrophoretic conditions), are amenable to mathematical analysis. This has attracted many physical scientists to study the electrophoretic behavior of DNA. The intense activity in this field has generated fascinating insights into electrophoretic processes. A DNA molecule free in solution is in a relaxed configuration. When the molecule is placed in the midst of an agarose gel, its shape becomes constrained by entanglements with the elements of the gel matrix (Noolandi, 1992; Burlatsky and Deutch, 1993). If a static electric field is impressed across the gel, the DNA molecule will be pulled toward the anode with a uniform force per unit of its length. The material of the gel will resist the forward motion of the DNA by imposing random obstacles along its length. (Recall that the gel matrix is not uniform, but rather a statistical meshwork of solid fiber bundles and open spaces.) Eventually a segment of the molecule will be pulled into a strategically located gel pore and will move ahead of the rest of the molecule. The field will pull this leading section ahead and force the rest of the molecule to follow it through the gel. The trailing segments of the DNA will disentangle from the gel matrix and follow the path taken by the leading segment. This type of motion is called reptation (Lerman and Frisch, 1982; Lumpkin et al., 1985), and has been compared to the motion of a snake moving through bamboo. Motion continues until entanglements with the matrix so severely impede the DNA molecule that it bunches up and must start the reptation process over again (Deutsch, 1988). Once the field is removed, the DNA molecule ceases moving and relaxes. The dynamics of reptation in agarose gels are such that, on the macroscopic level, it is not possible to distinguish the distances migrated by different DNA molecules longer than 20 kb.
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David E. Garfin Separation of large DNA molecules by gel electrophoresis becomes possible when the reptation process is disrupted. The technique of pulsed-field gel electrophoresis (PFGE) allows resolution of DNA molecules millions of base pairs long (Burmeister and Ulanovsky, 1992; Gemmill, 1991; Lai and Birren, 1990; Lai et al., 1989). In PFGE, the applied electric field is pulsed so that it alternately points in one of two different directions. Each size of DNA molecule in a sample takes a characteristic time to reorient to the differing field directions. Schwartz (1985) was the first to exploit the length-dependent reorientation time of DNA in electrophoresis. The advantages of PFGE for resolving large DNA molecules were quickly recognized. Variants of Schwartz and Cantor's (1984) original method were soon developed and several sophisticated PFGE apparatuses are commercially available (Anand and Southern, 1990; Birren and Lai, 1993). Reptating DNA molecules orient along the direction of the applied electric field. If the field is turned off, and a new field, whose vector points in another direction, is applied, DNA molecules must first relax, then reorient along the new field. Return of the original field direction forces the DNAs to again relax and reorient along the field that now points in the original direction. Switching of the fields back and forth produces an alternation of the motion of the DNA molecules. The net motion of the DNA is along the resultant of the field vectors. The time required for any particular DNA molecule to reorient along a newly applied field is a sensitive function of the length of the molecule; short molecules reorient faster than large ones. The length of time that either of the alternative fields is on is called the switching time. Different populations of molecules can follow fields alternating with different switching times. For any given switching time, molecules below a certain critical size will completely align along the field and migrate appreciable distances in the gel. Somewhat larger molecules will spend a greater proportion of the switching time reorienting than the smaller ones and have less time in which to move in the direction of the field. The largest molecules spend all of their time trying to reorient to the alternating fields and hardly move at all. PFGE exploits the size dependence of reorientation times to resolve DNA molecules in the megabase pair size range. The entire genomes of some small organisms, such as yeast, have been resolved by PFGE. The simplest configuration for PFGE is that of field-inversion gel electrophoresis (FIGE) (Carle et al., 1986). A standard subcell can be used for FIGE. An electronic controller switches the applied voltage back and forth between the two electrodes to give fields pointing alternately in the forward and backward directions (180~ reorientation angle). The magnitude of the field in the forward direction and the time that this field is applied are greater than for the reverse direction, giving net forward motion to the molecules (Lalande et al., 1987). Lanes are straight, but run times are long with FIGE, because the molecules spend part of their time moving backward. The range for best resolution is up to about 100 kb. A more sophisticated configuration for PFGE is the so-called d a m p e d homogeneous electric field (CHEF) apparatus (Chu et al., 1986). In the CHEF apparatus, a gel is centered within a hexagonal electrode array (Fig. 7A and B). Each leg of the hexagon consists of four individual electrodes. An electronic controller divides the applied voltage among opposing pairs of electrodes in
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Fig. 7 Electrode configurations for CHEF (A and B) and PACE ( A - D ) pulsed-field gel electrophoresis. These two types of PFGE both make use of the same basic layout of parts. The methods differ in the number of available electric field patterns. Both techniques employ fields in the horizontal plane to separate large DNA molecules. With PACE, the electric field can point in any direction, whereas CHEF is limited to only two field orientations. Gels (stippled) are centered within hexagonal arrays of electrodes. Standard gels are 14 cm wide and 13 cm long. Other gel sizes available are 21 cm wide by 14 cm long and 14 cm wide by 21 cm long. Sample wells are formed at the tops of the gels during casting. Electrolyte buffer (usually 0.5 x TBE) covers the gels and electrodes. The hexagonal electrode arrays are 33 cm across and consist of 24 individual platinum wire segments (4 segments per leg of the hexagon). The voltage of each electrode segment is controlled electronically. For every field orientation, the electronics adjust the individual electrode voltages so as to generate a homogeneous field approximating that between infinitely long parallel wire conductors. In the CHEF method, illustrated in the upper two configurations (A and B), the sense of the net field in the gel points alternately southeast-to-northwest and southwest-to-northeast. The directions of the forces on DNA molecules are shown by arrows [(A) + 60 ~ and (B) - 60 ~ where the angles are referred to a vertical axis]. [The direction of an electric field is defined as the direction of the force on a positively charged particle. The force on a DNA molecule is opposite to the field direction.] In CHEF, the magnitudes of the two fields are the same, but can be varied. The switching time between the two directions can be also varied, but the reorientation angle is fixed at 120 ~ as shown. The net motion of DNA is in the forward direction (0~ along the resultant of the two force vectors. The PACE method allows variation of field direction, magnitude, and time. Two different applications of a PACE apparatus are illustrated. The upper two configurations (A and B) represent a PACE system operating in the CHEF mode. The lower configurations [(C) 0 ~ and (D) 180 ~ show a PACE system operating in the field-inversion (FIGE) mode. In both these applications, the force on DNA molecules alternates between two possible directions (A ~ B or C *-~ D). The net motion of DNA in both cases is in the forward direction (0~ With PACE, it is possible to program a variety of different field orientations in any predetermined sequence. This can be useful in certain situations. For example, in one particular application, combinations of the three force orientations, A, B, and D, were used to enhance resolution in a size range that was poorly resolved in a standard two-field run (Clark et al., 1988).
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David E. Garfin such a way as to produce a homogeneous field in the gel. Two electric fields of equal magnitude are used in CHEF. The field direction alternates between northwesterly and northeasterly. In each cycle, the electrical forces on DNA molecules drive them first along the + 60 ~ direction then toward - 6 0 ~ with respect to the vertical axis. Switching the fields back and forth between the two directions repeatedly reorients DNA molecules through an angle of 120 ~ Net migration of DNA molecules is along the resultant of the two field forces, along the axial (0 ~ direction. Optimal field magnitude and switching time vary depending on the size range of molecules to be fractionated. Chu et al. (1986) found the 120 ~ reorientation angle to give very good separation of DNAs in the 200- to 2000-kb size range. With CHEF, lanes are straight and many samples can be run simultaneously. Separations have been extended to 7000 kb. The programmable autonomously controlled electrode (PACE) system of Clark et al. (1988) is a very versatile modification of CHEF. The physical layout of the gel box is similar to that in CHEF (Fig. 7). Twenty-four electrode segments are arranged in a hexagonal contour, with four segments in each leg of the hexagon. Each electrode is independently controlled to allow a wide variety of fields to be produced in the gel. The PACE system can be programmed to perform all of the types of PFGE that have been described. Various pulsing schemes and combinations of field strengths (including unbalanced, asymmetric fields) are possible with PACE, thus allowing much flexibility in cases of difficult separations. Of nearly equal importance to PFGE technology as the electronics is the development of methods for keeping large DNA molecules intact once they have been released from the protective cellular matrix. As pointed out by Schwartz (1985; Schwartz and Cantor, 1984), the shear forces acting on DNA of genome size, while free in solution, are sufficient to fragment the molecules. The resultant electrophoresis pattern of such fragmented DNA will be a smear representing the multitude of fragment sizes. This problem is circumvented by never releasing genomic DNA into free solution. Instead, organisms or cells from which DNA is to be extracted are embedded in plugs of specially prepared, low-melting-temperature agarose. Cell lysis and deproteinization of DNA are accomplished by allowing detergents and enzymes to diffuse into the gel plugs. Liberated DNA is protected from shear forces by the surrounding gel matrix. DNA can be treated in various ways, such as being cleaved with restriction enzymes, while in the sample plug. The entire plug is inserted into slots formed in the electrophoresis gel and the electric field drives the DNA out of the sample-preparation plug into the electrophoresis gel.
VII. Capillary Electrophoresis Capillary electrophoresis (CE) is an instrumental technique for automating electrophoretic analyses (Foret and Bocek, 1989; Grossman and Colburn, 1992; Landers, 1993; Weinberger, 1993). CE separations are carried out in fused silica capillaries with internal diameters of 25-100/~m. The capillaries are coated with an external layer of polyimide for mechanical strength. The small internal diameter allows for efficient heat dissipation from the capillary, enabling sepa-
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rations to be carried out at high field strengths (up to 1000 V/cm). Separations are rapid, typically taking just a few minutes. The use of fused silica as the capillary material permits direct detection of separated components in the tubes. A section of the polyimide coating is removed at one end of the capillary and this "window" is positioned in the light path of an optical detector. Band peaks are recorded as they migrate past the detector window. Most CE applications use absorbance detection in the ultraviolet range. A major disadvantage of on-tube optical detectors is the short light paths of the capillaries, which reduce detection signals 100- to 400-fold compared to the more familiar 1-cm path length flow cells. Strategies used to enhance detection sensitivity in CE include short-wavelength UV detection (185200 nm) and the use of capillaries of extended path length (Albin et al., 1993). Laser-induced fluorescence detection is also employed in CE (Gassman et al., 1985). This technique can provide very high sensitivity when the molecules of interest have sufficient natural fluorescence or can be tagged with a fluorophore prior to the separation. Samples are introduced at the inlet ends of capillaries by electrophoretic injection or hydraulic injection. Electrophoretic injection is accomplished simply by dipping the capillary inlet into the sample solution and applying high voltage for a short time (typically several seconds). In electrophoretic injection, only ionic species are loaded into the capillary, and analytes are injected in proportion to their electrophoretic mobilities. Hydraulic injection is accomplished by dipping the capillary inlet into the sample solution and briefly applying pressure at the inlet or vacuum at the capillary outlet. An alternative approach is to raise the sample vial relative to the capillary outlet for a short time. Samples loaded by hydraulic injection contain analytes in the same concentrations as the sample solutions. Injection volumes are in the nanoliter range. To increase detection sensitivity, sample starting zones can be concentrated by buffer-regulated stacking, as is done with gel electrophoresis (Chien and Burgi, 1992). An important consideration in CE, in contrast to gel electrophoresis, is the magnitude of electroosmotic flow (EOF). EOF refers to a flow of liquid in a separation chamber resulting from interactions at charged groups on the chamber walls. At electrolyte values above about pH 3, the silanol groups on the inner wall of a capillary become ionized (negatively charged). Positively charged cations in the buffer, together with their waters of hydration, are attracted to the capillary wall. On application of high voltage, the cations move toward the negative electrode, dragging their hydration shells with them. The net effect is that of a liquid flow toward the cathode. The magnitude of EOF increases with increasing pH and field strength and with decreasing ionic strength. EOF causes variations in peak migration times and peak size. Control of the EOF level is therefore necessary for achieving quantitative precision in CE. Considerable effort has been spent in the development of stable, noninteractive coatings to control or eliminate EOF and to reduce adsorption (Chien and Burgi, 1992). Several coated capillaries are available commercially. CE is a very versatile separation technique. A variety of separation modes can be used with the same CE instrument. The most widely used mode is capillary zone electrophoresis (CZE), in which the capillary and electrolyte
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reservoirs are filled with a homogeneous buffer. Sample molecules are resolved into discreet zones by differences in their electrophoretic mobilities. CZE has been most successfully used for separation of peptides. For example, peptide digests and mixtures of synthetic peptides are rapidly analyzed (Frenz et al., 1989). Gels can be cast in capillaries employing a modification of the acrylamide polymerization chemistry used for conventional slab gels. A bifunctional silane, such as ~/-methacryloxypropyltrimethoxysilane, is first attached to the capillary wall. The acrylic functional group is then extended by polymerization with acrylamide and bisacrylamide. Gel-filled capillaries provide extremely high resolution for nucleic acids, and capillary gel electrophoresis (CGE) is used for analysis of synthetic oligonucleotides and polymerase chain reaction products (Turner, 1991). Capillary gel electrophoresis is not suitable for separation of proteins due to the strong UV absorption of polyacrylamide at the wavelengths required for high-sensitivity polypeptide detection. Separation of proteins and other biopolymers by size can be accomplished using solutions of hydrophilic polymers inside capillary tubes (Ganzler et al., 1992; Zhu et al., 1989). This technique is variously referred to as dynamic sieving, nongel sieving, or entangled polymer CE. The polymer solutions mimic the effects of cross-linked gels in that the migration of macromolecules is retarded in proportion to their molecular sizes. Dynamic sieving has been used for separation of oligonucleotides and polymerase chain reaction products. Resolution is not as high as that obtained with capillary gel electrophoresis, but the technique avoids the problems of short gel lifetimes and difficulty of use that is experienced with CGE. Because the polymers used for dynamic sieving are transparent in the low UV, this technique can be used for separation of SDSprotein complexes with detection in the 214- to 220-nm range. Dynamic sieving compares favorably with SDS-PAGE for many applications. Capillary isoelectric focusing is analogous to conventional IEF. Ampholytes are used to establish stable pH gradients within the capillaries, and proteins migrate to form focused zones at their isoelectric points. The capillary approach differs from conventional IEF in that focused zones must be transported past the monitoring point to detect the separated proteins. This has been achieved by hydraulic mobilization of zones (using gravity, pressure, or vacuum) (Chen and Wiktorowicz, 1992) or by using EOF as a pump for mobilization (Thormann et al., 1992). An alternative method, termed chemical or electrophoretic mobilization, induces a pH shift in the gradient by changing the composition of the catholyte and anolyte, which causes proteins to migrate past the detection point in sequence (Zhu et al., 1991). Capillary IEF has been used successfully for the characterization of related proteins with subtle differences in structureme.g., hemoglobin genetic variants (Zhu et al., 1992) and glycoforms of recombinant biopharmaceutical proteins (Yim, 1991). CE instruments can also be used for the separation of uncharged molecules by micellar electrokinetic chromatography (MEKC) (Terabe et al., 1984). In this technique, the electrolyte is supplemented with an ionic detergent such as SDS. The detergent is added at concentrations well above its critical micelle concentration, and analyte molecules become partitioned into the micelles by hydrophobic interactions. The bulk electrolyte is carried toward the cathode by a high EOF, while micelles move electrophoretically toward the anode, in a
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direction c o u n t e r to that of EOF. M E K C is u s e d for analysis of l o w m o l e c u l a r m a s s p h a r m a c e u t i c a l s . S e p a r a t i o n of e n a n t i o m e r i c d r u g s can be effected b y the a d d i t i o n of chiral selectors of the electrolyte, a n d chiral s e p a r a t i o n s can be easily d e v e l o p e d (Nishi et al., 1991). C a p i l l a r y e l e c t r o p h o r e s i s offers m a n y a d v a n t a g e s as an i n s t r u m e n t a l techn i q u e in t e r m s of q u a n t i t a t i v e analysis a n d h i g h - t h r o u g h p u t a u t o m a t i o n . It is often u s e d as a c o m p a n i o n analytical t e c h n i q u e w i t h h i g h - p e r f o r m a n c e liquid c h r o m a t o g r a p h y to c o n f i r m p e a k purity. A limitation of CE is the r e q u i r e m e n t that m u l t i p l e s a m p l e s be a n a l y z e d serially, as c o m p a r e d to the m a n y s a m p l e s that can be a n a l y z e d in parallel b y P A G E on slab gels. N e v e r t h e l e s s , the capability of CE for u n a t t e n d e d a u t o m a t i o n , w i t h r e p r o d u c i b l e l o a d i n g a n d r u n n i n g m e c h a n i s m s , short r u n times, a n d direct quantification, is m a k i n g CE p o p u l a r for r o u t i n e analyses.
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Tas, S. (1990). Separation of the DNA molecules beyond conventional size limits by gel electrophoresis with sodium dodecyl sulfate. Anal. Biochem. 188, 33-37. Terabe, S., Otsuka, K., Ichikawa, K., Tsuchiya, A., and Ando, T. (1984). Electrokinetic separations with micellar solutions and open-tubular capillaries. Anal. Chem. 56, 111-113. Thormann, W., Caslavska, J., Molteni, S., and Chmelik, J. J. (1992). Capillary isoelectric focusing with electroosmotic zone displacement and on-column multichannel detection. J. Chromatogr. 589, 321-327. Timmons, T. M., and Dunbar, B. S. (1990). Protein blotting and immunodetection. In "Methods in Enzymology" (M. P. Deutscher, ed.), Vol. 182, pp. 679-688. Academic Press, San Diego, CA. Turner, K. A. (1991). New dimensions in capillary electrophoresis columns. LC-GC 9, 350-356. Vesterberg, O. (1989). History of electrophoretic methods. J. Chromatogr. 480, 3-19. Vesterberg, O. (1993). A short history of electrophoretic methods. Electrophoresis 14, 1243-1249. Weber, K., and Osborn, M. (1969). The reliability of molecular weight determinations by dodecyl sulfate-polyacrylamide gel electrophoresis. J. Biol. Chem. 244, 4406-4412. Weinberger, R. (1993). "Practical Capillary Electrophoresis." Academic Press, San Diego, CA. Wilson, C. M. (1983). Staining of proteins on gels: Comparisons of dyes and procedures. In "Methods in Enzymology" (C. Hirs and S. Timasheff, eds.), Vol. 91, pp. 236-247. Academic Press, New York. Woolley, P. (1987). Thermal instability of electrophoresis gels. Electrophoresis 8, 339-345. Wyckoff, M., Rodbard, D., and Chrambach, A. (1977). Polyacrylamide gel electrophoresis in sodium dodecyl sulfate-containing buffers using multiphasic buffer systems: Properties of the stack, valid Rf-measurement, and optimized procedure. Anal. Biochem. 78, 459-482. Yim, K. W. (1991). Fractionation of the human recombinant tissue plasminogen activator (rtPA) glycoforms by high-performance capillary zone electrophoresis and capillary isoelectric focusing. J. Chromatogr. 559, 401-410. Zhu, M., Hansen, D. L., Burd, S., and Gannon, F. (1989). Factors affecting free zone electrophoresis and isoelectric focusing in capillary electrophoresis. J. Chromatogr. 480, 311-319. Zhu, M., Rodriguez, R., and Wehr, T. (1991). Optimizing separation parameters in capillary isoelectric focusing. J. Chromatogr. 559, 479-488. Zhu, M., Rodriguez, R., Wehr, T., and Siebert, C. (1992). Capillary electrophoresis of hemoglobins and globin chains. J. Chromatogr. 608, 225-237.
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GLOSSARY Absorption optical system As used in this chapter, one of the principal methods used to detect concentrations of a molecule in an ultracentrifuge experiment. For proteins and nucleic acids the optical absorbance, A, in the ultraviolet is used to measure concentrations of the solutes using the standard equation A = Ecd (see Chapter 6), where E is the molar extinction coefficient at the wavelength selected, c is the concentration, and d is the path length through the centrifuge cell in the direction of the incident light. When the incident beam is Introduction to Biophysical Methods for Protein and Nucleic Acid Research
111
Copyright 9 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.
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Walter F. Stafford and Todd M. Schuster
scanned along the direction of the centrifugal force, direct plots of c vs x are possible at wavelengths selected to be optimal for different species. Activity coefficient Activity coefficients are parameters that connect the thermodynamic activities of dissolved molecules to their physical concentrations. They are discussed in detail in Chapter 1. Brownian motion Classically, Brownian motion is the irregular movement that small particles of microscopic size carry out when suspended in a liquid. This phenomenon was first described in 1828 by the botanist Robert Brown, who was observing pollen of different plants dispersed in water. Due in great measure to the theoretical work of Albert Einstein beginning in 1906, the physical principles underlying Brownian motion have been quantitatively applied to the random motions of molecules in liquids and gases. We now speak of Brownian motion to mean random motions of atoms or molecules in a gas or liquid. Chemical Potential In a solution, the chemical potential of species i,/d,i, is the partial molal free energy given by the expression 1.1,i = ( 3 G / 3 n i ) ,
where n i is the number of moles of molecular species i and G is the total free energy of the solution. The chemical potential refers to the increase in total free energy when I mol of component i is added to an infinite amount of solution at fixed temperature and pressure and the numbers of moles of all other components kept fixed. Diffusion coefficient In this chapter "diffusion coefficient" refers only to that for translational motion. The basic relation defining the diffusion coefficient, D, may be stated in the form Jdiff
=
--
D(3c/Ox)t,
where Jdiff is the flux of material passing through a surface of unit area per unit time and where O c / O x is the gradient of concentration. D has the dimensions c m 2 s e c -1. The equation above is called Fick's first law. The second law (see text) can be easily derived from the first law by differentiation. Donnan equilibrium The Donnan equilibrium (sometimes called the Donnan effect) results from the unequal concentration of salts on each side of a semipermeable membrane when a charged macromolecule, such as a protein, is only on one side. The Donnan equilibrium becomes negligible when the protein solution is dialyzed in the presence of low molecular mass salts in sufficiently high concentrations. Entrained water In aqueous solutions the solvent within the macromolecule is called entrained water. In order to interpret hydrodynamic measurements discussed in this chapter in terms of molecular shape, it is necessary to use a parameter called the hydrodynamic volume whose radius is the hydrodynamic radius. In this chapter relations are used for the hydrodynamic properties of dissolved macromolecules. These relations are expressed in terms of the volume of the macromolecules. This volume therefore involves the volume of the molecules, including the volume of solvent incorporated within them.
Chapter 3 HydrodynamicMethods
113
Flux In most hydrodynamic experiments, one must assume that the molecular mass of the solute is unknown. This means that the number of solute molecules in a sample is also unknown. In this situation, it is convenient to describe solute transport in response to diffusion or centrifugal force as mass transport. The flux of a solute, J, is defined as the rate of mass transport across a surface of unit area. The units of flux are then g s e c -1 c m -2. In this chapter the concept is used in Fick's laws and the Lamm equation describing sedimentation and diffusion transport.
Frictional coefficient
Refers to both translational and rotational frictional coefficients. These parameters contain information on the viscous drag on a body moving either by translation or rotation in a fluid.
Hydrodynamically equivalent sphere
See Hydrodynamic radius.
Hydrodynamic radius It is often useful to suppose that the shape of a macromolecule approximates that of an ellipsoid of revolution and to interpret hydrodynamic measurements in terms of the volume and axial ratio of the hydrodynamically equivalent ellipsoid of r e v o l u t i o n - - t h a t is to say, the volume and axial ratio of the ellipsoid that has the hydrodynamic properties identical to those of the real macromolecule. If the ellipsoid has an axial ratio of one, then the resulting sphere can be characterized by a hydrodynamic radius. See also Stokes radius. Johnston-Ogston effect
In ultracentrifugation, the J o h n s t o n - O g s t o n effect is a phenomenon complicating quantitative analysis of mixtures due to the decreases in sedimentation coefficients with increases in concentration.
Molecular mass averages The simplest average molecular mass is the number average; this is defined by the relation, Mn = E m i M i / E mi, where Ni is the mole fraction of species i whose molecular mass is Mi. IL instead, the molecular mass average is weighted according to the mass fraction fi of the species, the mass average molecular mass is defined by
Mw - E f i M i / E fi The z-average molecular mass is defined by
Mz - ~ fiM 2/ ~ fi M i" For a monodisperse macromolecular solution, all these different averages are equal; for a polydisperse solution, on the other hand, the higher members of this series of averages are greater than the lower members because they give more statistical weight to the higher molecular mass species. Thus, Mn ~ Mw ~
8+
Or) (--
c-
§
.............
'500
,---- ...................
1100
m/z
0
1700
10,000
500
1100
m/z
1700
lo+
pH 5.2
>, Or) C
16§
0
500
12+
8+
&_x
11O0
m/z
1700
Fig. 23 ESI mass spectrum of bovine cytochrome c obtained at different acid concentrations, at 4% acetic acid, pH 2.6; 0.2% acetic acid, pH 3.0; and no acetic acid, pH 5.2. (Reprinted with permission from Chowdhury et al., 1990. Copyright 1990 American Chemical Society.)
groups to the solvent. Other experiments have examined similar phenomena, including heat- and solvent-induced conformational changes of proteins, using ES MS, but it is not yet clear what specific factors are involved. The results are certainly interesting, but the interpretation of gas-phase structure in terms of known liquid-phase structures must be approached with caution.
2. Posttranslational Modifications A number of chemical changes to a protein can occur after synthesis on the ribosome, including partial proteolytic hydrolysis, glycosylation, acylation, phosphorylation, cross-linking through disulfide bridges, etc. What these have in common is that they change the mass of the original molecule. Table V summarizes some of the more common modifications in terms of their effect on the molecular mass of a protein or peptide (Krishna and Wold, 1993). Further, using the proper procedures, the position of these modifications within the polypeptide chain can be identified. Depending on the specific analytical task, approaches may include analysis of the intact protein before and after treatment with a chemical agent or enzyme, or hydrolysis of the protein to peptides, thus localizing the alteration to a specific small peptide, followed by identification of the specific residue modified, if necessary. One of the most common modifications of proteins that is of interest is that of glycosylation. Analysis of the oligosaccharides can be quite a difficult task
192
Richard M. Caprioli and Marc J.-F. Suter Table V C o m m o n M o d i f i c a t i o n s of Proteins and Their M a s s C h a n g e to Total Molecular Mass a
Nominal mass change (Da) -42 - 30 - 18 - 2 - 1 1 14 16 28 32 35 and 37 42 44 56 64 + isotopes 74 78 and 80 80 90 96 100 104 105 121 126 132 134 146 149 154 161 162 166 176 177 178 188 203 204 210 226 229 238 242 266 291 305 324 329 454 541 617 784
Common modifications and residues Ornithine replaces Arg Homoserine replaces Met Loss of water (cross link, dehydration, pyro-Glu replaces Glu) Disulfide formation, dehydroalanine replaces Ala Amide group replaces acid Acid group replaces amide, citrulline replaces Arg Methylene group (methylation, homolog, etc.) Oxygen atom (hydroxylation, Met sulfoxide formation, etc.) Formyl, 2-methyl groups, ethyl Addition of two oxygen atoms (dihydroxyl addition) Chlorine atom Acetyl Carboxyl addition
tert-Butyl
Selenocysteine replaces serine Glyceryl group Bromine atom Phosphoryl, sulfonyl groups Benzyl Trifluoroacetyl Butyloxycarbonyl Benzoyl Pyridylethyl Nitrophenyl Iodine atom Pentosyl Benzyloxycarbonyl Deoxyhexocyl Nitrobenzoyl Toluenesulfonyl Hexosaminosyl Hexosyl Pentafluorophenyl Glucuronosyl Glycosyloxy Trichlorophenyl Lipoyl N-Acetylhexosaminosyl Farnesyl Myristoyl Biotinyl Pyridoxyl Palmitoyl Triphenylmethyl Stearoyl phosphoryl-N-acetylglucosyl N-Acetylneuraminosyl Glutathionyl Pantetheinephosphoryl Adenosyl Coenzyme A ADP-ribosyl Heme FAD
a Adapted from Krishna and Wold (1993), with permission.
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193
because there are many potential sites of attachment of carbohydrates to proteins, two types of linkages (N and O linked), considerable heterogeneity in the numbers of sugars at even one specific attachment site, and, with respect to the carbohydrate group, many possible linkage arrangements. The specific strategy for the approach to such an analysis may be different, depending on the nature of the specific glycoproteins, the complexity of the carbohydrate groups, the amount of sample available, and information already known about the structure of the glycoproteins. Often, the amino acid sequence is known either from direct sequence analysis or is inferred from the DNA sequence. This is a major advantage because it helps pinpoint potential linkage sites for both N- and O-linked oligosaccharides. Although there are now many examples in the literature that illustrate the use of mass spectrometry in determining postribosomal modifications of proteins, recent work with recombinant human macrophage colony-stimulating factor (rhM-CSF) is noteworthy because it illustrates several uses of mass spectrometry (Martin et al., 1994). From standard biochemical methods, it was known that the active protein was a homodimer consisting of subunits of 223 residues each, covalently attached by disulfide bonds. From the DNA sequence, the protein sequence for the subunit contained two consensus sites for N-linked glycosylation and several potential O-linked sites. A MALD MS spectrum of the active protein contained a broad peak centered at m / z 64,900, suggesting heterogeneity in structure. Subsequent MALD analysis of the reduced, alkylated protein also showed a broad peak at m / z 33,200 (which includes the mass added from the alkylating agent). For further information on the nature of the carbohydrate groups, the strategy relied on sequential hydrolysis using enzymes that release specific carbohydrates or hydrolyze specific linkages, i.e., neuraminidase and other glycosidases and MALD analysis. From the known specificity of the enzyme and mass differences observed after enzyme treatment, conclusions could be drawn regarding the types of carbohydrate and the extent of glycosylation of the molecule. The protein was also cleaved to smaller peptide fragments by use of a specific protease, in this case, lysine-specific Achromobacter protease I. Figure 24 shows the MALD spectrum of the peptide Asn138-Lys163before and after treatment with N-glycosidase F, with both spectra obtained on about I pmol of sample. The structures of the carbohydrate groups attached to Asn-140, determined from subsequent work, are indicated in this figure. The differences of 365, 656, and 291 mass units are typical of structures Hex-HexNAc, N e u A c - H e x - H e x N A c , and NeuAc, respectively. Further, permethylation of the released carbohydrate groups at Asn-140 followed by FAB MS analysis indicated a predominantly biantennary, sialylated oligosaccharide containing fucose residues. The most abundant mass recorded corresponds to a carbohydrate composition of (Hex-NAc)4, (Hex) 5, (Fuc) 1, (NeuAc)2. Several higher molecular mass species were also recorded, showing the heterogeneity at this single site. Further detailed structure analysis of these oligosaccharides was accomplished by high-field NMR, providing anomeric configurations and linkage information. A similar approach was used with the other N-linked site and O-linked sites. In the latter case, FAB and MS/MS were used to analyze chymotryptic fragment peptides to further pinpoint sites of glycosylation on Ser-4 and Ser-9, providing some structural information on the carbohydrate group.
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Richard M. Caprioli and Marc J.-F. Suter
Fig. 24 MALD MS spectrum of (A) the [M + H] + ion region of the glycopeptide (Asn138-Lys163) from the proteolytic digest of recombinant human macrophage colony-stimulating factor, and (B) the molecular ion region after treatment of this peptide with N-glycosidase F. (Martin, S. A., Vath, J. E., Yu, W., and Scoble, H. Co-translational and post-translational processing of proteins. In "Biological Mass Spectrometry: Present and Future" (T. Matsuo, R. M. Caprioli, M. L. Gross, and Y. Seyama, eds.). Copyright 1994 John Wiley & Sons, Ltd. Reprinted by permission of John Wiley & Sons, Ltd.)
3. Location of Disulfide Linkages The determination of the numbers and positions of disulfide links in proteins, both intra- and intermolecular, can be accomplished quite effectively by mass spectrometry (Smith and Zhou, 1990). The number of cysteinyl residues in a protein can be quickly determined by alkylation of the protein, for example, with vinylpyridine. Each pyridylethyl group adds 105 Da for each modified cysteinyl residue. The molecular mass analysis, before and after alkylation using ES or MALD MS, thus provides the total number of cysteinyl residues modified. Of course, it is possible that not all residues will be completely modified. The strategy for position assignment is straightforward in that it involves digestion of the sample protein with one or more specific proteases, and mass spectrometric analysis of the peptide fragments. A second sample of the digested protein is then treated with a reducing agent such as dithiothreitol or dithioerythritol and again analyzed by mass spectrometry. Peptides containing intramolecular disulfide bonds will shift up two m/z units if converted to sulf-
Chapter 4 Mass Spectrometry
195
hydryl groups. The ion resulting from two different peptides linked by a disulfide bridge will disappear after reduction, and two new lower mass ions will appear, each containing the reduced or alkylated cysteinyl residue. If the protein sequence is known, then production of peptides containing the individual cysteinyl residues will uniquely position the disulfide bridge. If further pinpointing of the position of the disulfide is necessary because of unknown or ambiguous sequence data, or the presence of two disulfide bonds in one peptide, further hydrolysis by other endopeptidases and exopeptidases followed by mass spectrometric analysis is done. Alternatively, MS/MS sequencing of a small peptide will enable the position of the cysteinyl residue to be assigned. Although mass spectrometry offers some important advantages for the location of disulfide bonds, it does not eliminate the complex and troublesome disulfide exchange that can occur in a protein, i.e., the ability of these linkages to scramble so that the isolated sample contains disulfide links not present in the original protein. This can occur during protein isolation, sample preparation, and analysis. Also, disulfide linkages can be easily reduced to the corresponding thiols by a number of reagents, as discussed above, and although this is used to advantage to assign disulfide links, it also may occur inadvertently during handling of the sample. In addition, reduction of disulfide bonds can occur directly as a result of the sample conditions and ionization process, especially with FAB, further complicating this analysis procedure.
4. N o n c o v a l e n t Interactions Many proteins bind other molecules, such as low molecular mass ligands or other protein molecules, to form multicomponent complexes. Although a number of techniques have been used over the years to measure the stoichiometry and kinetics of these interactions, mass spectrometry has begun to be used to measure the molecular masses of these complexes. At the present time, it is not yet clear to what extent mass spectrometry will be successful because only a relatively small number of examples have been reported in the literature. Generally, measurements of nonconvalently bound multimeric complexes of proteins using MALD MS have not been successful. In part, this results from the fact that matrices used with the N 2 laser system are soluble in organic solvent/water mixtures; indeed, sample preparation employs conditions that can lead to dissociation of the complexes. However, cross-linking of noncovalently associated complexes using specific chemical reagents has proved useful. In one such approach, glutaraldehyde has been employed to bridge lysyl residues and covalently link proteins in aqueous solution (Farmer and Caprioli, 1991). If protein concentrations are kept -< 5/.~M, nonspecific associations are minimized and therefore only the subunits within the complex will be crosslinked. Figure 25 shows the MALD mass spectra of bovine hemoglobin, a n ~2/~2 complex, before and after treatment with glutaraldehyde as a cross-linker. Before reaction, the experimental conditions involved in sample preparation a n d / o r the ionization process lead to complete dissociation of the tetramer into the a and fl subunits. After cross-linking, the tetramer is clearly observed, along with monomer and aft dimer. These latter species are believed to result from some dissociation of the complex as a result of reaction conditions. The peaks are broad in the spectrum of the cross-linked protein because glutaraldehyde polymerizes and cross-links with a wide variety of cross-linking
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Richard M. Caprioli and Marc J.-F. Suter
Fig. 25 MALDMS spectrum of bovine hemoglobin before and after treatment with glutaraldehyde.
structures. Of course, intramolecular cross links can also occur. Nevertheless, the technique clearly establishes the multimeric state of the complex. The situation with ion spray and electrospray ionization is considerably better in that a number of protein-ligand complexes have been measured. Protein-ligand complexes involving binding of drugs and cofactors have been recorded using ES MS. For many of these, the complexes are of rather low intensity and probably do not reflect the actual solution concentration. It has been pointed out by numerous investigators that use of gentle conditions during analysis, i.e., elimination of organic solvents, salts, and use of low temperature, are essential to the measurement of these complexes. Nevertheless, not all attempts have been successful, and it appears that factors other than the solution-phase association constant for the protein-ligand can be very important. For example, the noncovalently bound ras protein-GTP complex has been measured by ion spray MS (Ganguly et al., 1993). This technique allows pure aqueous solutions to be sprayed into the mass spectrometer, eliminating organic solvents. Figure 26 shows spectra obtained from a change in pH of the sample. The spectrum at pH 4 shows the complex at m / z 19,374 of high intensity, decreasing as the pH is lowered, until only the ras protein at m / z 18,853 can be observed. This is exactly what has been found in other studies of this complex involving other analytical methods. Other types of interactions reported to be measured by ES MS are globin and heme (Katta and Chait, 1991), ribonuclease A and CMP (Haskins et al., 1994), lysozyme and carbohydrate (Li and Henion, 1991b), and immunosuppressive binding protein and drugs (Li and Henion, 1991a). Some protein-protein interactions have also been measured by ES or ion
Chapter 4 Mass Spectrometry
197
Fig. 26 Molecularmass analysis of ES spectrum from the ras-GTP complex in solution at (A) pH 4.0, (B) pH 3.4, and (C) pH 2.8. (Reprinted from Tetrahedron 49, Ganguly, A. K., Pramanik, B. N., Huang, E. C., Tsarbopoulos, A., Girijavallabhan, V. M., and Liberles, S., Studies of the Ras-GDP and Ras-GTP noncovalent complexes by electrospray mass spectrometry, 7985-7996; Copyright 1993, with kind permission from Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington OX5 IGB, UK.)
spray MS, although it is not yet clear h o w effective MS will be as a general tool in such studies. For example, concanavalin A is a h o m o t e t r a m e r with a monomer molecular mass of 25,500 Da. The ES spectrum in 10 m M a m m o n i u m acetate, p H 6.7, showed both dimer and tetramer (Smith et al., 1992). It is noted that the e v e n - n u m b e r e d charge states of both dimer and tetramer overlap, i.e., the m / z values of (dimer + 20H+) 2~ and (tetramer + 40H+) 4~ are the same, but these can be distinguished by the odd charge states, i.e., the m / z of (dimer + 21H+) 21+ does not overlap with (tetramer + 41H+) 41+. Although the application of mass spectrometry to m e a s u r e m e n t s of noncovalent interactions is still relatively new, the results are intriguing and considerable progress can be expected in studying p r o t e i n - l i g a n d and p r o t e i n protein interactions.
D. N u c l e i c A c i d s The use of mass spectrometry for the analysis of nucleic acids has come in two general areas: the first involves nucleosides, nucleotides, and small oligonucleotides, and the second involves polynucleotides. By far, most w o r k has involved small molecules, due primarily to their highly charged, polar nature. Generally these c o m p o u n d s do not desorb efficiently and, compared to peptides, are considerably less sensitive with current methods and ionization processes. Only recently have ES and MALD been applied with some success to polynucleotide analysis. The results are encouraging, but are not yet at the same level of sensitivity and structural selectivity attained for protein analysis and sequencing.
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Richard M. Capri01i and Marc J.-F. Suter
1. Nucleosides, Nucleotides, and Oligonucleotides The basic approach to the measurement of nucleosides and nucleotides involves use of chemical agents or enzymes to release low mass molecules from RNA and DNA so that they are amenable to mass spectrometric techniques (e.g., LC/MS, MS/MS, and high-resolution measurements for elemental composition). Applications include structure determination of modified bases from postribosomal processing of RNA and DNA, and identification and quantitation of known bases in digests of nucleic acids (McCloskey, 1990b). The derivatization of nucleosides using trimethylsilyl (TMS) groups with analysis by EI and CI has been quite successful over the years (McCloskey, 1990c). These derivatives usually give low-intensity molecular ions, and somewhat more intense fragment 15 m/z units below that of the molecular ion. Structurally significant ions such as the B series, which contains the base moiety with various fragments of the sugar, and the S series, the sugar ring with fragments of the base, are also readily formed. Figure 27 shows the EI mass spectrum of uridine-(TMS)4, with the characteristic molecular (M), base (B), and sugar (S) ion series labeled (Pang et al., 1982). High-resolution accurate mass measurements of some of these ions establish their elemental compositions. For example, the (B + 132) ion has been shown to contain the intact base, carbon atoms 1 and 2 of the sugar, and the ring oxygen of the sugar, giving an ion of mass (B + 132.0607)Da with the composition (B + C5H1202Si). Many such identifications can be made from a single spectrum. Further details of these mass spectra can be found in a review by McCloskey (1990c). GC/MS technology, in conjunction with the use of stable isotopically labeled analogs, has been used for the high-sensitivity quantitative analysis of methylated bases in DNA. The isotope dilution method is essential because of the difficulties in performing microscale derivatization on picogram quantities of material. This procedure has also been used for the identification of other minor bases present in nucleic acids. Analyses of complex mixtures of nucleosides from RNA and DNA digests have utilized LC/MS with thermospray, CF-FAB, and electrospray ionization sources. Nucleic acids can be digested to nucleosides using a combination of nucleases and alkaline phosphatase. To illustrate the technique, the thermospray LC/MS analysis of the enzymatic digestion of a tRNA sample will be
Fig. 27 Mass spectrum of uridine-(TMS)4 with molecular (M), base (B), and sugar (S) series ions indicated. (Reprinted with permission from Pang et al., 1982. Copyright 1982 American Chemical Society.)
Chapter 4 Mass Spectrometry
199
described. Thermospray mass spectra of nucleosides are relatively simple in that, in the presence of an a m m o n i u m acetate buffer, a protonated molecular ion [M + H] + is formed, with fragment ions for the protonated free base [BH2] + and a sugar ion [ ( S - H ) . NH4] + resulting from the loss of a h y d r o g e n from a hydroxyl group plus addition of an NH4 + adduct (Pomerantz and McCloskey, 1990). A few other fragment ions are formed in the thermospray process, but these are of relatively low intensity. Figure 28 shows the UV chromatogram (254 nm) for the LC separation of the digest of 18/zg of tRNA from Sulfolobus solfataricus. The peak assignments were m a d e from their thermospray mass spectra and are listed in the legend for Fig. 28. These applications represent impressive uses of mass spectrometry for the analysis of quite complex mixtures having components in a wide range of concentrations. The procedure is not trivial, and considerable experience is required to perform it effectively.
2. Oligonucleotides Direct analysis of oligonucleotides and fragments of RNA and D N A can be accomplished by mass spectrometry, but have not yet been developed to the state of protein analysis. Desorption ionization techniques such as FAB and PD have been effective only with relatively small oligonucleotides (8 to 10-mers), and most of their use has been in the analyses of synthetic preparations. Oligonucleotides are highly negatively charged and therefore are generally measured in the negative ion mode. The two techniques, which currently hold promise and have given some encouraging results, are MALD and ES, and work in this area is described below. MALD MS has shown some impressive results with respect to desorbing intact large polynucleotides. In one report the (M - H ) - ion of an RNA 104-mer
lOO
10
20
c" ~3 k_ 0 t,... k.
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19
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8 8
2
13 1 14 15
7
11
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I '' 10
''
I .... 15
~/
21
18
I .... 20
2
23
~ 29
24
i .... 25
I .... 30
I 35
Time, minutes
Fig. 28 Chromatographic separation of nucleosides from the LC/thermospray MS analysis of the enzymatic digest of unfractionated S. sulfataricustRNA (UV profile at 254 nm). Some of the peaks are identified: 2, pseudouridine; 3, cytidine; 4, uridine; 7, 1-methyladenosine; 8, 2'-O-methylcytidine; 10, guanosine; 13, deoxyguanosine; 17, 1-methylguanosine; 18, N4-acetylcytidine; 22, N2,N 2dimethylguanosine; and 28, Na,N2-O-trimethylguanosine. (Reprinted from Pomerantz and McCloskey, with permission.)
200
Richard M. Caprioli and Marc J.-F. Suter was recorded at about m / z 33,500 using succinic acid as the matrix and an infrared laser (Nordhoff et al., 1993), as shown in Fig. 29. This is not yet routine and, at this point, analysis of 50-mers are the practical limit in size one can expect to achieve with current methods. Size is important from the view of potential sequencing strategies; the larger the fragment the less overlapping data needed to link these fragments and the faster the sequencing process. Of course, the other challenge is to produce chemical/enzymatic methods that yield all of the truncated molecular species required to sequence the polynucleotides that are also compatible with the mass spectrometric techniques used. Although it is possible that MS/MS methods can be devised to sequence polynucleotides directly, progress thus far has been slow. Several factors have limited polynucleotide analysis by mass spectrometry and are being urgently addressed by many laboratories. First, ions from polynucleotides tend to fragment easily, and not always in a coherent manner. Second, the highly charged nature of the molecules not only makes them difficult to bring into the gas phase, but leads to the association of many different cations, giving a broad, diffuse peak when observed. Also, because most of the initial effort of MALD has been on proteins, the matrices used have not been optimal for polynucleotides. In this regard, several new matrices have been reported for specific use with polynucleotides. One of these, 3-hydroxypicolinic acid (Wu et al., 1993), appears quite effective for oligonucleotides up to about 70-mers. This matrix shows a significant improvement in performance, not only in analyzing a wider mass range, but also shows greater sensitivity in the negative ion mode. A truly intense effort is underway to develop such techniques by MALD MS, and the expectation of success is high. Electrospray has also shown some interesting results for polynucleotides in the 50- to 80-mer range (Stults and Marsters, 1991). These samples were prepurified and sodium ions were replaced with ammonium ions. The deconvoluted ES mass spectrum of a 77-mer obtained from a solution of 50 p m o l / ~ l infused at a rate of 2 ~ l / m i n gave a molecular mass of 24,058 + 8 Da (theoretical: 24,039 Da). This suggests the presence of one sodium ion, with the peak at m / z 924.5, corresponding to (M - 27H + + Na) 26-, i.e., this ion contains 26 negative charges. High-purity samples, devoid of mixtures of not only other poly-
100-
Z [..
z
> [..
10 -9 sec) and nuclear magnetic resonance phenomena (~ 10 -6 sec). Thus, vibrational spectroscopy is suitable for time-resolved studies of biological processes that are inaccessible by fluorescence and magnetic resonance methods. 5. There exists a large database of infrared and Raman spectra of proteins, nucleic acids, and their constituents, for which reliable band assignments, normal mode analyses, and spectra-structure correlations have been made. This facilitates interpretation of the often complex vibrational spectra obtained from proteins, nucleic acids, and their complexes. The following advantages are specific to Raman spectroscopy: 1. Both H 20 and D 20 generate very weak Raman scattering, thus producing relatively little interference with the Raman spectrum of the dissolved solute. This constitutes a significant advantage over infrared absorption spectroscopy, where both H 2 0 and D20 are highly problematic solvents. The innocuous Raman characteristics of H 20 and D 20 likewise facilitate the exploitation of Raman spectroscopy for monitoring hydrogen isotope exchange processes in proteins, nucleic acids, and their assemblies. Similarly, hydrogen isotope exchanges can be employed in the Raman effect for purposes of measuring isotope shifts to establish or confirm definitive vibrational spectroscopic assignments. 2. The fundamental selection rule for Raman spectroscopy, i.e., that relatively high Raman intensity accrues from molecular vibrations with which there is associated a large change in molecular polarizability, favors the electron-rich substituents of proteins and nucleic acids. Thus, the Raman spectrum of a typical protein is dominated by spectral bands assignable to main-chain peptide groups, aromatic side chains (Trp, Phe, Tyr), sulfur-containing side chains (Met, Cys), and side-chain carboxyls (Asp, Glu, Asn, Gln). Raman intensities associated with saturated hydrocarbon groups are intrinsically rather weak. However, the large numbers of such groups typically present in a protein result in a few relatively intense Raman bands associated with groups frequencies of the methylene and methyl substituents. In the case of nucleic acids, the Raman spectra are dominated by bands attributable to vibrations of the backbone phosphate groups and of the purine and pyrimidine rings, especially in-plane skeletal stretching and exocyclic carbonyl stretching modes of the latter. 3. Raman intensities are enhanced dramatically (by several orders of magnitude) when the energy of the incident photon is selected in resonance with a molecular electronic transition of a protein or nucleic acid chromophore. This constitutes the resonance Raman (RR) effect. Therefore, structural information about the chromophore can be obtained by use of relatively dilute protein or nucleic acid solutions through the RR mechanism. This technique is particularly
Chapter 6 Opticaland Vibrational SpectroscopicMethods
293
valuable for proteins containing chromophores that absorb in the visible (metalloproteins, retinal proteins, etc.) or near-ultraviolet (nucleotide-binding proteins, nucleoprotein complexes, etc.). Ultraviolet resonance Raman (UVRR) spectroscopy has found more extended use in applications to nucleic acids and nucleoprotein assemblies. Vibrational spectroscopy for protein and nucleic acid structure analysis has the following notable disadvantages: 1. Although band resolution in vibrational spectra is superior to that achievable in electronic spectra of condensed phases, the spectral resolution of vibrational spectroscopy is still inferior to that of high-field magnetic resonance spectroscopy. Inadequate resolution is especially problematic in infrared spectra of proteins and nucleic acids and can severely limit the usefulness of the data. To overcome this limitation, the experimentalist may employ a strategy based on chemical or biological modification, such as isotope editing or sitedirected mutagenesis. 2. The Raman process of inelastic light scattering is inherently weak compared to other light absorption and emission processes. Thus, considerable effort in sample purification and care in sample handling are necessary to avoid even minute traces of fluorescent impurities or other chromophores that may interfere with detection of the Raman scattering. 3. The inherent weakness of the Raman scattering mechanism in comparison to other mechanisms of interaction of radiation with matter also imposes a requirement for sophisticated and relatively costly instrumentation. 4. Although small sample volumes are sufficient for Raman and infrared analyses, relatively high solute concentrations are required (~ 10-100 p~g//zl).
C. Instrumentation and Sample Handling
1. Raman Spectroscopy The instrumentation required for measuring a Raman spectrum consists of a monochromatic light source (laser) that excites the Raman spectrum, a diffraction grating spectrometer that analyzes the Raman scattered frequencies, and a detector that captures the Raman photons. Laser excitation wavelengths extending from the near-infrared (~ 1000 nm) to the near-ultraviolet (~ 200 nm) have been employed. The choice of excitation wavelength is determined by the absorption characteristics of the sample and the objectives of the experiment. Inert gas lasers providing excitation wavelengths in the visible are most often employed for off-resonance Raman spectroscopy of nonabsorbing proteins and for resonance Raman spectroscopy of proteins that absorb in the visible. In the latter case, the Raman spectrum is dominated by resonance-enhanced bands of the visible chromophore, usually a metalloporphyrin or retinal cofactor. Typical excitation wavelengths include the continuous wave (CW) argon ion laser emission lines at 488.0 (blue) and 514.5 nm (green) and the helium-neon laser line at 632.8 nm (red). Intracavity frequency-doubled argon lasers, which provide CW emission in the near-ultraviolet (e.g., the second harmonics of the 488.0- and 514.5-nm emissions occurring at 244 and 257 nm, respectively), have become available for ultraviolet resonance Raman (UVRR) spectroscopy of
294
Takashi Miura and George J. Thomas, Jr. proteins and nucleic acids absorbing in the near-UV. In the UVRR spectra of such molecules, the spectrum is dominated by the resonance-enhanced Raman bands of the UV chromophores, namely, the aromatic amino acid side chains of proteins, or purine and pyrimidine bases of nucleic acids. A Raman spectrometer must be capable of efficiently rejecting the very intense Rayleigh scattering that accompanies the Raman scattering [Eq. (20)]. For this purpose, one employs either a highly dispersive (double) grating configuration in the analyzing spectrometer, or a narrow cutoff filter (holographic edge filter) before the detector. The latter are available commercially for use with excitation wavelengths in the visible and near-IR regions. Detectors for Raman spectroscopy are gradually evolving from the singlechannel photomultiplier and multichannel diode-array technologies to the more efficient charge-coupled device (CCD) detector. In recent years, the liquid nitrogen-cooled CCD camera, which virtually eliminates dark current noise and permits rapid multichannel detection, has come into wide use for detection of Raman-scattered photons. Because Raman spectroscopy of biological molecules requires a laser source of relatively high power and stability, optical components with superior stray light rejection, and sophisticated photon detection capability, the instrumentation is relatively costly in comparison to that of infrared or UV/visible absorption spectroscopy. In order to acquire state-of-the-art Raman spectroscopic data, it is advisable to establish an appropriate collaboration with a specialist in the field. More detailed discussion of instrumentation requirements for Raman spectroscopy has been given by Carey (1982). In the preparation of solutions of biomolecules for Raman spectroscopy, one generally avoids the use of high concentrations of complicated buffers. To manipulate ionic strength, monatomic cationic and anionic species are preferred whenever possible, because polyatomic species generate Raman bands that may interfere with those of the protein or nucleic acid. Thus, NaC1 would be preferred over NH4C1 or NaNO3 to increase the solution ionic strength. Low concentrations of chelating agents (~ 2 mM EDTA) are also acceptable. Although a low concentration of buffer is tolerable (e.g., 5 mM Tris), use of such buffers is largely cosmetic because they would provide negligible buffering capacity in a protein solution of ~ 100 /~g//~1 (equivalent to ~ 10 mM of a 10-kDa protein and probably much greater than 10 mM with respect to the acidic and basic side chains for which the buffering capacity is intended). Sample handling procedures for Raman spectroscopy of proteins and nucleic acids have been surveyed by Carey (1982) and Thomas and Kyogoku (1977). Special procedures for viral samples have also been discussed (Thomas, 1987). The sample solution is transferred to the Raman cell, ordinarily a glass or quartz capillary, by pipette, syringe, or direct suction; the cell is then sealed. Only I ~1 of solution is required for obtaining a high-quality Raman spectrum. The sample is irradiated by the focused laser beam and the scattered light is collected at 90 ~ from the direction of the incident beam. The time required to record a Raman spectrum varies from seconds to hours, depending upon the intrinsic strength of the Raman signal (determined by sample concentration, excitation wavelength, etc.) and the spectral resolution required. The rejection of fluorescence, due to impurities or to the sample, and the mode of detection of
Chapter 6 Optical and Vibrational Spectroscopic Methods
295
the Raman-scattered photons are also factors that determine the time required to obtain the Raman spectrum.
2. Resonance Raman Spectroscopy In addition to the foregoing, the following considerations apply to visible and ultraviolet resonance Raman experiments. First, if the laser excitation wavelength is close to or within the wavelength interval of electronic absorption by the sample, then the photons may be more efficiently absorbed than Raman scattered. In such a case, increasing the sample concentration would serve only to increase photon absorption rather than photon scattering. This is in contrast to the situation applicable in off-resonance Raman spectroscopy, where the Raman intensities increase with increasing sample concentration. Second, photon absorption in resonance Raman experiments tends to be minimized if the sample illumination scheme is in the so-called "back-scattering" geometry, i.e., if the propagation directions of incident and scattered beams are at approximately 180 ~ to one another. This minimizes collection of photons that have passed through the absorbing medium. Third, because the risk of photodecomposition is high in RR experiments, a spinning cell or flow cell is preferable to a static sample. This in turn requires a much greater volume of material (albeit lower concentration) than in off-resonance experiments. Finally, RR experiments should be conducted with the incident laser power sufficiently low that the population of molecular energy levels is not altered from the equilibrium value appropriate to the experimental objectives. A high laser power can significantly affect the distribution of molecules in electronic energy levels and thereby alter the Raman band intensities (Raman saturation). In RR experiments it is advisable to demonstrate that the observed Raman intensities are not dependent on the laser power.
3. Infrared Spectroscopy A conventional scanning instrument for recording infrared spectra consists of a source of continuous radiation over the mid-infrared region, a sample chamber, a monochromator, and a detector. The infrared beam, which passes through the sample, is dispersed by a grating monochromator and then focused by a spherical mirror onto a slit, which serves both as the exit slit of the monochromator and entrance slit to the detector. The spectrum is scanned by continuously changing the angle of the grating or by moving the focusing mirror. Although the scanning instrument requires a relatively long time to obtain a complete spectrum and is little used in biological applications, it is still convenient for routine analytical applications. At present, infrared spectroscopic studies of proteins and nucleic acids are carried out by use of Fourier transform instruments. A Fourier transform infrared (FTIR) spectrometer employs an interferometric device, such as a Michelson interferometer, rather than a grating. The infrared beam emitted by the source is divided into two beams and the optical paths of the two beams (from the light source to the detector) are changed continuously by a moving mirror. Consequently, because of interference, the intensity of infrared radiation reaching the detector changes as a function of the relative path lengths between the two beams. The measured interferogram is converted into an infrared spectrum
296
Takashi Miura and George J. Thomas, Jr. through the Fourier transformation procedure. Because radiation of all infrared frequencies (typically the interval 400-4000 cm- 1) is detected simultaneously, a complete spectrum can be obtained in a very short time. Signal averaging procedures to enhance band intensities and minimize noise are therefore rapid and convenient, even for weakly absorbing samples. The FTIR method has been discussed in detail by Griffiths and deHaseth (1986). As noted previously (Section III,B), both H a O and D 2 0 are problematic solvents for infrared spectroscopy because of their very strong infrared absorption. Infrared spectra of aqueous solutions of proteins and nucleic acids can be obtained satisfactorily in limited intervals of the mid-infrared region, namely, 500-1000 cm -1 for H 2 0 solutions and 800-1100 and 1300-2000 cm -1 for D20 solutions. Also, a relatively high solute concentration is usually required. An infrared sample cell usually consists of a uniformly narrow chamber achieved by sandwiching an inert gasket between two optically flat plates (windows) fabricated from nonabsorbing material. The window material is chosen on the basis of its high infrared transmission, low refractivity, durability, insolubility, nonreactivity, and so forth. Calcium fluoride (CaF2), barium fluoride (BaF2), zinc selenide (ZnSe), and silver chloride (AgC1) windows are commonly employed for aqueous samples. Advantages and disadvantages of these and other window materials have been discussed (Griffiths and dellaseth, 1986). The optical path within the infrared cell (gasket thickness) is generally chosen to be between 20 and 100 txm, depending on the sample concentration and molar extinction coefficient of the band(s) to be measured. Infrared absorption, like UV/visible absorption, is governed by the Beer-Lambert relationship [Eq. (14)]. Cells thicker than 100 Ixm ordinarily do not transmit sufficient energy due to strong infrared absorption by the solvent. The sample volume is of course dependent on the cell path and cross-section. Typically, an infrared cell volume is 10/xl or greater. Thin and ultrathin films of the biological sample can also be layered on a suitable window material or reflectance device for infrared analysis.
D. Analysis of Data The successful application of vibrational spectroscopy in protein and nucleic acid analysis presumes definitive band assignments and requires a combination of experimental and theoretical approaches. Tactics employed toward this objective include (1) comparison of Raman frequencies and intensities with corresponding infrared data when available; (2) determination of vibrational frequency shifts accompanying stable-isotope substitutions, such as 1H 2H(D), 12C ~ 13C, 14N ~ 15N, and 160 ~ 180; (3) evaluation of the effects of pH, temperature, and other environmental factors on the spectra; (4) detailed and well-analyzed Raman and infrared spectra of smaller, more symmetrical molecules that are structurally related to the biomolecular constituents; (5) normal coordinate calculations; (6) measurements of depolarization ratios of the Raman bands in isotropic solutions of the molecules; (7) collection and analysis of polarized spectra of oriented samples when feasible; and (8) measurement of Raman excitation profiles that correlate Raman intensities with laser excitation wavelengths.
Chapter 6 Optical and Vibrational SpectroscopicMethods
297
Digitally computed difference spectra can facilitate the visualization of changes in vibrational band intensities or frequencies accompanying changes in sample temperature, molecular environment, or the like. However, because the Raman spectrum is not an absorption spectrum, its intensities are not governed by the Beer-Lambert law, and the comparison of two independently recorded Raman spectra by subtraction can be subject to considerable uncertainty. This is dealt with by comparing intensities in the two spectra only after normalization of both the minuend and subtrahend to a reliable internal intensity standard. A normalization procedure should be deemed reliable only after careful consideration of the origin of the band in question, and preferably after validation on a suitable model system. In the absence of reliable internal normalization, a process of trial and error may be the only recourse for computation of a Raman difference spectrum. Similar concerns apply to the procedure of solvent correcting a vibrational spectrum (infrared or Raman). It should be kept in mind that the protein or nucleic acid solute may influence the structure of the aqueous solvent, and therefore its vibrational spectrum, as much as the water molecules may influence the structure of the dissolved biomolecule. Accordingly, it is virtually impossible to compensate completely a solution spectrum for contributions of the aqueous solvent by simply subtracting therefrom the spectrum of the pure solvent. The computational power of microcomputers has ushered in an era of easy manipulation of all types of experimental data, including infrared and Raman spectra. A particularly popular procedure is the method of Fourier deconvolution, which is applied to enhance the resolution of overlapping bands. Also commonly employed is the method of least-squares curve fitting, which can be used to fit a complex bandshape to an arbitrary number of simpler band components. While the utility of such procedures cannot be questioned, considerable caution must be exercised in their application. The vibrational spectroscopist is well advised to avoid these computational approaches whenever the collection of additional experimental data can serve the same objective.
E. Information Obtainable from Vibrational Spectra In this section, we discuss molecular structural and environmental factors that can affect the frequencies a n d / o r intensities of bands in infrared and Raman spectra of proteins and nucleic acids. We also consider the usefulness of vibrational spectral data for gaining an improved understanding of molecular force fields and dynamical processes in biological molecules. Spectral bands that are particularly useful as markers of residue structure or environment are tabulated in Tables III-VI. The selection is representative, rather than comprehensive. More detailed discussions of these and other marker bands of proteins and nucleic acids can be found in recent review articles on the following subjects: infrared spectroscopy of nucleic acids (Taillandier and Liquier, 1992); infrared and Raman spectroscopy of proteins (Thomas and Kyogoku, 1977); Raman spectroscopy of nucleic acids, nucleoproteins, and viruses (Thomas, 1987; Thomas and Wang, 1988; Thomas and Tsuboi, 1993); Raman spectroscopy of proteins (Miura and Thomas, 1995); resonance Raman spectroscopy of nucleic acids (Tsuboi et al., 1987); and resonance Raman spectroscopy of proteins (Harada and Takeuchi, 1986; Austin et al., 1993).
298
Takashi Miura and George J. Thomas, Jr.
Table III Vibrational Modes of Trans Peptide Group a Description
Observed frequency
Calculated frequency
Amide A Amide I Amide II Amide III N C N stretch CN stretch Amide V Amide IV Amide VI C~CN bend C N C N bend Amide VII
3236 1653 1567 1299 1096 881 725 627 600 436 289 206
3254 1646 1515 1269 1070 908 721 637 655 498 274 226
Potential energy distribution b NH CO NH NH
s (100) a (83), CN s (15), C~CN d (11) ib (49), CN s (33), CO ib (12) ib (52), C~C s (18), CN s (14) N C N s (77), C~C (17) CN s (31), C~C s (17), CO s (16) CN t (75), NH ob (38) CO ib (44), C~C s (34), C N C N d (11) CO ob (85), CN t (13) C~CN d (63), CO ib (11) C N C N (71), CO ib (19), C~CN d (13) NH ob (64), CN t (15), CO ob (12)
a Based on the observed and calculated frequencies (cm -~) of N-methylacetamide, C~CONHCN, where Ca and CN refer to the acetyl and amide methyl groups, respectively, as reported by Bandekar (1992). b Relative (unnormalized) contributions to the potential energy; s, stretch; d, deformation; t, torsion; ib, in-plane bend; ob, out-of-plane bend.
Table IV Ranges of Infrared and Raman Amide Modes for Different Protein Secondary Structures a Secondary structure c~-Helix
/3-Strand
Irregular
Amide mode Amide Amide Amide Amide Amide Amide Amide Amide Amide Amide Amide Amide
I II III V I II III V I II III V
Infrared (cm -1)
Raman (cm -1)
1648-1655 1540-1545 1270-1320 ~ 660 1630-1635(_1_ ), 1690-1695( II) 1520-1525( II ), 1550-1555(_t_) 1220-1235( II ) ~ 700 1655-1660 1550-1570 1240-1255 u
1648-1655 n 1270-1320 ~- 660 1660-1680 n 1225-1240 u 1655-1665 n 1240-1250 u
a Compiled from data in Carey (1982), Thomas (1987), Bandekar (1992), Arrondo et al. (1993), Miura and Thomas (1995), and references therein, n, Not observed in the off-resonance Raman effect; u, undetermined; (II), parallel component; (_t_), perpendicular component. The UVRR-determined amide II modes in model compounds are discussed by Austin et al. (1993). Additional correlations for various types of turns are also discussed by Bandekar (1992).
299
Chapter 6 Optical and Vibrational Spectroscopic Methods Table V Raman Markers of Backbone Conformation in D o u b l e Helical Nucleic Acids a Group
A DNA
O-P-O
B DNA
706 + 5 807 + 3 b
790 828 835 839 1092 1422
1099 + 1 1418 + 2
PO 2CH 2
Z DNA
+ 5 +_ 2 (GC) + 2 (GC + AT) + 2 (AT) + 1 + 2
745 + 3
1095 + 2 1425 + 2
a Frequencies (in c m - 1 ) a r e determined from Raman spectra of D N A and RNA crystals and fibers of known structure. b This vibration occurs at 813 + 2 c m -1 in A RNA structures. A very weak line also occurs at approximately 810 c m -1 in Z D N A structures.
1. M o l e c u l a r In applying
Force Fields
the simple harmonic
cal bond
between
diatomic
molecule),
atoms
A and
oscillator approximation B of masses
the classical vibrational
m A and
to an isolated chemi-
mB, r e s p e c t i v e l y
frequency
(e.g., a
is g i v e n b y
v = o c = (1/2rr)(K/la,) 1/2, where reduced
K is t h e H o o k e ' s mass
molecules,
law
of the system,
expressions
cated, can be derived
force constant defined
analogous
as 1/~
and
(21)
1/~
is t h e r e c i p r o c a l
t o E q . (21), b u t c o n s i d e r a b l y
for each of the 3N -
of the
= 1/m A + 1/mB. In polyatomic
6 normal
modes
more
compli-
( W i l s o n et al., 1 9 5 5 ) .
Table VI Raman Markers of Nucleoside Conformation in Nucleic Acids a Base G A C T
C3'-endo/anti 664 1318 644 1335 780 1252 668 745 777 1239
+ + + + + +
2b 2 4 2 2 2 -+- 2e + 2f + 2 + 2
C2'-endo/anti 682 1333 663 1339 782 1255 668 748 790 1208
+ 2 + 3c + 2a ___2 + 2 + 5 + 2 + 2 + 3 + 2
Cl'-exo/anti 670 + 2 1343 + 2
C3'-endo/syn 625 1316 624 1360 784 1265 660 745
+ + + + + + + +
3 2 3 5 2 2 5 5f
C2'-endo/syn 671 + 2 1324 + 2
677 + 2 737 + 2
Frequencies (in c m -1 ) are determined from Raman spectra of DNA and RNA crystals and fibers of known structure, reviewed in Thomas and Wang (1988), and from unpublished spectral data obtained by T. Miura and G. J. Thomas, Jr. b Observed at 668 + 1 c m -1 in structures containing rG. c A weak companion line near 1316 c m -1 is also observed in B D N A structures. Very low intensity compared to the 664 and 668 cm -1 lines of C2'-endo/anti dG and C2'-endo/anti dT, respectively. e Very low intensity compared to the 668 cm -1 line of C2'-endo conformer. f Very low intensity compared to the 748 c m -1 line of C2'-endo conformer. a
300
Takashi Miura and George J. Thomas, Jr. The frequencies of the molecular normal modes of vibration are determined rigorously by the nuclear masses and geometry~specifically, by the forces between bonded and nonbonded atoms (Herzberg, 1945). If the molecular geometry and the force field (i.e., the complete set of nonzero force constants) are reasonably well known, the 3N - 6 normal modes can, in principle, be calculated. The results of such normal coordinate calculations can then be tested against the experimental vibrational frequencies obtained from infrared and Raman spectra, and the force constants or geometry can be subsequently refined and the normal modes recalculated. Ultimately one hopes to obtain a detailed quantitative understanding of the nature of each normal mode of vibration, namely, which atoms are in motion in a given normal mode, and how the potential energy is distributed among the various internal coordinates that constitute the normal coordinate for that mode. Although such approaches have long been feasible for small molecules (Wilson et al., 1955), it is only relatively recently that complete normal coordinate analyses have been attempted for biological macromolecules (Krimm and Bandekar, 1986; Bandekar, 1992), sometimes with mixed success. This limitation is due in part to the paucity of experimental data needed to provide reliable force constants for large molecules and the resulting inadequacy of macromolecular force fields employed in the calculations. Microbiological and chemical methods have led to the incorporation of stable isotopes of hydrogen, carbon, nitrogen, and oxygen into the sugar and base residues of nucleic acids (Kellenbach et al., 1992; Nikonowicz et al., 1992). Similarly, isotope labeling of specific side chains in proteins and their assemblies (Aubrey and Thomas, 1991; Overman et al., 1994) has facilitated the refinement of key vibrational assignments in protein spectra. The new experimental data afforded by these methods make feasible the development of improved molecular force fields for accurate normal coordinate calculations of biological macromolecules. The more accurate normal mode analyses in turn provide reliable bases for both ab initio and molecular mechanics calculations. The latter are finding increased use in energy minimizations applied to problems of macromolecular folding and dynamics.
2. Macromolecular Conformations a. P r o t e i n s The vibrational modes associated with the trans peptide group of proteins (amide modes, Table III) are generally sensitive to the detailed conformation of the polypeptide backbone. Many of the amide modes in infrared spectra (reviewed by Arrondo et al., 1993) and Raman spectra (reviewed by Bandekar, 1992; Austin et al., 1993) of proteins have been correlated with specific main-chain conformations or secondary structures. Several are listed in Table IV. In principle, protein secondary structure may be estimated quantitatively from analysis of the conformation-sensitive amide I and amide III bands. In practice, however, a rigorous quantitative analysis is highly problematic and methods so far described have not been widely applied. Quantitative amide band analyses do provide, however, a complement to CD methods and may be especially useful for systems not amenable to CD spectroscopy. Surveys of infrared and Raman spectrophotometric methods employed for protein secondary structure analysis have been given by Bandekar (1992) and Arrondo et
Chapter 6 Optical and Vibrational Spectroscopic Methods
301
al. (1993). Further discussion of this subject is also given by Miura and Thomas (1995). b. Nucleic Acids The principal families of nucleic acid double helical structures (A, B, and Z conformations) are readily distinguished by their characteristic vibrational spectra. Table V lists the most prominent Raman marker bands of the different helical conformations. Table VI contains Raman marker bands identified for different conformers of the purine and pyrimidine nucleosides that are present in the helical duplexes. Detailed discussions of these nucleic acid spectra-structure correlations, established on the basis of known three-dimensional X-ray structures of oligonucleotide single crystals, are given elsewhere (Thomas and Wang, 1988; Thomas and Tsuboi, 1993). 3. S i d e - C h a i n
Conformations and L o c a l
E n v i r o n m e n t s in P r o t e i n s
A number of reliable correlations have been established to relate specific vibrational band frequencies a n d / o r intensities with the conformations and local environments of various protein side chains. A comprehensive overview of these correlations, which deal primarily with Raman and resonance Raman bands, can be obtained from the reviews by Harada and Takeuchi (1986), Austin et al. (1993), and Miura and Thomas (1995). (Owing to the difficulties associated with quantitative measurements in infrared spectra of aqueous proteins, relatively little is known about the possible conformational dependencies of corresponding infrared bands.) To illustrate this type of spectral information we consider two examples, cysteine and tryptophan. a. Cysteine The S - H stretching vibration of the cysteinyl side chain is particularly well suited to Raman analysis. The normal mode is a nearly pure group frequency; the Raman intensity associated with the vibration is intrinsically high; and the frequency occurs in a region of the Raman spectrum (25002600 cm -1) that is essentially devoid of interference from any other Raman bands of the protein or aqueous solvent. The structural value of the Raman S - H stretching band rests on two key factors: First, the band frequency is highly sensitive to hydrogen bonding of the S - H donor and S acceptor groups. Second, the band intensity is a measure of the molecular concentration of thiol groups in the protein. The first of these factors may be exploited to determine the environment and hydrogen-bonding interactions of the S - H group(s) within the protein structure; the latter may be exploited to measure the pK a of thiolate titration or the equilibrium constant governing oxidation of a cysteinyl thiol group. The S - H stretching frequency is also sensitive, though to a lesser extent, on torsions ,u (Co _C13) and X 2 (C]3-S~/) of the C ~ - C ~ - S r - H side chain (Li and Thomas, 1991; Li et al., 1992). The C - S stretching vibration of the cysteine side chain, which is also relatively easily measured in the region 640-725 cm-1 of the Raman spectrum, is much more highly sensitive to side-chain conformation. Normal coordinate and empirical analyses of the cysteine side chain lead to the structural correlations summarized in Table VII. As noted above, the vibrational frequency is a function of the nuclear masses, internuclear force constants, and molecular configuration. Accordingly, if the force constants and configuration are known for a molecule, the
302
Takashi Miura and George J. Thomas, Jr. Table VII Conformation-Sensitive Raman Bands of Cysteine Side Chain ~ Dependence of the Raman S-H Frequency and Bandwidth on Hydrogen Bonding Hydrogen bonding S-H frequency Bandwidth state of S-H group ( c m -1 ) (cm-1 ) Examples No hydrogen bond S acceptor Weak S-H donor
2581-2589 2590-2595 2575-2580
12-17 12-17 20-25
Moderate S-H donor
2560-2575
25-30
Strong S-H donor
2525-2560
35-60
S-H donor and S acceptor
2565-2575
30-40
Mode S-H stretch C-S stretch
Thiols in C C l 4 (dilute) Thiols in CHC13 Thiol neat liquids; thiols in thioethers Thiols in acetone; crystal structures c Thiols in dimethylacetamide; crystal structures c Thiols in H20
Dependence of Raman S-H and C-S frequencies on side-chain conformationb Rotamer (cm-1) Gauche X2 Trans X 2 Gauche X 1 Trans X 1
2581 2589 650 704
a From results of Li and Thomas (1991) and Li et al. (1992). b Data for 1-propanethiol and 2-methyl-l-propanethiol in dilute C C l 4 solution. c See references cited in Li and Thomas (1991) and Li et al. (1992).
n o r m a l m o d e s of vibration a n d their frequencies can be calculated (normal m o d e analysis). Figure 11 s h o w s the calculated relationship b e t w e e n the C - S stretching frequencies a n d the X1 torsions of 1-propanethiol and 2-methyl-1propanethiol, w h i c h are m o d e l c o m p o u n d s of cysteine. In this n o r m a l m o d e analysis, X1 w a s rotated b y increments of 20 ~ w i t h o u t a n y change of the force constants. Still, the calculated results are in g o o d a g r e e m e n t w i t h the experim e n t a l l y observed frequencies for C - S stretching m o d e s in molecules exhibiting g a u c h e (X1 = 60 ~ a n d trans (X1 = 180 ~ geometries. The a s s u m p t i o n that c o n f o r m a t i o n a l change has little or no effect on force constants g o v e r n i n g the f r e q u e n c y of the C - S m a r k e r b a n d w o u l d a p p e a r to be reasonable for the molecules studied. b. T r y p t o p h a n C o n f o r m a t i o n - and environment-sensitive b a n d s of the t r y p t o p h a n side chain (indole ring) are listed in Table VIII. The intense b a n d o b s e r v e d near 1550 cm-1 in R a m a n spectra of proteins is a sensitive m a r k e r of t r y p t o p h a n side-chain conformation (Miura et al., 1989). Specifically, the freq u e n c y of this m o d e , w h i c h is designated W3 a n d consists m a i n l y of stretching of the C 2 - C 3 b o n d of the indole ring (Takeuchi and H a r a d a , 1986), is correlated w i t h the absolute value of the X2,1 side-chain torsion, as s h o w n in Fig. 12. H o w ever, m o d e l c o m p o u n d analysis based on k n o w n crystal structures s h o w s clearly that the X 2'1 correlation cannot be r e p r o d u c e d by n o r m a l coordinate calculations using a fixed set of force constants. Therefore, in this case, the
303
Chapter 6 Optical and Vibrational Spectroscopic Methods
720
/ t
T
700
9 liD"
-
9 "0
tI
O'~
68O
\
x
~"i
i ~II/
660
640
i I
0
I
I
80
160
I
X
240
320
1
Fig. 11 Calculated dependence of the C - S stretching frequencies of 1-propanethiol (C)) and 2methyl-l-propanethiol (@) on the C - C - C - S torsion angle (t,1). See Li et al. (1992) for details of the normal coordinate analysis.
change of side-chain torsion angle apparently affects the frequency of the W3 mode through changes of the force constants. The molecular configuration and force constants are not always independent of one another and the influence of conformational change on force constants cannot generally be ignored in normal coordinate calculations.
4. Hydrogen Bonding Interactions Hydrogen bonding interaction between an appropriate donor hydrogen X - H (where X is O, N, or S) and an acceptor atom Y (usually O or N) is conveniently studied by methods of vibrational spectroscopy. The X - H stretching mode is particularly sensitive to hydrogen bonding. This dependency has been extensively investigated and correlated quantitatively with internuclear distances in X - H . 9.Y linkages (Pimentel and McClellan, 1960).
Table VIII Conformation-Sensitive
R a m a n B a n d s of T r y p t o p h a n S i d e C h a i n a
i
Mode
Interval
Assignment
Conformational sensitivity b
W3 W7 W17 W18
1545-1560 1360/1340 870-885 750-760
Pyrrole localized Fermi doublet Ring and N 1 - H motions Ring breathing
I X2,11 torsion Hydropathy of indole ring N 1 - H hydrogen bonding Hydropathy of indole ring
Based on normal coordinate and model compound analyses of Harada and coworkers, as indicated in Harada and Takeuchi (1986) and Miura et al. (1988, 1989). b See Miura and Thomas (1995) for detailed discussion.
a
304
Takashi Miura and George J. Thomas, Jr.
1555
T E u (J
c 1550
O"
B
L
LI,.
~Z.1 ,..-5"C~
iv)
r
1545,
~J 6~ ~
i
9'0 ~
'
'
1do" "
Ix .,I
Fig. 12 Experimentally determined relationship between the frequency of the tryptophan normal mode W3 and the side-chain torsion t ,2,1 (Miura et al., 1989). Different symbols refer to different tryptophan model compounds, as indicated in Miura et al., 1989. [Miura et al. (1989). Journal of Raman Spectroscopy, 20, 667-671. Copyright 1989 John Wiley & Sons, Ltd. Reprinted by permission of John Wiley & Sons, Ltd.]
As a recently investigated example, we consider the case of the imino N - H donor of 3-methylindole, a model compound for the indole ring in tryptophan (Miura et al., 1988). Infrared spectra in the region 3100-3600 cm -1 of 3-methylindole dissolved in mixed CS2-dioxane solutions are shown in Fig. 13A. In pure CS2, where hydrogen bond donation is disfavored, a relatively narrow band is observed at 3476 cm -1, corresponding to the imino N - H stretching vibration of nonhydrogen-bonded 3-methylindole. As the mole fraction of dioxane is increased and hydrogen bonds of the type N - H . . -O are formed between imino N - H donors and dioxane endocyclic acceptors, a characteristic infrared absorption band appears at 3346 cm -1 due to the hydrogen-bonded N - H groups. As the sharp band due to nonhydrogen-bonded groups (3476 c m -1) decreases, the broader band due to hydrogen-bonded groups (3346 cm-1) increases. The latter infrared band is distinguished from the former not only by its lower frequency and greater bandwidth, but also by its much greater intrinsic (integrated) intensity. It is generally true of stretching vibrations of hydrogen bond donor and acceptor groups that, on hydrogen bond formation, they give rise to infrared bands of lowered frequency and increased integrated intensity. Conversely, bending vibrations are elevated in frequency on hydrogen bond formation. These phenomenon can be rationalized in terms of the electronic perturbations occurring at the donor and acceptor sites (Pimentel and McClellan, 1960). In the Raman effect, however, although hydrogen bonding interactions also give rise to similar perturbations of lowered frequency and increased bandwidth for stretching vibrations, the integrated Raman band intensity is much less sensitive to hydrogen bonding than is the case in infrared spectra. [This can be appreciated, for example, by simply comparing the infrared and Raman spectra
305
Chapter 6 Optical and Vibrational Spectroscopic Methods A
B
006 f
I00:0/i1
1(0:0 0.05
--
9
~ 0.03
9 ):10
0:I00
/~--/-
5:5 -
,
(A1)
where ~ ' and 9 are the total wave functions, i.e., containing both electronic and nuclear coordinates for the excited and ground electronic states, respectively, and/z is the dipole moment operator. In the Born-Oppenheimer approximation, the total wave function can be factored into electronic and nuclear terms as given in Eq. (A2)" (D = (De(I) v
and
~'
--" r
,
(A2)
where (D e and ~v are the electronic and vibrational wave functions, respectively, and the prime symbols denote excited states. Nuclear motions other than vibrations are neglected. Note that (D e is a function of both electronic and nuclear coordinates, whereas ~v depends only on the nuclear coordinates. Using Eq. (A2), the transition moment integral of Eq. (A1) is given by Eq. (A3)0
= -
(9 t'v
z
U.I
l
ILl
/~ 2 odd
~ ~ .
~ I
even
Fig. A1 Representation of the lowest lying 7r-electron energy levels and wave functions of a conjugated diene molecule (e.g., butadiene). The symmetry-allowed absorption transitions are depicted by the vertical arrows.
Because ~s is independent of the dipole m o m e n t operator/z, (e' I/x I e) m a y be rewritten as
(e'l ~ l e ) = ( o ' 1 / ~ l o ) . ( s ' l s ) .
(A5)
Because the orbital electronic wave function ~o is classified as even if dPo(- x, - y, - z) = Cbo(X, y, z) and odd if CI)o(- x, - y, - z) = - Cbo(X, y, z), and because the operator/x is always odd with respect to coordinate interchange, the first integral on the right in Eq. (A5) will vanish due to odd parity unless ~o and ~o' have different parities. Thus, the integral on the left of Eq. (A5) will be nonzero only if the combining electronic orbital wave functions differ in parity, i.e., transitions in absorption are allowed only between even and odd states. To exemplify this selection rule, we show in Fig. A1 a representation of the four 7r-electron orbital wave functions of butadiene, the simplest conjugated 7r-electron system. In the g r o u n d electronic state of the molecule, the two lower energy 7r orbitals (bonding orbitals, 7rl and 7r2) are each occupied by two 7r electrons, whereas the two higher energy orbitals (antibonding orbitals, 7r3 and 7r4) are empty. In accordance with the electronic orbital selection rule, transitions
I~4
uJ
z
LLI
t
r
~,
t
\r
t
So Fig. A2 The lowest lying 7r-electronenergy levels and corresponding electron spin multiplicities of a conjugated diene (butadiene).
Chapter 6 Optical and Vibrational Spectroscopic Methods
313
erl (even)--~ er4(odd) and er2(odd)~ erg(even) are allowed, but transitions erl --~ er3 and era ~ er4 are forbidden. The second integral of Eq. (A5), (s' I s), is nonzero only when the total spin angular momenta of the combining states are identical (Fig. A2). Otherwise, orthogonality of spin wave functions causes this term and consequently the right side of Eq. (A5) to vanish. Normally, in the ground electronic state of a molecule each bonding orbital is occupied by an electron pair with opposing spin angular momenta, which cancel one another and lead to a total spin angular momentum (S) of zero. Such a spin state is categorized, in accordance with its spin degeneracy or multiplicity (2 I S I + 1 = 1), as a singlet or "S" state. A transition originating from an S state must terminate in an S state; and similarly a transition originating from a triplet or T state (parallel electron spins yielding S = 1 and multiplicity = 3) must terminate in a T state. Thus, the So ~ $1 transition is spin-allowed, while the So --> T1 transition is spin-forbidden (Fig. 2). The allowed So --~ $1 transition can be regarded as one in which a ground-state bonding electron is promoted to an excited-state antibonding orbital without change in its spin direction. Combining Eqs. (A3) and (A5), the selection rules are summarized as follows: 0 = (v'lv).(o'l
a lo}.(s'ls}.
(A6)
Rigorously, a transition between two electronic states is allowed only if each integral on the right of Eq. (A6) is nonzero. However, transitions that are rigorously forbidden may occur with low probability (resulting in relatively weak spectral bands) in certain circumstances. A principal cause of such "forbidden" transitions is coupling between electronic and vibrational states (vibronic coupling), which can eliminate the symmetry constraints discussed above.
References Arnold, G. E., Day, L. A., and Dunker, A. K. (1992). Tryptophan contributions to the unusual circular dichroism of fd bacteriophage. Biochemistry 31, 7948-7956. Arrondo, J. L. R., Muga, A., Castresana, J., and Goni, F. M. (1993). Quantitative studies of the structure of proteins in solution by Fourier-transform infrared spectroscopy. Prog. Biophys. Mol. Biol. 59, 23-56. Aubrey, K. L., and Thomas, G. J., Jr. (1991). Raman spectroscopy of filamentous bacteriophage Ff (fd, M13, fl) incorporating specifically-deuterated alanine and tryptophan side chains. Biophys. J. 60, 1337-1349. Austin, J. C., Jordan, T., and Spiro, T. G. (1993). Ultraviolet resonance Raman studies of proteins and related model compounds. Adv. Spectrosc. (Chichester, U.K.) 20, Part A, 55-127. Bamford, J. K. H., Bamford, D. H., Li, T., and Thomas, G. J., Jr. (1993). Structural studies of the enveloped dsRNA bacteriophage q~6 of Pseudomonas syringae by Raman spectroscopy. II. Nucleocapsid structure and thermostability of the virion, nucleocapsid and polymerase complex. J. Mol. Biol. 230, 473-482. Bandekar, J. (1992). Amide modes and protein conformation. Biochim. Biophys. Acta 1120, 123-143. Brand, L., and Gohlke, J. R. (1972). Fluorescence probes for structure. Annu. Rev. Biochem. 41, 843-868. Campbell, I. D., and Dwek, R. A. (1984). "Biological Spectroscopy," Benjamin/Cummings, Menlo Park, CA. Cantor, C. R., and Schimmel, P. R. (1980). "Biophysical Chemistry. Part II. Techniques for the Study of Biological Structure and Function." Freeman, San Francisco.
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Takashi Miura and George J. Thomas, Jr. Carey, P. R. (1982). "Biochemical Applications of Raman and Resonance Raman Spectroscopies." Academic Press, London. Clegg, R. M. (1992). Fluorescence resonance energy transfer and nucleic acids. In "Methods in Enzymology" (D. M. J. Lilley and J. E. Dahlberg, eds.), Vol. 211, pp. 353-388. Academic Press, San Diego, CA. Davies, M. M., and Sutherland, G. B. B. M. (1938). The infra-red absorption of carboxylic acids in solution. J. Chem. Phys. 6, 755-770. Dawson, R. M. C., Elliott, D. C., Elliott, W. H., and Jones, K. M., eds. (1969). "Data for Biochemical Research," 2nd ed. Oxford University Press, New York. Fasman, G. D., ed. (1992). "CRC Practical Handbook of Biochemistry and Molecular Biology." CRC Press, Boca Raton, FL. F6rster, T. (1966). In "Modern Quantum Chemistry" (O. Sinanoglu, ed.), Part 3. Academic Press, New York. Glasel, J. A. (1995). Validity of nucleic acid purities monitored by 260 nm: 280 nm absorbance ratios. BioTechniques 18, 62-63. Greenfield, N., and Fasman, G. D. (1969). Computed circular dichroism spectra for the evaluation of protein conformation. Biochemistry 8, 4108-4116. Griffiths, P. R., and deHaseth, J. A. (1986). "Fourier Transform Infrared Spectroscopy." Wiley (Interscience), New York. Harada, I., and Takeuchi, H. (1986). Raman and ultraviolet resonance Raman spectra of proteins and related compounds. Adv. Spectrosc. (Chichester, U.K.) 13, 113-175. Harada, I., Miura, T., and Takeuchi, H. (1986). Origin of the doublet at 1360 and 1340 cm-1 in the Raman spectra of tryptophan and related compounds. Spectrochim. Acta, Part A 42A, 307-312. Herzberg, G. (1945). "Molecular Spectra and Molecular Structure. II. Infrared and Raman Spectra of Polyatomic Molecules." Van Nostrand, Princeton, NJ. Herzberg, G. (1950). "Molecular Spectra and Molecular Structure. I. Spectra of Diatomic Molecules." Van Nostrand, Princeton, NJ. Herzberg, G. (1966). "Molecular Spectra and Molecular Structure. III. Electronic Spectra and Electronic Structure of Polyatomic Molecules." Van Nostrand, Princeton, NJ. Howard, F. B., Frazier, J., and Miles, H. T. (1969). Interbase vibrational coupling in G :C polynucleotide helices. Proc. Natl. Acad. Sci. U.S.A. 64, 451-458. Johnson, W. C., Jr. (1990). Protein secondary structure and circular dichroism: A practical guide. Proteins: Struc. Func. Genet. 7, 205-214. Johnson, W. C., Jr. (1992). Analysis of circular dichroism spectra. In "Methods in Enzymology" (L. Brand and M. Johnson, eds.), Vol. 210, pp. 426-447. Academic Press, San Diego, CA. Kellenbach, E. R., Remerowski, M. L., Eib, D., Boelens, R., van der Marel, G. A., van den Elst, H., van Boom, J. H., and Kaptein, R. (1992). "Synthesis of isotope labeled oligonucleotides and their use in an NMR study of a protein-DNA complex. Nucleic Acids Res. 20, 653-657. Krimm, S., and Bandekar, J. (1986). Vibrational spectroscopy and conformation of peptides, polypeptides, and proteins. Adv. Protein Chem. 38, 181-363. Kyogoku, Y., Lord, R. C., and Rich, A. (1968). Specific hydrogen bonding of barbiturates to adenine derivatives. Nature (London) 218, 69-73. Li, H., and Thomas, G. J., Jr. (1991). Cysteine conformation and sulfhydryl interactions in proteins and viruses. 1. Correlation of the Raman S - H band with hydrogen bonding and intramolecular geometry in model compounds. J. Am. Chem. Soc. 113, 456-462. Li, H., Wurrey, C. J., and Thomas, G. J., Jr. (1992). Cysteine conformation and sulfhydryl interactions in proteins and viruses. 2. Normal coordinate analysis of the cysteine side chain in model compounds. J. Am. Chem. Soc. 114, 7463-7469. Li, H., Hanson, C., Fuchs, J. A., Woodward, C., and Thomas, G. J., Jr. (1993a). Determination of the pKa values of active-center cysteines, cysteine-32 and cysteine-35 in Escherichia coli thioredoxin by Raman spectroscopy. Biochemistry 32, 5800-5808. Li, T., Johnson, J. E., and Thomas, G. J., Jr. (1993b). Raman dynamic probe of hydrogen exchange in bean pod mottle virus: Base-specific retardation of exchange in packaged ssRNA. Biophys. J. 65, 1963-1972. Lord, R. C., and Thomas, G. J., Jr. (1968). Spectroscopic studies of molecular interaction in DNA constituents. Dev. Appl. Spectrosc. 6, 179-199. Manning, M. C., and Woody, R. W. (1989). Theoretical study of the contribution of aromatic side chains to the circular dichroism of basic bovine pancreatic trypsin inhibitor. Biochemistry 28, 8609-8613.
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Miura, T., and Thomas, G. J., Jr. (1995). Raman spectroscopy of proteins and their assemblies. In "Subcellular Biochemistry: Proteins: Structure, Function, and Engineering" (B. B. Biswas and S. Roy, eds.), Vol. 24, pp. 55-99. Plenum, New York. Miura, T., Takeuchi, H., and Harada, I. (1988). Characterization of individual tryptophan side chains in proteins using Raman spectroscopy and hydrogen-deuterium exchange kinetics. Biochemistry 27, 88-94. Miura, T., Takeuchi, H., and Harada, I. (1989). Tryptophan Raman bands sensitive to hydrogen bonding and side-chain conformation. J. Raman Spectrosc. 20, 667-671. Miyazawa, T., and Blout, E. R. (1961). The infrared spectra of polypeptides in various conformations: Amide I and II bands. J. Am. Chem. Soc. 83, 712-719. Miyazawa, T., Shimanouchi, T., and Mizushima, S. (1958). Normal vibrations of N-methylacetamide. J. Chem. Phys. 29, 611-616. Nikonowicz, E. P., Sirr, A., Legault, P., Jucker, F. M., Baer, L. M., and Pardi, A. (1992). Preparation of 13C and 15N labelled RNAs for heteronuclear multi-dimensional NMR studies. Nucleic Acids Res. 20, 4507-4513. Overman, S. A., Aubrey, K. L., Vispo, N. S., Cesareni, G., and Thomas, G. J., Jr. (1994). Novel tyrosine markers in Raman spectra of wild-type and mutant (Y21M and Y24M) Ff virions indicate unusual environments for coat protein phenoxyls. Biochemistry 33, 1038-1042. Pimentel, G. C., and McClellan, A. L. (1960). "The Hydrogen Bond." Freeman, San Francisco. Rosenheck, K., and Doty, P. (1961). The far ultraviolet absorption spectra of polypeptide and protein solutions and their dependence on conformation. Proc. Natl. Acad. Sci. U.S.A. 47, 17751785. Schoenlein, R. W., Peteanu, L. A., Mathies, R. A., and Shank, C. V. (1991). The first step in vision: Femtosecond isomerization of rhodopsin. Science 254, 412-415. Taillandier, E., and Liquier, J. (1992). Infrared spectroscopy of DNA. In "Methods in Enzymology" (D. M. J. Lilley and J. E. Dahlberg, eds.), Vol. 211, pp. 307-352. Academic Press, San Diego, CA. Takeuchi, H., and Harada, I. (1986). Normal coordinate analysis of the indole ring. Spectrochim. Acta, Part A 42A, 1069-1078. Thomas, G. J., Jr. (1987). Viruses and nucleoproteins. In "Biological Applications of Raman Spectroscopy" (T. G. Spiro, ed.), Vol. 1, pp. 135-201. Wiley (Interscience), London. Thomas, G. J., Jr., and Agard, D. A. (1984). Quantitative analysis of nucleic acids, proteins and viruses by Raman band deconvolution. Biophys. J. 46, 763-768. Thomas, G. J., Jr., and Kyogoku, Y. (1977). Biological science. In "Infrared and Raman Spectroscopy" (E. G. Brame, Jr. and J. G. Grasselli, eds.), Part C, Vol. 1, pp. 717-872. Dekker, New York. Thomas, G. J., Jr., and Tsuboi, M. (1993). Raman spectroscopy of nucleic acids and their complexes. In "Advances in Biophysical Chemistry" (C. A. Bush, ed.), Vol. 3, pp. 1-70. JAI Press, Greenwich, CT. Thomas, G. J., Jr., and Wang, A. H.-J. (1988). Laser Raman spectroscopy of nucleic acids. Nucleic Acids Mol. Biol. 2, 1-30. Tinoco, I., Jr., Bustamante, C., and Maestre, M. F. (1980). The optical activity of nucleic acids and their aggregates. Annu. Rev. Biophys. Bioeng. 9, 107-141. Tsuboi, M., Nishimura, Y., Hirakawa, A. Y., and Peticolas, W. L. (1987). Resonance Raman spectroscopy and normal modes of the nucleic acid bases. In "Biological Applications of Raman Spectroscopy" (T. G. Spiro, ed.), Vol. 2, pp. 109-179. Wiley (Interscience), London. Valeur, B. (1989). In "Fluorescence Biomolecules: Methodologies and Applications" (D. M. Jameson and G. D. Reinhart, eds.). Plenum, New York. Warburg, O., and Christian, W. (1942). Isolation and crystallization of enolase. Biochem. Z 310, 384-421. Weber, G. (1952). Polarization of the fluorescence of macromolecules. Biochem. J. 51, 145-167. Wetlaufer, D. B. (1962). Ultraviolet spectra of proteins and amino acids. Adv. Protein Chem. 17, 303-390. Wilson, E. B., Jr., Decius, J. C., and Cross, P. C. (1955). "Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra." McGraw-Hill, New York.
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GLOSSARY Absolute value mode
Representation of a nuclear magnetic resonance (NMR) peak as the absolute value or magnitude: [(real) 2 + (imaginary)2] 1/2, which is insensitive to the phase of the peak. Some two-dimensional NMR experiments result in peaks that cannot be phased, and these spectra must be displayed in absolute value mode to be useful.
Absorption
The process in which a nuclear spin takes energy from an electromagnetic field and goes to a higher energy state; also, the name of one of the
Introduction to Biophysical Methods for Protein and Nucleic Acid Research
317
Copyright 9 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.
318
B. W. Bangerter two orthogonal lineshapes for a peak in an NMR spectrum; as in "absorption mode peak". See also Dispersion.
Analog
A property that varies in a continuous way, rather than in discrete steps; often applied to an electrical signal (voltage or current) representing some physical quantity.
Analog-to-digital converter (ADC) The device in an NMR spectrometer that converts an analog voltage representing a free induction decay NMR signal into a numerical value, which can be processed in a computer. An ADC is characterized by its resolution in bits. A 16-bit ADC, as is typically used in NMR, converts an analog voltage to a digital value having a numeric range from -32,768 (for the maximum negative input voltage) to + 32,767 (for the maximum positive input voltage), with 216 (65,536) total discrete values possible. The dynamic range of a 16-bit ADC is 32,768, or 215.
Angular momentum
A measure of the rotational inertia of an object about an axis. According to the laws of quantum mechanics, for an atomic nucleus, the measurable component of its angular momentum is restricted to some halfintegral (1/2, 1, 3/2, etc.) multiple of Planck's constant/2~r, or h. A nucleus that has a spin of 1/2 has a measurable component of angular momentum of h/2.
Antiphase
The appearance of a scalar coupling multiplet where the symmetry-related peaks have opposite phases (i.e., for a doublet, one component of positive absorption phase, the other component of negative absorption phase).
Autocorrelation function
A way is needed to measure the frequency and strength of thermal motions of molecules in liquids. If f(t) is some random property that fluctuates about a mean value of zero, a measure of its value is the mean square average of f(t). The time average value of the product of f(t) and f(t + z) is called the autocorrelation function, G(z). The function f(t + z) stands for the value of the function f(t) at a small time interval z after t. G(z) is defined as
G(z) = (fit)fit + z)), where the brackets ( . . . ) signify an average over time for an ensemble of molecules. For example, f(t) might be a quantity (e.g., spatial orientation) related to the random motion of a molecule. Then f(t) f(t + ~') differs for each molecule and each value of t, but on the average the mean value of G(~-) is the same for all molecules and is independent of t. Thus, the autocorrelation function measures the persistence of the fluctuations; G(z) is large for short times, and then decays toward zero as z increases. Frequently, G(z) decays exponentially with a characteristic time zc. In this case, Zcis called the correlation time. It is the time taken for a typical fluctuation to die away. As brought out elsewhere in this volume and in this chapter, the time course of a fluctuation can be represented as a frequency distribution via the Fourier transform. The frequency distribution of the fluctuations is called the spectral density function for the particular fluctuation. The spectral density function due to molecular rotation is important for understanding spin relaxation phenomena in NMR.
Chemical shift The resonance frequency of a particular nucleus in a molecule relative to some reference frequency, expressed in parts per million (ppm): [(~' - ~'ref)/ Vref] • 106. Chemical shifts result from diamagnetism (see Chapter 1) induced in molecules by the external static magnetic field of the NMR spec-
319
Chapter 7 NuclearMagnetic Resonance
trometer. Nuclei in different chemical environments in a molecule experience local magnetic fields that deviate from the applied external magnetic field due to a variety of effects. A partial list of these effects include diamagnetism induced in molecules by the external static magnetic field, paramagnetic effects due to unpaired electrons that may exist in some molecules or ions, and proximity of a nucleus to an aromatic ring distribution of electron density.
Classical As applied to NMR spectroscopy, this descriptive term indicates that the motions of an ensemble of nuclear spins under the influence of static and radio frequency magnetic fields are described by differential equations involving vector sums of spin components along the axes of a cartesian coordinate system fixed in space. The macroscopic magnetization vector M induced by the interaction of the ensemble of spins with a static magnetic field vector B0, M = Mxi + My j + Mzk,
obeys linear differential equations of classical physics that describe the motions of M as a function of time. These are called the Bloch equations.
Coherence When the magnetization of a spin system is brought into the x,y plane by a 90 ~ pulse, the phases of the spins of different chemical shifts are all the same (coherent) at the end of the pulse. They then begin a time evolution in the x,y plane and lose this phase coherence. Connectivity An indication in a two-dimensional NMR spectrum that two nuclei interact with one another, manifested by the appearance of a cross-peak in the spectrum at frequencies corresponding to the chemical shifts of the two nuclei. The interaction is generally either through scalar coupling (scalar or J connectivity) or cross-relaxation (NOE connectivity). See also Correlation. Continuous wave (CW) NMR A method of measuring the one-dimensional NMR spectrum of a sample by applying a constant radio frequency field of low amplitude and measuring the response of an electrical circuit surrounding the sample as the strength of the static magnetic field is varied. The absorption of energy by the sample is detected as the field is varied, bringing nuclei with different chemical shifts into resonance, thus tracing out the NMR spectrum of the sample. This method has largely been eclipsed by pulsed NMR. Correlation An indication, from the appearance of a cross-peak in a twodimensional NMR spectrum, that two nuclei resonating at frequencies ~Oland eo2 have a connectivity through scalar coupling or cross-relaxation, depending on the particular experiment; not to be confused with the rotational correlation time of a molecule in solution. COSY Correlation SpectroscopY. A two-dimensional NMR experiment that reveals scalar coupling interactions between nuclei. This term is usually restricted to the homonuclear (i.e., 1H) case, with the term HETCOR used to describe a heteronuclear (i.e., 1H/13C) scalar coupling experiment.
Coupling constant The value of the energy of the scalar electron-coupled magnetic interaction between two nuclei, expressed in hertz and represented by the symbol J. Cross-peak
A peak in a two-dimensional NMR spectrum occurring at fre-
320
B. W. Bangerter quencies co~ =~ oh, indicating a correlation or connectivity between the nuclei that resonate at these two frequencies.
Cross-relaxation A process in which each member of a pair of magnetic nuclei contributes to the spin relaxation of the other. Digital A representation of some quantity in terms of a number. Also, electronic circuits that function in a discrete or discontinuous way, in contrast to analog. Digital resolution
The separation of discrete data points in a digital NMR spectrum, expressed as hertz/point.
Dispersion The spread or distribution of NMR peaks along one or more frequency axes in a spectrum. Also, the name of a type o f lineshape as in "dispersion mode peak." See Absorption. DQF-COSY Double Quantum-Filtered COSY. A two-dimensional NMR experiment that reveals scalar coupling interactions, similar to the basic COSY experiment but with certain advantages (see text).
Dynamic range
A measure of the ratio of the largest signal to the smallest signal that can be detected in an experiment. The primary limitation on the dynamic range in an NMR experiment is the resolution of the analog-to-digital converter.
Energy level diagram
A graphical device used to describe NMR phenomena and experiments for a particular system of nuclear spins in terms of the populations of the various energy levels (resulting from the interactions of the spins with a magnetic field and with each other), and the frequencies v or energies h z, of the transitions between levels.
Ensemble
A large number of identical systems (molecules, atomic nuclei, etc.) studied in an experiment, which give a result representing a statistical average of the responses of the individual systems to the experiment.
Ethernet
The physical means commonly used to connect computers in a high-speed data network.
Extreme narrowing
In NMR, the motional regime in which the frequency of molecular reorientation (1 / Zc) (see Autocorrelation) is much higher than the NMR resonance frequency, expressed as ~OCZc~ 1, where COLis the resonance frequency and Zc is the rotational correlation time for the molecule. In this regime, T~ = T2.
Field/frequency lock A system in an NMR spectrometer that ensures that the magnetic field strength Bo and the spectrometer frequency ~0r are held at a constant ratio. This eliminates the detrimental effect of drift or external disturbance of either field or frequency on an NMR spectrum (which appear as shifts or broadening of NMR peaks). To accomplish this the NMR spectrometer incorporates a very simple 2H NMR spectrometer, which excites and detects the 2H resonance of the deuterated solvent of the sample and continually adjusts the strength of the Bo field to hold the solvent 2H resonance at a constant radio
frequency.
A mathematical operation used in NMR to convert Fourier transform (FT) between the time domain and frequency domain representations of a time-varying quantity, such as the amplitude of an electromagnetic wave or a free
Chapter7 NuclearMagneticResonance
321
induction decay NMR signal. The two representations are called a Fourier transform pair, F(~o) and f(t). The mathematical relation between F(~o) and f(t) has the form
F(o~) = ~~~ f(t)
e -i~
dt
or
f ( t ) = ( 1~) f ~
F(~o) e§i ~ t d o g .
The mathematical operation within the integral is the Fourier transform that converts each representation into the other. The exponential term e +-i~t may be expressed in its alternative form a s e +-i~ = cos(o~t) + i sin(oJt). In the simplest form of Fourier transform NMR (FTNMR) spectroscopy, all of the nuclei of a given isotope are excited simultaneously by a single, short pulse of radio frequency radiation. In response to this pulse, nuclei within the sample having different chemical shifts are detected as a time-varying signal (i.e., a plot of amplitude vs time) that decays to zero over a time typically within the range of 0.1 to 30 sec. This time-varying signal contains all the frequency components corresponding to an NMR spectrum (i.e., a plot of amplitude vs frequency). A computer program called a fast Fourier transform (FFT) performs the discrete analog of integration and this produces a discrete NMR spectrum from the sample for further analysis. See Chapter 1.
Free induction decay (FID) The signal detected in a pulsed N M R experiment; an oscillating voltage induced in an electrical circuit by nuclear spin magnetization precessing about a static magnetic field while relaxing toward equilibrium. Gauss A unit of magnetic field strength. Presently units of tesla are preferred, where 1 gauss = 1 • 1 0 - 4 tesla. Heteronuclear In NMR spectroscopy this refers to experiments involving interactions between nuclear spins of at least two different isotopes. The opposite of homonuclear in which the magnetizations of nuclei of just a single isotype are perturbed. HOHAHA HOmonuclear H A r t m a n n - H A h n spectroscopy. A two-dimensional N M R experiment that reveals both direct and relayed scalar coupling connectivities. See RELAY, TOCSY. Hz, kHz, MHz Units of frequency; 1 Hz = 1 cycle sec-1, 1 kHz = 1 • cycles sec- 1, 1 MHz = 1 • 106 cycles sec- 1.
10 3
Isotropic mixing Transfer of magnetization among all the members of a system of scalar coupled nuclear spins brought about by application of a spin lock pulse or pulse sequence. J coupling
See scalar coupling.
In NMR, a cartesian coordinate system with the z axis Laboratory frame defined parallel to the direction of the static magnetic field and the x and y axes fixed in space perpendicular to one another and to z.
Larmor frequency
The frequency Vc of precession of a magnetic nucleus in
322
B. W. Bangerter a magnetic field B0, generally expressed in MHz: VL = (~//2vr)B0, where ~/is the magnetogyric ratio of the nucleus.
Lattice In discussions of nuclear spin relaxation, those molecular motions in an NMR sample to or from which energy may be transferred by nuclear spins oriented in a static magnetic field. In a liquid, these are the translational and rotational motions of the molecules. Lineshape A mathematical description of the shape of a line or peak in an NMR spectrum. Longitudinal magnetization The component of the magnetization of an ensemble of nuclear spins that lies along the direction of the static magnetic
field. Longitudinal relaxation
The return of the longitudinal magnetization of an ensemble of nuclear spins toward its equilibrium value.
Longitudinal relaxation time The reciprocal of the rate constant characterizing the process of longitudinal relaxation. The diamagnetic fields induced by an external Magnetic anisotropies magnetic field interacting with certain groups of atoms within a molecule may be highly dependent on the orientation of the molecule with respect to the field direction (see Chapter 1). This can have important effects on chemical shifts of other nuclei near such a group in the molecule.
Magnetic dipolar coupling A direct interaction through space between two magnetic moments (in the case of NMR, electron-nuclear or nuclearnuclear magnetic moments are the most important cases). If the two moments are designated/-/'1 and/d,2, the interaction energy depends on the moments, the intermoment distance r, and the angle 0 between the intermoment vector and the static magnetic field as E
~
~1~2(1
-
3
COS2 0 ) / r
3.
Magnetic dipolar couplings between nuclei, modulated by random molecular motion, usually provide the main mechanism of spin relaxation for spin 1/2 nuclei in liquids. However, because the electron magnetic moment is approximately 2000 times that of a proton, electron-nuclear dipolar interactions are very potent inducers of nuclear relaxation. Such interactions may come from gases (such as oxygen) or transition metal ions that have unpaired electrons.
Magnetic field A force field that acts to align magnetic moments. The static magnetic field (B0 is the symbol used in this chapter for a static magnetic field directed along the z axis) gives rise to the various energy levels for a system of nuclear spins, and one or more rf magnetic fields (B1, B2, etc.) induce transitions between these levels in an NMR experiment. These rf magnetic field vectors oscillate in magnitude. Their directions with respect to B0 are determined by the particular NMR experiment being done.
Magnetic field gradient Variation in the strength of a static magnetic field along one or more axes in the laboratory frame. Undesirable static magnetic field gradients are reduced by the process of "shimming" the field to achieve narrow lines in NMR spectra. Pulsed magnetic field gradients are employed in certain NMR experiments to reveal selected interactions of nuclear spins.
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Magnetic moment
The magnetic dipole m o m e n t / z of a nucleus due to its spin:/z = yhI. Both/z and the spin I are vectors; y is the magnetogyric ratio of the nucleus and h is Planck's constant/2vr. An equivalent expression is /z = gNfiNI, where fiN is the nuclear magneton and gN is the (dimensionless) "g value" for that nucleus. The nuclear magnetic moment has the same dimensions as the nuclear magneton, joule tesla-1. The term magnetic moment is also used to represent the net magnetization of an ensemble of nuclear spins.
Magnetization transfer The mechanism that gives rise to the appearance of cross-pe~ks in a multidimensional NMR spectrum, arising from scalar coupling o~' cross-relaxation interactions between the nuclei. Magnetogyric ratio A physical constant for an atomic nucleus, with the symbol y, which expresses the ratio of the magnetic m o m e n t / z to the angular m o m e n t u m hi for the nucleus: y = la,/hI. The magnetogyric ratio is also commonly expressed as y~ 2 vr or ~ in units of MHz tesla- 1 (106 sec- 1 tesla- 1). Molecular modeling
The use of computational procedures to derive threedimensional structures of molecules, based on considerations of covalent bonding, steric interactions, and other physical forces. See Chapter 9 and computer programs included with this book.
Multidimensional N M R NMR experiments in which the resulting spectra show signal intensities as a function of two or more frequencies. One frequency axis shows the Larmor resonance frequencies of the nuclei detected in the experiment, most often 1H. The other axes may represent the resonance frequencies of protons, or the resonance frequencies of other nuclei, such as 13C, 15N, or 31p, depending on just what experiment is performed. Multidimensional NMR experiments allow interactions between various pairs of nuclear spins to be determined simultaneously in a single experiment and increase resolution by dispersing NMR peaks along two or more frequency axes. Multiple quantum transition In NMR, a transition between energy levels of a nuclear spin system, where the spin state of one nucleus changes by ___2, +__3, etc., or where the spin states of two or more nuclei change simultaneously. Multiple quantum (MQ) transitions are forbidden by q u a n t u m mechanical selection rules, and thus are not directly observed in one-dimensional NMR spectra. MQ transitions can be observed in certain m u l t i d i m e n s i o n a l N M R spectra. Multiplet A set of peaks in an NMR spectrum for a particular nucleus in a molecule, resulting from scalar couplings with other nuclei in the molecule. The multiplet may be referred to as a doublet, triplet, quartet, doublet of doublets, etc., depending on its appearance. NOESY Nuclear Overhauser effect spectroscopy. A two-dimensional N M R experiment that reveals cross-relaxation interactions between protons in a molecule.
Nuclear Overhauser Effect (or Enhancement) (NOE) A change in the intensity of the NMR signal of a particular nucleus observed under conditions wherein the resonance of another nucleus in the same molecule or different molecule is subjected to a continuous high-amplitude radio frequency irradiation at its NMR resonant frequency. The NOE results when cross-relaxation occurs between the observed and irradiated nuclei. The NOE is a through-space
324
B. W. Bangerter effect, depending only on the distance between the nuclei and not on chemical bonds, hence its use in determining internuclear distances for structural determinations.
Nuclear spin A property of many atomic nuclei, which rotate about a spin axis and possess angular momentum. Nuclear spin is expressed by a spin quantum number L which is some integral multiple of 1/2 (1/2, 1, 3/2, 2, . . . ). Nuclear spin results in a nuclear magnetic moment. One-dimensional NMR spectrum A plot of the absorption of energy from an rf magnetic field by a magnetic isotope (1H, 13C, 31p, etc.), versus the frequency of the rf field, at a fixed value of the static magnetic field B0. Phase
In NMR, phase is used in several contexts: (a) the position of an rf
magnetic field or a nuclear magnetic moment vector in the rotating frame; (b) the appearance of an NMR resonance peak as having an absorption or dispersion lineshape (which differ in phase by 90 ~ or some intermediate shape; (c) the process by which the peaks in an NMR spectrum are made to have the same lineshape (ordinarily absorption) by taking a suitable linear combination of the two orthogonal representations of the spectrum that result from the Fourier
transform. Phase cycle The systematic variation of rf transmitter and receiver phases from one scan to the next in an NMR experiment, designed to select certain signal components in the experiment and cancel others. Precession Motion of a spinning object (one having angular momentum) when subject to a force tending to change the axis of spin, as observed with a top or gyroscope. In NMR, nuclear spins individually precess about a static magnetic field. The precession of the ensemble average of all the spins in a sample (the macroscopic spin magnetization) is also used to describe NMR experiments. Probe
The component of an NMR spectrometer that surrounds the sample, couples radio frequency magnetic fields to the sample, and detects the response of the nuclei. The probe and sample are positioned in a uniform or homogeneous magnetic field, usually produced by a superconductive magnet. A probe is described by the diameter of the sample (in millimeters) it will accommodate, by the nucleus or nuclei it is designed to excite a n d / o r detect, and by other relevant characteristics.
Pulse sequence A sequence of time intervals consisting of rf pulses and periods of free nuclear precession, designed to put a system of nuclear spins in some particular state. Pulsed NMR A method of observing NMR spectra whereby all the nuclei of a given type (i.e., 1H) in a sample are observed simultaneously, as a free induction decay (FID) response to one or more brief, intense pulses of rf energy. The spectrum is obtained by application of the Fourier transform to the FID. Quadrature phase detection In NMR spectroscopy, the simultaneous measurement of the components of nuclear spin magnetization along two orthogonal axes in the rotating frame (i.e., x and y). This allows positive and negative frequencies of the same absolute value to be distinguished, and has the important practical consequence of permitting the spectrometer frequency to be
Chapter 7 NuclearMagnetic Resonance
325
placed in the center of the spectrum rather than at one end. This allows the pulsed rf magnetic field to excite the spins more uniformly and also leads to a 40% improvement in sensitivity.
Radio frequency (rf) Oscillating electrical voltages, currents, or electromagnetic fields with frequencies characteristic of those used for radio communication. In NMR spectroscopy, resonance frequencies of nuclei generally fall in the range 10-1000 MHz or 107-109 sec -1, in the radio frequency range. Relaxation time A quantitative measure of the approach toward equilibrium of the magnetization of an ensemble of nuclear spins in a magnetic field. See Longitudinal relaxation and Transverse relaxation. RELAY Relayed coherence transfer spectroscopy. A two-dimensional NMR experiment that reveals correlations between nuclei that do not have a direct scalar coupling but share a common coupling partner.
Resolution
A measure of the ability to distinguish resonance peaks that are close together in an NMR spectrum. As an example, consider two protons that give single peaks in an NMR spectrum with a chemical shift difference of 0.01 ppm. At 60 MHz, the peaks would be separated by 0.6 Hz. If the line widths were 1 Hz for both peaks (measured at half the peak height), the peaks would overlap strongly. At 600 MHz, the 0.01-ppm chemical shift is 6 Hz and the two 1-Hz-wide peaks would be well separated or resolved.
Resonance In NMR the application of an oscillating magnetic field to a system of nuclei in a static magnetic field at a frequency corresponding to the energy difference between spin states for a particular nucleus; also, a peak observed in an NMR spectrum. rf pulse A short burst of radio frequency energy, generally with a duration of a few microseconds to a few milliseconds, used to perturb nuclear spins in an NMR experiment. ROESY Rotating frame nuclear Overhauser Effect SpectroscopY. A two-dimensional NMR experiment that reveals cross-relaxation interactions between protons in a molecule. This experiment is particularly useful for study of molecules of ~ 2 - 3 kDa mass, where the NOE in the laboratory frame measured by the NOESY experiment is very small.
Rotating frame A cartesian coordinate system with the z axis defined parallel to the direction of the static magnetic field and with the x and y axes rotating relative to the laboratory frame at the Larmor frequency. In the rotating frame, the apparent effect of the static magnetic field on the motion of the nuclear spin magnetization vanishes. Because of this simplification, NMR experiments are generally described in the rotating frame. Rotational correlation time ~c, the average time a molecule takes to undergo a rotation of one radian in solution; a quantitative measure of rotational diffusion. The rotational correlation time is a parameter that enters into the rotational autocorrelation function. Scalar coupling An interaction between two magnetic nuclei in a molecule, giving rise to splittings of the resonance peaks for the two nuclei in liquids. The scalar coupling results from magnetic interactions of the nuclei with electrons
326
B. W. Bangerter in the molecule and is generally observed between nuclei separated by four or fewer chemical bonds.
Sequence-specific (or sequential) resonance assignment Assignment of an NMR resonance peak to a particular residue at a specific position in a biopolymer. Shielding The effect of the motions of the electrons of a molecule in a magnetic field in reducing (diamagnetic shielding) or increasing (paramagnetic shielding) the intensity of the magnetic field experienced by the nucleus, relative to the applied magnetic field B0. See Chapter 1 for discussion of diamagnetism and paramagnetism.
Shielding constant A parameter representing the difference between an applied static magnetic field B0 and the effective field Bef f experienced by an a nucleus in an atom or molecule placed in that field. The shielding constant o-is dimensionless, o- = (B0 - B e f f ) / B 0 , and is expressed in parts per million. Shimming The process of making the magnetic field B0 uniform in intensity, or homogeneous, over the volume of an NMR sample. This is done by adjusting electrical currents in coils designed to create specific magnetic field gradients in the region of the sample, to cancel gradients inherent in the magnet or gradients created by the NMR probe or by the sample. Signal-to-noise ratio A quantitative measure of the sensitivity of an NMR experiment, calculated by dividing the amplitude of a peak representing an NMR signal by the root-mean-square amplitude of the random noise present. In a modern NMR experiment repeated FIDO or spectra are averaged together by computer. Because the noise in a good spectrometer is random, whereas peak signals are always present at a their particular frequencies in the spectrum, the signal-to-noise ratio increases as N 1/2, where N is the number of FIDO or spectra that are averaged. Single quantum transition In NMR, a transition between energy levels of a nuclear spin system whereby the spin state of one nucleus changes by _ 1. Such transitions give rise to the signals observed in a free induction decay and to the peaks in a one-dimensional NMR spectrum. Spectral density function As applied to NMR, a mathematical function describing the frequency distribution of the fluctuations perturbing a nucleus in a molecule. For the most familiar application to NMR spectroscopy consider two nuclei separated by a distance r situated in the same molecule in a liquid. The nuclei have an energy of interaction due to magnetic dipolar coupling. The energy of this interaction is dependent on the orientation of the internuclear vector with respect to the external static magnetic field. As the molecule in question undergoes random rotational reorientations, so does the internuclear vector. Suppose that the autocorrelation function of the random rotational reorientations of the molecule is an exponential with a characteristic time ~'c. The Fourier transform of such a time-fluctuating function corresponds to a frequency distribution function. In this case, the frequency distribution function is called the spectral density function. The characteristic of major interest for the spectral density function is that frequencies over a wide range of values are represented. Indeed, there is a finite amplitude at the Larmor frequency of
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327
the nuclei coupled by magnetic dipole interaction. Thus the random molecular rotational motions result in a magnetic field fluctuation, at the nuclei that are paired, that has the exact frequency necessary to cause an NMR transition. When this transition is from an excited state to a lower energy state, the result is
nuclear spin relaxation.
Spectral width The range of frequencies over which the peaks in an NMR spectrum are observed. Spin diffusion Transfer of magnetization from one nucleus to others of the same type through efficient spin-spin relaxation. Spin-lattice relaxation
See longitudinal relaxation.
Spin lock Application of a long (several milliseconds), moderately intense rf pulse, or sequence of pulses, along some axis in the x,y plane of the rotating frame. This has the effect of dephasing nuclear spin magnetization not aligned along the axis of the applied rf magnetic field. Spin relaxation The process by which an ensemble of nuclear spins returns to an equilibrium condition following a disturbance. Spin saturation
Equalization of the populations of the energy levels for an
ensemble of nuclear spins, usually by application of an rf magnetic field at a frequency corresponding to the energy difference between the levels. Because the frequency v corresponding to the difference between energy levels for a nuclear spin in a magnetic field is small, the probability of spontaneous emission of a photon of radiation of frequency v (which has a ~3 dependence) is negligibly small. Thus, in contrast to optical spectroscopy, where the frequencies are much higher and spontaneous emission is an important process, it is easy to pump nuclear spins to saturation.
Spin-spin coupling
See Scalar coupling.
Spin-spin relaxation Spin system
See Transverse relaxation.
A group of magnetic nuclei in a molecule that interact with
one another. Spin temperature A fictitious temperature (in degrees Kelvin) corresponding to the population of the two allowed energy levels by an ensemble of spin 1/2 nuclei in a magnetic field, as described by the Boltzmann distribution. This concept is useful in qualitative discussions of spin relaxation.
Tesla (T) The unit of magnetic field strength. In NMR spectroscopy, magnetic fields of ~ 1.4-17.6 tesla (corresponding to proton resonance frequencies of 60-750 MHz) are generally used. See Gauss. Tip angle A measure, in degrees or radians, of the angle through which a vector representing nuclear spin magnetization is rotated by application of a pulsed rf magnetic field. TOCSY TOtal Correlation SpectroscopY. A two-dimensional NMR experiment that reveals both direct and relayed scalar coupling r showing cross-peaks between all members of a scalar-coupled spin system. See RELAY, HOHAHA.
Transverse magnetization
The component of the magnetization of an en-
328
B. W. Bangerter
semble of nuclear spins that is perpendicular (transverse) to the direction of the static magnetic field. Transverse relaxation The decay toward zero of the transverse magnetization of an ensemble of nuclear spins. Transverse relaxation time The reciprocal of the rate constant characterizing the process of transverse relaxation, also called T 2. Two-dimensional N M R spectrum A plot of the absorption of energy by a type of magnetic nucleus (i.e., 1H) as a function of two frequencies. One frequency axis displays the Larmor frequencies of the nuclei observed, whereas the other axis may correspond to the same frequency range (in a homonuclear two-dimensional experiment) or to the frequency range of another type of nucleus (i.e., ~3C) with which the observed nuclei interact (in a heteronuclear two-dimensional experiment). Vector notation In this chapter vectors are written in capital bold and their components along axes are written in capital italic. For example, a static magnetic field directed along the z axis is written as B0 and its component along this axis is written as B0. Zeeman interaction The interaction of a nuclear magnetic m o m e n t / z with a magnetic field B0, having the energy E = - / z - B0, where 9represents the scalar or dot product of the two vectors. This can also be written E = - I/z li BoB cos ~, where 0 is the angle between the magnetic moment and magnetic field vectors and I/~1 and I B0i are the magnitudes of the vectors. The magnetic moment is quantized, and/z can adopt only certain orientations with respect to B0, leading to discrete energy levels for a nuclear magnetic moment in a magnetic field.
2D, 3D, 4D Two-, three-, or four-dimensional NMR; classes of multidimensional N M R spectroscopy.
I. Introduction An understanding of biological processes at the molecular level requires knowledge of the three-dimensional structures of the molecules involved, the dynamic properties of the molecules, and the intermolecular interactions in which the molecules participate. The two methods presently available for determining three-dimensional structures of proteins and nucleic acids at the level of atomic resolution are X-ray diffraction and nuclear magnetic resonance (NMR) spectroscopy. Although X-ray crystallography can provide precise structural information, many biological molecules of interest do not yield crystals suitable for X-ray work, or there may be significant differences between structures in a crystal and in solution. The use of NMR does not require crystals, and molecules can be examined in solution under near-physiological conditions where effects of solvent composition, pH, temperature, and other factors on structure can be probed. Dynamic processes occurring over a wide range of time scales (picoseconds-seconds) can be studied by NMR methods as well. These characteristics have made NMR a useful adjunct or alternative to X-ray crystallography for determination of biomolecular structure.
Chapter7 NuclearMagneticResonance
329
NMR has been successfully used for structure determination of small and medium-sized organic molecules for more than 30 years, but only in the past decade or so have methods been developed to determine the secondary and tertiary structures of proteins and nucleic acids by NMR. The potential utility of NMR spectroscopy for studying the structures of biopolymers was widely recognized very early in the development of the technique. It was clear that information derived from certain NMR parameters, such as chemical shifts, scalar spin-spin coupling constants, and rates of spin relaxation, could in principle become as useful for deducing the structural features of biological macromolecules as had been demonstrated for smaller molecules. The highly localized nature of NMR, in which a nucleus is affected by influences in its immediate vicinity, and the sensitivity of NMR parameters to dynamic processes occurring over a very wide range of time scales can provide unique structural and dynamic information not available from other spectroscopic methods. The major difficulty in studying biopolymer structure by NMR has always been (and remains today) resolution. An NMR spectrometer is usually described in terms of the frequency at which protons resonate in the magnetic field of that instrument, with higher frequency (or field) instruments providing both higher sensitivity and increased resolution. A small protein of 50 residues (~ 5500 Da) has about 300 protons, which can result in a proton NMR spectrum
Fig. 1 ProtonNMR spectra of three proteins at 600 MHz and 27~ (A) Magainin 2 (23 amino acids) in 75% H20/25% trifluoroethanol-d3; (B) basic pancreatic trypsin inhibitor, (58 amino acids) in D20 , (C) staphylococcal nuclease (156 amino acids) in 90% H20/10% D20. Most amide protons have been replaced by deuterons in the basic pancreatic trypsin inhibitor spectrum. Identical digital filtering was used for the three spectra to narrow the resonances. Expansion of the regions between the dashed lines reveals scalar J couplings in these resolution-enhanced spectra. [Reproduced with permission from Bax (1989b).]
330
B. W. Bangerter
with more than 600 peaks. Even in a spectrum obtained at 600 MHz, where these peaks are spread out over a frequency range of ~ 6 kHz, there is a great deal of spectral overlap and not all of the r e s o n a n c e s can be resolved in a simple one-dimensional NMR spectrum. Representative proton NMR spectra at 600 MHz of three proteins of different size are shown in Fig. 1. At the field strengths available 30 years ago, corresponding to a resonance frequency of ~ 100 MHz for protons, most resonances could not be resolved. Nevertheless, useful NMR studies of proteins were conducted by exploiting unique resonances that could be resolved and assigned, such as those on side chains of aromatic amino acids. Chemical shifts, lineshapes, and relaxation times for these identifiable resonances were used to monitor changes in conformation and dynamics as temperature and pH were varied, or when an inhibitor was bound to an enzyme. In addition, studies of single- and double-stranded oligonucleotides explored the conformations and hydrogen-bonding properties of these molecules. Many small peptides and o!igonucleotides were extensively studied during the 1960s and 1970s, and assignments of chemical shifts and analyses of the dependence of scalar couplings on conformation from this work helped pave the way for the currently available comprehensive NMR-based structure determination methods for biopolymers in solution (James, 1975; W6thrich, 1976; Shulman, 1979; Jardetzky and Roberts, 1981). Progress in the application of NMR for determination of structures of proteins and nucleic acids in solution has been extremely rapid since about 1980, and developments continue at a fast pace. It is now possible to determine the three-dimensional structure of a protein of known sequence of molecular mass up to ~ 10 kDa (~ 90 residues) with a resolution of 2.5-3.0 A (expressing the root-mean-square deviation of an atom's coordinates from its calculated position) solely on the basis of NMR data. Methods recently developed push that practical limit up beyond 20 kDa. The general approach presently used to determine "NMR structures" of biopolymers is derived from a strategy first developed by W6thrich and co-workers in pioneering studies of small proteins. This strategy, which is based on application of two-dimensional (2D) NMR methods (discussed in Section III,A), is clearly described in a book by Wtithrich (1986) and in several review articles (Bax, 1989b; Clore and Gronenborn, 1987, 1989; Kessler et al., 1988; Markley, 1989; W6thrich, 1989a,b, 1990). The basic strategy has been extended through incorporation of new NMR methods; in particular, procedures employing multidimensional, Fourier transform NMR (FTNMR) experiments (3D and 4D), where the NMR peaks are dispersed along more than two frequency axes, along with uniform isotopic labeling with 13C a n d / o r 15N are making larger molecules amenable to study (Clore and Gronenborn, 1991a,b). Among the more recent treatments of the subject are books by Roberts (1993) and Evans (1995). The strategies and procedures directed toward determination of the three-dimensional structures of proteins and nucleic acids in solution are the main topics of this chapter. Developments in instrumentation and methodology and in computer modeling of molecular structure have provided the tools needed for determination of structures of proteins and nucleic acids by NMR: 1. Stable, homogeneous superconductive magnets suitable for NMR at fields of 11.7 tesla (T) and higher. Instruments operating at proton frequencies
Chapter 7 NuclearMagnetic Resonance
331
of 500 and 600 MHz are widely used to study large biomolecules, and 750-MHz instruments are now commercially available. 2. Spectrometer electronics systems ("CONSOLES") capable of performing the range of multidimensional pulsed NMR experiments used to study biopolymers. Stable and flexible radio frequency (rf), analog, and digital electronic systems are required, with control of rf frequency, phase, and amplitude in several rf channels and perhaps one or more magnetic field gradient channels. The spectrometer computer(s) must be capable of controlling complex multichannel pulse sequences and handling the large amounts of data generated in a multidimensional experiment. Connection of the spectrometer's computer to a standard computer network (generally ethernet) with standard protocols is a necessity for effective management of data. 3. Development of techniques for obtaining relevant NMR parameters from complex spectra. In particular, multidimensional NMR methods have greatly increased resolution, allowing individual resonances to be separated and identified in complex spectra. These methods also allow separation of the various interactions a nuclear spin has with neighboring spins, and determination of all the interactions of a given sort (such as scalar coupling through two or three chemical bonds) in a single experiment. 4. Computational methods for analysis of molecular structure. The advances made in computational procedures for molecular modeling (see Chapter 9 for details) constitute the final phase in a determination of the structure of a protein or polynucleotide in solution. Interatomic distances and torsional bond angles obtained by NMR are used along with covalent bond distances and various nonbonded interactions as constraints in the calculation of possible structures.
II. Basic Principles of Nuclear Magnetic Resonance Spectroscopy Although an accurate and complete description of NMR requires a quantum mechanical treatment (Ernst et al., 1987), a detailed knowledge of quantum mechanics is not a prerequisite to understanding NMR applications. Classical descriptions representing the net behavior of a large number or ensemble of identical nuclei are often very useful, and provide an adequate explanation of many NMR experiments after quantum mechanical rules are applied to the individual nuclei. Therefore, in keeping with the usual descriptions of NMR we will mix classical descriptions of NMR experiments with pictorial representations of quantum mechanical energy levels. Several good texts are available to serve as more advanced treatments of modern NMR spectroscopy (Derome, 1987; Farrar, 1987; Harris, 1986; Sanders and Hunter, 1987). The basic principles of NMR are briefly outlined here to provide a foundation for subsequent discussion. The reasons why NMR experiments can be described classically provide insight into the phenomenon and reveal why it differs from other spectroscopic methods. The electromagnetic radiation used to irradiate an NMR sample (i.e., the ensemble of nuclear spins) has a wavelength much greater than the size of the sample. Moreover, the radiation is generated by a macroscopic "broadcasting antenna" (called a transmitter coil in an NMR spectrometer) that produces
332
B.W. Bangerter phase-coherent radiation. In the basic NMR experiment, all the members of the ensemble can be exposed simultaneously to irradiation that varies in time with the same amplitude and same phase throughout the sample. That is, at any given time any of the spins in the ensemble are acted on by the same forces, in direction and magnitude, that act on any other spin. This combination compels the ensemble's response to the irradiation to be coherent with the irradiation, i.e., the response has a definite phase relation to the irradiation. In contrast, even with phase-coherent (laser) radiation, the sample being irradiated in electronic or vibrational spectroscopy is ordinarily much larger than the wavelength of the radiation. (See discussion in Chapters I and 6.) This means that the amplitude of the irradiation varies throughout the sample. Consequently, absorption and emission processes are taking place at different times throughout the sample, and there is not phase coherence between irradiation and response.
A. Nuclear Spins in Static Magnetic Field Most atomic nuclei possess a property called spin and can be thought of as rotating about an axis (the spin axis) like a top. Spin is an intrinsic property of these nuclei, in addition to their intrinsic properties of mass and electric charge. Because a nucleus has mass, a nucleus with spin has angular momentum. The angular momentum is a vector quantity directed along the spin axis. If a spinning mass carries electrical charge, as do all nuclei, it has a magnetic moment that is proportional to the angular momentum. Properties, such as nuclear angular momentum, are governed by the laws of quantum mechanics. Once the angular momentum behavior of a nucleus is described by simple application of quantum mechanical rules, the behavior of an ensemble of such nuclei, such as found in a macroscopic sample, can be described by considering only the behavior of the macroscopic magnetic properties of the ensemble. For nuclear magnetic dipole moments, the proportionality constant relating magnetic moment to angular momentum is a scalar quantity (i.e., one with magnitude but no direction, unlike a vector) called the magnetogyric ratio, with the symbol 7- The magnetic moment is a vector quantity that is parallel with the angular momentum vector. Thus, if I is the angular momentum vector of a nucleus a n d / z is the magnetic dipole moment vector, then in the correct units the proportionality is /z = 7hi,
(1)
where h is Planck's constant divided by 2~r. The magnitude of 7 must be determined experimentally for individual nuclei ~ nuclear theory is not yet good enough to predict the values. The interaction energy, E, of a magnetic moment vector with an external magnetic field B0 vector (in our vector notation) is given by an expression, called the Zeeman interaction, that is, the scalar vector product, E = - / z . B0.
(2)
From the proportionality of angular momentum vector to magnetic moment vector, if we take the maximum projection of I along any axis to be L then, E =
-
"yhIBo,
(3)
where now I is the projection of the angular momentum vector I on B0, and B0
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333
is the m a g n i t u d e of the magnetic field. The rules of q u a n t u m mechanics restrict the values of I a n d state that I m u s t be an integral or half-integral multiple of h. Because the a n g u l a r m o m e n t u m and magnetic m o m e n t vectors are coparallel, so are all their c o m p o n e n t s . We call the m a x i m u m c o m p o n e n t of I the spin q u a n t u m n u m b e r . The restriction is that in the presence of the external magnetic field, the projections of I on B0 m a y only have a total of 21 + I values that are L I - 1, I - 2, . . . , - I + 1, - I . Because of the scalar p r o p o r t i o n a l i t y bet w e e n the magnetic m o m e n t and a n g u l a r m o m e n t u m , this restricts the observable values o f / z to the same n u m b e r of levels. As an application of these rules, let I = 1/2. Then 21 + 1 = 2 a n d the a l l o w e d projections are I = - 1 / 2 and I = + 1/2. We therefore have the result that an I = 1 / 2 nucleus has t w o quant u m mechanically allowed projections of its a n g u l a r m o m e n t u m along B0, a n d b e c a u s e / z is parallel to I, there can only be t w o projections of the magnetic m o m e n t vector along B0 as well. A l t h o u g h the exact values for the m a g n e t o g y r i c ratios of nuclei cannot be theoretically predicted, there are certain regular features concerning nuclear spin q u a n t u m n u m b e r s that m a y be expressed in terms of nuclear charge n u m ber Z a n d mass n u m b e r A for different isotopes. In s u m m a r y , (1) if A is odd, the nuclear spin n u m b e r I is half integral; (2) if A a n d Z are b o t h even, I is zero a n d therefore no nuclear magnetic m o m e n t exists; (3) if A is even but Z is odd, I is integral. Examples of (1) are I = 1 / 2 (1H, 13C, 15N, 19F, 31p), I = 3 / 2 (7Li), I = - - 5 / 2 (170); examples of (2) are I = 0 (12C, 160); examples of (3) are I = 1 (2H, 14N). The N M R properties of several nuclei i m p o r t a n t in studies of proteins a n d nucleic acids are given in Table I. In the usual coordinate system u s e d in N M R spectroscopy, called the laboratory frame, the external static magnetic field defines the z axis. F r o m the discussion above, for a nucleus w i t h I = 1/2, the q u a n t u m mechanically all o w e d projections of the nuclear spin on this axis are Iz = + 1/2, resulting in a l l o w e d e n e r g y levels of E = + 89
(4)
w h e r e B0 is the static magnetic field strength along the z direction. Q u a n t u m mechanics allows transitions b e t w e e n these energy levels w i t h a b s o r p t i o n or
Table I Nuclear Properties of Selected Isotopes Receptivity Isotope 1H 2H
13C
Spin
~, (rad sec -1
89 1 1
26.75 4.11 6.73
15N
89
31p
89
-2.71
10.84
T -1 )
v at 11.74 T (MHz)
Natural abundance (%)
Relativea
500.0 76.8 125.7
99.98 0.015 1.11
1.00 9.67 • 10 -3 1.59 • 10 -2
50.7
202.4
0.37
100.0
1.04 • 10 -3
6.63 • 10-2
i
a Relative sensitivity at constant field for equal numbers of nuclei: --- (~,x/ ~/H)3~ b Absolute sensitivity: product of relative sensitivity and natural abundance.
Absoluteb
1.00
1.45 • 10 -6 1.76 • 10 -4 3.85 • 10 -6 6.63 • 10 -2
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B.W. Bangerter emission of a quantum of electromagnetic energy, AE = 7hB0 = hto0 = huo,
(5)
where the frequency tOo = 7B0 (in radians sec-1), or equivalently u0 = (7/2It)B0 (in Hz). We can now inquire about the motion of the nuclear magnetic moment vector. An ordinary bar magnet placed in the magnetic field B0 would simply align with the z axis. However, the nuclear magnet differs in possessing intrinsic angular momentum and its resultant motion depends on the interaction between the force trying to align it and its intrinsic angular momentum. Analogous to how the force of gravity interacts with a spinning top, the aligning force of the external magnetic field interacts with the spin angular momentum to produce a precession of the angular momentum vector about the magnetic field direction. The result, as for the top, is that the angular momentum vector, and therefore the magnetic moment, precesses about the field direction with a characteristic angular frequency proportional to the strength of the magnetic field. An exact solution of the equation of motion shows that the frequency is o~ = tOo = 7B0,
(6)
where toz is the precessional frequency, called the Larmor frequency. Thus, the frequency of precession about the static external magnetic field is equal to the electromagnetic radiation frequency required to induce a transition between energy states, according to the fundamental quantum relation, A E = hu.
(7)
However, we already have seen that the only transition allowed is between two energy levels characterized by different projections of I on the external static magnetic field direction. In the NMR experiments discussed here we are not concerned with experiments performed on single nuclear spins, but on macroscopic samples containing many nuclei. If a sample containing a large number No of identical spin 1/2 nuclei, which interact only with the magnetic field and not with one another, is placed in a static external magnetic field B0, the spins will populate the two allowed energy levels according to the Boltzmann distribution (see Chapter 1), N ~ / N ~ = e (aE/kT),
(8)
where N~ and N~ are the numbers of spins in the I = 1/2 (lower energy state) and I = - 1/2 (upper energy state) states, respectively; k is the Boltzmann constant; T is the absolute temperature; and N~ + N~ = No. At an external magnetic field strength corresponding to a Larmor frequency of 500 MHz for 1H (corresponding to a contemporary high field NMR spectrometer) and T = 298 K, A E / k T ~, 10 -5. Thus, under these conditions only a small excess of spins occupies the lower energy state. This small excess consists of nuclear magnetic moments, precessing about the external field, with all their projections on the z axis in the same direction. Without further perturbation, beyond the existence of the external magnetic field, the Boltzmann distribution results in a net macroscopic magnetic moment along the z axis, with a value M0 = N0"yRhaB0/4kT.
(9)
The phenomenon resulting in a net macroscopic nuclear magnetization is called
Chapter7 NuclearMagneticResonance
335
spin polarization and M0 is called the induced magnetic moment. The object of NMR experiments is to observe the properties of induced magnetic moments. Because each nuclear magnetic vector is precessing about the z axis at the Larmor frequency in the presence of the external static magnetic field, it has a projection on the x,y plane of the laboratory frame that is also rotating in that plane at the Larmor frequency. In the absence of any perturbing force, at any instant, each precessing nuclear magnetic vector projection will be randomly oriented in the x,y plane with respect to any other rotating nuclear magnetic vector projection in the same plane. As a result, without any perturbation, the vector sum of the projections from all the nuclear magnetic vectors in the system add up to zero and this is time invarient. In NMR language, the x,y plane is transverse to the static external magnetic field, so we say that without any perturbation, there is no net transverse macroscopic nuclear magnetization. Associated with the ratio of the populations of the two energy levels is the concept of spin temperature. Spin temperature is the temperature (in degrees K) that would correspond to a particular N~/N~ being an equilibrium condition, according to the Boltzmann distribution. Thus, an equal population of the two levels corresponds to an infinite spin temperature, and a population inversion (N~ > N~) corresponds to a negative spin temperature. This idea is useful for understanding spin relaxation, which is discussed later.
B. Nuclear Magnetic Resonance Experiment The simplest and most pictorial descriptions of the NMR phenomenon and of many simple NMR experiments are based on energy level diagrams showing populations for various levels (a quantum mechanical picture), along with depiction of the motion of macroscopic magnetization vectors in a coordinate system that rotates about the static magnetic field vector, B0, at the Larmor frequency (a classical picture). In this coordinate system, called the rotating frame, the effect of the static magnetic field B0 on precession of the nuclear spins disappears. The basic NMR experiment, depicted in Fig. 2, is performed by applying to the sample a magnetic field that oscillates at a frequency OJr near the Larmor frequency o& of the nuclei of interest in a direction in space perpendicular to the static field B0. This oscillating magnetic field is depicted as a motionless, or stationary, vector B 1 in the x,y plane of the rotating frame. The magnetization M0 precesses about the field B 1 at a frequency v = (T/2"rr)B1 (Fig. 2b). The B 1 field of constant amplitude is applied for a short time to place the magnetization at the desired orientation in the rotating frame. Because Larmor frequencies are in the radio frequency range (10 7 - 1 0 9 sec-1, or 10-1000 MHz, at the magnetic field strengths presently used), this is called an rf pulse. The strength of the rf field is usually given in terms of the frequency of precession in the rotating frame that it brings about, v = (T/2"rr)B1; rf fields corresponding to v = ~ 25 kHz are generally used. An rf pulse is usually described in terms of the tip angle of the magnetization vector produced by the pulse, the angle (in degrees or radians) by which the magnetization is rotated away from the z axis during the pulse. The effect of a 90 ~ pulse is shown in Fig. 2c. For a B 1 field of 25 kHz, this is a 10-/zsec pulse. For all the nuclei of the species being examined, the pulse converts the longitudinal magnetization lying along B0 to transverse magnetization in the x,y plane. Therefore it is called a nonselective pulse (in
336
B. W. Bangerter
lz
b
Bo
B.
C
T
/
B1
d
Bo
e
v
Mo
y
f
90o
-]lA
t
Fourier transform
/~Aa . . . . ~
F(~) =
f(t) e -i'''t dt
0
t
Fig. 2 Behavior of nuclear spin magnetization under the influence of static and radio frequency (rf) magnetic fields in the rotating frame. (a) At equilibrium, a net magnetization M0 is aligned along the static magnetic field B0 (z axis). (b) Application of an rf magnetic field B1 along the x axis causes M0 to precess away from B0 toward the y axis. (c) B 1 is turned off when M0 reaches alignment with the y axis (a 90 ~ pulse). M0 then precesses in the x,y plane at a frequency ~c -- OJr,where ~OCis the Larmor (resonance) frequency of the nuclei and ~r is the frequency of the applied B1 field, which defines the rotating frame. (d) Representation of this experiment as a simple pulse sequence, with the 90 ~ pulse followed by the free induction decay. (e) Components of M0 along the x and y axes are recorded to give the complex free induction decay (quadrature phase detection). (f) Fourier transformation of the free induction decay gives the complex spectrum, with the resonance represented as both an absorption mode (upper) and a dispersion mode (lower) peak.
NMR jargon a "hard pulse"). This transverse magnetization, which appears stationary in the rotating frame if the frequency of the B1 field is exactly on resonance (~r = OIL),is in fact precessing about B0 in the laboratory frame at the Larmor frequency. This precession induces an electric current in a coil having its axis perpendicular to B0 (the same coil is used to produce B1); this is the NMR signal. The magnetization relaxes or returns to its equilibrium condition along B0, (discussed in Section II,D), by decaying toward zero in the x,y plane {transverse relaxation} and recovering toward M0 along the z axis (longitudinal relaxation}. The NMR signal, also called the free induction decay (FID), is amplified, converted from rf to the audio frequency range ( ~ - O~r = 0--20 kHz or so) by electronically subtracting the frequency of the B 1 field, digitized incrementaly in an analog-to-digital converter over a total time T, and stored in computer memory as a time increment-varying digital amplitude, s(t). In most molecules of interest, there will be several (or many) protons in different chemical environments with slightly different resonance frequencies, oJi, due to the chemical shift, which is discussed below. The magneti-
Chapter7 NuclearMagneticResonance
337
zation observed following a 90 ~ pulse then has several components that precess in the rotating frame, at frequencies corresponding to the differences between the resonance frequencies 0 9 i and the rf transmitter frequency (.Or that defines the rotating frame. A pulse is applied to the sample every second or so and the successive FIDs are added together in the computer memory. This is done to improve the signal-to-noise ratio or sensitivity of the experiment, which increases as the square root of the number n of coadded scans. Signal voltages add directly and increase in amplitude proportional to the number of coadded FIDs. Noise, being random, does not; rather, noise powers add directly, and noise voltages increase a s //1/2. The FID is sampled at a rate corresponding to the range of frequencies 0 9 i - - O ) r , called the spectral width, which is ~ 5 kHz for protons at 500 MHz. Signal components along two orthogonal axes in the rotating frame are sampled simultaneously; these complex data points lead to quadrature phase detection, which allows positive and negative frequencies 09 i - (.Dr t o be distinguished and permits the transmitter frequency O.)r t o be placed in the middle of the resonance frequency range. The accumulated FID has many frequency components, corresponding to the various resonance frequencies of the nuclei in the sample. The FID is subject to a mathematical operation called a Fourier transform (FT), which converts the time domain NMR signal to the frequency domain and yields the NMR spectrum. The FT operation produces a complex (in the mathematical sense) spectrum, with both real and imaginary parts. This spectrum is phased by taking suitable linear combinations of the two parts, leading to two representations of the spectrum, one with peaks in absorption mode and the other with peaks in dispersion mode, as shown in Fig. 2f. The digital resolution in the spectrum (spacing of data points in the frequency domain, in units of Hz) is given by the ratio of the spectral width to the number of complex data points collected. Digital resolution would typically be 1 Hz for a protein or nucleic acid, corresponding to ~ 5000 complex data points at 500 MHz and ~ 1 sec acquisition time per scan. Because the Fourier transform algorithm used (a numerical method called the fast Fourier transform, or FFT) operates on sets of data points containing 2n values, the number of data points collected is generally a power of 2, so 4K (212 = 4096) or 8K (213 -8192) FID data points would be collected.
C. Two Basic Nuclear Magnetic Resonance Parameters: Chemical Shift and Scalar Spin Coupling The various magnetic nuclei in a molecule interact with one another as well as with the magnetic field B0. For spin 1/2 nuclei, these interactions are the Zeeman interaction, scalar s p i n - s p i n coupling, and magnetic dipolar coupling. The scalar couplings cause the resonance line for a nuclear spin to be split into a multiplet. In solution, where molecules tumble rapidly, the dipolar couplings average to zero and do not cause splitting of spectral lines. The dipolar interactions are important in NMR of solutions, however, because the fluctuating dipolar magnetic fields lead to spin relaxation as discussed in Section II,D.
1. Chemical Shift The static magnetic field seen by a particular nucleus is modified by the behavior of electrons in the molecule. This effect is called shielding, because the magnetic field experienced by a nucleus in a molecule is generally slightly
338
B. W. Bangerter smaller than the static applied field B0 due to the motion of the electrons. This shielding gives rise to the chemical shift, so that chemically different nuclei of a given kind have slightly different resonance frequencies o~i = ~/Bi = ~1 - cri)B0, where O"i is called the shielding constant. The chemical shift for a chemically distinct nucleus is expressed in parts per million (ppm) relative to some reference compound by 8 = [(o2i - COrer)/Ogref] X 106. For protons, the reference compound used in aqueous solutions is generally either 3-trimethylsilyl propionate (TSP) or 2,2-dimethyl-2-silapentane 5-sulfonate (DSS), both watersoluble derivatives of tetramethylsilane (TMS), the chemical shift standard ordinarily used in nonaqueous solvents. Chemical shift values for nearly all protons range from 0 to 15 ppm relative to these standards. The chemical shift, expressed in terms of frequency units (Hz) rather than ppm, is proportional to magnetic field strength, so increasing the field B0 increases the dispersion of a spectrum, thereby improving resolution. The range of shielding constants and chemical shifts is larger for heavier nuclei than for protons, because nuclei such a s 13C, 15N, and 31p are surrounded by many more electrons. 2. S c a l a r S p i n - S p i n
Coupling
Scalar, spin-spin, or J couplings are pairwise interactions between two nuclei with energies hJI1 912, where J is the coupling constant in Hz. This scalar coupling is brought about by interactions between bonding electrons and the nuclei involved, and is independent of the orientation of the molecule relative to the static magnetic field B0. The magnitude of J is independent of B0. The resonance peak for a particular proton is split into a doublet with components separated by J Hz due to scalar interaction with each spin 1/2 nucleus to which it is coupled, and a scalar coupling multiplet appears in the NMR spectrum at the chemical shift for that proton. Homonuclear proton-proton scalar couplings are generally 15 Hz or less, with resolved couplings > 2 Hz involving separations by two or three bonds. One-bond couplings between protons and heteronuclei are much larger; 1 j ( 1 H - 1 3 C ) ~ 140 Hz and 1 j ( 1 H - 1 5 N ) ~ 90 Hz are typical. A group of nuclei among which scalar couplings exist is called a spin system. For n spin 1/2 nuclei in a spin system, there are 2 n energy levels. Transitions between any two of these levels can be observed, either directly or indirectly, by NMR. Transitions between two levels where a single spin "flips" or changes its spin state a ~ / 3 are single quantum transitions and are directly observed in a normal one-dimensional NMR spectrum. Transitions between levels where more than one spin flips are multiple quantum transitions and may be observed in two-dimensional (or higher) NMR spectra. The magnitude of the coupling constant between two protons separated by three chemical bonds (a vicinal coupling, with the symbol 3j), as, for example, in a molecule fragment H - C - C - H , is related to the dihedral or torsion angle 0 defined by the H - C - C and C - C - H planes. A relationship of the form J(O) = A COS2(0) -- B cos(0) + C
(10)
has been shown to describe satisfactorily the dependence of the 3j coupling constant on 0, with the parameters A, B, and C determined empirically for the particular molecular fragment (Karplus, 1963). The angle 0 is 0 ~ for the cis conformation of the two protons and 180 ~ for the trans conformation.
Chapter 7 NuclearMagnetic Resonance
339
One of the key data sets that must be obtained to solve the structures of complex molecules by NMR is the set of conformational angles around each rotatable bond in the molecule. For example, in a protein the peptide bonds are normally considered fixed. However, the goal of NMR bond angle experiments is to obtain an accurate set of ~b, ~, and X angles for every residue in the protein. (See Chapter 1 for definitions of these angles.) Although this is possible for small peptides using one-dimensional NMR, multidimensional NMR experiments have made this formidable task approachable in proteins.
D. Nuclear Overhauser Effect and Spin Relaxation
1. Magnetic Dipole Interactions The ability to obtain structural information on macromolecules depends to a great extent on the ability to measure relative interproton distances using the nuclear Overhauser effect (NOE). The NOE is a phenomenon that changes the intensity of a given NMR resonance signal when the magnetization of a nucleus spatially close to the given one in the same molecule is perturbed in a particular way by an rf field. We will find that two different classes of experiment cover essentially all the NOE measurements currently performed. NOEs are caused by magnetic dipolar interactions between nuclei. Magnetic dipolar couplings relate to the distance, rq, between pairs of nuclei in a molecule and to rates of molecular motions that bring about changes in the angular orientation, O(t), of the nuclei relative to the external magnetic field. The energy of interaction, Eq, between two magnetic dipole moments is
E
~
[J.,i[d,j(1-- 3 COS2 0 / r~,
(11)
where the symbols have all been defined previously. Using basic theory, NOE caused by nuclear magnetic dipolar interactions has enabled experiments to be designed that provide relative internuclear distances in complex molecules. Conformational information provided by the set of separate bond rotational angles in a macromolecule are obtained from separate experiments described in this chapter. Combined with the set of bond angles, the internuclear distance information allows determination of macromolecular structure.
B0
~j
rij Fig. 3 Two nuclear spins shown as magnetic dipoles in a magnetic field B0, with the internuclear vector rij making an angle 0 with the static field.
340
B. W. Bangerter
Fluctuating local magnetic fields produced by nearby magnetic nuclei as the molecule undergoes random molecular rotational motion are caused by the sum of pairwise magnetic dipole interactions. Two protons in a molecule that interact through their mutual dipolar coupling are shown in Fig. 3. The field at spin i produced by the magnetic moment of spin j (and conversely) depends on the internuclear distance rij and on the angle 0 the internuclear vector makes with the static magnetic field B0, as described by Eq. (11). For a rigid molecule, modulation of 0 by molecular motions results in a modulation of the dipolar field experienced by each spin. In this analysis, we will make the simplifying assumption that O(t) varies randomly in direction as the molecule tumbles in solution. We further restrict the discussion to nuclei that are not coupled by s p i n - s p i n interactions. Finally, the magnetic field experienced by each spin depends on the orientation of each nuclear dipole moment. We will use the symbols ~ and ]3 to indicate the components of the ith nuclear magnetization opposed to and along the external field direction, respectively. The energy levels of protons differing in chemical shift, which interact through magnetic dipolar coupling modulated by rapid molecular motion, provide an example of an NMR problem that must be dealt with at the quantum mechanical level. The reason is that quantum mechanical rules govern how the components of spin angular m o m e n t u m for two (or more) spins may be added. Q u a n t u m mechanics then describes the resulting energy levels between which transitions may occur when the levels are made nondegenerate (are separated) in an external magnetic field. However, as mentioned previously, once we know the energy levels, the time behavior of the total magnetization from ensembles of spin pairs can be described by a macroscopic differential equation of motion. The results for the two-spin system, interacting via magnetic dipolemagnetic dipole coupling as shown in Fig. 3, are given by the energy level diagram of Fig. 4. There are four energy levels, determined by the orientations of the spin components, c~and ]3 of i and j. The allowed transitions that can take place between excited and ground states are shown. The rate constants for the transitions are shown in Fig. 4 as W0, W1, and W2, called the rate constants for
/
i
W
Fig. 4 Two spin 1/2 nuclei represented by an energy level diagram. Each level is labeled with its corresponding spin state (i.e., a]3:I/ = + 1/2; I~ = - 1/2), and the transition probabilities are shown for the relaxation pathways that result from modulation of the magnetic dipolar coupling of the two spins by molecular motion.
Chapter 7 Nuclear Magnetic Resonance
341
zero-, one-, and two-quantum transitions, respectively. W0 is the rate constant at which spins i and j exchange energy. W1 values are a group of equal rate constants for just one spin changing its energy state in transitions having the same energy level difference. Finally, W2 is the rate constant for the transition where both spins change energy state at the same time. Knowing the allowed energy levels and having defined the transition rate constants we can turn to a classical analysis of the time behavior of the total magnetization. A simple kinetic analysis of this system of two spins involving the rate constants leads to a differential equation that describes the rate of change of observable magnetization, dM/dt, along the z laboratory axis as a function of time (Noggle and Schirmer, 1971). We choose to follow the magnetization of the spin i. Its equation of motion is given by dMi/dt = -(2W~
+ W0 + W 2 ) [ M i -
Mi,ol -
(W2 -
W o ) [ M j - My, o],
(12)
or, redesignating the rate constant terms, dMi/dt = -pi[Mi-
Mi,0] - crij[Mj - Mj,0],
(13)
so that, p, = (2w~ + Wo + w2)
(14)
crij = ( W 2 - W0).
(15)
and
In these equations Mi, o and Mj,0 are the equilibrium components of magnetization for spins i and j, respectively. The rate constant terms tOi and crij determine what are called the spin-lattice and cross-relaxation rates, respectively. It is the existence of the cross-relaxation term that allows relative internuclear distance determinations by NMR. The rate constant terms have quantitative expressions for the general case of many nuclei coupled by magnetic dipolar interactions, and if the rotational motion of the molecule they are located in is random,
oij
=
h2~/4/lO{~l/r~j{~'c + 3Zc/[1 + (COLZc)2] + 6~'c/[1 + 4(r
(16)
J
crij-- ~2~/4/10{ E
1/r~{6zc/[1
+ 4(COL~'c)2] -- 7"c},
(17)
J
where the Zcis the overall rotational correlation time for the molecule in which the nuclei are located. The terms involving ~'care derived from spectral density functions with the assumption that the rotational autocorrelation function is an exponential with a characteristic rotational correlation time of Zc. The dependence of the rate constants on a~CZcshown in Eqs. (16) and (17) becomes very important in applications of NMR to macromolecules. The size of the macromolecule determines Zcand the frequency of the NMR spectrometer determines ~c. As we will see, the success of certain NMR experiments depends on advantageous combinations of ~Ocand Zc. For protons, the constant h 2 ~ / 4 / 1 0 = C --
5.688 • 1010
sec -2
/~k6o
(18)
Using this value, the magnetogyric ratios given in Table I enable calculation of the analogous constants for other nuclei of interest.
342
B.W. Bangerter
2. Steady-State Nuclear Overhauser Effect Using the results just obtained, consider the following application to a molecule where the terms ~C~'cin the longitudinal and cross-relaxation rate constants are much smaller than one. We will discuss the physical meaning of this later. For this case, the rate constants approximate to pi ~ 10~-cand ~rij = 5~'c. In this application, a steady rf field is applied at exactly the Larmor frequency of spin j with sufficient amplitude that Mj becomes zero (because the field equalizes the populations of all upper and lower states for the j spin). The j spin system is said to be saturated and the rf field doing this is a saturating field. At equilibrium, dM i/dt = 0, so, from the differential equation of motion for spin i, -- pi[Mi - Mi,0] + crij[Mj, o] --
O,
(19)
or
M i = Mi, o q- o-ij/Pi[Mj,o].
(20)
The normalized intensity of the i spin's magnetization (observable as the intensity of its NMR signal) is then Mi/Mi, o =
1 + fi(j)= 1
+ ((rij/Pi)(Mj, o / M i , o),
(21)
where fi(j) is the fractional change in intensity of M~ due to saturation of the j resonance. If the spins are identical, Mj, o / M i , o -- 1 and we have the important result for this special case where ~Oc%> 1, O'ij --- - - P i [Eqs. (16) and (17)], and the fractional steadystate NOE enhancement becomes f~(j) = - 1. That is, in the two-spin case, the i resonance signal disappears on strong irradiation of the j resonance. In a transient NOE experiment, the initial slope is negative, and the time-dependent NOE approaches the steady-state value of zero at long irradiation times. Typical correlation times for molecular rotation in aqueous solutions are rc ~ 3 • 1 0 - 1 2 s e c for a water molecule ~c ~ 10-1~ sec for small peptides and oligonucleotides, and ~c ~ 10-9 sec for a globular protein of 10 kDa mass. In using NOEs for structural determination, there is an additional important effect that exists for macromolecules when COC~'c>> 1. Under these conditions, theory shows that mutual spin flips a]3 ~ ]3a become highly probable. That is, referring to Fig. 4, the W0 process, with no net energy change, dominates. In a molecule with many protons the cross-relaxation of a given proton depends on a sum of pairwise dipolar interactions with all of the other protons in the molecule. When mutual spin flips are highly probable, saturation of a given spin leads to saturation of nearby spins, and this spin saturation propagates rapidly throughout the molecule. This is called spin diffusion. A simple thermal analogy for spin diffusion is the consequence of a brief application of intense heat to corner I of a metal triangle whose corners are labeled 1, 2, and 3. The heat travels to corner 3 in two ways: it diffuses from corner 1 to corner 3, and around the longer path from corner I to corner 2 and then to corner 3. If the heat conductivity were somehow greater via the longer path, that path could be a better mechanism for transfer of energy to corner 3, compared to the shorter path. The same principle applies to cross-relaxation. If the efficiency of energy transfer were greater via spin diffusion through other spins than through direct transfer between two selected spins, the internuclear distance derived from NOE measurements on the selected spins could be badly skewed. For this reason steady-state NOE experiments are not useful for complex biological macromolecules. For a molecule with a large number of protons, a complete theoretical analysis of NOE behavior, including explicit consideration of spin diffusion, can be carried out. Such treatments have been applied to biopolymers (Borgias and James, 1990). However, the simpler s p i n - p a i r model, described above, is used more often. If the successive time intervals, ~-, in both the TOE and transient NOE experiments span < 200 msec, spin diffusion effects are usually not very important. Minimization of the effects of spin diffusion is the reason transient experiments are used in NOE measurements on complex molecules.
346
B. W. Bangerter In structural determinations on macromolecules, ratios of pairs of internuclear distances are calculated from ratios of NOE buildup rates. For example, (l'ij/ l'ik) 6 = O'ik/ O'ij
(31)
is determined from the initial slopes of the NOE buildup rates for resonance signals from nuclei j and k when irradiating i. If one of these distances is known in a molecule, the other can be determined from this ratio. The treatment assumes that the reorientations of the two internuclear vectors rij and rik are described by the same correlation time %, which may not always be the case. Because of the steep r -6 dependence, the effects of the failure of such simplifying assumptions about ~c and errors in the measurement of NOE enhancements on determination of proton-proton distances are substantially reduced. For example, a 50% error in a measured NOE corresponds to an approximately 6% error in the calculated internuclear distance. In practice, p r o t o n - p r o t o n distances determined by NOE measurements need not be very precise; the simple observation that one particular proton-proton distance is shorter or longer than another can have a profound influence on determination of secondary and tertiary structure of proteins and nucleic acids.
6. Longitudinal Relaxation Time The longitudinal relaxation time or spin-lattice relaxation time, T1, expresses the rate at which magnetization M for a nuclear spin returns toward its equilibrium value M0 along B0 after it has been perturbed in an NMR experiment. Longitudinal relaxation involves gain or loss of energy by the nuclear spin system through transfer of heat to or from the surroundings (the lattice). Generally this is loss of energy, after the spin system has been perturbed in an experiment by equalizing or inverting the populations of the two spin levels. The recovery toward equilibrium is usually exponential, with a rate constant 1/T1. Typical values of T1 are ~ 1 sec for protons in liquids. A simple analogy for spin-lattice relaxation is immersion of a warm metal bar (representing the spin system) in a water bath at a lower temperature (the lattice). The temperatures of the metal bar and the bath approach some final value exponentially; if the heat capacity of the bath is much greater than that of the metal bar, that final temperature is only slightly higher than the initial bath temperature. This is the case with nuclear spins; the heat capacity of the nuclear spin system is many orders of magnitude smaller than the heat capacity of the sample as a whole (the lattice), which would typically be ~ 0.5 ml of a solution. Thus, the temperature of a spin system with a nonequilibrium population will approach that of the sample, with the rise in temperature of the sample being unmeasurably small. For a spin 1/2 nucleus, the most important contribution to this relaxation process comes from magnetic dipolar coupling with other nuclei in the molecule, these interactions being modulated by random molecular motions as discussed above. An important experimental complication can arise because of electronnuclear dipolar magnetic coupling. This is commonly due to dissolved molecular oxygen or paramagnetic ions in the solution being studied. The unpaired electrons on either of these entities can cause extremely efficient relaxation of nuclei in any molecule under study in the same solution. The reason is that the electron magnetic moment is 2000 times greater than the proton magnetic mo-
347
Chapter 7 NuclearMagnetic Resonance
ment and the dipolar relaxation rate involves the squares of the two dipole moments involved. The longitudinal relaxation rate, 1/T1, for two identical spins interacting solely by magnetic dipole coupling is given by 1/T1
= oij -}- Pi.
(32)
It is clear from this equation that the longitudinal relaxation time is closely related to the NOE. Therefore, an effect o n T 1 as O~L'rc changes may be expected. In fact, minimum value of Z 1 is reached when Zc ~ oh~1 9 7. Transverse R e l a x a t i o n Time
In order to speak quantitatively about the transverse, or spin-spin relaxation, time, T2, we would have to present a differential equation that would describe the time behavior of the x and y components of the total nuclear magnetization. Transverse relaxation processes are energy conserving ones as far as the nuclear spin system is concerned. For the two-spin 1/2 case, energy is being transferred by mutual spin flips, a]3 *-+ ]3a between spins i and j. The process is accompanied by a loss of phase coherence (the components of magnetization for i and j in the x,y plane become uncorrelated). Thus detected magnetization in this plane decays. The functional dependences of spin-lattice and transverse relaxation on the rates of random molecular motion differ. However, although T2 is of considerable practical importance, it is rarely measured to obtain structural or dynamic information concerning macromolecules. Consequently, we will just state the most important practical aspects here. Theoretically, in the extreme narrowing region (see above) T2 = T1. Theory also tells us that the line width, LW, of an NMR signal, expressed as its full width at half-height, is related to T2 by LW = 1 / ('/rT2).
(33)
As a practical matter, measured line widths are frequently greater than Eq. (33) predicts. The reason for this is that inhomogeneities in the static external magnetic field B0 broaden a resonance line, so a line-width measurement gives an "effective T2," called T~, where 1/T~ = 1/T2 + 1/T~.
(34)
The term 1/T~ represents the contribution to the measured line width from B0 field inhomogeneity over the volume of the sample. With modern instruments this contribution is typically less than I Hz. The natural proton line widths for proteins and nucleic acids of a size amenable to study by NMR are several hertz, corresponding to T2 values of < 0.1 sec. As OkZc increases through the T1 minimum, T2 levels off briefly at OJCZc= 1, corresponding to the Z 1 minimum, and then, in contrast to Z l , Z 2 continues to decrease as OkZcincreases. Finally, it is observed that for macromolecules, 1/T2 and therefore the line widths are roughly directly proportional to molecular mass. This effect, along with the increase in the number of protons with increasing molecular size, means that the ability to resolve peaks in the NMR spectrum of a protein or polynucleotide decreases rapidly with increasing molecular size.
348
B. W. Bangerter
-% Sequence-Specific ! Assignments 1 Distance and DiConstraints hedralAngle
"
!
Secondary and Supersecondary Structure
1
1
Distance Geometry1 InitialStructures ~ Restrained Dynamics"~
(SimulatedAnnealing) i
FINAL 1 STRUCTURES
Fig. 6 Flow chart showing the various steps involved in determination of the three-dimensional structure of a macromolecule. The structures generated at intermediate stages of the calculations are often used to help resolve spectral ambiguities and extend the assignments. [Reproduced with permission from P. E. Wright (1989). Trends in Biochemical Sciences, 14, 255-260.]
III. Experimental Methods for Structure Determination As shown in Fig. 6, the general strategy used to determine structures of biopolymers in solution proceeds in several stages: (a) assign proton resonances within a residue (amino acid, nucleotide, monosaccharide) using chemical shifts and scalar couplings; (b) establish sequence-specific resonance assignments through use of distance information derived from NOEs between protons on adjacent residues and from scalar couplings involving 13C and/or 15N; (c) deduce secondary and tertiary structure from "long-range" NOEs (cross-relaxation interactions between protons far apart in the sequence but close to one another in space), as well as from intraresidue and short-range NOEs and the magnitudes of scalar coupling constants. Although the potential utility of such an approach was appreciated many years ago, application of the strategy to biomolecules of significant size became possible only when development of NMR instrumentation and methods and computers reached an adequate level. The development of Fourier transform NMR in the early 1970s brought about major changes in the way NMR spectroscopy was done (Ernst, 1992). The introduction of pulse methods allowed manipulation of nuclear spins in ways not possible using the continuous wave (CW) NMR spectrometers previously available, making many NMR parameters more accessible, and greatly increased the sensitivity of NMR through rapid repetitive signal averaging. But the result was still a one-dimensional spectrum, and the problem of resolution in proton spectra of biopolymers remained. During the late 1970s, two-dimensional (2D) NMR methods were developed (Ernst et al., 1987) that revolutionized the use of NMR as a structure determination tool for biopolymers, particularly proteins (Bax and Lerner, 1986). These methods greatly improve resolution by dispersing NMR spectra along two frequency axes rather than one, and allow the simultaneous measurement of NMR parameters and interactions that can only be determined by individual experiments with 1D meth-
Chapter 7 NuclearMagnetic Resonance
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ods. The 2D methods have been extended to higher dimensions, and 3D and 4D experiments have allowed further improvements in resolution so that larger molecules can be profitably studied by NMR. The great proliferation of NMR experiments has been accompanied by an elaborate jargon to describe the methods and purposes of the experiments, and many fanciful acronyms have been devised. These terms may be amusing, confusing, or annoying, but they cannot be avoided; those used here are explained in the glossary, or in the text as they arise.
A. T w o - D i m e n s i o n a l Nuclear Magnetic Resonance As a review, in a typical homonuclear one-dimensional NMR experiment, the magnetizations of all the spins, which at equilibrium are initially aligned along B0, are simultaneously flipped into the x,y plane by a 90 ~ observation pulse. This is called the preparation period of the experiment. The magnetization in the x,y plane is measured over a detection period (t 2) as a signal that varies with time, s(t 2), called the FID, by being sampled at discrete points in time, digitized, and stored in a computer. The time variable, t2, is used here to allow our notation for this one-dimensional experiment to agree with two-dimensional NMR terminology; t 2 is just the detection period discussed previously. When subjected to a Fourier transform, s(t 2) gives S(o~2), which is the spectrum of the spin system. In a more complex example, we saw that in the one-dimensional transient NOE experiment, a selective 180 ~ pulse was applied to the system (initially at equilibrium along B0) at some time prior to the detection period. In the language of multidimensional NMR, the 180 ~ pulse defines the end of the preparation period for the experiment. The interval we called ~-is termed the evolution period and is given the symbol t I . The result of this experiment, repeated for various values of ~-or t l , is a two-dimensional array of data S(tl, t 2), which are the several FIDs corresponding to the different values used for t I . The rows of this array (the FIDs) are transformed to give another array S(tl, r , which are simply the one-dimensional spectra acquired for various values of the evolution time t 1 . O f interest in this particular example is the intensity of a resonance peak at some particular value of oJ2, which varies as a function of t l , as discussed previously. Although we are working with a two-dimensional array of data here, this is not truly a two-dimensional NMR experiment because there is only one frequency axis. A two-dimensional NMR experiment is one designed to produce a two-dimensional array of data, S(tl, t2) , to which are applied two sets of Fourier transforms, resulting in an array S(COl, oJ2) with two frequency axes, which is a two-dimensional NMR spectrum. Virtually all 2D NMR experiments contain the elements discussed above: a preparation period, at the end of which coherences are created between the various spin energy levels with rf pulses, often as x,y magnetization (transverse magnetization); an evolution period during which the coherences evolve according to chemical shifts and perhaps scalar couplings; and a mixing period not discussed previously. In the mixing period, spins are correlated with one another. Finally, as mentioned before, there is a detection period during which a free induction decay of n data points is collected and stored. A number of experiments m are performed in which the evolution time, t l, is incremented to generate an m • n data matrix we can call S(tl, t2). Two-dimensional Fourier
350
B. W. Bangerter transform of this matrix gives the 2D spectrum S(o91, o92). The rows of s(tl, t2) a r e the m FIDs, which are transformed first to give an array S(tl, r This results in a series of spectra in which the resonance peak for a spin i is modulated (in amplitude a n d / o r phase) as a function of t I by the interactions the experiment is designed to reveal. The modulation is generally at frequencies corresponding to the chemical shift of spin i and to the chemical shifts of the other spins that interact with spin i. The columns of the S(tl, co2) matrix are corresponding points in the m spectra, and are called interferograms. Fourier transformation of the columns converts the modulations in t I to frequencies in the 091 dimension. In most homonuclear 2D experiments the frequency ranges 091 and oJ2 are identical and therefore S(~Ol, o~2)is a rectangular matrix with the normal 1D spectrum appearing along the diagonal. Off diagonal cross-peaks (~Ol # ~o2)reveal the interactions between different spins selected by the experiment. Generally 2D experiments are designed to result in amplitude modulation of a peak in S(tl, co2) as a function of tl, rather than phase modulation. Peaks in the 2D spectrum resulting from phase modulation in t I have a mixed absorption/dispersion lineshape and cannot be phased; they must be displayed in absolute value mode, and such peaks have broad wings at the base that reduce both resolution and sensitivity. Peaks resulting from amplitude modulation in t I can be phased in the 2D spectrum, yielding a pure-phase absorption spectrum of higher quality. Two-dimensional NMR spectra are usually presented as contour plots, with the two chemical shift axes defining the plane of the plot and sets of contours at various heights above this base plane indicating the resonance peaks. Although hundreds of 2D NMR experiments have been devised, perhaps 30 are commonly used in studies of protein and polynucleotide structure. Two general classes of proton homonuclear 2D NMR experiments are used to study biopolymers in solution. In the first class of experiments, cross-peaks arise between protons correlated through scalar J-coupling networks. The scalar J-couplings are related to bond rotational angle information. Therefore, this class of experiment is used to obtain the sets of bond angle information necessary for structural determination. In the second class of experiments, crosspeaks result from cross-relaxation between protons within ~ 5 A of one another. The cross-relaxation information (i.e., NOE data) is used to obtain sets of internuclear distance ratios necessary for structural determination. A few of the most important experiments will be described.
1. Scalar Coupling Correlated Spectroscopy a. COSY Among the most common forms of 2D NMR are correlation experiments. In these experiments the spectrum shows chemical shift positions of nuclei that interact with each other. The correlating interaction may be scalar J coupling, magnetic dipole interactions, or others not discussed in this chapter. The simplest experiment used to reveal scalar coupling correlations is the COSY experiment (so named from the term correlated spectroscopy), with the pulse sequence shown in Fig. 7A. Figure 8 shows the entire process of obtaining the 2D spectrum in a COSY experiment. The correlating influence is, of course, the J coupling between spins. We will describe this experiment in some detail, and then present other important experiments more briefly. During the preparation period, the populations of the spin energy levels are allowed time to equilibrate with their surroundings via longitudinal (spin-lab
Chapter 7 Nuclear Magnetic Resonance A
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351 90 ~
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Fig. 7 Pulse sequences for several 2D NMR experiments that reveal scalar coupling correlations between protons. (A) COSY; (B) double-quantum filtered COSY (DQF-COSY); (C) relayed COSY; (D) homonuclear Hartmann-Hahn spectroscopy (HOHAHA).
tice) relaxation processes. At the end of this time a nonselective 90 ~ pulse is applied that flips the magnetization along z (the direction of B0) into the x,y plane. This marks the end of the preparation period. There follows an evolution period t l, during which time the various nuclei precess at their characteristic Larmor frequencies. At the end of the evolution time a second nonselective 90 ~ pulse is applied. This pulse constitutes the mixing period in the COSY experiment; it has the effect of transferring magnetization between spins that are scalar coupled to one another. The detection period, t2, follows the second 90 ~ pulse, during which time the FID is accumulated; perhaps 2048 data points might be collected during t 2 . This experiment is repeated many times, with t 1 increased incrementally. In a typical experiment, 1024 such t I increments might be used, with t I increasing from 0 to 204.6 msec in steps of 0.2 msec. The FIDs collected are different for each t I increment because of the different extent of precession of the spins in the x,y plane during each t 1 period. In this example, we have generated a rectangular matrix of data points of dimension 1024 • 2048. Each of the 1024 rows of this matrix is Fourier transformed, to give 1024 frequency-domain spectra corresponding to the various values of t I . In this new matrix S(tl, oJ2), the columns contain information revealing how the FIDs were modulated as a function of tl. A second set of 2048 Fourier transforms performed on the columns of this matrix yields the two-dimensional spectrum S(o~1, o~2). The spectrum can be represented as a stacked plot or a contour plot, as shown in Fig. 8. All the nuclei in the sample, whether they have J couplings
352
B. W. Bangerter
,""
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Fig. 8 Schematic representation of the generation of a two-dimensional correlated (COSY) spectrum in which the correlating influence is the scalar J coupling between chemically shifted nuclei. [Reprinted with permission from L. W. Jelinski (1984). Chemical and Engineering News, 62, 26-47. Copyright 9 American Chemical Society.]
Chapter 7 NuclearMagnetic Resonance
353
or not, give peaks along the diagonal of the 2D plot at frequencies 091 -- 092, corresponding to their chemical shifts. Those pairs of nuclei that exchanged magnetization during the mixing period because they are J coupled also give off-diagonal contours or cross-peaks at frequencies (01 :# 092, corresponding to the different chemical shifts of the two nuclei. All the J connectivities in a molecule can be obtained from one experiment of this type. The COSY experiment has consequently become one of the most widely used 2D NMR methods. In the pure-phase version of COSY, cross-peaks appear as antiphase absorption peaks (for a doublet, one peak up and one peak down) and diagonal peaks appear in dispersion mode. Not shown in the pulse sequences of Fig. 7 are the phases of the various rf pulses and of the detection period (receiver). Pulse and receiver phases are varied systematically in all 2D NMR experiments, both to detect desired signal components and to suppress artifacts due to instrumental imperfections. The phase cycles used may be as crucial as the pulse sequence, but they are less easily represented in a graphical way and are thus often not shown in representations of 2D NMR experiments. b. DQF-COSY DQF-COSY (double-quantum filtered COSY; Fig. 7B) is a variant of the original COSY experiment; it affords improved resolution, better detection of cross-peaks near the diagonal, and suppression of singlet signals (from protons without scalar coupling partners) along the diagonal n most importantly the water peak. Both cross-peaks and diagonal peaks appear in pure absorption phase, so the dispersive tails of diagonal peaks that may obscure cross-peaks near the diagonal in normal COSY spectra are absent. (The short, fixed delay A between the second and third 90 ~ pulses simply allows time for the rf phase to be changed for the third pulse.) c. R E L A Y In RELAY (relayed coherence transfer spectroscopy, or relayed COSY), cross-peaks correlate spins that are not directly coupled but that share a common coupling partner. The one-step RELAY experiment is shown in Fig. 7C. This experiment is useful in establishing a network of scalar coupling connectivities when the common coupling partner is obscured by overlap with another peak. Overlap situations frequently occur in COSY experiments with proteins, for example, in a N H - C ~ H - C ~ H fragment of an amino acid residue, where the a proton is not resolved. The delay z in the RELAY experiment is set to ~ 1/(2Jav), where Jav is the average of the two coupling constants involved, for optimal magnetization transfer. A second RELAY step may be incorporated by inserting z2-180~ ~ intervals before the acquisition period t 2 in the scheme of Fig. 7C. d. H O H A H A / T O C S Y The two-dimensional HOHAHA (homonuclear Hartmann-Hahn) magnetization transfer experiment shown in Fig. 7D (Bax,
1989a) reveals both direct and relayed scalar coupling connectivities. The mixing period (typically 50-100 msec) consists of a sequence of composite 180 ~ pulses preceded and followed by spin lock trim pulses; this brings about isotropic mixing, which causes all spins in a coupled system to exchange magnetization. A given proton will then show correlations with all other protons in that spin system in the resulting 2D spectrum. There are a number of variants of this experiment with different sorts of mixing periods; all are derived from the
354
B. W. Bangerter
original TOCSY (total correlation spectroscopy) experiment, and all provide equivalent information about J connectivities. An advantage of HOHAHA over COSY and relayed COSY experiments is that HOHAHA cross-peaks are in phase, so the reduction in sensitivity that results in COSY-type experiments from signal cancellation of antiphase cross-peaks when J is small and line widths are large is avoided. There are also a number of experiments that reveal heteronuclear correlations through scalar coupling, as between 1H and 13C or 15N. The proton-detected versions of these experiments are far more sensitive than those involving detection of the heteronucleus. These methods are incorporated in 3D and 4D experiments employed to establish sequential resonance assignments in proteins through scalar coupling and to increase resolution so that proton-proton interactions in larger proteins can be resolved. Finally, methods of multiplequantum (MQ) spectroscopy (Rance et al., 1989) can be used to reveal both homo- and heteronuclear correlations between scalar coupled spins. The homonuclear MQ methods are useful for spin system assignment when simpler methods give ambiguous results, and reveal scalar connectivities close to the o~1 = ~o2 diagonal, because diagonal peaks are absent in MQ spectra.
2. Cross-Relaxation Correlated Spectroscopy When the magnetization of a spin i is perturbed, transfer of magnetization between spin i and another spin j through chemical exchange or cross-relaxation will change the intensity of the j spin resonance. Both transfer processes are detected by the same experiment. Although measurement of a chemical exchange rate is useful in a particular situation wherein such a dynamic process is occurring, determination of cross-relaxation rates is of great general utility for determining relative proton-proton distances in multispin systems.
a. NOESY NOESY (nuclear Overhauser enhancement, or effect, spectroscopy) is the name given to the 2D experiment used to detect cross-relaxation processes between protons. The pulse sequence is shown in Fig. 9A. The first
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Fig. 9 Pulse sequences for two 2D NMR experiments that reveal cross-relaxation correlations between protons. (A) Nuclear Overhauser effect spectroscopy (NOESY). (B) Rotating frame NOE spectroscopy (ROESY).
Chapter7 NuclearMagneticResonance
355
two 90 ~ pulses are separated by the incremented delay t I . During t I the transverse magnetizations of all the protons precess in the rotating frame at their characteristic frequencies. The second 90 ~ pulse places the component of each magnetization that is orthogonal to the phase of that pulse along the z axis. The result is that after the second 90 ~ pulse the magnitude of the magnetization for spin i along the z axis varies as cos(coit 1) between -mi0 and + m~. During the mixing period ~'m magnetization is transferred between spins by cross-relaxation or chemical exchange. The third 90 ~ pulse transfers the magnetization along z to the x,y plane, and the resulting FID is collected during t 2. The 2D data set is transformed to give a 2D spectrum in which the 1D spectrum appears along the diagonal, and off-diagonal cross-peaks indicate magnetization transfer between the corresponding spins. The NOESY experiment is ordinarily performed in a phase-sensitive mode, and when the spectrum is phased for positive pure absorption peaks along the diagonal, the cross peaks also have pure absorption phase. For negative NOEs, as is the case for molecules where OJC~'c.>> 1, the cross-peaks are positive. The mixing time ~'m must be short to minimize spin diffusion due to the efficient cross-relaxation process W0; ~'m values between 50 and 200 msec are generally used. The intensities of NOESY cross-peaks are proportional to the cross-relaxation rate between the two spins for short mixing times. The 2D NOESY experiment is quite analogous to the selective 1D transient NOE experiment discussed in Section II,D, wherein the magnetization of one spin is inverted and changes in the intensities of other resonances due to cross-relaxation are observed. b. R O E S Y ROESu an alternative to the NOESY experiment, involves measurement of cross-relaxation rates between protons when the spin magnetization vectors are aligned in the x,y plane rather than along z (Brown and Farmer, 1989). The ROESY (rotating frame nuclear Overhauser effect spectroscopy) experiment is shown in Fig. 9B. At the end of the evolution period t 1 a strong rf field is applied in the x,y plane. This causes the spin magnetization components lying along the direction of the applied rf field to become spinlocked along that axis. Because of their different precession frequencies during t l, the different spins will have different fractions of their magnetizations aligned with the rf field at the beginning of the mixing period. During the mixing period, transfer of magnetization between spins occurs through crossrelaxation. This cross-relaxation takes place transverse to the static field direction, and is therefore governed by spin-spin relaxation processes. Thus, crossrelaxation in the rotating frame has a different dependence on molecular motion than does cross-relaxation in the laboratory frame (along z), which occurs in the NOESY experiment. The cross-relaxation rate in the rotating frame is always positive, so for molecules of a size such that ~JC~c"~ 1.12, where ~rij ~ 0 [as per Eq. (17)], the NOESY experiment fails, but the 2D ROESY experiment gives useful information. In addition, the effects of spin diffusion are less severe in the rotating frame NOE experiment.
B. Experiments of Higher Dimensionality The basic scheme for 2D experiments can be extended by adding additional evolution and mixing periods to a 2D pulse sequence. For example, a 3D exper-
356
B. W. Bangerter iment can be constructed from two 2D experiments by omitting the detection period of the first 2D experiment and the preparation period of the second. The result is a 3D pulse sequence with two independently incremented evolution periods tl and t 2 t o label two axes with chemical shifts, two corresponding mixing periods to reveal two distinct types of interaction between nuclear spins, and the t 3 acquisition period to establish the third chemical shift axis. A variety of 4D experiments have been constructed in a similar fashion. Such multidimensional NMR experiments may be homonuclear, where all axes represent proton chemical shifts, or heteronuclear, where one or more axes represent chemical shifts of 13C, 15N, o r 31p nuclei. Multidimensional NMR experiments generate a large amount of data. For example, a 32 • 256 • 1024-point 3D data set has a size of 64 Mbytes. Storing and processing these data are often a problem for older instruments because of computer limitations, but newer NMR data systems and off-line NMR data processing have largely removed this impediment. A lot of instrument time is required to perform these experiments, even when the digital resolution in one or two of the dimensions is low (as few as 64 or 32 data points may suffice to resolve chemical shifts in a 13C, 15N, or 31p dimension). The committment of 3 - 5 days of time on an expensive instrument to a single experiment is justified by the fact that a well-designed 3D or 4D experiment may allow spectra of large molecules to be resolved and assigned when 2D methods fail. Several 3D and 4D heteronuclear experiments have proved to be quite useful in studies of larger biomolecules, as discussed for proteins in Section IV,D.
C. Water Signal Suppression NMR measurements in solution are usually made using deuterated solvents. There are several reasons for this. An 2H resonance is used to maintain a field/ frequency lock for long-term instrument stability and to facilitate shimming of the static magnetic field. In addition, the molar concentration of protons in water or a nondeuterated organic solvent is very high and the intense solvent resonance dominates the 1H NMR spectrum and makes it difficult to discern the resonances of dilute solute molecules. A high level of deuteration of the solvent greatly reduces this interference from the solvent peak. However, protons that exchange with water (peptide and side-chain NH and NH2 in proteins; imino and amino base protons in nucleic acids) cannot be observed in D20 solution due to replacement of 1H by 2H from the solvent. Although the exchange rates provide important information about structure, exchange of labile protons with D20 solvent leads to loss of J coupling and NOE connectivities vital to establishing both sequential assignments and secondary and tertiary structure. Consequently, many of the spectra required for determination of protein or polynucleotide structure must be obtained in H20 solution, generally with 5-10% D20 added to provide the field/frequency lock for the spectrometer. Because H20 is ~ 110 M in protons and typical solute concentrations are ~ 1 mM, the potential range of signal intensities is ~ l0 s. This intensity range cannot be accommodated by spectrometer electronics systems, particular the analog-to-digital converter, which generally has a dynamic range of 16 bits, or + 32K. Consequently, some means of suppressing the large water
Chapter 7 Nuclear Magnetic Resonance
357
signal is required in order to obtain proton spectra in H20 solution. A variety of schemes have been devised to accomplish this (Hore, 1989; Meier and Marshall, 1990), involving (1) presaturation of the water signal, (2) selective excitation methods whereby the water magnetization is maintained along or returned to the z axis while solute magnetizations are placed in the x,y plane, (3) methods based on differences in T1 for H20 and solute protons, and (4) methods based on manipulation of data after digitization. Using one or several of these methods in combination, it is possible to achieve an overall reduction in H20 signal intensity by a factor of 25,000 or greater. Although water suppression methods are necessary in H20 solution, undesired consequences may include loss in intensity of solute signals due to saturation transfer through chemical exchange, cross-relaxation with H20 protons, and either direct saturation or failure to excite resonances near the H20 peak, depending on the method used. For this reason, it is generally necessary also to obtain spectra in D20 to observe nonexchangeable protons that are not seen because of water suppression. On suitably equipped spectrometers, use of pulsed magnetic field gradients can provide exceptionally effective water suppression (~ 10S-fold), revealing solute resonances at the H20 frequency. Suitably modified 2D experiments have been devised to incorporate water suppression, and many of these are very effective.
D. Instrumental Requirements Spectrometers operating at proton frequencies of 500 or 600 MHz are generally used to acquire the NMR data used for structure determination of a protein or a nucleic acid. For very small proteins, peptides, and oligonucleotides, lower field instruments (300-400 MHz) may provide adequate resolution. Studies of larger molecules will usually benefit from use of the highest magnetic fields available. Modern high-field spectrometers (500 MHz and above) are generally well configured for NMR studies of biopolymers, with 1H probes optimized for water suppression and consoles having performance adequate for the demands of 2D proton spectroscopy in H20 solution. Multidimensional experiments involving 13C- and 15N-labeled proteins or nucleic acids require a spectrometer with an adequate number of independent rf channels (three, four, or more) and a triple (or quadruple) resonance probe for observation of 1H and irradiation of 13C, 15N, and perhaps 31p, as well as 2H. Spectrometer data systems of the newer instruments are generally capable of controlling complex experiments and handling the large amounts of data generated. Although spectrometer computers are in most cases capable of processing the NMR data sets generated, this is usually not done on the instrument. Off-line data processing using graphics workstations is now the norm, and offers many advantages both in terms of computer hardware capabilities and in the use of a wide range of software from both commercial and noncommercial sources for NMR data processing and analysis and for molecular modeling computations used in determination of structure. NMR methods using pulsed magnetic or rf field gradients may significantly reduce data acquisition times when high concentrations of sample are available (several millimolar) and can
358
B. W. Bangerter greatly improve water suppression, as noted above; these capabilities may be present on the newest spectrometers. An NMR structure determination requires that a number of 2D spectra be acquired under virtually identical conditions, and it is best to collect these data with the same sample and in the same time frame, ideally running experiments in sequence without removing the sample from the magnet. Because the various experiments may take from 8 to 12 hr for a 2D COSY or other J-correlated experiment, to 1 89 days for a NOESY, 2 - 3 days for a 3D experiment, and 3 - 5 days for a 4D experiment, this is generally not feasible in practice. It is most important, however, to keep experimental conditions as nearly identical as possible when obtaining the various data sets. Collection of NMR data required to determine a "high-resolution" tertiary structure for a ~ 10 kDa protein may require 30 days of spectrometer time; determination of a structure of equivalent quality for a protein of twice that size would likely require use of 3D or 4D experiments with a uniformly 13C- and 15N-enriched protein and 60-90 days of spectrometer time. It should be clear from the foregoing discussion that determination of the structure of a protein or nucleic acid by NMR is not a simple matter. A very substantial committment of instrumental resources and particularly of a researcher's time must be made to complete such a project successfully. In any laboratory where the NMR instrumentation and computational resources required for biomolecular structure determination are present, scientific personnel experienced in this use of NMR are also likely to be available. A researcher wishing to apply NMR methods to the study of biomolecular structure would be prudent to discuss the project with an "expert" early in the process, and a collaborative approach might be suitable.
E. Sample Preparation Proper preparation of a protein or polynucleotide solution for NMR studies is most important, and may greatly affect the results obtained. Important considerations for NMR, apart from purification of the molecule of interest and control of pH and ionic composition of the solution, include ensuring stability of the sample over the long period of time the NMR experiments may require, avoidance or removal of paramagnetic and suspended particulate impurities, and exchange of deuterons for protons for experiments in D20 solution. Deterioration of the sample can result from proteases or nucleases produced by microbial growth. This is not usually a problem in D20 solution because this medium inhibits growth of microorganisms, but in H20 solution the addition of sodium azide at a concentration of ~ 20-50/zM can substantially reduce sample degradation by suppressing microbial growth. Elimination of even trace amounts of paramagnetic impurities (primarily metal ions with unpaired electron spins, such as Cu 2+ and Fe2+,3+) from the sample is particularly important for NMR experiments because such impurities provide a very effective pathway for relaxation of nuclear spins due to the large magnetic moment of the electron. Proton and heteronuclear line widths can be substantially increased if paramagnetic ions are present, and NOE intensities due to proton-proton cross-relaxation may be
Chapter 7 NuclearMagnetic Resonance
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greatly reduced. Contact with possible sources of contamination during sample preparation should be minimized, and Chelex resin is quite effective in removing polyvalent metal ions. The presence of dissolved 02, which is detrimental to measurement of NOEs for small organic molecules, is not usually a problem with biopolymers, for which T 1 and T2 < 1 sec, so samples are not usually degassed. Suspended or colloidal material in an NMR sample will increase line widths due to local magnetic field gradients resulting from the inhomogeneity of the solution. Filtration using a syringe filter, as is often used for HPLC samples, is suitable for the small volumes (~ 0.5 ml) typically used for NMR. Exchange of D20 for H20 is generally accomplished by repeated lyophilization, which may be done on the sample in the NMR tube to achieve the greatest reduction in the residual H20 content. These and other aspects of sample preparation for protein NMR studies are well described by Oppenheimer (1989).
IV. Nuclear Magnetic Resonance of Proteins We turn now to the use of NMR spectroscopy for the study of biopolymer structure. The applications discussed here are limited to the use of high-resolution multidimensional NMR methods to determine the structures of proteins and nucleic acids in solution, an area of research that has progressed rapidly over the past decade. But this is just one of several approaches to the use of NMR as a tool for biomolecular structure determination. NMR can also be applied to molecules in solid or semisolid environments, such as membranes, lipid vesicles, and other molecular aggregates (Smith and Griffin, 1988; Smith and Peersen, 1992). Though the structural information available from these studies is generally less detailed than that obtained for molecules in liquid solutions, such approaches are necessary for entities such as membrane-bound proteins, which undergo structural changes when removed from the cellular environments in which they function. Development of NMR methods for the study of biomolecules in solution has often focused on protein structure first, with subsequent application to nucleic acids and polysaccharides, and that approach is followed here.
A. Proton Nuclear Magnetic Resonance Spectrum of Protein The chemical shifts of the various protons in a protein fall in characteristic ranges determined by the chemical environment of each proton. Corresponding protons of a particular type of amino acid residue show a dispersion in their chemical shifts due to local influences such as hydrogen bonding, side-chain conformation, nature of neighboring residues, and conformational factors related to secondary and tertiary structure. Chemical shift ranges for the different kinds of protons in a protein are shown in Table II. The dispersion of resonances of corresponding protons is highly dependent on the composition and structure
360
B.W. Bangerter Table II Proton Chemical Shifts in Proteins Type of proton
Chemical shift (ppm)
CH 3 ]3; other aliphatic protons a; 13 in Ser, Met Aromatic CH NH (side chain) NH (backbone) NH (Trp)
0-1.5 1-4 3.5-5.4 6.5-7.7 6.6- 7.6 8.1-8.8 --- 10
of the protein, and the utility of NMR methods for determining structure hinges on the ability to resolve and assign resonances. For example, a run of c~-helix with several adjacent Ala residues could present a significant assignment problem due to resonance overlap. Magnetic anisotropies of particular groups of atoms, particularly CO groups and the side chains of aromatic amino acids, have a major influence on chemical shifts of nearby protons. Thus heterogeneity of both amino acid composition and secondary structure aid in dispersing the proton NMR spectrum. Proteins that have only c~-helices, loops, and turns as secondary structural elements generally show poor dispersion of resonances and a high degree of spectral overlap, whereas the dispersion of resonances in proteins with ]3-sheet regions is quite good.
B. Proteins Suitable for S t u d y Proton NMR spectroscopy has been successfully used to determine the threedimensional structures of many small proteins or protein domains of < 10 kDa mass, and several in the 10-25 kDa range. The difficulties encountered in applying NMR methods increase greatly as molecular size increases. Both the number of protons and the resonance line widths increase approximately linearly with molecular size. Assignment of the spectrum becomes difficult because of resonance overlap and a reduction in the effectiveness of 2D methods based on scalar coupling correlations, which require that line widths be not much greater than J couplings. Methods involving 13C and 15N nuclei (described in Section IV,D) are central to the successful application of NMR to structure determination of larger proteins. Aside from being of suitable size and known sequence, the protein must be soluble to a concentration of ~ 1 mM without aggregating and must remain stable in solution for many days at temperatures up to 30-40~ It is helpful if the proton spectrum exhibits a good dispersion of chemical shifts, for the reasons discussed above. It is possible that some regions of a protein may be structurally well defined and thus amenable to NMR structure determination, whereas other regions are not. The ill-defined regions will show few of the long-range NOE interactions that allow tertiary structure to be determined, and
Chapter 7 Nuclear Magnetic Resonance
361
positioning such regions relative to the rest of the protein cannot be done with confidence. C. Structure D e t e r m i n a t i o n M e t h o d s The procedure that is generally used for protein structure determination by NMR has several phases: (1) assign all resonances in the proton spectrum of the protein; (2) determine proton-proton distance constraints from NOE measurements and dihedral or torsion angle constraints from three bond scalar couplings; (3) calculate a family of structures using the NMR constraints along with various geometric constraints dictated by the covalent structure; and (4) refine the structures obtained by use of computational procedures based on energy minimization. The various phases of this overall approach will be outlined, with particular attention given to the NMR methods involved.
1. Sequence-Specific Resonance Assignments Determination of structural constraints from NMR requires that the particular protons involved in cross-relaxation or scalar coupling interactions be associated with particular resonances in the NMR spectrum. Thus, a prerequisite for a successful structure determination is that all, or nearly all, proton resonances be assigned to specific residues in the protein (Robertson and Markley, 1990). The sequential assignment procedure described by W~ithrich (1986) for small proteins (K 10 kDa) relies on several 2D NMR experiments for its success. The first step is to identify as many spin systems corresponding to the amino acid residues as possible by using proton-proton scalar coupling correlation. Some residues have unique spin-coupling interactions, such as Gly, wherein the two nonequivalent C~ protons couple with the NH proton, and Val, wherein the C~ proton is coupled to NH and to C~H, and C~H is also coupled to two groups of methyl protons attached to C~ atoms. Other residues are more difficult to identify. For example, Ser, Cys, Asp, Asn, Phe, Tyr, His, and Trp all have spin systems wherein C~H is coupled to NH and to two C~ protons, and the C~ protons show no couplings with the other sidechain protons. The second step begins with a knowledge of the primary structure of the protein. The problem is to assign resonance signals to sequential residues. Because observable J couplings between protons extend over two or three bonds, interresidue connectivities cannot be determined simply from proton-proton scalar coupling correlations. If 13C a n d / o r 15N enrichment of a protein can be achieved, scalar coupling correlations involving these nuclei can be used to establish sequential connectivities. Such methods are particularly useful for larger proteins, as discussed in Section IV,D. In the usual situation, where 13C and lSN are present only in natural abundance, through-space connectivities are established from cross-relaxation interactions revealed by the NOESY experiment. Interresidue NOEs are present regardless of the peptide backbone conformation, so this procedure is generally applicable. The key to beginning the sequential assignment process is to find unique dipeptide segments, then use these as starting points for further assignments. Unique pairings of amino acid residues are not rare. In a protein of ~ 100 residues, a few amino acids will
362
B.W. Bangerter likely occur only once; in larger proteins there may be only two or three occurrences of a particular amino acid. a. Scalar Coupling Correlations Identification of scalar coupled spin systems is made from COSY (generally DQF-COSY, to exploit the advantages of this method) and H O H A H A spectra, and perhaps RELAY spectra as well. These experiments show patterns of connectivity specific to the various amino acid residues, as indicated schematically in Fig. 10. It is necessary to perform these experiments in H20 to establish the crucial N H - C ~ H scalar connectivities, and data are also usually obtained in D20 solution to permit observation of connectivities involving resonances close to the water peak at ~ 4.8 ppm. For those cases wherein the spin system type does not permit a unique assignment as to amino acid, intraresidue NOE connectivities may be useful. For example, the aromatic protons in positions 2 and 6 of Tyr and Phe do not show scalar
Gly
'Ala'
a S
Val
'
Thr
13/
,2
.
,
y.#-
N n
lie
6,
(~ O H 3 / ,
i
Cys, Asp, Phe His, Asn, Trp Tyr .,
Ser
,
i
i
| J
, , '
, ,
J
I m
Glu, Met, Gin y'
Lys
Pro, Arg
fl (ppm) COSY o RELAY x HOHAHA r~ I 5
I 4
I 3
I 2
I 1
f2 (ppm)
1 0
Fig. 10 Schematicrepresentation of scalar coupling connectivities used to identify amino acid spin systems in proteins. The chemical shift range shown is 0-5 ppm for both fl and f2. Shown are diagonal peaks, COSY connectivities, relayed COSYconnectivities, and additional connectivities revealed by HOHAHA experiments.
Chapter 7 Nuclear Magnetic Resonance
363
coupling to the C~ protons, but they do have cross-relaxation interactions with those protons. An example of the way in which J-correlated data are analyzed is shown for the protein magainin-2 (23 amino acids) in the COSY spectrum of Fig. 11. The spin system of Val-17 is traced by the set of successive scalar couplings shown. Connectivities between N H and Ca protons of the peptide backbone are revealed in the "fingerprint region" of the COSY spectrum, which is expanded in Fig. 12. There is a single correlation here for each amino acid, except for the glycine residues, which have two Ca protons. Note that the Ca protons of Ala-15 and Glu-19 both resonate at 4.24 ppm, so identification of the N H protons of the two residues is ambiguous from this spectrum. The H O H A H A spectrum, of
Fig. 11 COSYspectrum of magainin 2 (23 amino acids) in 75% H20/25% trifluoroethanol-d3, recorded at 600 MHz and 27~ The lines show connectivitiesbetween the J-coupled spins of Val-17. The peaks marked ALA are C~H-CH3 cross-peaks of the two alanine residues, Ala-9 and Ala-15. [Reproduced with permission from Bax (1989b).]
364
B. W. Bangerter
'~1~, K 11 F5 N22
;~.
. ' ~ ' E 19
- -
~,~o
~,.,,7
S 23 , , l ~ . : ~ : $ 8 F16 ~F12
'
t
7.8
8.0
G18
e.oK4 A15o-~ 8.2 qlie" t 9I ~ H 7
O~K14 :-- = = A 9
.~M21 lltL6
8.4
.-8.6 ~ I ~ G 3 qP~o omo
r
!
1
4.8
4.6
1 4.4
i 4.2
| 4.0
! 3.8
! 3.6
8.8
PPM
Fig. 12 Expansionof the "fingerprint region" of the COSYspectrum of Fig. 11, showing connectivities between NH and C~H protons. A single cross-peak (actually a cross-multiplet, consisting of a number of closely spaced components) is observed for each nonglycine amino acid, with the exception of the two N-terminal residues (Gly-1 and Ile-2) whose NH protons exchange rapidly with the solvent, substantially broadening these NH resonances. Two cross-multiplets appear for each glycine residue, corresponding to the two nonequivalent C~H protons. The two C~H protons of Gly-18 differ in chemical shift by only 0.04 ppm, and the two multiplets nearly overlap. [Reproduced with permission from Bax (1989b).] which a small region is shown in Fig. 13, reveals relayed N H - C ~ H connectivities for these amide protons that resolve the assignment question. In fact, with the exceptions of Gly-1 and Ile-2, for each N H proton nearly all side-chain resonances connected directly or indirectly by scalar couplings are observed in this H O H A H A spectrum. b. Cross-Relaxation Correlations Once the spin systems have been identified as to residue type, sequential assignments can be made by identifying through-space cross-relaxation connectivities involving the NH, C~H, and C~H protons from NOESY experiments. The most important cross-relaxation interactions between residues close to one another in the sequence are the C~H(i)-NH(i + 1,2,3,4), N H ( i ) - N H ( i + 1,2), C~H(i)-NH(i + 1), and C~H(i)C~H(i + 3) connectivities. Several short-range NOE connectivities used to establish sequential assignments are shown in Fig. 14. Short interresidue distances involving backbone protons that are revealed by NOESY spectra are those between C~H, C~H, and N H protons of one residue and the N H proton of the next residue, designated deN, d~N, and dNN, respectively. These are in general the most useful distances for establishing sequential connectivity. There is much redundancy in NOEs between sequential residues, so this assignment
Chapter 7 Nuclear Magnetic Resonance
365
Fig. 13 Region of the HOHAHA spectrum of magainin 2 (in 75% H20/25% trifluoroethanol-d3, recorded at 600 MHz and 27~ showing amide to side-chain connectivities. With the exceptions of Gly-1 and Ile-2, nearly all side-chain resonances connected directly or indirectly by scalar couplings to the NH resonance are observed. [Reproduced with permission from Bax (1989a).]
s c h e m e is generally quite effective for small proteins. The major p r o b l e m is again resolution, as even for small proteins f e w e r t h a n half the residues m a y h a v e u n i q u e chemical shifts for both the N H a n d C ~H protons. It is often necessary to m e a s u r e several NOESY spectra u n d e r different conditions of t e m p e r a ture or p H to resolve these ambiguities. As discussed in Section II,D, the cross-relaxation rate ~rij b e t w e e n t w o protons can be d e t e r m i n e d f r o m the initial slope of the d e v e l o p m e n t of the N O E
I
I
H C H-,-,~
--
N
t
HI'
t
C%-/C
~'/,'\
H
/f
I-- N --
i
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t
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C"---- C - -
N --
C ~-
H
H
H
H
HI'+~ Oli'+~
i ,+, i,+, ,,+~ i,+~ i,+~ ,,+~ i,+~
O -H
i
C ~--- C - -
O
O
C --
Fig. 14 Illustration of several short-range NOE connectivities useful in establishing sequential resonance assignments and secondary structure of the polypeptide backbone in a protein.
366
B. W. Bangerter with increasing mixing time. o'ij is proportional to rij-6 and to reff(i,j), the effective correlation time of ri/. Ratios of NOE cross-peak intensities for short mixing (Orkl/O'ij)1/6, times rm can thus yield ratios of interproton distances by ri//rkl provided reff(i,j) and reff(k,l) are similar. The model described for the NOE in Section II,D presumes a rigid molecule, with a single rotational correlation time ~'ccharacterizing the motion of the internuclear vectors. This is of course a gross simplification; proteins in solution are certainly not rigid, and effective correlation times vary significantly throughout the molecule. Similarly, an internuclear distance rij fluctuates over some range. Mobility increases (and reff decreases) in moving from the backbone outward along a side chain, particularly for residues with long side chains. This variation in rates of motion in a protein limits the accuracy with which interproton distances can be calculated from NOE intensities, but the steep t " - 6 dependence considerably reduces the effect of variations in reff. In practice, the calculations of structure based on NMR data do not require that the constraints on p r o t o n - p r o t o n distances be very precise. It is sufficient to simply classify relative NOE intensities as strong, moderate, or weak, corresponding to interproton distances of --- 1.8-2.7, 1.8-3.3, and 1.8-5.0/~, respectively (Gronenborn and Clore, 1990). A NOESY experiment with a short mixing time ~'m (typically ~ 50 msec) will show correlations over relatively short distances (< 3-3.5 A), with a longer mixing time (typically ~ 200 msec) revealinog a much larger number of correlations corresponding to distances up to ~ 5 A. The three distance ranges used in this NOE classification scheme specify the same lower limit, corresponding to the sum of van der Waals radii of two hydrogens, or to the distance between two protons in a methylene group, rather than tighter ranges such as 2-3, 3-4, or 4 - 5 / ~ . The reason for this is twofold. First, the distance geometry method generally used to calculate structures from NMR-derived distances uses these values as constraints for maximum distances between protons. Second, local motion in a protein causes reff for an affected interproton vector to be smaller than the overall rotational correlation time ~'c. NOE intensities observed between two protons experiencing a shorter reff are smaller than if the molecule were truly rigid, so local motion leads to weaker NOEs and thus to distance estimates that are too long. ~
2. D e t e r m i n a t i o n
of
Secondary Structure
Features of secondary structure can be identified from characteristic patterns of interresidue NOEs extending over two to five residues, and from vicinal scalar couplings.
a. N O E Intensities Regions of a-helix are characterized by a sequence of strong to moderate N H ( i ) - N H ( i + 1) NOEs corresponding to the ~ 2.8-/~ interproton distance. Moderate to weak C~H(i)-NH(i + 3), C~H(i)-NH(i + 1), and C ~H(i)-C~H(i + 3) connectivities are also characteristic of a helical region, as is a strong intraresidue N H - C ~ H NOE corresponding to a distance of 2.4 A. Strands show strong C~H(i)-NH(i + 1) NOEs and an absence of other shortrange NOEs involving these protons. The various ]3-sheet regions are characterized by strong C~H(i)-NH(i + 1) sequential NOEs, and by interstrand NOEs involving C~H and N H protons, which allow the alignment of the two strands forming the sheet region to be determined.
Chapter 7 Nuclear Magnetic Resonance
367
b. J Couplings Three-bond vicinal scalar coupling constants relate to the torsional angle of the central bond according to a Karplus-type relationship [Eq. (10)]. Values of J couplings can be obtained from analysis of the antiphase multiplet structure of COSY cross-peaks. The intraresidue coupling between N H and C~H protons is related to the backbone torsion angle ~bby 3JHNc ~ =
6.4 cos2(~b- 60 ~ - 1.4 cos(q~- 60 ~ + 1.9,
(35)
where the constants have been determined empirically to give good agreement between measured couplings and the X-ray structure of the protein BPTI. Values of 3JHNo ~ < 6 Hz and > 8 Hz correspond to ~branges of - 10 ~ to - 90 ~ and - 8 0 ~ to - 1 8 0 ~ respectively. Side-chain torsion angles X1 can be obtained in similar fashion from 3j~ coupling constants. Intraresidue NOEs between N H or C~H protons and C~H protons also relate to X1. Estimation of torsion angles from measured J couplings cannot be as precise as might be implied here, because the measured J couplings may well represent a time average value over a range of conformations, and a particular value for J may correspond to two different torsion angles. In fact, the presence of multiple conformations may lead to NOEs and J couplings that are not simultaneously consistent with a single conformation.
3. Determination of Tertiary Structure a. Measurement of Long-Range NOEs
A globular protein is generally folded into a tertiary structure, wherein protons far apart in the sequence may be close together in space. Measurement of NOEs involving such pairs of protons is essential for deducing the polypeptide folds of the protein. Once the assignment stage is complete, it is straightforward to determine a large number (often several hundred) of such "long-range" (in terms of sequence, I i - j I > 5) NOEs. Resonance overlap may make assignment of many of these long-range NOEs ambiguous, and it is often useful to calculate a low-resolution structure at this stage based on a few NOE interactions assigned with confidence. This low-resolution structure may then serve to resolve some of the more ambiguous assignments.
b. Computational Procedures Constraints on p r o t o n - p r o t o n distances from NOEs and torsion angles from scalar couplings are used along with structural constraints of standard bond lengths and bond angles from the covalent structure to calculate tertiary molecular structure by several methods. These calculations are discussed in detail in Chapter 9. i. Model Building The simplest approach is model building, generally using interactive molecular graphics. This is useful in the first stages of structure determination, wherein identified long-range NOEs can be used to orient regions of the protein of identified secondary structure. The resulting low-resolution structure may then lead to assignment of more of the long-range NOEs. Of course, model building procedures are highly biased, and more objective procedures must be employed to incorporate constraints in a quantitative way. ii. Distance Geometry (DG) The metric matrix distance geometry method is generally the first computational procedure used to determine a protein structure (Braun, 1987). This method does not rely on an initial conformation as a starting point, and is thus unbiased. In the DG procedure, upper and lower
368
B. W. Bangerter bound matrices are first set up for all a t o m - a t o m distances in the molecule, with many elements determined from the covalent and NMR constraints. A "bound smoothing procedure" extends the constraints to all elements of the two matrices. Then a distance matrix is constructed, with distances chosen randomly between the upper and lower bounds, and a structure corresponding to these distances is computed. The structure is optimized by using an error function based on distance constraints. The computation is repeated a number of times with different random choices of the distance matrix to generate a set of structures. The root-mean-square (rms) deviation of atomic coordinates from mean positions in this set of structures is used to judge the "quality" of the set of NMR structures. A related method minimizes a distance constraint error function by varying torsion angles in the molecule. A "variable target function" is used in which only short-range constraints (between residues close together in the sequence) are used at first, with longer range constraints incorporated as the computation proceeds. Results of the two methods are quite similar. iii. Restrained Molecular Dynamics (RMD) These methods involve simultaneous solution of the classical equations of motion for all atoms in the molecule over a suitable period of time. The potential energy function incorporates terms derived from the NMR constraints as well as bond length, bond angle, van der Waals, and electrostatic terms. A starting structure is ordinarily required, which is usually determined by DG methods. The RMD approach is generally regarded as a means of refining DG structures, though it has been successfully used with an extended polypeptide strand as a starting point. The RMD method is effective in overcoming the small energy barriers that create local minima, giving good convergence on the global energy minimum.
D. Study of Larger Proteins The 2D NMR methods that have been used so effectively to study small proteins break down for proteins of higher molecular mass (more than ~ 100 residues) because of extensive resonance overlap and failure of correlation methods based on proton-proton scalar coupling. Both of these limitations can be overcome by utilizing NMR experiments of higher dimensionality (Bax and Grzesiek, 1993; Fesik and Zuiderweg, 1990; Otting and W6thrich, 1990; Wagner, 1989) to reduce resonance overlap and exploit through-bond correlations involving heteronuclear couplings that are larger than the line widths. Use of these methods requires the availability of protein uniformly labeled with lSN, 13C, or both isotopes. Effective procedures for the preparation of labeled proteins (> 95% incorporation of 13C and ~5N) by expression in bacterial systems have been developed using methods of molecular biology (McIntosh and Dahlquist, 1990). With a suitably labeled protein available, several useful 3D and 4D experiments can be performed; these overcome the limitations of 2D experiments based solely on proton-proton interactions (Clore and Gronenborn, 1991a,b). All these experiments incorporate one or two heteronuclear correlation components that relate proton chemical shifts to the chemical shifts of attached 13C o r 15N nuclei (Griffey and Redfield, 1987). A few examples may serve to show the utility of these methods.
Chapter7 NuclearMagneticResonance
369
1. Isotope-Edited NOESY Spectra NOE interactions involving backbone amide NH protons are particularly important in establishing sequential resonance assignments. In larger proteins, many of these NOEs are ambiguous because of resonance overlap. A 3D experiment that combines 1H-15N correlation with an 1H-1H NOESY experiment yields a 3D 15N-separated NOESY spectrum, wherein ambiguities from overlapping amide proton resonances can be resolved if their directly bonded 15N J coupling partners have different chemical shifts. This idea can be extended to create a 4D experiment that also incorporates 1H-13C correlation, Whereby each NOE interaction is simultaneously labeled by four chemical shift coordinates along four orthogonal axes, those of the originating and receiving protons involved in cross-relaxation and those of the corresponding 13C or 15N nuclei directly bonded to these protons.
2. Sequential Assignments Based on Heteronuclear Scalar Coupling In proteins smaller than ~ 30 kDa, uniformly enriched in 13C and 15N, one-bond scalar couplings are significantly larger than the line widths, so magnetization can be transferred efficiently between directly bonded nuclei. A number of 3D J-correlated experiments have been devised to connect 1H and 15N amide resonances of one residue with 13CO, 13Ca, 13C]3, H~, and H~ resonances of the preceding residue, and thus establish sequential resonance assignments.
V. Nuclear Magnetic Resonance of Nucleic Acids Structural features of a variety of nucleic acids have been profitably studied by NMR (Wemmer, 1992). Species investigated include synthetic helical DNA and RNA duplexes (both self-complementary and non-self-complementary, including species with extra nucleotides, base pair mismatches, and unusual or modified bases), single-stranded oligomers, various tRNAs, 5S rRNA (Marshall and Wu, 1990), and fragments of naturally occurring DNA and RNA molecules. Work prior to 1988 has been reviewed by Van de Ven and Hilbers (1988). Nuclei that may be observed are 1H and 31p at natural abundance, 13C and 15N with isotopic enrichment, and other nuclei (most notably 19F) that may be introduced as labels. As with proteins, proton spectra have been the most extensively studied and provide the greatest range of structural information through protonproton NOEs and scalar couplings. The nomenclature of nucleic acid structure is discussed in Chapter 1.
A. Proton Nuclear Magnetic Resonance Spectrum of Nucleic Acid Structures of the (deoxy)ribose phosphate backbone and Watson-Crick base pairs of DNA and RNA are shown in Fig. 15. The base amino and imino protons exchange with water and can be observed only in H20 solution, though the exchange is sufficiently slow on the NMR time scale that distinct narrow resonances are observed for these protons. The 2'-OH proton in RNA exchanges so rapidly with water it does not give a distinct resonance in H20. Resonances for
370
B. W. Bangerter c
Hs
H6
0 Base
13
HgN~ /
N- H .
"0 SugarJNN'~N'"'. H . ~
ei
Hs'~
H
v2 ~/~l \Hi'
/ ~
8/v3 O ~
H2,,
(OH)
H..N~NAN~ H8 H Sugar T (U) (Hs) CH3 ~''",
H6"~
O''''' H"N"H
Sugar'/N~ N" ""
Pi+I
i i
sugar phosphate
~N G
backbone
0
N
. iJQff > "
He
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\
Sugar
Watson-Crick base pairs
Fig. 15 Sugar phosphate backbone and Watson-Crick base pairs found in nucleic acids. Structural features pertaining to RNA are shown in parentheses. Torsion angles defining the backbone conformation are shown as c~-~'; torsion angles describing the (deoxy)ribose ring conformation are v0-v4. See discussion in Chapter 1.
the various protons of D N A and RNA fall in characteristic regions of the spectrum, as shown in Table III. The dispersion of the sugar proton resonances is not very great; whereas the deoxyribose protons span a chemical shift range of 4.5 ppm, the ribose proton range is only ~ 2.5 ppm. The HI' protons are well separated from the others, but the H2', H3', H4', H5', and H5" resonances all fall in a narrow range of ~ 1.5 ppm, making their assignment difficult. The base protons are well separated and easily identified, however. Thymine C H 3 r e s o n a n c e s in D N A are readily identified by their unique chemical shifts and intenTable III Proton Chemical Shifts in Nucleic Acids Type of proton
Chemical shift (ppm)
CH 3 (T) H2', H2" in DNA H4', H5', H5" in DNA H3' in DNA H2', H3', H4', H5', H5" in RNA HI', H5 (C, U) H6 (C, T, U), H8 (A, G) H2 (A) NH2 (A, G, C) (exposed) NH2 (A, G, C) (hydrogen bonded) NH (G, T, U)
1.2-1.6 1.8-3.0 3.7-4.7 4.4-5.2 3.7-5.2 5.2-6.3 7.0-8.3 6.5-7.0 8.0-9.0 10-15
Chapter 7 Nuclear Magnetic Resonance
371
sities, H5(C,U) resonances overlap those of the H I ' protons but are doublets from J coupling to the H6 proton, and the H6(C,T,U), H8(A,G), and H2(A) base protons occur between 7.0 and 8.5 ppm. The chemical shift range for the amino protons of A, G, and C overlaps that for the nonexchangeable base protons, but of course the N H 2 proton resonances are not present in D20 solution. The imino protons, NIH(G) and N3H(T,U), occur in the range of 10-15 ppm, well separated from all other resonances. The NIH(G) imino protons of G + C base pairs generally fall on the high-field side of 13 ppm, and the N3H(T,U) imino protons of A + T or A + U base pairs generally fall on the low-field side. The proton spectrum of the d (GGAATTCC)2 self-complementary DNA duplex is shown in Fig. 16. In double helices formed by self-complementary strands the base pair sequence is symmetry related (palindromic), and the two ends of the oligomer are indistinguishable. Corresponding protons of the symmetry-related pairs of nucleotide residues thus have identical chemical shifts;
Fig. 16 Proton NMR spectra of the d(GGAATTCC)2 duplex in 0.1 M NaC1/10 mM phosphate buffer at pH 7, observed at 500 MHz. (A) Low-field region recorded in H20 at 20~ with exchangeable NH and NH 2 protons indicated by asterisks. (B) Spectrum of nonexchangeable protons recorded in D20 at 25~ [From Patel et al. (1987). Quarterly Reviews of Biophysics, 20, 35-112. Copyright 91987Cambridge University Press. Reprinted with the permission of Cambrige University Press.]
372
B.W. Bangerter this can be seen in Fig. 16 most clearly from the appearance of four imino proton resonances. The N3H imino proton of the terminal G + C base pair is broadened by exchange, because the hydrogen bond involving an imino proton of a terminal base pair is less stable than those of interior base pairs. Resonances of amino protons are broadened by chemical exchange, with rotation about the C - N bond interchanging the hydrogen-bonded and non-hydrogen-bonded protons of the NH 2 pair.
B. Sequential Assignment Methods The sequence-specific assignment of proton resonances in nucleic acids relies on scalar and cross-relaxation connectivities, and the methods used derive from those originally developed to study proteins (Wiithrich, 1986). Of course, the structures of proteins and nucleic acids are very different, and the NMR approaches consequently differ as well (Reid, 1987; Patel et al., 1987). There is less diversity among the monomeric units in nucleic acids (four bases compared to 20 amino acids), and the repeating backbone unit in DNA and RNA (sugarphosphate) has six or seven protons compared to the two protons (NH, C ~H) of the protein backbone. These factors, along with the poor chemical shift dispersion among the sugar protons, make identification of spin systems and assignment to specific residues considerably more difficult in nucleic acids than in proteins. In nucleic acids, several scalar coupling networks (spin systems) correspond to a single nucleotide, and scalar coupling connectivities alone cannot be used to identify a residue. Except for H5 and H6 of cytosine (3JH5_H6 8 Hz) and H6 and CH3 of thymine (4JH6_CH3 ~ 1--2 Hz), the exchangeable and nonexchangeable base protons show no scalar coupling to other protons. The (deoxy)ribose protons form a J-coupled spin system, which can be identified by scalar coupling correlation methods. The exchangeable and nonexchangeable protons effectively constitute two separate sets that are assigned independently.
1. Assignment of Exchangeable Protons The amino, imino, and H2(A) protons of a base pair can in principle be identified by NOEs due to short (2.4-2.6 A) N H - N H 2 distances and the ~ 2.8-A H2(A)-NH(T,U) distance. The H2(A)-NH(T,U) NOE is readily observed, and serves to identify A + T or A + U base pairs. The N H - N H 2 NOEs are often not observed due to chemical exchange of the NH 2 protons with H20 protons competing with cross-relaxation. In any event, once the A + T or A + U imino protons are identified, the other imino protons can be attributed to G + C base pairs. NOE connectivities between imino protons of adjacent base pairs and between an imino proton and the H2(A) of an adjacent A + T or A + U base pair allow sequential assignments to be made for these protons. For double-helical DNA in the canonical B form, adjacent base pairs are separated by ~ 3.4 and the sequential N H - N H or NH-H2(A) distances are typically 3.5-4.5 A, so the NOE intensities are weaker than those between protons within a base pair. Thus, intra- and interbase pair NOEs are rather easily distinguished. By measuring NOEs involving the imino protons either selectively (transient NOE difference spectra) or in a NOESY experiment, it is possible to proceed along a
Chapter 7 Nuclear Magnetic Resonance
373
segment of double-helical DNA or RNA and sequentially assign all of the NH, H2(A), and often the NH2 protons.
2. Assignment of Nonexchangeable Protons Scalar coupling correlated (COSY, RELAY, HOHAHA) and NOESY experiments performed in D20 solution allow the nonexchangeable protons to be assigned. A COSY experiment shows connectivities between pyrimidine base protons and between coupled protons of the sugar. A simple example is the COSY spectrum of d(GGAATTCC)2 shown in Fig. 17. The off-diagonal crosspeaks correspond to protons coupled through two bonds (H2'-H2" and HS'H5"), three bonds [H5(C)-H6(C); H I ' - H 2 ' , H2"; H3'-H2', H2"; H3'-H4'; and H4'-HS', HS"], or four bonds [H6(T)-CH3(T)]. The expanded region shows the correlations between the 8 HI' protons and the 16 H2', H2" protons. The NOESY experiment allows assignment of the H6 and H8 protons and provides the sequential assignments of the nonexchangeable protons. In dou-
Fig. 17
Magnitude COSY spectrum of the d(GGAATTCC)2 duplex in 0.1 M NaC1/10 mM phosphate buffer at pH 7 in D20 at 25~ observed at 500 MHz. (A) Plot of the entire spectrum, from 1.0 to 8.5 ppm. (B) Expansion of the boxed region, correlating the sugar HI' protons (5.2-6.3 ppm) and the sugar H2', H2" protons (1.9-3.0 ppm). The upfield H2' protons and the downfield H2" protons exhibit different crosspeak patterns due to differences in the values of their couplings with HI' and H3'. [Reproduced with permission from Patel et al. (1986).]
374
B. W. Bangerter ble-helical DNA in the usual right-handed B form, the deoxyribose ring assumes the 2 ' - e n d o conformation. In this structure, each base is positioned above the base and sugar of the residue on its 5' side in the same strand, and the H8 proton of a purine or the H6 proton of a pyrimidine shows NOE connectivities with the H I ' , H2', and H2" protons of the same residue and of the preceding residue. The approximate (~- + 0.2 A) intraresidue distances are 3.7 A to H I ' , 2.2 A to H2', and 3.5 A to H2"; the approximate interresidue distances are 3.8 to H I ' , 3.9 A to H2', and 2.2 A to H2". Thus, there results a ladder of NOE connectivities along a strand that can be followed from sugar (HI', H2', H2") to base (H6 or H8), to sugar, to base, etc., to permit sequential assignments. Because the H I ' proton chemical shifts are usually well dispersed, this path is generally preferred. The NOESY spectrum of Fig. 18 shows how this assign-
Fig. 18 Phase-sensitiveNOESYspectrum (mixing time, 250 msec) of the d(GGAATTCC)2duplex in 0.1 M NaC1/10 mM phosphate buffer at pH 7 in D20 at 25~ observed at 500 MHz. (A) Plot of the entire spectrum, from 1.0-8.5 ppm. (B) Expansion of the boxed region, showing NOE connectivities between the base protons (7.1-8.2 ppm) and the sugar HI' and cytosine H5 protons (5.2-6.3 ppm). [Reproduced with permission from Patel et al. (1986).]
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ment scheme is followed for the d(GGAATTCC)2 oligomer. The expanded region shows NOEs between the base protons (7.1-8.2 ppm) and the HI' protons (5.2-6.3 ppm). The NOESY cross-peaks are labeled with the residue to which the HI' proton belongs. The peak marked G1 includes both the H8(G1)HI'(G1) NOE and the HI'(G1)-H8(G2) NOE, because the H8 protons of G1 and G2 have nearly identical chemical shifts; the peak marked G2 is the H8(G2)-H1 '(G2) NOE, the peak to the left of G2 is the H1 '(G2)-H8(A3) NOE, and so on. In this manner the entire eight-residue strand can be traced. In double-helical RNA regions the helix conformation is usually in the A form, with a 3'-endo-ribose conformation, a somewhat different base stacking geometry, and H2" replaced by an OH. The H6 and H8 to sugar HI' and H2' NOEs are evident, though the corresponding distances are different. The approximate intraresidue distances are 3.7 A to HI' and 3.8 A to H2', whereas interresidue distances are about 4.6 A to HI' and 2.1 A to H2'. The same sort of sequential assignment method as used for DNA can be applied to RNA, with the added complication that the H2' resonances now fall in a very crowded region of the spectrum.
3. Correlation of Sequential Assignments The sequential assignment strategies discussed yield three independent parallel linear networks of NOE connectivities along the axis of a double helix. Although these networks are largely isolated from one another, there are generally several NOE connectivities that can be used to correlate the assignments of the individual networks. Two examples are evident in the expanded NOESY plot of Fig. 18B. Several NOE cross-peaks are evident for the H2(A4) proton at 7.66 ppm. Peaks C and A connect H2(A4) with HI'(A4) and HI'(T5), respectively, whereas peak B is the NOE between H2(A4) and HI'(T6) on the opposite strand. Similarly, the H2(A3) proton shows an intraresidue NOE to HI'(A3) and a NOE to H1'(C7) on the opposite strand, both in peak E, and a sequential NOE to HI'(A4), peak F. Thus, the adenine H2 protons bridge sugar HI' protons on the two strands, correlating the three networks.
C. Secondary and Tertiary Structure 1. Scalar Coupling Constants The conformation of the sugar phosphate backbone of a nucleic acid is described by six torsion angles, a-~', by five endocyclic torsion angles v0- v4 which characterize the conformation of the sugar ring, and by the glycosidic torsion angle X, as shown in Fig. 15. Specification of these 11 torsion angles (~ and v3 being redundant) for each nucleotide in a polynucleotide chain defines the conformation of the molecule. The torsion angles v0- v4 of the sugar ring are not independent because the closed covalent structure must be maintained. The furanose ring conformation is most conveniently expressed by pseudorotation (Altona and Sundaralingam, 1972), which describes the pucker of the deoxyribose ring in terms of the pseudorotation angle P and the amplitude cI)m. The ring conformations most commonly encountered in nucleic acids are C2' endo (the C2' atom displaced from the approximate plane formed by the other four atoms of the ring, toward the C5' side) characteristic of the B form of helix
376
B. W. Bangerter
adopted by most double-helical DNA molecules, and C3' endo, which characterizes the A form of helix most commonly adopted by RNA molecules. It is seen from Fig. 14 that 1,1, z,2, 3/~'3, and ~/relate vicinal protons, and the Karplus equation [Eq. (5)] has been parameterized (Van de Ven and Hilbers, 1988) so that the torsion angles can be determined from the three-bond couplings, which are generally measured from cross-peaks in phase-sensitive COSY-type experiments. The torsion angles ]3 and E can be determined from 3 1 p - 1 H couplings by 3JHco P =
15.3 cos 2 (~- 6.1 cos q~ + 1.6,
(36)
but there are no suitable J couplings that could constrain the angles ~ and ~'.
2. Cross-Relaxation Correlations As discussed in Section V,B, a number of short intra- and internucleotide proton-proton distances lead to NOEs that can be used to determine local structure. Specific examples were given to distinguish A and B forms of a double helix. Long-range NOE constraints important for determining tertiary structure are far less abundant in nucleic acids than in proteins, particularly in double-helical oligomers that have extended structures. Exceptions to this are the few interactions between the two strands, as discussed above for the H2(A) proton in d (GGAATTCC)2. Because of this scarcity of long-range distance constraints, greater emphasis has been placed on obtaining precise proton-proton distances from cross-relaxation rates in nucleic acids than in proteins (Borgias and James, 1990). Determination of an unknown distance rq can be made by comparison of two initial NOE buildup rates (often simply by comparison of NOE cross-peak volumes for short mixing times) by rij/rkl (O'kl/O'ij)1/6 if rkl is known. Two such internal "yardsticks" have been used in nucleic acids, the cytosine H 5 - H 6 distance of 2.48 A and the deoxyribose H2'-H2" distance of 1.80 A. Interproton distances thus obtained are used as constraints in the computational procedures. ~
3. Calculation of Structure The same computational procedures used for proteins are also applied to determination of nucleic acid structures from NMR constraints (Van de Ven and Hilbers, 1988; Patel et al., 1987). Oligomeric DNA duplexes do not have a tertiary structure in the same sense that proteins do, though this is an important consideration for nucleic acids that fold, such as tRNAs and 5S rRNAs. In double-helical molecules, greater emphasis has been placed on determining the finer details of structure, such as local variations in helix parameters with sequence and the effects of mispairing and the formation of loops.
VI. Conclusion The application of NMR spectroscopy to the study of biological systems is truly a broad and diverse subject. In this chapter the focus has been narrowed to the application of high-resolution multidimensional NMR methods to determination of the structures of proteins and nucleic acids in solution. Active and productive areas of research such as solid-state NMR, magnetic resonance imaging, and in vivo NMR spectroscopy have not been discussed at all. Development of new experimental and computational tools for biomolecular structure deter-
Chapter 7 Nuclear Magnetic Resonance
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m i n a t i o n is o n g o i n g , a n d a p p l i c a t i o n of t h e s e m e t h o d s to a w i d e v a r i e t y of m o l e c u l e s a n d m o l e c u l a r a g g r e g a t e s is e x p a n d i n g r a p i d l y . O v e r the next f e w years, m o d e s t i n c r e a s e s in the field s t r e n g t h of N M R m a g n e t s m a y be e x p e c t e d , w i t h s p e c t r o m e t e r s o p e r a t i n g at p r o t o n f r e q u e n c i e s of ~ 1000 M H z b e c o m i n g available. W i d e s p r e a d u s e of 3D a n d 4D N M R m e t h o d s to s t u d y u n i f o r m l y 13Ca n d 15N-enriched p r o t e i n s at the h i g h e s t a v a i l a b l e m a g n e t i c fields will a l l o w the s t r u c t u r e s of l a r g e r m o l e c u l e s to be d e t e r m i n e d , a n d c o m p u t a t i o n a l a d v a n c e s will l e a d to i m p r o v e m e n t s in the p r e c i s i o n of the r e s u l t i n g s t r u c t u r e s . N M R i n s t r u m e n t s will be easier to o p e r a t e , a n d c o m p l e x N M R e x p e r i m e n t s will bec o m e s i m p l e r to p e r f o r m t h a n t h e y p r e s e n t l y are. D a t a analysis, m u c h of w h i c h is p r e s e n t l y d o n e b y h a n d , will be g r e a t l y facilitated b y a d v a n c e s in c o m p u t e r s o f t w a r e . G r e a t a d v a n c e s in the u n d e r s t a n d i n g of v a r i o u s a s p e c t s of " m o l e c u l a r r e c o g n i t i o n " m a y be e x p e c t e d ( p r o t e i n / n u c l e i c acid, d r u g / r e c e p t o r , a n t i g e n / a n t i b o d y , cell/cell, etc.), a n d N M R s t u d i e s will p l a y a central role in this w o r k .
References Altona, C., and Sundaralingam, M. (1972). Conformational analysis of the sugar ring in nucleosides and nucleotides. A new description using the concept of pseudorotation. J. Am. Chem. Soc. 94, 8205-8212. Bax, A. (1989a). Homonuclear Hartmann-Hahn experiments. In "Methods in Enzymology" (N. Oppenheimer and T. James, eds.), Vol. 176, pp. 151-168. Academic Press, San Diego, CA. Bax, A. (1989b). Two-dimensional NMR and protein structure. Annu. Rev. Biochem. 58, 223-256. Bax, A., and Grzesiek, S. (1993). Methodological advances in protein NMR. Acc. Chem. Res. 26, 131-138. Bax, A., and Lerner, U (1986). Two-dimensional nuclear magnetic resonance spectroscopy. Science 232, 960- 967. Borgias, B. A., and James, T. L. (1990). Structure determination via Complete Relaxation Matrix Analysis (CORMA) of two-dimensional nuclear Overhauser effect spectra-DNA fragments. In "Biological Magnetic Resonance" (L. J. Berliner and J. Reuben, eds.), Vol. 9, pp. 119-154. Plenum, New York. Braun, W. (1987). Distance geometry and related methods for protein structure determination from NMR data. Q. Rev. Biophys. 19, 115-157. Brown, L. R., and Farmer, B. T., II (1989). Rotating-frame nuclear Overhauser effect. In "Methods in Enzymology" (N. Oppenheimer and T. James, eds.), Vol. 176, pp. 199-216. Academic Press, San Diego, CA. Clore, G. M., and Gronenborn, A. M. (1987). Determination of three-dimensional structures of proteins in solution by nuclear magnetic resonance spectroscopy. Protein Eng. 1, 275-288. Clore, G. M., and Gronenborn, A. M. (1989). Determination of three-dimensional structures of proteins and nucleic acids in solution by nuclear magnetic resonance spectroscopy. CRC Crit. Rev. Biochem. Mol. Biol. 24, 479-564. Clore, G. M., and Gronenborn, A. M. (1991a). Two-, three-, and four-dimensional NMR methods for obtaining larger and more precise three-dimensional structures of proteins in solution. Annu. Rev. Biophys. Biophys. Chem. 20, 29-63. Clore, G. M., and Gronenborn, A. M. (1991b). Structures of larger proteins in solution: Three- and four-dimensional heteronuclear NMR spectroscopy. Science 252, 1390-1399. Derome, A. E. (1987). "Modern NMR Techniques for Chemistry Research." Pergamon, New York. Ernst, R. R. (1992). Nuclear magnetic resonance Fourier transform spectroscopy. Angew. Chem., Int. Ed. Engl. 31, 805-823. Ernst, R. R., Bodenhausen, G., and Wokaun, A. (1987). "Principles of Nuclear Magnetic Resonance in One and Two Dimensions." Oxford University Press, New York. Evans, J. N. S. (1995). "Biomolecular NMR Spectroscopy." Oxford University Press, New York. Farrar, T. C. (1987). "Pulse Nuclear Magnetic Resonance Spectroscopy: An Introduction to the Theory and Applications." Farragut Press, Chicago.
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B. W. Bangerter Fesik, S. W., and Zuiderweg, E. R. P. (1990). Heteronuclear three-dimensional NMR spectroscopy of isotopically labelled biological macromolecules. Q. Rev. Biophys. 23, 97-131. Griffey, R. H., and Redfield, A. G. (1987). Proton-detected heteronuclear edited and correlated nuclear magnetic resonance and nuclear Overhauser effect in solution. Q. Rev. Biophys. 19, 51-82. Gronenborn, A. M., and Clore, G. M. (1990). Protein structure determination in solution by two-dimensional and three-dimensional nuclear magnetic resonance spectroscopy. Anal. Chem. 62, 2-15. Harris, R. K. (1986). "Nuclear Magnetic Resonance Spectroscopy: A Physicochemical View." Wiley, New York. Hore, P. J. (1989). Solvent suppression. In "Methods in Enzymology" (N. Oppenheimer and T. James, eds.), Vol. 176, pp. 64-77. Academic Press, San Diego, CA. James, T. L. (1975). "Nuclear Magnetic Resonance in Biochemistry." Academic Press, New York. Jardetzky, O., and Roberts, G. C. K. (1981). "NMR in Molecular Biology." Academic Press, New York. Jelinski, L. W. (1984). Modern NMR spectroscopy. Chem. Eng. News 62, 26-47. Karplus, M. (1963). Vicinal proton coupling in nuclear magnetic resonance. J. Am. Chem. Soc. 85, 2870-2871. Kessler, H., Gehrke, M., and Griesinger, C. (1988). Two-dimensional NMR spectroscopy: Background and overview of the experiments. Angew. Chem., Int. Ed. Engl. 27, 490-536. Markley, J. (1989). Two-dimensional nuclear magnetic resonance spectroscopy of proteins: An overview. In "Methods in Enzymology" (N. Oppenheimer and T. James, eds.), Vol. 176, pp. 12-64. Marshall, A. G., and Wt/, J. (1990). Investigation of ribosomal 5S ribonucleic acid solution structure and dynamics by means of high-resolution nuclear magnetic resonance spectroscopy. In "Biological Magnetic Resonance" (L. J. Berliner and J. Reuben, eds.), Vol. 9, pp. 55-118. Plenum, New York. McIntosh, L. P., and Dahlquist, F. W. (1990). Biosynthetic incorporation of 15N and 13C for assignment and interpretation of nuclear magnetic resonance spectra of proteins. Q. Rev. Biophys. 23, 1-38. Meier, J. E., and Marshall, A. G. (1990). Methods for suppression of the H20 signal in proton FT/NMR spectroscopy. In "Biological Magnetic Resonance" (L. J. Berliner and J. Reuben, eds.), Vol. 9, pp. 199-240. Plenum, New York. Noggle, J. H., and Schirmer, R. E. (1971). "The Nuclear Overhauser Effect--Chemical Applications." Academic Press, New York. Oppenheimer, N. J. (1989). Sample preparation. In "Methods in Enzymology" (N. Oppenheimer and T. James, eds.), Vol. 176, pp. 78-89. Academic Press, San Diego, CA. Otting, G., and W~ithrich, K. (1990). Heteronuclear filters in two-dimensional [1H-1H]-NMR spectroscopy: Combined use with isotope labelling for studies of macromolecular conformation and intermolecular interactions. Q. Rev. Biophys. 23, 39T96. Patel, D. J., Shapiro, L., and Hare, D. (1986). Sequence-dependent conformation of DNA duplexes: The AATT segment of the d(GGAATTCC) duplex in aqueous solution. J. Biol. Chem. 261, 1223-1229. Patel, D. J., Shapiro, L., and Hare, D. (1987). DNA and RNA: NMR studies of conformations and dynamics in solution. Q. Rev. Biophys. 20, 35-112. Rance, M., Chazin, W. J., Dalvit, C., and Wright, P. E. (1989). Multiple-quantum nuclear magnetic resonance. In "Methods in Enzymology" (N. Oppenheimer and T. James, eds.), Vol. 176, pp. 114-134. Academic Press, San Diego, CA. Reid, B. R. (1987). Sequence-specific assignments and their use in NMR studies of DNA structure. Q. Rev. Biophys. 20, 1-34. Roberts, G. C. K., ed. (1993). "NMR of Macromolecules; A Practical Approach." Oxford University Press, New York. Robertson, A. D., and Markley, J. L. (1990). Methods of proton resonance assignment for proteins. In "Biological Magnetic Resonance" (L. J. Berliner and J. Reuben, eds.), Vol. 9, pp. 155-176. Plenum, New York. Sanders, J. K. M., and Hunter, B. K. (1987). "Modern NMR Spectroscopy." Oxford University Press, New York. Shulman, R. G., ed. (1979). "Biological Applications of Magnetic Resonance." Academic Press, New York.
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Smith, S. O., and Griffin, R. G. (1988). High-resolution solid-state NMR of proteins. Annu. Rev. Phys. Chem. 39, 511-535. Smith, S. O., and Peersen, O. B. (1992). Solid-state NMR approaches for studying membrane protein structure. Annu. Rev. Biophys. Biomol. Struct. 21, 25-47. Van de Ven, F. J. M., and Hilbers, C. W. (1988). Nucleic acids and nuclear magnetic resonance. Eur. J. Biochem. 178, 1-38. Wagner, G. (1989). Heteronuclear nuclear magnetic resonance experiments for studies of protein conformation. In "Methods in Enzymology" (N. Oppenheimer and T. James, eds.), Vol. 176, pp. 93-113. Academic Press, San Diego, CA. Wemmer, D. E. (1992). NMR studies of nucleic acids and their complexes. In "Biological Magnetic Resonance" (L. J. Berliner and J. Reuben, eds.), Vol. 10, pp. 195-264. Plenum, New York. Wright, P. E. (1989). What can two-dimensional NMR tell us about proteins? Trends Biochem. Sci. 14, 255-260. Wfithrich, K. (1976). "NMR in Biological Research: Peptides and Proteins." Elsevier, New York. Wfithrich, K. (1986). "NMR of Proteins ancl Nucleic Acids." Wiley, New York. Wfithrich, K. (1989a). Protein structure determination in solution by nuclear magnetic resonance spectroscopy. Science 243, 45-50. Wfithrich, K. (1989b). The development of nuclear magnetic resonance spectroscopy as a technique for protein structure determination. Acc. Chem. Res. 22, 36-44. Wfithrich, K. (1990). Protein structure determination in solution by NMR spectroscopy. J. Biol. Chem. 265, 22059-22062.
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GLOSSARY Amplitude
The magnitude of a structure factor; the square root of the corresponding intensity.
Anomalous scattering
A change in the phase of the imaginary component of scattered radiation that occurs when the wavelength is close to the edge of an absorption band of an atom. It gives rise to small differences in the intensities of the otherwise identical Friedel pairs that can be used to calculate phases. Introduction to Biophysical Methods for Protein and Nucleic Acid Research
381
Copyright 9 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.
382
Norma M. Allewell and Jaishree Trikha Asymmetric unit
The basic repeating structural unit within a crystal, from which all other structural elements can be generated by symmetry operations and translations of unit cell lengths.
Atomic coordinates
Coordinates that specify atomic positions, either as dimensionless fractions of the unit cell axes or in an orthogonal coordinate system with units of angstroms.
Atomic parameters Occupancy factors. Bessel function
See Atomic coordinates, Temperature factors, and A mathematical series of the form
In(X)
2m
n
e ix
cos
y + iny
dy
Substituting y = q~ - 6, where q~ and 6 are cylindrical coordinates in real and reciprocal space, respectively, and x = 2~rrR, where r and R are radii in real and reciprocal space, generates a function with spherical symmetry and a periodic nature. The maximum nearest the origin is the highest; the remaining maxima decrease in magnitude as r increases. The distance of the first maximum from the origin increases as n increases. The Fourier transforms of helices can be expressed as Bessel functions.
Birefringence A property of crystals with anisotropic refractive indices that causes plane polarized light to be extinguished when the plane of polarization is perpendicular to one of the crystal axes. Body-centered {cell}
A unit cell with a lattice point at its center as well as at
its corners.
Bravais lattice A regular repeating three-dimensional array of points in which the arrangement of points about any given point is identical to that around any other point and which extends indefinitely through space. There are 14 such lattices. Charge-coupled device (CCD) camera A sensitive, state-of-the-art detection device in which X-rays induce the release of electrons from a screen into fiber optics that transmits them to a detector. The detector generates an electronic signal that is transmitted to and stored by a computer. Chiral A structure that cannot be superimposed on its mirror image. See Chapter 1 for further discussion. Collimator
An apparatus used to produce a narrow, parallel beam of radi-
ation.
Convolution A mathematical operation involving two functions in which the product of the two functions, with the origin of one function placed at every point on the second function, is calculated. Crystal system A classification of unit cells based on relationships between the lengths of their axes, the angles between them, and their rotation axes. There are seven crystal systems that can generate a macroscopic threedimensional object. Densitometer A device that measures the optical density of photographic film by determining the ratio of the intensity of incident light to that of light
Chapter 8 Diffraction Methods
383
transmitted by the film within the sample area. It is used to measure the intensities of diffraction spots on the photographic film.
Difference Fourier A Fourier synthesis in which the amplitudes are the differences between either observed and calculated structure factors or the structure factors of two isomorphous structures. Phases are those of the calculated structure or those of the isomorphous structure with known phases, respectively. Direct methods Methods of predicting unknown phases from relationships between their Miller indices and the indices of a set of known reflections and between the structure factor amplitudes of the more intense reflections in the set. These methods are based on the assumptions that every atom in the structure contributes to the diffraction pattern and that the electron density is positive or zero. Electron crystallography Analogous to X-ray diffraction, except that the radiation used is a beam of electrons. Used to determine large macromolecular structures such as viruses. Electron density map A contour represention of the electron density of the unit cell in three dimensions. Ewald sphere Also known as sphere of reflection. A geometric construction of Bragg's law in reciprocal space. If a sphere of radius 1/A is constructed and the origin of the reciprocal lattice is positioned at the point where the incident beam emerges from the sphere, Bragg's law will be satisfied at points where the reciprocal lattice intersects the sphere.
Face-centered (cell) A unit cell with lattice points at the center of one or more faces of the unit cell, in addition to the corners. Cells with lattice points at the center of all six faces are designated F; those with centering on the faces perpendicular to the a, b, and c axes are designated A, B, and C, respectively. Fourier series A summation that approximates a periodic function and that consists of weighted sine and cosine terms with wavelengths that are integral fractions of a periodic function. Because both the crystal and the reciprocal lattice are periodic, they can be represented by Fourier series. Fourier synthesis A periodic function generated by a Fourier series. In crystallography, it usually refers to the electron density generated by performing a Fourier transform on the structure factors of all of the reflections in the diffraction pattern. Fourier transform A mathematical operation that converts one periodic function into another. Used in crystallography to calculate electron density maps from structure factors, and structure factors from electron density. Friedel's law The intensities of centrosymmetric reflections in a diffraction pattern are equal, because these are reflections from opposite faces of the h, k, l planes [I(h, k, l) = I ( - h, - k, - l)]. Glide plane A symmetry operation that reflects a structure across a plane and translates it parallel to the plane by one-half of the unit cell edge, so that two successive reflections and translations are equivalent to one unit cell translation.
384
Norma M. Allewell and JaishreeTrikha An instrument used to rotate a mounted crystal about three Goniometer mutually perpendicular axes during data collection. Heavy atom (derivative) A derivative of the molecule whose structure is being determined in which one or more atoms of high atomic number have been introduced, either by chemical modification or noncovalent interactions. When the crystal structure of the derivative is isomorphous with that of the unknown structure, it can be used to determine phases in the multiple isomor-
phous replacement method. A symmetry operation in which a structure is reflected through a Inversion point. When the point is at the origin, inversion changes (x, y, z) to (-x,-y,-z).
Lattice The regular repeating three-dimensional array of points on which the contents of the unit cell can be imagined to be laid down so that the regularly repeating structure of the crystal is obtained. Laue diffraction Diffraction of X-rays with multiple wavelengths. Used for phasing and to monitor conformational changes in real time. Least-squares refinement A statistical method for refining the parameters of a model to obtain the best agreement with experimental data, by minimizing the sums of the squares of the differences between observed and calculated values. In crystallography, the model parameters are the atomic coordinates, temperature factors, and occupancies. Miller indices (h, k, 1)
Index lattice points in reciprocal space and the corresponding sets of parallel planes in real space that intersect the unit cell axes at a/h, b/k, and c/l.
Mirror plane A symmetry operation that causes structures to be reflected across the plane of the mirror, designated by the symbol m. Mirror planes convert a chiral structure into its enantiomorph. Molecular averaging A procedure used to improve initial phases in which subunits in the asymmetric unit related by noncrystallographic symmetry elements are averaged. Molecular replacement method A method to derive phases in which the known structure of a similar protein is used as a model. Rotation and translation functions are used to orient and position the model relative to the unknown structure. Monochromatic radiation
Consists of a single wavelength.
Motif
The structural unit that is translated within the crystal lattice to generate the crystal. It must contain an integral number of asymmetric units. Distinguish from the catalogs of structural motifs that have been identified in proteins whose structures have been solved. See Chapter 1.
Multiple isomorphous replacement (MIR) method A method of obtaining phases from measurements of the contributions to the intensities of several heavy atom derivatives. Noncrystallographic symmetry Local symmetry that relates identical elements in the asymmetric unit. For example, a two-fold axis which related two dimers in the asymmetric unit is a noncrystallographic symmetry element.
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Nucleation Formation of an aggregate (nucleus) of molecules of critical size that can grow spontaneously to form macroscopic crystals. Usually the rate-limiting step in crystal growth. Occupancy factor Defines the extent to which a given atom or structural element occupies a defined site. Values range from 0 to 1, with low values usually indicating disorder. Patterson function A Fourier transform calculated with intensities rather than structure factors as coefficients. Generates a map of the interatomic vectors, weighted by the product of the atomic numbers of the two atoms. Phase The difference in position of the crests of two waves of the same wavelength, or the point to which the crest of a given wave has advanced relative to some fixed point, for example, the origin. Generally expressed in radians (see Chapter 1). Phase problem The structure factors required to calculate electron density in the unit cell in the Fourier synthesis are waves with both amplitudes and phases. This term refers to the fact that the phases are not directly observable, but must be inferred, through the use of either isomorphous or molecular replacement methods. Point group symmetry The set of 32 symmetry operations that when applied to a point in space brings the point back to its original position. All of the points generated by the symmetry operation lie in the same plane. Precession camera Records a section through reciprocal space. Precession photographs are used primarily to determine the unit cell dimensions and space group of the crystal and to screen potential heavy atom derivatives. Produced with a camera introduced by Buerger, in which the film and one axis of the crystal precess about the beam while the film is maintained perpendicular to the precessing axis. Primitive (cell) cell.
A unit cell with motifs only at the eight corners of the unit
Radiation damage Disordering of the crystal as a result of overheating or free radical formation induced by irradiation with X-rays, resulting in a loss of intensity with increasing resolution. Real space refinement A refinement procedure in which only the geometrical parameters of the model (torsional and interbond angles) are adjusted to obtain the best fit to the electron density map. Reciprocal lattice A lattice with dimensions inversely proportional to the dimensions of the real lattice. Its axes are a*, b*, and c*; a* is perpendicular to the bc plane, b* is perpendicular to the ac plane, and c* is perpendicular to the ab plane. The Miller indices (h, k, l) are used to index lattice points. Reciprocal space The mathematical space in which the Fourier transform of the crystal structure (the diffraction pattern) is defined. It is called reciprocal space because its dimensions are the reciprocal of dimensions in real space; for example, the vectors from the origin of reciprocal space to its lattice points which are perpendicular to the imaginary reflecting planes in real space have a
386
Norma M. Allewell and Jaishree Trikha
nagnitude equal to 1/d, where d is the distance between the reflecting planes. Refinement The process of adjusting the parameters of the model (atomic coordinates, occupancies, and temperature factors) and hence the phases to improved agreement between the amplitudes of the observed reflections and the values calculated from the model parameters.
Resolution The smallest interplanar spacing for which data have been collected, expressed in angstroms. Usually substantially greater than the uncertainty in atomic coordinates. R factor A measure of the agreement between the amplitudes (or intensities) calculated and observed, and hence of the reliability of the model.
llrol hkl
IFcll/
, Ifol hkl
The subscripts o and c correspond to observed and calculated structure factors. Ribbon diagram A ribbonlike trace of the protein backbone showing no atoms, used to emphasize secondary structure. Rotamer A side-chain conformation in proteins defined by its torsional angles and observed in known crystal structures. Rotamer library A compilation of side-chain conformations observed in known crystal structures.
Rotation function The first calculation in the molecular replacement method. The overlap integral of the Patterson functions corresponding to intramolecular vectors of the known and unknown structures is maximized as a function of their relative orientation. Scintillation counter A device used to measure the intensity of X-rays and other radiation. It contains a material that fluoresces when radiation is absorbed and a detector that measures the intensity of the fluorescence.
Screw axis An n t-fold screw axis is a symmetry operation that rotates a structure through an angle equal to 360~ and translates it parallel to the rotation axis by t/n of the unit cell length, where t is an integer -~ n. Simulated annealing A refinement procedure in which a molecular model is refined by simulating in a computer, first heating it to disrupt intramolecular interactions and then slowly cooling it, minimizing internal energy at each stage. It is a powerful method of refinement that can produce large changes in the structure by overcoming local minima.
Solvent accessible surface The surface swept out by the center of a solvent molecule that is rolled across the van der Waals surface of the molecule. Solvent flattening A procedure used to improve phases in structures that have high solvent content. The method assumes that any density in the solvent region represents noise, eliminates this density, and recalculates phases. It requires that the molecular envelope (boundary of the molecule) be defined. Space group
An arrangement of points such that each point is in exactly the
Chapter 8 Diffraction Methods
387
same environment and the same orientation as every other point. Space groups are generated by a combination of external symmetry elements (the 32 point groups), internal symmetry elements (the 14 Bravais lattices), and translational symmetries (screw axes). There are 230 space groups, of which only 65 are compatible with the chirality of macromolecules.
Structure factor The Fourier transform of the unit cell sampled at reciprocal lattice points h, k, l. Structure factors are waves, with both amplitudes and phases.
Symmetry operation (operators) An operation that, when performed on a structure, brings a structure into coincidence with itself. There are four symmetry operations: rotation, reflection, inversion, and rotation-inversion. The latter two are not allowed in crystals of chiral molecules. Synchrotron radiation Radiation emitted when subatomic particles accelerated in high-energy storage rings strike a target. A source of very intense multichromatic X-rays. Systematic absences A regular pattern of reciprocal lattice points with intensities of zero, produced by the symmetry of the crystal lattice (screw axes, glide planes, and nonprimitive lattices). Temperature factor A correction for disorder or atomic motion applied to atomic scattering factors via the term 8 -B(sin~ Its units are/~2. Torsional angle
Also known as the dihedral angle. For a series of bonded atoms A - B - C - D , the torsional angle about the bond B - C is defined as the angle of rotation required to make the B - A bond coincide with the C - D bond when viewed along the B - C direction. Positive values correspond to clockwise rotation. Torsional angles of enantiomers have equal absolute values but opposite signs (see Chapter 1).
Translation function The second function calculated in the molecular replacement method for deriving initial phases. The overlap integral of the Patterson functions of the known and unknown structures is calculated for reflections that correspond to structural elements in different molecules and maximized as a function of the vector connecting the origins of the known and unknown structures. It requires that the orientation of the unknown molecule relative to the known cell be known. Unit cell The boxes enclosed by adjacent pairs of lattice points along the three unit cell axes. Six parameters define the unit cell: three axial lengths and three interaxial angles. The lengths of the unit cell edges are designated a, b, c; the interaxial angles are designated a (between b and c),/3 (between a and c), and ~/(between a and b).
van der Waals surface
The surface of the molecule calculated by summing the solvent exposed van der Waals surfaces of constituent atoms.
Vapor diffusion
A method of crystallization in which solvent is gradually transferred through the vapor phase from the protein solution to a more concentrated salt solution until the two are in equilibrium.
Weissenberg rotation-oscillation camera
A camera that records the diffraction pattern of a crystal oscillated about one of its unit cell axes.
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Norma M. Allewell and Jaishree Trikha
SYMBOLS F(h,k,l)
structure factor at reciprocal lattice point h, k, l corresponding to reflections from the h, k, l plane
I(h,k, l)
intensity of the reflection from the h, k, l plane
P(u, v, w)
value of the Patterson function at point u, v, w in Patterson space phase of a structure factor
p(x, y, z)
electron density at fractional coordinates x, y, z within the unit cell
I. Introduction A. From Crystals to Structures X-Ray and neutron diffraction are unique among the methods of molecular biophysics in that they can be used to develop structural models that position tens of thousands of atoms in large macromolecules to within tenths of angstroms. In both cases, the structural models are derived from the interference patterns of radiation scattered from crystals of the material. In the early days of crystallography, progress was slow because very few biological molecules could be crystallized, data collection was tedious, and computers were slow and had limited memory. As a result of the development of restriction enzymes and ligases, the polymerase chain reaction, site-directed mutagenesis, monoclonal antibodies, machines for synthesizing peptides and oligonucleotides, and improved methods of protein purification, a tremendous range of vitally important problems in cell and molecular biology has become accessible. Crystallography is being used with increasing frequency to rationalize the biological activity of hormones, drugs, and proteins and in drug design. At the same time, data collection has become infinitely less laborious because of the development of powerful X-ray sources, including synchrotron radiation, and of very efficient detection devices. Both the speed and size of the memory of computers have increased exponentially and the development of powerful computer software has made the computational aspects of crystallography much less daunting. Simultaneously, the coming of age of computer graphics (Chapter 9) has resulted in what is essentially a paradigm shift in the way solved structures are analyzed, with visual approaches now being as important as mathematical analyses. These changes have brought crystallography into the mainstream of biomedical research and make it a subject with which every molecular biologist needs to become conversant. All the other methods that are used to probe the structures of biological molecules are either more limited in the range of problems to which they can be applied or are of lower resolution. Nuclear magnetic resonance spectroscopy (Chapter 7) can be used to determine structures of molecules with molecular mass less than ---25 kDa; extended X-ray absorption fine structure (EXAFS), which measures the absorption of X-rays by atoms at energies just above that required to produce an electronic transition, can yield bond lengths for individual bonds correct to tenths of angstroms; fluorescence energy transfer yields distances between fluorescence donors and acceptors that are correct to within
Chapter 8 Diffraction Methods
389
a few angstroms when these groups are separated by less than --- 80 A (Chapter 6); scanning tunneling microscopy and atomic force microscopy, which measure the force between a probe and individual atoms in a structure, yield structures at resolutions of several angstroms. However, none of these methods has the generality or resolution of X-ray and neutron diffraction, which can be used to determine structures of any size up to a resolution of 1.2 A. What is required to determine a structure by diffraction? The most stringent requirement is the availability of crystals with dimensions of a few tenths of a millimeter that diffract well. This in turn usually requires milligrams or more of a highly homogeneous preparation of the molecule of interest, the patience to carry out a systematic search of crystallizing conditions, and at least a little luck. Both the size of the crystal and the regularity of the molecular packing are important, because the phenomenon of diffraction depends on a regular pattern being repeated over and over again in exactly the same way. Crystals of biological molecules are quite different from crystals of small molecules. Of the volume of macromolecular crystals, 25-70% is typically solvent, and macromolecular crystals lose their crystallinity when the solvent is removed. To maintain their solvent content, macromolecular crystals used in diffraction experiments are mounted either in sealed capillaries containing a drop of solution from which the crystals were grown (mother liquor), or in flow cells that allow the liquid medium to be changed. The presence of solvent in the crystals of proteins minimizes the conformational perturbations produced by crystallization, because intramolecular interactions vastly outnumber intermolecular interactions. The high concentrations of precipitant required for crystallization generally also have little effect on the overall structure of proteins, although small conformational differences between the conformation of the protein in solution and in the crystal are always possible. Nucleic acid structures are often quite sensitive to solvent conditions, as exemplified by the differences in the structures of A and B DNA (see Chapter 1), which have different solvent and salt content. The conformational heterogeneity of biological macromolecules and the presence of solvent make crystals of biological macromolecules less ordered than those of small molecules. Although the diffraction pattern of small crystals often extends to the limit set by the wavelength of the radiation, so that individual atoms can be resolved, the resolution of macromolecular crystals is always much less. When suitable crystals become available, the first step is to determine the arrangement of molecules within the crystal; that is, to determine the space group of the crystal. This in turn determines how much data must be collected. Precession cameras are often used at this stage. The raw data consists of the intensities of the X-rays that are diffracted at various angles from the crystal. The large number of atoms in crystals of biological macromolecules requires a correspondingly large number of experimental observations. Moreover, the intensities of the diffracted rays are weak. Development of high-energy X-ray sources, sensitive detectors, and automated data collection methods was essential for solving the crystal structures of biological macromolecules. Many different devices have been used to collect data: precession cameras, diffractometers, multiwire area detectors, charge coupled device (CCD) cameras, and image plates. At present, multiwire area detectors are most widely used (Section III,E). The goal of the analysis of an X-ray diffraction pattern is to compute a
390
Norma M. Allewell and JaishreeTrikha three-dimensional electron density map of the structure under study by summing the waves diffracted from the crystal. Although the summation is carried out in a computer, it is analogous to the operation performed by the lens of a microscope, which generates an image of the object being viewed by summing the waves of visible light scattered from it. The information required to compute electron density maps consists of both the amplitudes of the diffracted waves (usually known as reflections) and their phases. When both the amplitudes and the phases are known, the crystallographer can reconstruct the electron density of the crystal by computing a Fourier transform. The amplitudes can be calculated directly from the intensities of the diffracted rays, but the phases cannot be directly measured (the so-called phase problem). Phases must be computed, either by comparing the diffracted intensities of the original crystals with those of other crystals into which heavy atoms have been introduced without disturbing the crystal packing, or from the atomic coordinates of a molecule with a similar known three-dimensional structure. The first approach is known as the multiple isomorphous replacement (MIR) method, the second as the molecular replacement method. As many structures and powerful computer programs have become available, molecular replacement has become increasingly popular. Refinement of the initial structure is an important part of the process. By adjusting the structure and recomputing the phases, the crystallographer is able both to improve agreement between observed and calculated intensities and to eliminate energetically unfavorable interactions. Progress of the refinement is evaluated by calculating the R factor, a measure of the agreement between observed and calculated amplitudes. During the refinement, the crystallographer adjusts not only the atomic coordinates of the macromolecule, but also the occupancies and temperature factors of all the atoms, parameters that define their disorder or motion. Solvent molecules and ions that are bound to the macromolecule are also incorporated into the model. The principles of neutron diffraction are similar to those of X-ray diffraction. Neutron diffraction requires a nuclear reactor as a source of neutrons and larger crystals, but has the advantage of allowing hydrogens in the structure, which generally cannot be visualized with X-rays, to be located. When well-ordered three-dimensional crystals cannot be obtained, accurate structural models can sometimes be derived from the diffraction pattern of fibers that are ordered in only one or two dimensions. This approach was used to develop the double helical model of DNA. In this chapter, we will begin by discussing the steps involved in determining the structure of a macromolecule by X-ray diffraction: obtaining and characterizing crystals, collecting data, determining phases, calculating electron density maps, refining the initial model, and analyzing final structures (Fig. 1). Our emphasis will be on proteins, although most statements also apply to nucleic acids. Special features of neutron diffraction will be discussed next, followed by a brief discussion of fiber diffraction. We will conclude by discussing new directions that are emerging. X-Ray crystallography is like most other fields: it is easy when you know how! Crystallography has the advantage of having a powerful and elegant theoretical base; with a good understanding of a few basic principles, one can solve any number of seemingly complex problems. These principles are most easily expressed and grasped when they are expressed mathematically, and so
Chapter 8 Diffraction Methods
391
I'Grow crystals I~-~
Preliminary examination -single crystal ? -does the crystal diffract ?
Determine unit cell dimensions
]
Measure intensities of reflections I
l
Determine phases using - isomorphous replacement -anomalous scattering -molecular replacement -any combination of the above
Calculate and fit electron density map repeat until convergence is achieved [ Refine phases and initial modelt::-
] Analyzethefinalmodel ] Fig. 1
F l o w d i a g r a m of the s t e p s i n v o l v e d in d e t e r m i n i n g the structure of a m a c r o m o l e c u l e diffraction.
by
this chapter contains mathematics that may be new to some readers. The mathematics m geometry and integral calculusmcomplement and reinforce each other. We have tried to present the mathematics as an overview without becoming bogged down in detail. This necessarily requires that the discussions be less rigorous than they would be in standard crystallographic textbooks (cf. Blundell and Johnson, 1976; Cantor and Schimmel, 1980; McPherson, 1982; Glusker and Trueblood, 1985; Wyckoff et al., 1985; Stout and Jensen, 1989).
II. Crystals A crystal is a three-dimensional ordered array of molecules. This type of packing is best for diffraction experiments because it results in the scattered rays interfering constructively at discrete angles to produce intense diffraction spots whose intensities can be measured very accurately.
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Norma M. Allewell and Jaishree Trikha
A. G r o w i n g Crystals The search for conditions under which a macromolecule will crystallize is much like looking for the proverbial needle in a haystack. Conditions under which a given macromolecule will crystallize cannot be predicted in advance, for two reasons: macromolecules are complex physicochemical systems whose structure, dynamics, and state of self-association change with temperature, pH, solvent composition, ionic strength, and the addition of ligands in ways that cannot be predicted a priori; in addition, the forces that form and maintain crystals are poorly understood. Crystallizing a macromolecule thus requires varying the parameters that influence crystal formation, with the goal of finding one or more sets of initial conditions that produce crystals of some sort, and then optimizing variables to obtain the best possible crystals (cf. McPherson, 1990). Macromolecules are usually crystallized from supersaturated solutions, obtained by altering a concentrated solution of the macromolecule in a way that reduces the solubility of the macromolecule. This is generally accomplished by changing pH or temperature or adding precipitating agents. The concentration of the macromolecule is generally 5-15 m g / m l ; the precipitating agent is often a salt, organic solvent, or polyethylene glycol. The process of growing crystals can be divided into two phases: nucleation and growth. Formation of stable nuclei is the rate-limiting step, but unfortunately is poorly understood. When nuclei do not form spontaneously, micro- or macrocrystals of the same protein, or a homologous protein, can serve as nuclei. Once crystal nuclei have formed, the emphasis shifts to maintaining conditions that will sustain continued, ordered addition of single molecules or ordered aggregates so that large, single crystals are obtained. This is most likely to be achieved when only a few nuclei have formed. Supersaturated conditions can be achieved by evaporation, dialysis, or vapor diffusion. The hanging drop method, which depends on vapor diffusion between a microdrop containing the macromolecule and a much larger reservoir of precipitating agent (Fig. 2), is frequently used to screen crystallization conditions. A drop of a solution of the molecule to be crystallized is mixed on a coverslip with a drop of the solution containing the precipitating agent, the coverslip is placed over an aliquot of the precipitating solution in a microtiter well, and the two solutions are equilibrated. Compilations of conditions that are often successful allow a wide range of conditions to be tested quickly (Jancarik
Fig. 2 The hanging drop vapor diffusion method of crystallization. A cross-section through one well in a tissue culture plate is shown. High-vacuumgrease (petroleum jelly) is used to create a seal between the siliconized coverslip and the lip of the well.
393
Chapter 8 Diffraction Methods
and Kim, 1991). When conditions that induce the formation of crystalline precipitates or microcrystals have been found, a grid search in which these conditions are varied over a narrow range often yields diffraction-quality crystals (Weber, 1991). A robotic crystallization apparatus facilitates the search and increases precision and reproducibility. When conditions that yield satisfactory crystals have been identified, crystallization is often carried out by dialysis, free interfacial diffusion between a solution of the protein and a solution containing the precipitant, or the sitting drop method, in which the macromolecule and precipitating solution are mixed in the well of a depression slide or microtiter plate that is sealed with a coverslip (Fig. 3). These procedures tend to yield fewer but larger crystals and are often used in seeding experiments. When crystals do not form readily, modifying the molecule sometimes leads to success. Limited proteolysis is sometimes the key, particularly for membrane proteins or proteins with multiple domains connected by flexible loops. Single-site mutants designed to facilitate crystallization are also being used with increasing frequency. To observe X-ray diffraction, the dimensions of the crystal must be in the range of a few tenths of a millimeter. Crystals used for neutron diffraction often have dimensions of a few millimeters. The crystal need not have well-defined faces. Examples of diffraction-quality crystals are shown in Fig. 4. A polarizing microscope is useful in evaluating quality and in defining the orientation of the unit cell axes relative to the faces of the crystal. Unless they are cubic, the crystals should exhibit birefringence so that they extinguish (do not transmit) polarized light at certain angles. Twinned crystals, composed of two or more smaller crystals, can sometimes be identified because their patterns of birefringence will be discontinuous and different parts of the crystal will extinguish at different positions. The volume occupied by solvent in macromolecular crystals is generally 50%, although crystals with 25-70% solvent have been obtained. Solvent content can be determined from the weight lost by crystals on drying, and density can be determined with a density gradient column constructed from two miscible liquids. The presence of solvent in the crystal has several consequences. On the one hand, macromolecular crystals tend to be fragile, because only a few intermolecular contacts maintain their structure. On the other hand,
A coverslip grease
plasticbox
dropofasolutionof proteinandprecipitating agent glassrod reservoirof precipitatingsolution Fig. 3 The sitting drop vapor diffusion method of crystallization. (A) An individual well. (B) Three wells in a depression slide enclosed in a plastic box.
394
Norma M. Allewell and Jaishree Trikha
Fig. 4 Two diffraction-quality crystals. (a) Amphibian red cell L ferritin. (b) Amphibian red cell H ferritin. Magnified 100 times. (Courtesy of J. Trikha and N. M. Allewell.)
Chapter 8 Diffraction Methods
395
because of their aqueous environment, macromolecules in crystals behave much as they do in solution, although their conformational repertoire may be restricted by the crystal lattice. For example, enzymes are often catalytically active in crystals but have reduced catalytic efficiency. The presence of solvent channels also makes it possible to diffuse small molecules into crystals. By varying solution conditions, both heavy atom derivatives and complexes of the macromolecule with various ligands, (enzyme-inhibitor complexes), can be prepared.
B. Crystal Lattices and Unit Cells All crystals can be thought of as being generated by placing a structural motif on a lattice with the same orientation in each position (Fig. 5). A lattice is a regular repeating arrangement of points in three dimensions. Its geometry is defined by the distances between adjacent points along its principal axes and by the angles between the axes. The axes are designated a, b and c; the angles between are designated c~ (between b and c), ]3 (between a and c), and ~/(between a and b). A lattice point is a point at which the three principal axes intersect. (The principal axes are generally the axes with the shortest distances between lattice points.) There are only 14 lattices with geometries that generate a three-dimensional object in space. These lattices are known as the Bravais lattices (Table I). The nature of the structural motif depends on the type of molecule being studied. In inorganic crystals it may be simply a pair of ions; in organic crystals it is usually a cluster of atoms; in macromolecule crystals it is likely to be a single molecule or a collection of molecules. A crystal can also be considered to be built up from unit cells, the boxes bounded by adjacent lattice points along the principal axes of the Bravais lattice
Fig. 5 The crystal lattice and unit cell.
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Norma M. Allewell and Jaishree Trikha
Table I Bravais Lattices Symbol
Type
Crystal system
Comment Lattice points only at the corners of the unit cell Lattice points at the center of the faces of the unit cell Lattice points at the center of the unit cell Lattice points at the center of all of the faces of the unit cell Lattice points at corners of the unit cell with three-fold axis along the body diagonal
P
Primitive
A, B, or C
Face centered
Triclinic, monoclinic, orthorhombic, tetragonal, hexagonal, cubic Monoclinic, orthorhombic
I
Body centered
Orthorhombic, tetragonal, cubic
F
All faces centered
Orthorhombic, cubic
R
Rhombohedral
and containing the portions of the structural motifs centered on these lattice points that fall within their bounds. The sides of the unit cells are called its faces. The dimensions and symmetry of the unit cell are determined from the spacing and symmetry of the diffraction pattern (see Section III,F). Seven of the Bravais lattices are simple lattices in which all of the structural motifs are located at lattice points along the principal axes of the lattice. They generate the seven primitive crystal systems defined below and illustrated in Fig. 6. 1. In triclinic crystals, the three unit cell axes are unequal, none of the angles between them equals 90 ~, and the unit cell has no symmetry elements. 2. Monoclinic crystals have three unequal unit cell axes, but one of the unit cell axes is at right angles to the other two, and there is a twofold rotation axis parallel to b. 3. Orthorhombic crystals have three mutually perpendicular unequal unit cell axes, with twofold rotation axes parallel to the unit cell axes. 4. The axes of tetragonal crystals are also at right angles; two of the three are equal and there is a fourfold rotation axis parallel to the c axis. 5. In hexagonal crystals, one axis is inclined at an angle of 120 ~ to the other two, which are equal and at right angles to each other. There is a sixfold rotation axis parallel to the c axis and two twofold rotation axes perpendicular to it. 6. Rhombohedral crystals have equal axes and equal interaxial angles, but the interaxial angle is not equal to 90 ~ and there is a threefold rotation axis along the body diagonal. 7. In cubic crystals, all three axes are equal; the interaxial angles are all 90 ~ and there is a threefold axis along the body diagonal and fourfold axes parallel to each crystal axis. The remaining seven Bravais lattices have lattice points that lie off the principal axes. These additional lattice points are located either at the centers of the faces of the unit cell or at the center of the unit cell. These lattices generate nonprimitive crystal systems. The unit cell in a nonprimitive crystal system can
397
Chapter8 DiffractionMethods
Triclinic
Monoclinic
Fig. 6 given
Crystal
systems.
a ~ b r c; o~ ~ 13 ~ 7 ~
a ~b r
c~r
90*
~ 90"; 7 = 90 ~
Orthorhombic
a ~ b r c; c~ = 13 = y = 90 ~
Tetragonal
a = b ~: c; cc = 13 = 7 = 90"
On the left-hand
side are diagrams
of unit cells; the unit cell restrictions
are
on the right.
be defined in more than one way, because the scattering pattern does not depend on how the unit cell is defined.
C. Space Groups The overall symmetry of the crystal, called its space group, will depend on both the symmetry of the lattice and any additional symmetry within the unit cell. The symmetry of the crystal is defined by a set of symmetry operators that is sufficient to'generate all of the molecules in the unit cell from a single asymmetric unit. All of the repeating units generated by a symmetry operation have exactly the same environment. The asymmetric unit is the smallest unit from which the crystal structure can be generated through symmetry operations. The asymmetric unit can
398
Norma M. Allewell and Jaishree Trikha
Hexagonal
Rhombohedral
Cubic
a = b ~ c; t~ = 13 = 9 0 ~ 7 = 1 2 0
a=b
=c;t~r
r
~
~
90 ~
a = b = c; t~ = ~ = ~, = 9 0 ~
Fig. 6 (Continued)
correspond to one molecule, more than one molecule, a subunit of an oligomeric molecule, or even a domain of a molecule. More than one molecule or subunit of an oligomeric molecule within the asymmetric unit can be related to each other by noncrystallographic symmetry elements (symmetry elements that are not part of the crystal symmetry). Alternatively, when the molecule is a multimer made up of monomers that are related in the crystal by crystallographic symmetry elements, the asymmetric unit will consist of only part of the molecule. Point group symmetry operators (rotation axes, inversions through a center of symmetry, mirror planes, and combinations of these symmetry operators) are manipulations of an object (a molecule or group of molecules) that ultimately regenerate the object. The N-fold rotation axes rotate the molecule through 360~ about the axis; the geometry of the unit cell restricts the possible values of n to 1, 2, 3, 4, or 6 (Fig. 7). Because macromolecules contain chiral atoms, macromolecular crystals cannot contain centers of symmetry or mirror
Chapter 8 Diffraction Methods
399
Fig. 7 Rotational symmetry elements. (A) Twofold, (B) threefold, (C) fourfold, and (D) sixfold.
planes, because these operations convert right-handed molecules into lefthanded molecules, and vice versa. Space group symmetry operators involve a translation. They are either screw axes (a rotation plus a translation) or glide planes (translations accompanied by a reflection). Only screw axes need be considered in macromolecular crystals, because glide planes change the handedness of chiral centers. An n t screw axis generates molecules related by an n-fold rotation about the axis and a translation of t / n of the unit cell length parallel to the axis. For example, a twofold screw axis rotates the molecule by 180 ~ and translates it by one-half the unit cell axis, so that two successive operations bring the structure to its original position in the next unit cell (Fig. 8). All the possible symmetry operations, including the operations that are not allowed in crystals of macromolecules (inversions through a center of symmetry, mirror planes, and glide planes) generate 230 unique space groups that are compiled in the International Tables for X-Ray Crystallography (Hahn, 1987). Biological molecules can crystallize in only 65 of these space groups, because inversions, mirror planes, and glide planes are ruled out by their chirality. Usually no assumptions are made about symmetry when the first data are collected. However, once the symmetry has been determined, it can be used to
400
Norma M. Allewell and Jaishree Trikha
A
C
3600
B
(x',y',z')
180~
(-x,-y,z+1/2)
360" ~
~
(x,y,z)
I
(x',y',z')
270~
(y,-x,z+3/4)
180" ~
(-x,-y,z+l/2)
90~ 0"
C
0~
!
I ~(-y,x,z+l/4 )
~
(x,y,z)
I
Fig. 8 Two examples of screw operators. (A) A 21 screw axis rotates the asymmetric unit by 180~ and translates it by one-half of a unit cell length. (B) A 43 screw axis rotates the asymmetric unit counterclockwise by 90 ~ about the screw axis and translates it by one-quarter of the unit cell length. Coordinates are expressed in fractions of the unit cell axes.
reduce the amount of data that must be collected, because the diffraction pattern will have the same symmetry as the crystal.
III. Collecting Diffraction Data In this section, we will begin by discussing the physical basis of diffraction in the context of Bragg's law to provide a framework for discussing data collection. We will finish with a discussion of two powerful but more abstract concepts, the reciprocal lattice and Ewald sphere. Although there are some important differences between neutron and X-ray radiation, as discussed in Section III,A, the same fundamental theory applies to both. Specific applications of neutron diffraction are discussed in Section X.
A. Introduction X-Rays are electromagnetic radiation with wavelengths in the range of 0.1100 A. Neutrons, one of the fundamental particles of atoms, have properties of waves as well as particles (see Chapter 1). The wavelengths of the nearly monochromatic neutrons that can be obtained from nuclear reactors are in the range of 2 - 4 A. X-Rays and neutrons that strike the crystal are absorbed and emitted as waves emanating in all directions. Diffraction of X-rays depends on scattering of radiation by electrons, whereas neutron diffraction results from scattering by atomic nuclei. The intensity of scattered X-rays is proportional to the number of electrons in the structure. There is no simple relationship between the amplitude of neutron scattering and the structure of the atom. Waves scattered by different atoms in the structure interfere both constructively and destructively, generating a diffraction pattern in which the intensity of the scat-
401
Chapter 8 Diffraction Methods
tered radiation is nonzero only w h e n the conditions for constructive interference are met. Bragg's law, which applies to all diffraction phenomena, is one w a y of defining these conditions.
B. Bragg's Law According to Bragg's law, waves reflected from a set of planes with a spacing d interfere constructively only w h e n the sine of the angle 0 between the plane and the incident or reflected ray is given by 2d sin 0 = n A, where n is an integer and h is the wavelength of the radiation (Fig. 9). In a crystal there are no real planes from which X-rays or neutrons are reflected. However, the diffraction pattern is what w o u l d be expected if the radiation were reflected from all the families of planes that intersect the unit cell axes a, b, and c, at a/h, b/k, and c/l, where h, k, and l are integers (Fig. 10) k n o w n as the Miller indices. The interplanar spacings corresponding to any set of Miller indices d e p e n d only on the unit cell dimensions, the interaxial angles of the unit cell, and the indices themselves (Table II). Bragg's law relates the angles at which diffraction is observed to the spacings of the planes that give rise to the diffraction pattern. It provides no information about the w a y atoms are arranged within the molecule.
C. Sources X-Rays are generated w h e n electrons traveling at high velocity strike a metal target. In an X-ray tube, electrons generated by heating a tungsten filament enclosed in a v a c u u m tube are accelerated by a high voltage applied between the cathode, the source of electrons, and the anode, which emits X-rays w h e n
l
2
2'
Fig. 9 Bragg'slaw. Rays 1 and 2 are incident beams; rays 1' and 2' are reflected beams. The angles of incidence and reflection (0) are equal. The path difference between rays scattered by points X and Y (aY + bY) is 2d sin 0. Constructive interference requires that the path difference be equal to nA, where n is an integer. Hence, 2d sin 0 = nA.
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Norma M. Allewell and Jaishree Trikha
'b
020
022
005
Fig. 10
Some possible planes in the unit cell and their Miller indices (h, k, l). The Miller indices are defined by the number of times the planes intersect the respective axis within the unit cell; for example, the 022 planes do not intersect the a axis, but intersect the b and r axes twice.
the electrons strike. The anode is usually made of copper or molybdenum, two metals that generate X-rays with wavelengths comparable to chemical bond lengths. Although the longer wavelength of the X-rays produced by copper allows larger molecules to be studied and is the most common choice, X-rays from molybdenum have the advantage of being of higher energy and shorter wavelength so that they are less readily absorbed and can be used to determine structures at higher resolution. On the other hand, the higher energy X-rays from molybdenum sources disorder crystals and weaken the diffraction pattern more rapidly. Modern X-ray tubes have rotating anodes, in which the anode is a plate that rotates rapidly, so that the electrons strike different parts of its surface, allowing heat to be dissipated more rapidly. Because the generated X-rays are of more than one wavelength, filters made of nickel or the Bragg reflections from a crystal are frequently used to produce monochromatic radiation. Collimators produce a narrow and focused beam. X-Ray beams can also be generated by the electrons or positrons that circulate at very high velocities within the circular chamber of synchrotrons, driven by radio frequency generators and maintained in a circular orbit by powerful magnets. The wavelength of the X-rays is a function of the curvature of the synchrotron chamber and the velocity of the atomic particles. Synchrotrons are at least as large as several football fields and exist only at specialized facilities; for example, at Cornell and Stanford, at some of the National Laboratories
Chapter 8 Diffraction Methods
403
Table II Interplanar Distance Formulas for Crystal Systems a Interplanar spacing of (hkl) plane
Crystal system Cubic
d =
Tetragonal
d =
Orthorhombic
a=
Hexagonal
d = d =
Rhombohedral Monoclinic
a2 ) 1/2 h2 + k2 + 12
(
d=
a2 c ~ ) 1/2 h 24- k24-
(aabac2)
V+V+F
1/2
l~.i a2 C2 1/2 3h24-hk4_k24--~) a2(1 + cos ~, - 2 cos 2 ~/) "~ 1/2 4- cos T)[(h 24- k24- /2) _ (1 - tan 2 T/2)(hk + kl + hi)] J I a2(sin ]3) b2 c2(sin 2 ]3) ac sin 2 ]311/2 h2 + -~ + ' T l~ - 2hl cos ]3
aThe complex formula for the triclinic system has been omitted.
(Argonne, Brookhaven, and Los Alamos, Daresbury in England, and Grenoble in France). Using these facilities requires that an application be peer reviewed and approved. Radiation from synchrotron sources is several orders of magnitude more intense than from conventional rotating anodes. The intensity of the beam and the sensitive detectors used at synchrotrons increase the speed at which data can be collected, making synchrotrons particularly useful when only small or fragile crystals are available. Data can be obtained so rapidly that synchrotrons are beginning to be used to define the conformational changes that occur during catalysis. Because they generate radiation of multiple wavelengths, they can also be used to obtain phases from anomalous scattering. Macromolecular crystals are subject to radiation damage, disordering of the crystal as a result of chemical changes induced by overheating or formation of free radicals or ions. Radiation damage is detected as a reduction in and smearing of the intensities of diffracted X-rays, particularly at high resolution. Neutrons do not produce appreciable radiation damage. The susceptibility of crystals to radiation damage varies enormously, with some crystals being stable for weeks and others deteriorating in a matter of hours or even minutes. In recent years, crystallographers have begun to chill crystals to reduce radiation damage, by directing either nitrogen gas boiling off liquid nitrogen or refrigerated air at the crystal, particularly when the crystal deteriorates rapidly in the X-ray beam. D. G o n i o m e t e r s , Diffractometers, and Cameras Bragg's law specifies very stringent relationships between the source, the crystal, and the detector. Because the position of the source is generally fixed, the Bragg conditions must be met by moving the crystal and the detector. Crystals are usually mounted, in either sealed capillaries or flow cells on goniometers (Fig. 11), which allow the crystal to be oriented in three dimensions by rotating
404
Norma M. Allewell and Jaishree Trikha
Fig. 11 The four-circle goniometer. The four angles, 2-theta (20),omega (~o),phi (q~),and chi (X) are varied independently to collect a complete data set.
it around two axes. Goniometers coordinate changes in 20, achieved by rotating both the detector and the crystal about an axis perpendicular to the plane of the source and the detector, with changes in the orientation of the crystal, achieved by rotations around the axis defined by the beam and around the axis perpendicular to the beam. The Buerger precession camera and Weissenberg rotation-oscillation camera record a set of reflections on film. The Buerger precession camera processes the crystal and the film about an axis parallel to the beam. These motions result in a set of intensities being recorded on the film as an undistorted two-dimensional lattice (Fig. 12). Precession camera photographs are now used primarily to assess the quality of the crystal, determine unit cell dimensions and the space group of the crystal, and scan for potential heavy atom derivatives. The mechanism of the Weissenberg camera is simpler in that the crystal is simply rotated back and forth by a few degrees. As a result, the pattern recorded on the film is more complex; however, as long as the unit cell dimensions are known, the reflections can be assigned Miller indices. The Weissenberg camera is most frequently used to assess crystal quality and to collect data at synchrotron sources.
E. D e t e c t o r s X-Rays are generally detected either by film or by an electronic device. Because tens to hundreds of thousands of weak reflections must typically be measured
Chapter 8 Diffraction Methods
405
Fig. 12 A precession PohOtographinthe hkO plane of a protein that crystallizes in a hexagonal unit cell, with a = b = 96 A; r = 106 A. c~= 13= 90~ ~, = 120~ A threefold screw axis generates sixfold symmetry in this plane.
and crystals of biological molecules gradually become disordered in the X-ray beam, recording simultaneously the intensities of as many reflections as possible is an important goal that has influenced the development of detectors. In principle, film methods have the advantage of allowing many intensities to be recorded simultaneously. Like visible light, X-rays will sensitize grains of silver halide in photographic film for subsequent reduction by the developer, and intensities can be measured with a densitometer. At low intensities, the number of grains sensitized is directly proportional to the intensity of radiation; however, at high intensities, this is no longer the case. Crystallographers deal with this problem by using a stack of X-ray films, so that the intensity of each diffracted ray is recorded accurately on at least one film. Other problems of film methods include chemical fog that results in a high background, inaccuracies in optical scanning, and scaling from film to film. Modern image plates, in which the intensities are detected by a phosphorescent screen and then transmitted to a computer via fiber optics, are being developed and are beginning to supplant other methods. Diffractometers use proportional or scintillation counters to detect X-ray photons. Proportional counters detect showers of ions produced by the incident X-rays. Scintillation counters contain materials that produce light when X-rays are absorbed and photocells that detect the signal produced. The number of photons produced is proportional to the intensity of the X-rays, although,
406
Norma M. Allewell and Jaishree Trikha again, the response may be nonlinear. Both single detector and linear diffractometers have been developed, as well as multiwire, television, and, most recently, charge-coupled device (CCD) area detectors. The principle of area detectors can be illustrated with the multiwire area detector (Fig. 13). In these detectors a scan is performed by moving the crystal in discrete rotational steps. Two sets of parallel wires with a large voltage drop between them are mounted at right angles in a box containing an inert gas. When X-rays enter the box through a w i n d o w that is transparent to X-rays, they ionize the inert gas, generating a shower of electrons that migrate to the anode. When the electrons strike the anode, they trigger an electric discharge that creates tens of thousands of ion pairs in the gas; these in turn stream to the anode and cathode, generating a signal in the wires that is transmitted to the detector. Signals from different points on the wires can be distinguished by the time they take to reach the detector, which is in turn determined by a delay time generated by a delay circuit. Although each pulse generates a response in several wires, the responses attenuate with distance from the initial ionizing event. Comparison of the responses from several wires after sensitivity corrections allows the initial ionizing event to be located accurately. Data are recorded efficiently by direct electronic readout into a computer with a large, high-speed m e m o r y system.
F. Reciprocal Lattice The rays reflected from each family of Miller planes with indices h, k, l in the crystal form a cone with an angle of 20. However, because all the reflections
Fig. 13 Schematicdrawing of a cross-section through a multiwire area dectector. Diffracted X-ray beams pass through a transparent window and are absorbed by a mixture of gases. The electrons that are released migrate to a mesh of wires, setting off signals that are detected and stored in a computer.
407
Chapter 8 Diffraction Methods
from a crystal can be assigned Miller indices, they can be arranged on a lattice analogous to the crystal lattice, the so-called reciprocal lattice, for mathematical convenience. The diffraction pattern in Fig. 12 is a section through this lattice, obtained with a precession camera designed to record sections through the reciprocal lattice directly without distortion (Section III,D). The reciprocal lattice is constructed so that the vector from its origin to any lattice point is perpendicular to the corresponding reflecting planes in the crystal and has a length equal to 1/d, the spacing between them (Fig. 14). The reciprocal lattice derives its name from the fact that its dimensions are the reciprocal of the dimensions of the crystal lattice. Intensities close to the origin in the reciprocal lattice encode low-resolution information about solvent and molecular shape; intensities far from the origin provide high-resolution information about details of the structure. The axes of the unit cell of the reciprocal lattice are designated a*, b*, and c*. When the axes of the crystal lattice are orthogonal, a* is parallel to a, b* to b, and c* to c. As noted above, lattice points in reciprocal space are identified by the same Miller indices (h, k, and 1) used to identify the reflecting planes in the crystal (Fig. 15). Because a precession photograph is an image of a single plane in the reciprocal lattice, the unit cell dimensions can be determined from the spacings between the spots, whereas the space group of the crystal can be determined from the s y m m e t r y of the diffraction pattern and its systematic absences (Fig. 16). The diffraction pattern is always centrosymmetric; that is, pairs of reflec-
(~o) i i
0 130)
>a(a*)
9
dh
~
L L
Lib
9L
L
(110)
(410) Fig. 14 Relationship between the crystal and reciprocal lattices and the Bragg planes. Crystal lattice points (O), reciprocal lattice points (D), the origin of the crystal lattice (B), and the origin of the reciprocal lattice (O) are depicted. Both the Bragg planes and the reciprocal lattice points are labeled with their Miller indices. The dashed lines connect reciprocal lattice points and the origin of the reciprocal lattice.
408
Norma M. Allewell and Jaishree Trikha h=0
1=2 c*
h=l
,
.
/
.
k=O
Fig. 15 (A) An orthorhombic unit cell in a crystal (fine lines) and the corresponding unit cell in reciprocal space (bold lines). (B) The reciprocal lattice, labeled with Miller indices. Relationships between the orthorhombic direct and reciprocal lattice cell are a* = l / a , ~ = ]3 = ~/= ~* = ]3* = ~,* = 90~ b* = l / b , V = l/V* = abc; c* = 1/r V* = 1 / V = a*b*c*.
t i o n s t h a t lie o n a l i n e t h a t p a s s e s t h r o u g h t h e o r i g i n a n d t h a t a r e e q u i d i s t a n t f r o m t h e o r i g i n w i l l h a v e t h e s a m e i n t e n s i t y (Friedel's law; s e e S e c t i o n V,B). R o t a t i o n a x e s in t h e c r y s t a l l e a d to a d d i t i o n a l s y m m e t r y ; for e x a m p l e , a t w o f o l d axis w i l l g i v e rise to t w o f o l d s y m m e t r y in t h e d i f f r a c t i o n p a t t e r n . F a c e - o r body-centered s p a c e g r o u p s a n d s c r e w a x e s r e s u l t in sets of r e f l e c t i o n s b e i n g m i s s i n g ( s y s t e m a t i c a b s e n c e s ) . F o r e x a m p l e , a t w o f o l d s c r e w axis p a r a l l e l to a in t h e c r y s t a l w i l l r e s u l t in e v e r y o t h e r r e f l e c t i o n a l o n g a* b e i n g m i s s i n g , w h e r e a s a
Fig. 16 The hkO plane in reciprocal space of a crystal with a twofold screw axis parallel to a. The diffraction pattern is centrosymmetric because of Friedel's law. The twofold screw axis results in every other reflection along a* being absent.
Chapter 8 Diffraction Methods
409
threefold screw axis parallel to r will result in two out of every three reflections along c* being absent.
G. Ewald Sphere The Ewald sphere defines the conditions for diffraction and provides an excellent opportunity to consider the relationship between Bragg's law, the crystal lattice, and the reciprocal lattice. Figure 17 shows a section through reciprocal space in the a'b* plane. The direction of the X-ray beam is defined by the vector XO that connects the X-ray source to the origin of the reciprocal lattice. If the point C on the vector XO that lies a distance of 1/A from O (the origin of reciprocal lattice) is located and a circle with radius 1 /A is drawn with this point as the center, it can be shown that only those reciprocal lattice points that fall on this circle (in this case the lattice point P) satisfy the conditions for diffraction defined by Bragg's law. If the angle between CO and CP is taken to be 20, then OP/2CP = sin 0. Moreover, because the circle was constructed so that CP = CO = 1/A, and OP, the vector between the origin of reciprocal space and a lattice point in reciprocal space, is by definition equal to l / d , OP/2CP = A/2d = sin 0, a rearrangement of Bragg's law, with n = 1. The Bragg planes corresponding to this particular reflection bisect the angle 20 and are parallel to the vector BP and perpendicular to the vector OP. When the crystal and hence the reciprocal lattice are rotated, as they are in most detection devices, different reciprocal lattice points intersect the Ewald sphere and satisfy the conditions for diffraction. Rotation around the point B in the a'b* plane generates a circle with radius 2/A; rotation about other axes sweeps out a sphere that also has a radius of 2/A, the limiting sphere (Fig. 18).
x-ray I[ ,, beam B
\'-"~
N
I
0
x
Sphere of reflection
Fig. 17 A section t h r o u g h the Ewald sphere in the plane of incident and diffracted beam vectors. This construction defines the conditions for constructive interference in reciprocal space. The sphere has a radius of 1/A. The origin of the crystal is at C; the origin of reciprocal space is at O. P(h, k, l) is a reciprocal lattice point that lies on the Ewald sphere. Because sin OBP = sin 0 = O P / 2CP = O P / 2 / A = n A / 2 d h k l , O P = 1 / d h k t.
410
Norma M. Allewell and Jaishree Trikha Ewald sphere (Sphere
x-ray
[/
~ I~"
\1
Limiting sphere
/
\
Fig. 18 A section through the sphere of reflection and the limiting sphere of reflection.
H. R e s o l u t i o n The resolution of a set of data is defined as the m i n i m u m interplanar spacing in the data set and is the m i n i m u m distance that can be resolved in the electron density map. For example, if data were collected to a 20 value of 30 ~ with CuK~ radiation with a wavelength of 1.54 A, the resolution would be d - ,~/2 sin 0 - 2.98 A. A resolution of 6 A is usually sufficient to define the molecular envelope (surface), crevices, subunits, and secondary structure; 3 usually allows the chain to be traced. At 2.5 A, most side chains and carbonyl oxygens of proteins and the functional groups on the bases and sugars of nucleic acids are visible and the endo and exo conformations of the sugars can be distinguished. At 1.5 A, many individual atoms can be seen, and much of the sequence of a protein can be deduced from the electron density map. The accuracy of the atomic coordinates is much greater, because of the knowledge of the chemical structure, bond lengths, bond angles, and noncovalent interactions expected in the structure that is incorporated into the refinement. The lower the temperature factor (Section VII,A), the greater the accuracy of the atomic coordinates. The positions of atoms with temperature factors in the range of 10-20/~2 a r e defined to within a few tenths of angstroms or less in a 2-A map. The uncertainty in coordinates can be established from Luzzati plots (Blundell and Johnson, 1976; Stout and Jensen, 1989). Several factors influence the resolution to which data are collected. The limiting sl~here is the ultimate restriction; for example, data beyond 0.77 (d = 1.54 A/2) cannot be collected with CuK~ radiation. Crystal quality imposes a second restriction; because all macromolecular crystals are imperfectly ordered, intensities become weaker as resolution increases, until eventually they are no longer above noise level. Time is also a consideration, although much less so now than in the past. The number of intensities that must be measured increases as the cube of the resolution, because the reciprocal lattice is three-dimensional. Furthermore, the average intensity decreases with resolution, so that more time is required to measure intensities accurately. The computational time required to process data, compute phases, and calculate maps also increases with resolution. However, the investment of time is usually well
Chapter 8 Diffraction Methods
411
worthwhile, because additional features of the structure are revealed, and so data are usually ultimately collected to the highest possible resolution. Use of synchrotron radiation improves resolution because its higher intensity allows weak, high-resolution reflections to be measured.
IV. Calculating Electron Density and Patterson Maps The electron density maps that are used to create models of the molecular structure are generated by carrying out a set of mathematical calculations of varying degrees of complexity on the intensities that have been measured experimentally. Initially symmetry-related reflections are simply averaged, background is subtracted, different sets of data are scaled, and the amplitudes of the reflections are calculated by taking the square roots of the reduced intensities. Phases are calculated indirectly by one of the approaches discussed in Section V. The phases and amplitudes are then combined to give structure factors and the electron density map is calculated by computing the Fourier transform of the structure factors. The following section outlines the mathematical basis of the Fourier transform.
A. Fourier T r a n s f o r m s and Structure Factors Jean Baptiste Joseph Fourier, a French mathematician, showed almost two centuries ago that all periodic functions, no matter how complex, can be decomposed into sums of sine and cosine functions (Fourier series). Because both the crystal lattice and the reciprocal lattice are periodic, they can clearly be described by Fourier series in three dimensions. What makes this so useful is that a mathematical operation called the Fourier transform can be used to calculate the Fourier series for the crystal lattice from the Fourier series for the reciprocal lattice, and vice versa. Fourier transforms relate the diffraction pattern and the atomic structure of the molecule. If we designate the Fourier series for the crystal as p, the Fourier series for the reciprocal lattice as F, and the Fourier transform operation as T, then p = TF and F T - l p . T -1 is called the inverse Fourier transform. Substituting for F in the first equation, we obtain p - TT-lp or p = p, as must be the case if the original equations are correct. What is the relationship between p and F and the structure of the crystal or the features of the reciprocal lattice? Because an X-ray diffraction pattern depends on scattering by the electrons of the structure, p is the electron density, which has large values only near atoms, p has a specific value at each point x, y, and z in the unit cell and can be represented as p(x, y, z). The terms in the Fourier series for p correspond to the periodic variations in electron density generated by the molecular structure and the symmetry of the unit cell. The physical meaning of F is a little harder to grasp. F corresponds to the Fourier transform of the crystallographic motif (generally called the molecular transform). At every point in reciprocal space, the molecular transform has both a magnitude (amplitude) and a phase relative to the origin of the unit cell. The magnitude is nonzero only at the lattice points of the reciprocal lattice, where its value is equal to the square root of the intensity of the corresponding reflection. The phase is determined by the orientation of the diffracted ray relative to the =
412
Norma M. Allewell and Jaishree Trikha
crystal lattice. The values of the molecular transform at reciprocal lattice points are known as structure factors; each structure factor can be identified by the indices of the reciprocal lattice point to which it corresponds, i.e., F(h, k, l). Structure factors are most easily manipulated in the Fourier transform if they are treated as complex numbers of the form I F I e i4'. I F I is the amplitude of the structure factor, the square root of the intensity of the corresponding diffracted ray, and 4, is its phase. The term e i4' is a complex number whose position in the imaginary plane is determined by the value of 4, (Fig. 19). Bec a u s e e i4~ = c o s ~b + i sin 4,, this term generates a wave. [For a more detailed discussion of complex numbers and their use in crystallography, see Stout and Jensen (1989).] Fourier transforms are integrals, of the general form A(x) =
a(x')e 2~xx' dx'. --co
Here the function A(x) is the Fourier transform of the function a(x'). In terms of the notation on the previous page, TF is equal to the entire integral; T and F are not separable. The inverse transformation, which generates a(x') from A(x), is given by a(x ') =
A ( x ) e - 2~xx, dx. --co
Note that only the sign of the exponent has changed. The two functions that we are concerned with are p(x, y, z) and F(h, k, l). By analogy, Fhk l =
p(X, y, z ) e 2"rri(hx+ ky + Iz)
dVc
and 1
P -- -~c ~-~ Fhkle-2"ai(hx+ky+lz)' hkl
where Vc is the volume of the unit cell. (Because the structure factors have
imaginary axis
~ B = i IFIsinq5 A = IFIcos~
real axis
Fig. 19 Vector diagram of a structure factor in the complex plane, where F ( h , k , l ) = I F I (cos 4, + i sin 4,).
413
Chapter 8 Diffraction Methods
nonzero values only at reciprocal lattice points, the integral can be replaced by a
sum.)
Note that the exponential terms in both equations establish a linkage between the crystal and reciprocal lattices because they involve both crystal coordinates and reciprocal lattice coordinates. Note also that the electron density at any point in the unit cell is a function of all the structure factors, just as each structure factor is a function of the electron density throughout the unit cell. This is in part what makes crystallography so labor intensive; to calculate the electron density at any point within the unit cell, one has to collect a full set of intensities and determine a complete set of phases. It is not possible to ask a specific structural question and answer it with a single experiment, as is possible with some forms of spectroscopy, for example, EXAFS or fluorescence energy transfer. On the other hand, once the structure factors are known, every aspect of the structure can be analyzed.
B. C o n v o l u t i o n s A convolution is a mathematical operation that is second only to the Fourier transform in terms of its usefulness in crystallography. The convolution is an integral that involves two functions and that generates a third function, a~(x') =
f+or a(x) b(x' --2
+ x) dx).
Here function a is convoluted with function b, to generate a new function a~. If b is periodic and a is not, it can be shown that function a will be repeated in the new function a~ with the periodicity of b. This property of convolutions makes them useful in describing crystal structures, because a crystal can be thought of as a motif convoluted with a three-dimensional point lattice. Convolutions have another property that makes them useful in predicting diffraction patterns from structures. The Fourier transform of the convolution of two functions is the product of their individual Fourier transforms. Apply this to a crystal and its diffraction pattern. We have just seen that a crystal can be thought of as the convolution of a motif with the crystal lattice. Then the theorem cited above predicts that the diffraction pattern of the crystal will correspond to the product of the Fourier transform of the crystal lattice and the Fourier transform of the motif. The transform of the crystal lattice is simply the reciprocal lattice. Because the motif is not periodic, its transform will be a continuous function that extends throughout reciprocal space. When the two transforms are multiplied together, the transform of the motif can be monitored in reciprocal space only at reciprocal lattice points. We now see why the geometry of the reciprocal lattice provides information only about the geometry of the crystal lattice, whereas the intensities of the diffraction pattern at the reciprocal lattice points encode information about the structure of the molecule. If we are correct, the same principles should operate in reverse. By analogy, the Fourier transform of the product of two functions should be the convolution of the two individual Fourier transforms. We have just seen that the structure
414
Norma M. Allewell and Jaishree Trikha factors in reciprocal space are the products of the Fourier transforms of the crystal lattice and the structural motif. The Fourier transform of the structure factors should then be the convolution of the inverse Fourier transform of the reciprocal lattice (i.e., the crystal lattice) with the inverse Fourier transform of the Fourier transform of the motif (i.e., the motif). As expected, then, the Fourier transform of the structure factors is the convolution of the motif with the crystal lattice, i.e., the crystal.
C. Patterson Function The first step in determining phases by isomorphous replacement with heavy atoms (discussed in Sections V,A and V,C,1) is to locate the heavy atoms in the unit cell. This can often be done with the Patterson function, a Fourier transform in which intensities, rather than structure factors, are the coefficients, P(u, v, w) = ~,, I(h, k, l)e -2~hu+kv+tw). hkl
What is the effect of substituting intensities for structure factors in this calculation? Recall that F(h, k, 1) = I(h, k, 1)1/2ei4'. Then I(h, k, l) = I F[ 2 = I F I e i4~ ] F I e -~. Now we have the product of two functions, one of which is the transform of the structure, the second of which is the structure inverted through the origin, as a result of the change in the sign of the exponent. The transform of this product, then, will be the convolution of the structure rotated through the origin with the original structure (Fig. 20). What will this convolution look like? We convolute structure I with structure 2 by placing the origin of structure 1 at each point in structure 2. If we think of the points as atoms, we have generated a map of the interatomic vectors, weighted by the product of the atomic numbers of the corresponding atoms. As a result, the heavier atoms give rise to higher peaks in the Patterson map (Fig. 20). Given this result, an alternative definition of the Patterson function in terms of electron density should be easy to accept. The Patterson function can also be defined as P(u, v, w) = I J~
p(x, y, z)p(x + u, y + v, z + w) dVc.
nit cell v o l u m e
This expression is equivalent to the first definition of the Patterson function, because the product within the integral has a value of zero except when (u, v, w) corresponds to an interatomic vector. Although this is not a useful calculation for complex structures, it can be very useful when the coefficients in the Patterson function are the changes in the intensities of the reflections from a crystal that result from binding a limited number of heavy atoms (that is, atoms with high atomic number and therefore high electron density) to the molecule being studied. Under these circumstances, the only significant peaks in the Patterson map correspond to the vectors connecting heavy atoms, because the products of their atomic numbers are much greater than the corresponding products for other pairs of atoms. This fact, plus knowledge about the symmetry of the unit cell, is often enough to allow determination of the coordinates of the heavy metal binding sites in the unit cell.
Chapter 8 Diffraction Methods
415
A
B
c
b
J .b cb
ar
c
~a I
0
0
0
0
0
0
or o
o
o
o
0
c~
0
o
~
L
o
o
0
0
~
o
o
l
o
0
0
0
0
o
o
o 'qF
0 o
0
r
~
0
o
0
0
/'Oo
lw,
w
0
0
c~
%/ ' o o
o
o d
0
0
0
0 o
Fig. 20
(A) A molecule consisting of three atoms, a, b, and c. (B) Interatomic vectors. (C) The Patterson map is derived by inverting the molecule about the origin and placing the origin of the inverted molecule on each atom of the original molecule. (D) The Patterson map for six unit cells, with the contents of one unit cell shaded. The high origin peak in each unit cell results from the self-vectors ( a - a , b - b , and c-c).
A difference Patterson map of a heavy atom derivative is shown in Fig. 21. There are two unique heavy atom positions within the orthorhombic unit cell and the two twofold axes generate four symmetry-related pairs.
V. O b t a i n i n g P h a s e s Although the amplitudes of structure factors can be calculated directly from measured intensities, their phases cannot be observed directly. Determining the phases of reflections is the principal obstacle that must be overcome in solving the structure of a crystal. The four principal approaches that have been used are discussed below. Which will be most useful in any particular project depends on the nature of the project.
A. Multiple Isomorphous Replacement The method of multiple isomorphous replacement (MIR) requires that a heavy (electron-dense) atom be introduced into the crystal without disturbing the
416
Norma M. Allewell and Jaishree Trikha
Fig. 21 Difference Patterson map for a protein that crystallizes in an orthorhombic unit cell. The Fourier coefficients are the differences in the intensities of the protein derivatized with tungstate salt and the underivatized protein. The peaks correspond to interatomic vectors involving heavy atoms (courtesy of T. Winter and L. Banaszak).
crystal packing, to p r o d u c e an i s o m o r p h o u s crystal w i t h observable changes in the intensities of the diffraction pattern. W h e n the differences in intensities b e t w e e n the diffraction patterns of crystals w i t h and w i t h o u t the h e a v y atoms have been m e a s u r e d and the positions of the h e a v y a t o m s have been defined, the phases of the reflections for the native crystal can be calculated. The a t t a c h m e n t of the h e a v y a t o m to the molecule can be either covalent or
417
Chapter 8 Diffraction Methods
noncovalent. Chemical modification has sometimes been used to attach a group covalently; for example, a number of compounds containing lead or mercury will bind to the thiol groups of cysteine residues while iodine reacts with tyrosine. Site-directed mutagenesis can be used to create sites that will react selectively with groups containing heavy atoms. More frequently, however, metal ions with high atomic numbers, often from the lanthanide series, are simply allowed to bind to naturally occurring polar or ionic sites on the protein. Such sites exist on all proteins, whether or not their function requires that they bind metals; the number of sites at which binding occurs can be restricted by adjusting the concentration of the metal ion in solution. Metal ions that have been used frequently include uranium, lead, platinum, and gold. The heavy metal derivative can be prepared either by growing the crystal in the presence of the heavy metal ion or by placing the crystal in a solution of the metal ion and allowing the metal ions to diffuse into the crystal through the solvent channels that are found between macromolecules in crystals. Crystals often survive this treatment, though occasionally they may crack. Even when crystals do not crack, it is important that the crystals remain isomorphous, i.e., that the unit cell dimensions do not change by more than --- 1%. Ideally, the only difference in electron density between the native and derivative crystals is at the site of heavy atom substitution. The bound metal ions alter both the magnitudes and the phases of the structure factors (Fig. 22). When their binding sites have been located by analyzing difference Patterson maps, their contributions to the magnitudes and phases of the structure factors can be calculated directly. These quantities and the magnitudes of the structure factors, in the presence and absence of the heavy atoms, reduce to two possible phases of each structure factor (Fig. 23). When the same procedure is carried out with a second heavy atom derivative, the phase will, in principle, be uniquely determined, because only one of the two possible phases will be common to both calculations. In fact, phases determined with heavy atom derivatives are usually accurate only to within ---40 ~ because of imperfect isomorphism and experimental errors in evaluating the small differences in intensities produced by the heavy atoms. The use of addi-
imaginary axis
A
~t
B
real axis
Fig. 22 A vector diagram illustrating how the structure factor of a heavy atom derivative, FpH is the vector sum of the structure factor of the native protein (Fp) and heavy atom (FH).
418
Norma M. Allewell and Jaishree Trikha imaginary
9
axis
..f-.,
>, real axis
Fig. 23 A vector map illustrating how the heavy atom method can be used to determine phases. Fp, FH, and FpH are the structure factors of the native protein, heavy atom, and heavy atom derivative of the protein, respectively, q~aand (~)b a r e the two possible phases of Fp determined with this derivative.
tional derivatives or other methods of phase determination is therefore highly desirable.
B. A n o m a l o u s Scattering A complementary method of determining phases also uses heavy atoms but makes use of anomalous scattering. The origin of the reciprocal lattice is generally a center of symmetry, so that reflections related by this center of symmetry with indices h, k, l and - h, - k, - l have equal intensities. The reason that this holds true is that these reflections correspond to reflections from opposite sides of the same set of planes in the crystal. This principle is often referred to as Friedel's law. When a significant amount of radiation is absorbed by a heavy atom, Friedel's law no longer holds. Resonance between the electrons excited by the X-ray beam and the natural frequencies of vibrations of other electrons in the atom creates small differences in the intensities of Friedel pairs. If the position of the heavy atom is known, two possible phases for each reflection can be derived from the differences in the intensities of Friedel pairs in a calculation analogous to the one shown in Fig. 23. Which of the two phases is correct can be determined by comparing the anomalous scattering calculation with the heavy atom calculation, or by using additional heavy atom derivatives. Because anomalous scattering effects are small, they are often close to the noise of the measurements; however, even under these circumstances they are often useful in phasing.
C. Molecular Replacement When a structure that is similar to the unknown structure is available, an initial set of phases can be generated from the known structure, an approach known as molecular replacement.
1. lsomorphous Structures The simplest molecular replacement model is one in which a crystal structure that has already been determined is altered slightly. The most frequent alter-
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ation is to allow binding of a ligand, such as a competitive inhibitor of an enzyme, a drug, or a metal ion. Often these derivatives can be created simply by equilibrating the crystal with a solution of the ligand. Determining these structures is of great value because of the light that they shed on mechanism. Note that although one would like to be able to examine the structures of e n z y m e substrate complexes, this is rarely possible, because the substrate turns over in minutes, whereas data collection generally requires days. There are a few examples, however, of such structures being determined with very poor substrates at very low temperatures and with synchrotron radiation. Experiments in which temperature is altered provide a means of probing molecular dynamics, whereas varying pH and ionic strength allows exploration of the influence of electrostatic effects on the structure of the protein. Addition of organic solvents has exciting potential as a method of identifying potential drug-binding sites. Site-directed mutagenesis also opens up the possibility of determining x 2~mutant structures for every protein containing x amino acids. Although not every mutant will crystallize in the same space group as the native protein, many will. As long as the unit cell dimensions of the derivative crystal differ from the original by no more than --~ 1A, an approximate electron density map can be generated by using the amplitudes of the derivative and the phases of the original crystal in the Fourier transform. The initial model derived from this map can then be improved by refinement. Several other transforms are useful in analyzing these structures. Difference Fourier maps are calculated by setting the coefficients in the transform equal to the differences between the magnitudes of the structure factors of the derivative and native structure and using the phases of the native structure. Only the differences in the two structures appear in the resulting electron density map. New elements of the structure, for example, a bound ligand, will appear as positive density, while conformational changes in the protein will result in pairs of positive and negative electron density on either side of the element of the structure that moves. Similarly, difference maps can be used to analyze mutant protein structures. An example is given in Fig. 24, which shows the negative electron density generated in a Fourier difference map when three Glu residues are replaced by Ala. Another approach is to calculate 2Fo - Fc maps, where the coefficients in the transform are 2Fo - Fc; Fo is the structure factor of the derivative and Fc is the original structure. This approach minimizes the bias introduced by substituting the phases of the native protein for the phases of the derivative. An example in stereo of the electron density of a dipeptidyl group calculated from a 2Fo - Fc map is shown in Fig. 25.
2. Nonisomorphous Models Frequently the only model available is one generated with crystals that are not isomorphous to those being investigated. Unfortunately, this precludes the use of the methods described above. This situation may arise when a given protein is crystallized in different crystal lattices under different sets of conditions to investigate the effects of crystal packing or solvent on the molecular structure. Single-site mutants may also crystallize with a unit cell different from the native protein. Finally, and most importantly, as more and more structures become available, one frequently finds oneself suspecting that an unknown structure is
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Fig. 24 Difference Fourier map of a mutant in which three Glu residues were replaced by Ala. Black contours are at 3o-. Note the negative density at the sites of the missing Glu residues.
v e r y s i m i l a r to that of a k n o w n s t r u c t u r e . To d e t e r m i n e w h e t h e r this is the case, o n e m u s t establish the o r i e n t a t i o n a n d p o s i t i o n of the k n o w n m o l e c u l e in the u n i t cell. A s c h e m a t i c r e p r e s e n t a t i o n of the steps t h a t are f o l l o w e d is s h o w n in Fig. 26. If the t w o s t r u c t u r e s are i n d e e d similar, their P a t t e r s o n f u n c t i o n s will also be similar, b e c a u s e P a t t e r s o n m a p s are s i m p l y m a p s of i n t e r a t o m i c vectors. I n a s m u c h as a P a t t e r s o n m a p of the u n k n o w n s t r u c t u r e can be c a l c u l a t e d sim-
Fig. 25 A stereo illustration of an electron density map at 2.2 A contoured at lo./A, showing Phe and His residues. Viewing this figure requires a stereoviewer or crossing the eyes.
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Fig. 26 The molecular replacement strategy. Zig-zag shading corresponds to the unknown molecule; fine stippling corresponds to the model. (a) The first step is to determine the orientation of the known structure in the unit cell of the unknown structure. (b) The orientation is refined with the Patterson correlation function, in which the atomic coordinates of the known structure are adjusted to maximize the correlation between the two Pattersons. (c) The refined orientation is used to position the known structure in the unit cell of the unknown molecule. (d) The rotated and translated model.
ply from its diffraction pattern, w i t h no k n o w l e d g e of phases, the relative orientations of the t w o structures can s o m e t i m e s be d e t e r m i n e d by c o m p a r i n g the t w o Patterson maps. The p r o b l e m has t w o parts; one m u s t d e t e r m i n e both h o w the u n k n o w n structure m u s t be rotated to m a k e it coincide w i t h the k n o w n structure a n d h o w it m u s t be translated. Fortunately, the t w o p r o b l e m s can be separated. The t w o structures can be t h o u g h t of as being related by the equation X 2 -- [C I X 1 -Jr- d ,
w h e r e [C] is a rotation matrix w h i c h operates o n X 1 a n d d is a vector defining a translation. The rotation matrix can be d e t e r m i n e d first w i t h o u t a n y k n o w l e d g e of the translation vector. W h e n the rotation matrix has been d e t e r m i n e d accurately, the translation vector can u s u a l l y be readily defined. Both calculations involve c o m p u t i n g the integral of the m e a s u r e d intensities of the u n k n o w n structure a n d calculated intensities of the k n o w n structure over a set of rotations a n d translations. Relatively large values of the integral indicate s u p e r p o s i t i o n s of all or part of the structure. The rotation function is calculated by integrating over only that region of Patterson space that is expected to c o r r e s p o n d to i n t r a m o l e c u l a r atomic vectors; the translation function uses i n t e r m o l e c u l a r atomic vectors to d e t e r m i n e the w a y in w h i c h the mole-
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Norma M. Allewell and Jaishree Trikha cules pack best within the unit cell. The translation vector is often harder to derive than the rotation matrix, because the value of the translation function is sensitive to small errors in orientation. A similar approach can be used to define noncrystallographic molecular symmetry. A self-rotation function is calculated by computing the integral of the product of the intensities of the unknown structure with the same set of intensities over a set of rotations within the region of Patterson space that is expected to contain only intramolecular atomic vectors. This information in turn improves the results obtained with molecular averaging (Section VII,D). When a protein contains several elements of secondary structure or more than one domain whose relative orientations may differ from those in the known structure, Patterson correlation refinement can be used to refine these orientations (Br6nger, 1990). The model parameters defining the relative orientations of the various elements of secondary structure or the domains are refined by minimizing the sum of the root-mean-square differences between experimental and calculated intensities. Initial phases obtained by molecular replacement are highly biased toward the known structure. Systematically omitting regions of the molecule and calculating new phases reduce the bias. Because all parts of the molecule contribute to each reflection, the density of the omitted residues will appear in the new map and can be used to adjust their positions in the model. An alternative and very powerful strategy is to use a single heavy atom derivative along with the molecular replacement method and to compare and combine the phases.
D. Direct M e t h o d s Direct methods depend on constraints imposed on the phases by the requirements that electron density maps have no negative density and have a nonrandom electron density distribution with isolated gaussian peaks at atomic positions. These conditions generate probabilistic relationships between the phases and amplitudes of certain pairs of structure factors that exist because every atom in the structure contributes to every structure factor. If a small set of phases can be determined for a structure, unknown phases can then in principle be calculated. This approach has been successful only with structures containing approximately 150 atoms or less, so that it is not useful in solving macromolecular structures. It is being used increasingly to refine and extend phases obtained from isomorphous replacement or anomalous scattering. The maximum entropy method is a relatively new approach that shows great promise for phasing macromolecular structures. It is most useful for improving phases at medium resolution.
VI. Building Models The Fourier transform calculates the value of the electron density within the unit cell at grid points of a three-dimensional grid whose resolution can be specified. A contour map is then drawn by computer. The contour map is analogous to a topological map, with regions in which the electron density
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(rather than the altitude) is above specified values enclosed by contours. The greater the number of electrons in an immobilized structural element, the more contours will enclose it. Before the development of computer graphics, electron density maps were analyzed by tracing sections of the electron density map onto sheets of plastic, laying the sheets of plastic on plexiglass plates, and stacking the plates to create a three-dimensional image. A half-silvered mirror inclined at an angle of 45 ~ with respect to the stack of plexiglass plates was used to superimpose the model on the electron density map. When an electron density map has been calculated, the primary sequence of the macromolecule must be fit to the map. This is a challenging task, because even high-resolution maps contain some ambiguities and low-resolution maps may be highly ambiguous. Examples of the molecular envelope being defined incorrectly, chains being traced in the wrong direction, and solvent molecules being identified as side chains have occurred. Usually the first step is to identify elements of secondary structure and then to trace the chain; that is, to decide which features of the electron density map correspond to which residues in the primary sequence. Bulky hydrophobic side chains and cysteinyl residues containing sulfur, which is relatively electron dense, are often the best landmarks. Building a model is a gradual process, in which elements of the structure are incorporated in the model as they become visible, as the electron density map improves through refinement. At the same time, errors in interpretation are corrected.
VII. Refinement Several approaches can be used to improve the electron density map by improving the initial phases and structures derived either by multiple isomorphous replacement or molecular replacement.
A. Least-Squares Refinement Least-squares refinement is a powerful general method for fitting a model defined by a set of parameters to a set of experimental observations. It was developed at the beginning of the nineteenth century by the French mathematician, Legendre. In this procedure, the parameters of the model are adjusted iteratively by minimizing the sum of the squares of the differences between the experimental quantities and the values of these quantities calculated from the parameters of the model until convergence is achieved. Least-squares refinement was the first approach used to refine macromolecular structures and is still very powerful. Because it is a purely mathematical procedure, it is more objective than other refinement procedures. The parameters of the structural model are the positions, temperature factors, and occupancies of all the atoms. Temperature factors reflect atomic motion or disorder; they modulate the contribution that each atom makes to a structure factor by a term e-B[sin 0/A]2, where B is the temperature factor. Temperature factors can also
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Norma M. Allewell and Jaishree Trikha be calculated for groups of atoms; these temperature factors are usually assumed to be anisotropic and contain several direction-dependent terms. The occupancy of each atom refers to the fraction of molecules in which the atom occupies the position specified in the model. This may be less than one when the atom is part of a noncovalently bound group (for example, a metal ion) or when an element of the structure (for example, an amino acid side chain) occupies more than one position. Both constraints and restraints can be imposed on the model during refinement. Constraints oppose changes in the values of certain parameters; for example, in the early stages of refinement, all occupancies might be constrained to be one. Restraints set limits on the values that certain parameters, such as bond lengths and bond angles, can assume. Use of constraints and restraints increases the probability of refining to the lowest energy structure. The progress of the refinement is monitored by calculating a weighted sum of residual differences between observed and calculated values, either intensities or amplitudes of structure factors, the so-called R factor. The smaller the R factor, the better the agreement between observed and calculated amplitudes, and therefore the better the model. R factors based on structure factors should be less than 0.20 for a fully refined structure at --- 2 A resolution and will sometimes be as low as 0.15. Because of the limited resolution of macromolecular structures and their conformational flexibility and hydration, R factors for macromolecules are larger than those for small molecules, which may be as low as 0.02. Luzzati plots (Section III,H) are used to estimate uncertainties in the coordinates. As in all least-squares calculations, a high degree of redundancy is important; i.e., the number of known intensities or structure factors should be greater than the number of model parameters (atomic coordinates, occupancies, and temperature factors) by a factor of 5 to 10. For example, refining the structure of a protein with 200 residues and therefore ---1500 atoms and 7500 degrees of freedom requires that at least 37,500 to 75,000 intensities be known.
B. Simulated A n n e a l i n g Recent advances in our ability to compute and minimize the energies of macromolecular structures can be used to improve the model through a procedure called simulated annealing, by analogy to the physical process of annealing. In the physical process, a solid in a heat bath is heated by increasing the temperature of the bath to a temperature at which the solid melts. When the system is cooled slowly, all the particles arrange themselves in the lowest energy state of the solid. Because steric effects are not considered in the initial fit of the model to the electron density map, simulated annealing, which minimizes the energy, is an important step in refinement. In simulated annealing, either a Monte Carlo or a molecular dynamics simulation (Brfinger et al., 1987) is used to generate Boltzmann distributions of structures at a series of temperatures (for a detailed discussion, see Chapter 9). The initial calculation is at a very high temperature (4000 K, for example); subsequent calculations are carried out at progressively lower temperatures to a final temperature of 300 K. The initial high temperature disrupts the structure and lifts it out of the local potential energy minimum, allowing a search
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for other minima. Simulated slow cooling provides access to more than one local minimum in the potential energy surface, thereby generating a larger radius of convergence than is obtained with nonlinear least-squares refinement. Shifts in atomic positions of as much as 5 A can occur. When this approach is incorporated into a crystallographic refinement, the potential energy that is calculated contains two terms,
Epotential
--
Echemical WEexperimental. -~
E chemical includes terms that depend on bond geometry, vibrations, hydrogen bonding, and nonbonded interactions; Eexperimental depends on the difference between the observed structure factors and those calculated from the atomic model. A scale factor, w, can be adjusted to strike the best balance between optimizing the geometry of the structure and minimizing the difference between observed and calculated structure factors.
C. Solvent Flattening This approach is based on the principle that regions of disordered solvent should have essentially no structure. Initial electron density maps are, however, likely to have noise in these regions, because of errors in the phases. The phases can be improved by depressing weak features that fall below a certain threshold, calculated from the estimated solvent content, recalculating phases, and repeating this calculation until convergence is achieved.
D. Molecular Averaging When the asymmetric unit contains more than one subunit, the signal-to-noise ratio can be increased by superimposing their structures, taking the average, and recalculating phases (see Glossary, Molecular averaging). The higher the symmetry, the more powerful this procedure is. It has been used to obtain structures of viruses at close to atomic resolution. It requires knowledge of the rotation and translation operators that relate the subunits.
E. Inspecting the Model Despite the power of computational methods, human intervention is still essential. No computer program is sufficiently sophisticated to incorporate all the principles of macromolecular structure that we understand today. It is important to use molecular graphics frequently in the course of the refinement to inspect the fit of the model to the electron density and to adjust the structure so as to obtain the best fit to the electron density map. The electron density gradients in difference Fourier maps indicate the directions in which atoms should be moved. These adjustments, known as real space refinement, move the structure outside local minima in the potential energy surface.
VIII. Evaluating the Model Several criteria can be used to assess the quality of the model at any stage of refinement. Backbone torsional angles can be plotted on Ramachandran plots (see Chapter 1) to assess how many fall outside allowed regions. Side-chain
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torsional angles can be compared with those observed in rotamer libraries (see also Glossary, Rotamer) derived by analyzing known structures. Although values different from those commonly observed are certainly possible, it should be possible to rationalize them in terms of interactions within the structure. Combinations of backbone and side-chain torsional angles should also be generally consistent with those observed in other structures. Temperature factors also shed light on the quality of the structure. Although high-temperature factors may reflect molecular motion or disorder in the crystal, they also indicate regions of the structure that are not well defined. The fit of the model to the electron density map is an extremely important consideration. When the fit has been optimized by real space refinement, the significance of missing density and density that the model does not account for must be carefully considered. Missing density often indicates molecular motion, whereas extra density may indicate bound solvent species or multiple conformers.
IX. Analyzing the Model Although there are no limits on the ways in which a molecular model can be used, there are certain questions that are generally asked about every new structure. The secondary structure is always mapped and interpreted in terms of known or new structural motifs (see Chapters 1 and 9). Distance plots are always generated to map long-range interactions. Relevant interatomic distances are calculated to define hydrogen and ionic bonds. The way in which the molecules pack in the crystal is scrutinized. Molecular graphics is a powerful tool as illustrated by Chapter 9 and the two computer programs included with this book. Ribbon diagrams are helpful in visualizing the overall fold, and ball-and-stick diagrams highlight side-chain positions. When cavities, solvent accessibility, or molecular interactions are the focus, the molecular surface must be defined. This is usually done by displaying dots on the surface so that the underlying structure is not obscured. The van der Waals surface is useful in identifying sterically forbidden contacts, and the solvent-accessible surface indicates positions on the surface where a solvent molecule can make contact. The extended surface maps potential binding sites. Electrostatic potential energy surfaces are useful in analyzing how electrostatic effects are involved in binding ions and ligands and in intermolecular interactions. Commercial packages with all of these capabilities are available.
X. Neutron Diffraction Although the principles of X-ray and neutron diffraction are similar, the advantages and disadvantages of the two methods are to some extent complementary. The greatest advantage of neutron diffraction is that scattering of neutrons by atoms is not a function of their atomic number. This makes it possible to distinguish atoms with similar atomic numbers that often cannot be differentiated in electron density m a p s m f o r example, nitrogen, oxygen, and
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carbon. Hydrogen can also be visualized and distinguished from deuterium. This last point is particularly important because the positions of hydrogens are often crucial in understanding the mechanism by which a macromolecule performs its function. Furthermore, the ability to distinguish hydrogen from deuterium makes it possible to use neutron diffraction to analyze molecular dynamics, by monitoring hydrogen exchange. Because hydrogen exchange in crystals tends to be slow, the kinetics cannot be defined with the same precision as in solution. Neutrons produce minimal radiation damage and have larger anomalous dispersion than do X-rays, facilitating phase determination. On the other hand, because the scattering amplitude is not proportional to atomic number, heavy atom derivatives cannot be used to determine phases. Neutron sources are few in number, difficult to maintain, and have low fluxes. Because absorption of neutrons by the sample is minimal, the low flux can be overcome to some extent by using crystals with dimensions of a few millimeters, rather than tenths of millimeters, as is the case for X-ray diffraction. Even then, measuring the intensity of a single reflection can take minutes to hours. However, collecting a complete data set from a single crystal minimizes scaling problems and the effects of variations between crystals. Neutron radiation is polychromatic and can be used for Laue diffraction, in which the diffraction patterns produced by radiation of different wavelengths are recorded simultaneously. This is useful both in determining phases and in monitoring conformational change. Monochromatic radiation is often produced by reflecting the beam off a crystal, so that the wavelength of the reflected radiation is restricted by Bragg's law. The greatest advantage of neutron diffraction for biological studies is the difference in scattering by hydrogen and deuterium. Although hydrogen, having only a single electron, scatters X-rays weakly, scattering of neutrons by hydrogen and deuterium is comparable to that of other atoms found in nucleic acids and proteins. The phase of neutrons scattered by hydrogen differs from that scattered by most other atoms by 180~ that of deuterium does not. This makes hydrogen readily identifiable as strong negative peaks in neutron Fourier maps. It also makes it possible to obtain phases by measuring differences in intensities produced by substituting deuterium for hydrogen. The difference in the phases of neutrons scattered by hydrogen and deuterium arises from differences in the interactions of their nuclear spins with the spin at the neutron. Neutron diffraction is not used to determine unknown structures at atomic resolution, because of its technical difficulty. However, it can be of great value in asking sophisticated questions about structures that have already been determined by X-ray diffraction. In these studies, initial phases can be calculated from the X-ray coordinates. An important application is in mapping the relative positions of subunits in large complexes such as viruses and ribosomes. The general approach is to disassemble the complex, selectively deuterate some components, and reassemble. Adjusting the level of deuteration adjusts the contrast between the deuterated components and the solvent. Phases can be determined by comparing the changes in intensity produced by deuteration. Neutron scattering is also useful in determining the radius of gyration of the solvent-impenetrable core of
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Fig. 27 X-Raydiffraction pattern from a polycrystalline fiber of the lithium salt of poly[d(AATT)]. This structure has the 10-fold helical symmetry of B-DNA (Chandrasekaran et al., 1994). The strong meridional reflection on the tenth layer line indicates that there are 10 base pairs per turn. The distance between spots on the zero layer line indicates the distance between helices.
the structure, a quantity that cannot be determined by other h y d r o d y n a m i c methods. The approach discussed above, of varying the H20/D20 content of the solvent (in these studies to exploit solvent contrast to highlight particular features of the structure), can also be used in these experiments.
XI. Fiber Diffraction Naturally occurring DNA, some fibrous proteins such as collagen, and some filamentous viruses form not three-dimensional crystals, but fibers, in which the long axis of the molecule is parallel to the fiber axis (see Chapter 1). Dep e n d i n g on the extent to which they are ordered, the fibers can be microcrystalline, semicrystalline, or noncrystalline. The molecules in microcrystalline fibers are ordered in three dimensions over short distances along the fiber axis, but order is not maintained over long distances. In semicrystalline fibers, the distances between molecules are fixed, but they are disordered in terms of position along the fiber axis and rotation around it. Not even the distance between molecules is maintained in noncrystalline fibers. As always, the transform of the structure is the product of the molecular and lattice transforms. Paradoxically, the more disordered the fiber, the more of the molecular transform that can be observed; however, disorder also averages the molecular transform. Because fibers are often ordered over short distances but disordered over long distances, frequently the molecular transform is sam-
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Fig. 28 Electrondensity map of an oligonucleotide (courtesy of J. Vojtechovsky and H. Berman).
pled by the lattice transform at low resolution but is continuous at high resolution. Because many of the molecules that form fibers are helical, transforms of helices have been intensively studied. The cylindrical structure of helices results in their structure factors being Bessel functions, one for each layer line in reciprocal space. Bessel functions are oscillatory, with one peak of high amplitude whose direction from the origin increases as the order of the Bessel function (or the layer line) increases, followed by a series of smaller peaks that gradually decrease in amplitude. The high-amplitude peaks form crosses in the diffraction pattern (Fig. 27). The helical parameters [radius, pitch (repeat distance), and residues per turn] and the distance between the axes of adjacent helices can be easily determined from the diffraction pattern. The distance between helices can be calculated from the distance of spots on the zero layer line from the origin. The distance between layer lines is a function of pitch, the angle between the arms is a function of the radius of the helix, and the distance between successive crosses is a function of the number of residues per turn.
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The development of automated methods for synthesizing oligonucleotides and peptides has reduced the use of fiber diffraction, because synthetic oligonucleotides and peptides usually crystallize as three-dimensional crystals whose structures can be solved at atomic resolution. Comparison of these structures with the models developed from fiber diffraction measurements provides a valuable cross-check of the biological relevance of the oligonucleotide and peptide structures and the validity of the models derived from fiber diffraction data. An electron density map of an oligonucleotide is shown in Fig. 28.
XII. Databases Several databases of three-dimensional structures that have been solved have been developed with funds from federal agencies. The major European database is located at the European Molecular Biology Laboratory (EMBL) at Heidelberg (hHp: / / www.embl-heidelberg.de). The major protein and nucleic acid structural database in the United States is based at Brookhaven National Laboratories [the Protein Data Bank (PDB)]. The database maintained by the National Library of Medicine at the National Institutes of Health will soon incorporate three-dimensional structural information (hHp://www.gdl.org). The Cambridge Structural Database (CSD) archives structures of organic and organometallic compounds, excluding biological macromolecules and long-chain polymers (htHtp: / / csdvx2.ccdc.cam.ac.uk). A nucleic acid structural database is being developed at Rutgers University, New Brunswick, N.J. (hHp: / / ndb.rutgers.edu). All the databases can be accessed through the Internet and files can be obtained with the file transfer protocol (FTP) command. The menu-driven interface of Gopher facilitates direct access to the databases through the Internet (for further discussion, see Chapter 12). Each structure is stored as a file, designated by a reference code, that includes unit cell type and dimensions, R factor, sequence or chemical structure, connectivity between atoms, atomic coordinates, temperature factors and occupancies, and bibliographic information. In addition to providing access to three-dimensional structures, the databases serve as centers for the coordination and development of database management and the development of tools to analyze three-dimensional structures effectively.
XIII. New Directions Progress on several fronts can be anticipated in coming years. At the technical level, more widespread use of CCD cameras and image plates and new methods of phase determination can be expected. Ab initio methods that rely on a combination of noncrystallographic symmetry and either direct methods or heavy metal derivatives are under development. The multiwavelength radiation produced by synchrotrons is being exploited to solve structures solely by anomalous dispersion. At the level of biological problems, membrane proteins and macromolecu-
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lar a s s e m b l i e s are likely to be t w o active areas. A l t h o u g h f e w s t r u c t u r e s of m e m b r a n e p r o t e i n s are k n o w n at this time, p r o g r e s s is b e g i n n i n g to be m a d e as a r e s u l t of d e v e l o p m e n t s in purification, t w o - d i m e n s i o n a l c r y s t a l l o g r a p h y , a n d electron c r y s t a l l o g r a p h y . The r e s o l u t i o n that can be a c h i e v e d b y i m a g e recons t r u c t i o n is i m p r o v i n g as a result of a d v a n c e s in e l e c t r o n m i c r o s c o p y a n d c o m p u t e r d e s i g n ( C h i u et al., 1993). This has b e e n p a r t i c u l a r l y u s e f u l in the area of v i r u s s t r u c t u r e . P r o g r e s s in d e t e r m i n i n g s t r u c t u r e s of p r o t e i n - n u c l e i c acid c o m p l e x e s has b e e n r a p i d in r e c e n t y e a r s a n d can be e x p e c t e d to c o n t i n u e . L a u e diffraction w i t h s y n c h r o t r o n s o u r c e s is b e g i n n i n g to be u s e d to m o n i t o r structural c h a n g e d u r i n g r e a c t i o n s (cf. Moffat, 1989). T h e d e v e l o p m e n t of large d a t a b a s e s a n d m e t h o d s of a n a l y z i n g all the inf o r m a t i o n t h e y c o n t a i n is o n e of the m o s t exciting areas at p r e s e n t . T h e d a t a b a s e s h a v e the p o t e n t i a l to m a k e p r e d i c t i n g a n d s o l v i n g s t r u c t u r e s m u c h easier, a n d , e v e n m o r e i m p o r t a n t l y , the p o t e n t i a l to g e n e r a t e n e w s t r u c t u r a l principles. T h e i r p r o g r e s s in t u r n d e p e n d s o n d e v e l o p m e n t s in c o m p u t e r d e s i g n a n d software.
References Blundell, T. L., and Johnson, L. N. (1976). "Protein Crystallography." Academic Press, New York. Br6nger, A. T. (1990). Extension of molecular replacement: A new search strategy based on Patterson correlation refinement. Acta Crystallogr., Sect. A: Found. Crystallogr. A46, 46-57. Br6nger, A. T., Kuriyan, J., and Karplus, M. (1987). Crystallographic R factor refinement by molecular dynamics. Science 235, 458-460. Cantor, C. R., and Schimmel, P. R. (1980). "Biophysical Chemistry. Part II. Techniques for the Study of Biological Structure and Function," Chapters 13 and 14. Freeman, San Francisco. Chandrasekaran, R., Radha, A., and Ratcliff, R. L. (1994). Sequence dependent conformational variation in the B-DNA double helix of poly a(AATT) 9poly a(AATT). J. Biomol. Struct. Dyn. 11, 741-766. Chiu, W., Schmid, M. F., and Prasad, B. V. V. (1993). Teaching electron diffraction and imaging of macromolecules. Biophys. J. 64, 1610-1625. Glusker, J. P., and Trueblood, K. N. (1985). "Crystal Analysis: A Primer," 2nd ed. Oxford University Press, New York. Hahn, T. (1987). "International Tables of Crystallography," Vol. A. Kluwer Academic Press, Dordrecht, Boston, and London. Jancarik, J., and Kim, S.-H. (1991). Sparse matrix sampling: A screening method for crystallization of proteins. J. Appl. Crystalogr. 24, 409-411. McPherson, A. (1982). "Preparation and Analysis of Protein Crystals." Wiley, New York. McPherson, A. (1990). Current approaches to macromolecular crystallization. Eur. J. Biochem. 189, 1-23. Moffat, K. (1989). Time-resolved macromolecular crystallography. Annu. Rev. Biophys. Biophys. Chem. 18, 309-332. Stout, G. H., and Jensen, L. H. (1989). "X-Ray Structure Determination: A Practical Guide," 2nd ed. Wiley, New York. Weber, P. C. (1991). Physical principles of protein crystallization. Adv. Protein Chem. 41, 1-36. Wyckoff, B. H. W., Hirs, C. H. W., and Timasheff, S. N., eds. (1985). "Methods in Enzymology," Vols. 114 and 115. Academic Press, New York.
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GLOSSARY Ab initio A term used to describe calculations that are based on first principles. Ab initio calculations can be used to represent the electrons of a molecule Introduction to Biophysical Methods for Protein and Nucleic Acid Research
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All rights of reproduction in any form reserved.
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by solving the Schr6dinger equation. These calculations are performed on small diatomic and other organic molecules. Algorithm The underlying iteration method or mathematical theory of any particular computer programming technique. Amphiphilir An amphiphilic a-helix has asymmetric polarity and projects mainly hydrophilic side chains in one direction, whereas the opposite surface projects mainly hydrophobic side chains. Binary file A type of file format that encodes all of the information in "computer code." This type of file format is more condensed than ASCII and often is used to store the instructions for executable computer programs such as MAGE. The FTP protocol requires a specific designation of "binary" to transfer binary files over the Internet. Conformational space An abstract description of all of the possible combinations of bond rotations and resultant conformations for a given molecule. Conjugate gradient Nonlinear optimization method that differs from the steepest descent by using both the current gradient and the previous search direction to drive the minimization. It also uses a scaling factor for determining the step size. Conservative substitutions Mutations that do not change the physicochemical character of an amino acid in a protein. For example, leucine is a conservative mutation from alanine or isoleucine and arginine is a conservative mutation from lysine. Convergence criterion When calculating a minimum energy conformation, the value of rms gradient at which the geometry optimization is considered to be complete. Disintegrins Snake venom proteins that inhibit fibrinogen interaction with platelet receptors expressed on the glycoprotein IIb-IIIa complex. They act by binding to the integrin glycoprotein IIb-IIIa receptor on the platelet surface and inhibit aggregation induced by ADP, thrombin, platelet-activating factor, and collagen. Distance matrix A two-dimensional matrix with the query and database sequences on the two axes. When a k-tuple from the database matches a k-tuple from anywhere in the query sequence, a point is plotted in the distance matrix. Docking Compared to the calculated binding affinity, ligand docking is a more qualitative description of the interaction of a ligand (drug, substrate, or peptide) with its receptor (protein or DNA). E-mail address A "mail box" name in the Intemet that describes the person and the location of the person's post office box. An example of an E-mail address is
[email protected]. This describes the E-mail address of Michael Bolger on the computer "zygote" at the Health Sciences Campus of the University of Southern California, an educational institution. Force field A completely "empirical" approach to calculating the behavior of large organic and biological macromolecules is encompassed in the molecular mechanics force field. The force field is described by a mathematical function that expresses all the energy contributions arising from geometrical and electrostatic forces on the atoms of a molecule.
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Fractional coordinates are used by crystalloFractional coordinates graphers to define the unit cell of a crystal, and must be converted into cartesian angstrom distances prior to visualization with a molecular graphics computer program.
Gap penalty A parameter used in macromolecule sequence alignment. A gap penalty is assigned for each gap that occurs in either the query or database sequence between positively scored matches in an alignment. The value of g can also be set by the user and is typically g = 4. Geometry optimization A static procedure that results in a new structure at a minimum energy that would be expected to be more populated than higher energy conformers. Hashed database Procedure for coding entries of a database into a binary or ASCII format that makes the searching algorithm run faster. Helical wheel A two-dimensional stacked circle diagram of a polypeptide secondary structure. The wheels are projections of the amino acid side chains onto a plane perpendicular to the axis of the helix. The vectors connecting each side-chain position correspond to the backbone of the polypeptide. Hydropathy
Measure of a amino acid polarity based on water-vapor transfer free energies of individual amino acids.
Hydrophilicity Characteristic physicochemical property that measures the tendency to associate with an aqueous phase. Highly hydrophilic molecules are usually polar or charged. Hydrophobicity Characteristic physicochemical property that measures the tendency to avoid an aqueous phase. Molecules with high hydrophobicity are more oily and associate with lipids. HyperChern An excellent commercial molecular modeling program (HyperCube Inc., Waterloo, Ontario, Canada) that integrates graphics, model building, geometry optimization, and molecular dynamics for the PC. Internet A network of computers interconnected by a variety of high-speed protocols; includes computers from all over the world. Computers attached to the Internet are assigned an identifying number called an IP address (Internet protocol address). The Internet is a publicly accessible source of shared information, news, and computer programs. Joining penalty A parameter used in macromolecule sequence alignment. Analogous to a gap penalty; in this fashion, sequences that have an optimal set of diagonals that can be joined to form a single alignment attain higher scores than do those sequences that have similar regions with large gaps.
k-tuple The number of consecutive nucleotide base matches that are required to be identical in a fast sequence search. Kinernages Kinetic images that show three-dimensional molecular structures and other 3D figures that serve as illustrations for specific scientific papers in the journal Protein Science. In addition, the user can create customized Kinemage files from any Protein Data Bank file. Macro language A type of computer program or script that is built into most word processing and spreadsheet programs and allows the user to automate repetitive keystrokes.
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Michael B. B01ger MAGE A computer program for viewing Kinemages. Copies of MAGE for execution on PC or Macintosh computers are included with this book.
Membrane spanning
A characteristic chain of amino acids (usually 22 amino acids) that form an a-helix, which spans a biological membrane.
Molecular dynamics
Methods that evaluate the force field energy and its analytical derivatives and move all atoms using Newton's laws of motion (i.e., in a direction and with a magnitude determined by the force or negative gradient).
Monte Carlo
Methods that use a random movement of the atoms of a molecule and, by comparing the new configuration to the old, either accept it or reject it, based on the Boltzmann factor for the relative energies.
Neural network A computer algorithm that is based on the types of connections that are observed in the nervous system. The neural network is used in a variety of computer programs related to this chapter. NEWMBB A completely hypothetical disintegrin protein, created as a thread of continuity for this chapter.
Operating system A computer program that controls the most basic functions of a computer, such as the disks, memory access, and i n p u t / o u t p u t devices. Parameterization A process of creating constants to be used in the empirical functions of a molecular mechanics force field. The parameters are generated by manual and computerized fitting to experimental data. PCGene A suite of programs for molecular biochemistry from Intelligenetics that calculate alignments and properties of macromolecules.
Polygon shading
A computer procedure that depicts the shadows on a solid object by "painting" the surface with small polygons that vary in color intensity depending on the degree of shading desired.
Potential energy surface
A mathematical description of potential energy IV(R)], as a function of molecular structure (described by coordinates R).
PREKIN A program that allows the user to create easily a Kinemage file from standard a Brookhaven Protein Data Bank (PDB) coordinate file.
Primary structure
Linear string of amino acids or nucleotides.
PROSITE A protein motif searching program and motif database. These are sequence motifs that sometimes predict function or structure.
Protein motif
A sequence of amino acids that is found in all members of a
superfamily. QUANTA A commercial molecular graphics software package (Molecular Simulations, Inc.).
Quaternary structure Noncovalent interactions between folded subunits of a multisubunit macromolecule create the oligomeric macromolecule thus defining its quaternary structure. Quenched dynamics A combination of high-temperature molecular dynamics and energy minimization.
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RasMol A molecular graphics program designed to produce publicationquality graphics. It can be executed on a wide variety of computer platforms, including personal computers. This program complements one called MAGE. Copies of RasMol for execution on PC or Macintosh computers are included with this book.
Real time A term used to describe movement or rotation of a molecular graphic image that responds interactively to commands from the user. This is opposite to movement that is prerecorded and played back as an animated motion picture. rms gradient The rate of change (first derivative) of the total energy with respect to displacement in the x, y, or z directions is a measure of the rootmean-square value of forces on all atoms, and is called the rms gradient. Secondary structure For proteins, secondary structure is created by local interactions of neighboring amino acids to produce helices, extended sheets, turns, and random coils. For nucleic acids, secondary structure is produced by H bonding between nucleic acid bases and stacking to produce helixes, loops, and bends. See Chapter 1 of this book for discussion of protein and nucleic acid secondary structures. Selective search A method of searching for sequence homology that is able to find exact matches to the query sequence. Semiempirical The most commonly used quantum mechanical calculations. These calculations make a variety of approximations to reduce the amount of computer time required and are used for calculation of atomic charges and molecular orbital energy levels. Sensitive search A method of searching for sequence homology that is able to find more distantly related sequences. These methods are used when one is attempting to trace the evolutionary origins of a particular protein or peptide. Similarity matrices Derived from an analysis of the frequency of evolutionary amino acid mutations for protein superfamilies. Dayhoff developed such a similarity matrix (PAM250) that is widely used in conjunction with searching algorithms.
Simulated annealing Cooling a computerized molecular structure slowly is called simulated annealing. Cooling is accomplished by changing the calculated velocities of the atoms of a molecule. The higher the velocity the "hotter" is the temperature of the molecule. Steepest descent Nonlinear optimization method that uses the first derivative of the potential energy with respect to the cartesian coordinates. Superfamily Proteins grouped in a superfamily generally have statistically significant sequence homology and thus presumably share a common evolutionary origin. Tertiary structure Folding of secondary structure elements to produce a variety of three-dimensional structures. See Chapter 1 of this book for discussion of protein and nucleic acid secondary structures.
Z-matrix file
Three-dimensional molecular representation that is built by
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specifying the geometrical relationships based on distance, angle, and dihedral angle.
ACRONYMS AMBER Assisted Model Building and Energy Refinement; for protein and nucleic acid computations. This force field was developed and parameterized by members of Peter Kollman's research group at the University of California, San Francisco. AMBER is the most widely used force field for macromolecular calculations, and extensive work has gone into developing it. Anonymous FTP File Transfer Protocol; a computerized method for transfer of ASCII or binary files between computers on the Internet. Private FTP is utilized by registered users of particular computers to exchange files. Anonymous FTP is a procedure that anyone with access to the Internet can use to exchange files on selected computers. The FTP command is followed by an Internet protocol (IP) address (128.200.80.20) or a computer name (orion.oac.uci.edu). ASCII text American Standard Code for Information Interchange; ASCII text is the lowest common denominator for exchange of information. The ASCII code covers 128 standard characters, including numbers, uppercase and lowercase letters, and some formatting characters such as line feed, tab, and space. CHARMM Chemistry at Harvard Macromolecular Mechanics; CHARMM is the force field that was developed in the laboratory of Martin Karplus as a united atom force field. EVB Electron Valence Bond; one of the most effective ways of simulating enzymatic reactions is provided by the empirical valence bond method. The EVB method represents the enzymatic reaction or the change in structure due to mutation in terms of valence bond resonance structures. FEP Free Energy Perturbation; a method used with molecular dynamics simulations to calculate the change in macromolecular properties following mutation or change in ligand structure. GUI Graphical User Interface; a user interface for a computer program that supports multiple-application windows and graphical input devices such as the mouse and trackball. MM2 Molecular Mechanics 2; MM2, developed by Norman Allinger, is one of the most widely used molecular mechanics force fields and has been parameterized primarily for small organic molecules.
OPLS Optimized Potentials for Liquid Simulations; OPLS is a united atom force field developed by the research group of William Jorgensen and is designed for calculations on proteins and nucleic acids. PDLD Protein Dipoles Langevin Dipoles; in contrast to macroscopic methods, the PDLD method divides the protein into three regions.
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QCFF/Pi Quantum mechanical extensions of the Consistent Force Field to Pi electron systems; one of the earliest and most sophisticated force fields, developed by Lifson and Warshel.
I. Introduction The preceding chapters of this volume have described a variety of techniques for determining the structure and properties of proteins and nucleic acids. In this chapter, the data collected by those techniques will be used in conjunction with computational and visualization tools in order to create a graphical representation of the experimental structures, to generate hypothetical model structures based on sequence homology methods, and to predict new physical properties. This discussion will focus on practical aspects needed to use existing computational tools for determination of sequence homology, secondary structure predictions, hydropathy analysis, three-dimensional computer modeling, macromolecular docking, and calculation of binding free energy and catalytic properties. The theoretical basis of selected tools and computational methods will be compared in terms of ease of use, computer resources required, and validity of resultant structures and properties. Most people associate molecular modeling with the beautiful pictures of biological molecules that are produced by the current generation of graphics workstations. Surprisingly, much of our understanding of function and homology can be determined from an analysis of primary structure, and such an analysis is an essential prerequisite to the procedures of secondary and tertiary structure analysis.
II. Sequence Homology The most basic knowledge of a new structure comes from its primary nucleotide or amino acid sequence. In the classification scheme devised by Dayhoff, the largest grouping of proteins is the superfamily (Schwartz and Dayhoff, 1978). Proteins grouped in a superfamily generally have statistically significant sequence homology and thus presumably share a common evolutionary origin. Proteins within a superfamily may have developed quite different specific functions, but often share similar three-dimensional structure. In spite of the specific differences in the function of superfamily members, the common aspects of their three-dimensional structure usually confer a common mechanism of action. For example, the nicotinic acetylcholine receptor and the 3,-aminobutyric acid (GABA) receptor are both members of the ligand-gated ion channel family, but have different biological actions. Thus, the common functional relationships between members of protein superfamilies are based on the comparable folding patterns of their primary sequences. Thermodynamic forces act on those sequences to create reproduci-
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Michael B. Bolger bly biomolecules capable of a vast array of important physiological functions. These biomolecules are responsible for all aspects of life (physical, mental, emotional, and perhaps even spiritual). In spite of its importance, there has been no success in understanding the "algorithm" of this natural process of information transfer (DNA ~ RNA ~ folded protein) for individual sequences (Lesk and Boswell, 1992). However, it has recently become clear that sequence homology, and knowledge of the structure of key members of a superfamily, can provide valuable structural information for previously unknown biomolecules. At the least, sequence homology methods provide knowledge of a biomolecular class and possible function. At best, sequence homology methods combined with molecular modeling provide detailed high-resolution threedimensional structures that have been highly predictive of experimentally determined structures (Benner and Gerloff, 1991).
A. Fast Database Searching Methods
1. Selective Searching Methods There is always a tradeoff between sensitivity and selectivity in biological sequence comparison. Highly selective search methods are able to search a database for exact matches to the query sequence. These methods are important when searching for proteins that contain specific peptides or consensus sequences. For example, a search for proteins that participate in cell adhesion would concentrate on proteins that contain a consensus sequence of Arg-GlyAsp (RGD). There would be no need to look for closely related or distantly related sequences. By contrast, highly sensitive methods are able to find more distantly related sequences. These methods are used when one is attempting to trace the evolutionary origins of a particular protein or peptide. In order to use computer-based sequence searching programs effectively, it will be important to understand qualitatively the computer algorithms and the variable parameters that can be adjusted by the user. One of the most important advances in our understanding of biological superfamilies involved the development of fast methods for searching sequence databases. Prior to 1983, the fastest computer algorithms required 8 hr of computer time on a VAX 11/750 to compare a 200-residue protein to the 2500 protein sequences (500,000 residues) that existed in the National Biomedical Research Foundation (NBRF) library at that time. In 1983, Wilbur and Lipman reported a new computer algorithm for the global comparison of sequences based on matching k-tuples of sequence elements. This method reduced the search time from 8 hr to approximately 3 min. Needless to say, this improvement in searching efficiency has produced a quantum leap in our understanding of the evolutionary relationships among protein families. Considering that the number of new sequences is growing exponentially (the SWISS-PROT protein database alone has 43,470 sequences as of Feb. 1995), efficient searching algorithms are very important in molecular modeling. A k-tuple is the first adjustable parameter that is found in all of the modern sequence-searching algorithms. In order to learn about the computerized methods used in molecular modeling, let us assume that we are conducting biophysical research on snake toxins and have isolated, purified, and sequenced a
Chapter 9 Macromolecular Structural Analysis NEWMBB
Arg Ile Cys CGA ATC TGC Asn AAC
5 Tyr Asn His TAC AAC CAC
i0 Leu Pro Thr Thr Glu Cys Thr Gln CTA CCA ACA ACA GAG TGC ACG CAG
25 Ile Trp Arg Asn Cys Thr ATC TGG CGT AAC TGC A C A
45 Pro Arg Gly Cys Arg Thr CCT CGT GGT TGC CGT ACT Asp Lys GAC A A G
Cys Asn TGC AAC
441
Ser Cys Tyr TCA TGC TAC
20 Lys AAG
30 35 Phe Gly Asn Cys Cys Arg Asn Cys Arg Phe Gly Thr TTC GGA AAC TGC TGC CGA AAC TGC CGA TTC GGA ACT
40 Lys AAG
50 Pro Arg Gly Asp Met CCT CGC GGC GAC ATG
15 Glu Asp GAG GAC
55 60 Pro Gly Pro Tyr Cys Ala Cys Glu Ser CCC GGC CCA TAC TGC GCA TGC GAG TCA
65 Leu CTA
Seq. $1 By convention, sequences are usually presented from the N-terminal amino acid to the C-terminal amino acid. Nucleotide sequences are stored in a 5' to 3' sequence order. Computer algorithms for finding the translated protein sequences can use one of three nucleotide frame shifts and can translate in the 3' to 5' sequence order as well for a total of 6 possible reading frames.
n e w protein from snake v e n o m with the D N A and protein sequences given in Seq. $1, NEWMBB. We need to find all of the protein sequences in the various protein databases that contain this exact sequence. In addition, we w o u l d like to k n o w if there are other sequences that are closely related to this sequence that might provide a clue to the structure or function of the n e w sequence. One strategy for searching the sequence databases w o u l d be to line up $1 with the N terminus of the first sequence in the database ($2) and check each position for a match. If all amino acids match, then we have found an identical sequence. If there is no match to all amino acids, then we might w a n t to k n o w if some of the amino acids matched. In addition, we w o u l d w a n t to m o v e the whole sequence d o w n by one amino acid and compare for a match again. It is easy to see w h y the n u m b e r of computations in this type of comparison w o u l d be proportional to N • M, w h e r e N and M are the n u m b e r of amino acids in $1 and $2, respectively. Wilbur and L i p m a n (1983) used the concept of k-tuple matches and distance matrix generation in order to reduce the n u m b e r of computations. The k-tuple p a r a m e t e r determines h o w m a n y consecutive identities are required in a match. For example, if k-tuple = 4 for a D N A sequence comparison, only those identities that occur in a run of four consecutive nucleotide base matches are examined. For proteins, using k-tuple = 2 corresponds to dipeptide matches that occur rarely between r a n d o m l y related proteins. In order to enhance the speed of the comparison algorithms, Wilbur and L i p m a n a d o p t e d a m e t h o d of encoding data into a lookup table of k-tuples. This means that they assigned a numerical value to all possible k-tuple sets for the alphabet that w o u l d be used ( D u m a s and Ninio, 1982). In D N A sequence searching, the " a l p h a b e t " is four letters (A, T, G, C). If k-tuple = 2, then the lookup table w o u l d be a one-dimensional matrix of numbers, w h e r e 1 = AA, 2 = AT, 3 = AG, 4 = AC, 5 = TA, 6 = TT, 7 = TG, . . . , and so on. The size of this matrix w o u l d b e / , where p is the n u m b e r of elements in the alphabet (usually 4 for DNA, and 20 for amino acids). Thus, for D N A k-tuple = 2, there w o u l d be 42 = 16 possible combinations, and for a protein search with k-tuple = 2, there w o u l d be 2 0 2 = 400 possible combinations. Next, in one pass t h r o u g h $1 the query sequence can be coded into n u m b e r s for each k-tuple in the sequence. For
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Michael B. Bolger example consider the following short DNA query sequence (Seq. Sq): Seq. Sq
A T G G C A T T A
This would correspond to the following integer-coded k-tuples: 2 711 1213 2 6 5 In like fashion, the database sequences can be hashed, or coded into numbers for the common k-tuples that are to be used. Now, in one pass through each database sequence ($2), all of the matching k-tuples in the query sequence (Sq) and their relative distances can be recorded and plotted in a distance matrix. A distance matrix is a two-dimensional matrix with the query and database sequences on the two axes. When a k-tuple from $2 matches a k-tuple from anywhere in Sq, a point is plotted in the distance matrix. A diagonal starting at position I with a slope of - 1 would indicate a perfect match between Sq and $2. Other diagonal elements in the distance matrix represent series of k-tuple matches that are not perfectly aligned but might represent a significant comparison. By this method the algorithm provides matching sequences that do not necessarily have to be exact matches. At this point some comparison of the quality of the matches must be determined. The second adjustable parameter in sequence searching is called the window space = w. In a comparison, some of the diagonal elements will contain many, and others only a few, k-tuple matches. A diagonal is considered to be significant if it contains a number of k-tuple matches that is a certain number of standard deviations above the mean for all diagonals with at least one k-tuple. The user sets the values of k and w prior to initiating the database search. Typically, when k > 1 and w is of reasonable size (---20), the search of a sequence database can be completed quite rapidly. Once the significant diagonals have been determined, an alignment of the query (Sq) and database ($2) sequences is produced and assigned a relative score. The alignment and scoring procedures are usually based on the method of Needleman and Wunsch (1970). A score of + 1 is assigned for all k-tuple matches that occur adjacent to each other and within the window space for that diagonal. A penalty of - g is assigned for each gap that occurs in either sequence between positively scored matches in an alignment. The value of g can also be set by the user and is typically g = 4. Most sequence searching programs produce only one possible alignment with the highest score. A score is generated for each sequence in the database and corrected for the relative length of the sequence. Naturally, most of these sequences will not be significantly related to the query sequence and by averaging all of the scores in a given database, a random matching score is generated. This random mean score is compared to the length-corrected score for each sequence by Eq. (1) to give a z score (Doolittle, 1981), z = (Corrected score - mean score)/standard deviation.
(1)
In this fashion, the best scoring sequence matches and their alignments can be ranked for more detailed analysis. An enhanced version of the method described above has been implemented in a publicly available program called FASTP and in a number of commercially available programs that run on UNIX, IBM-compatible, and Apple
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Macintosh computers (Lipman and Pearson, 1985). A search of the SWISS PROT database using NEWMBB (Seq 1) as the query sequence with k = 2, w = 20, and g = 4 produced the results shown in Table I. Table I lists the 20 top-scoring sequences retrieved by the program (IFIND, Intelligenetics) from 20,772 sequences in the SWISS PROT protein database (1991 version). Figure 1 shows the alignment for the top-scoring protein and a more distantly related protein, TXS5$DENJA and DISI$AGKRH, respectively. The first protein is a 61-amino acid short toxin ($5C1) with four disulfide bonds from Dendroaspis jamesoni kaimosae (eastern Jameson's mamba). This toxin is surprisingly nontoxic and has not been studied in very much detail. The second protein is a 68-amino acid disintegrin, kistrin, a platelet aggregation activation inhibitor from Agkistrodon rhodostoma (Malayan pit viper) with five disulfide bonds. The disintegrins all have a characteristic RGD (Arg-Gly-Asp) sequence near the C terminus and inhibit fibrinogen interaction with platelets, by binding to the gp-IIb-IIIa receptor on the platelet surface. Reduction of the disulfide bonds of the disintegrins effectively reduces the activity of the peptides several hundredfold. These two matches show the range of similarity that can be achieved by using a fast sequence-searching algorithm. One can see that the top-scoring match is very closely related to the query sequence in both the N-terminal and C-terminal domains (78% homology). The N-terminal domain is characteristic of snake toxins, and the C-terminal domain is typical of cell adhesion proteins that contain an RGD consensus sequence. Most of the high-scoring proteins were isolated from snake venom and belong to the class of disintegrin proteins. These matches obtained a score between 6 - 8 and are more distantly related but
Table I Top Scoring Sequences Retrieved by Program IFIND a RANK
SEQUENCE
LENGTH
SCORE
STD-DEV-FROM-MEAN
1 2 3 4 5 6 7 8 9 I0 ii 12 13 14 15 16 17 18 19 20
TXS5$DENJA DISI$AGKHA DISI$BITAR DISF$TRIFL DIST$TRIFL DISI$BOTAT DISI$TRIEL NXS2$DENJA NXSI$DENJA NXSI$DENPO NXSI$DENVI DISISAGKRH DISI$ECHCA NXSI$HYDLA NXSI$ACAAN NXS2$AIPLA NXS4$AIPLA PA2$ENHSC VE7$BPVl VE7$BPV2
L=61 L=71 L=83 L=70 L=70 L=71 L=73 L=58 L=60 L=60 L=60 L=68 L=49 L=60 L=62 L=81 L=81 L=II9 L=127 L=127
33 9 9 8 8 8 8 7 7 7 7 7 6 6 6 6 6 6 6 6
42.12 8.61 8.61 7.21 7.21 7.21 7.21 5.81 5.81 5.81 5.81 5.81 4.42 4.42 4.42 4.42 4.42 4.42 4.42 4.42
a Mean
score
= 2.84; standard
deviation
= 0.72.
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Michael B. Bolger I.
NEWMBB(I-65) TXS5$DENJA
S C O R E = 33 S H O R T T O X I N 5CI.
X I0 20 30 40 R I C Y N H L .... P T T E C T Q EDS C Y K N I W R N C T F G N C C R N C R F G T K P R G
llfilfl
lllillllIillilillJ
JJ J
RI C Y N H L G T K P P T T E C T Q E D S C Y K N I W R N I T F D N I R R G C X I0 20 30 9 9 NEWMBB
(i-65)
DISI$AGKRH
SCORE
X i0 RI C Y N H L P T T E C T Q E D S
: i
i
- 7
DISINTEGRIN
I
KISTRIN
I I
50 60 X CRT PRGDM PGPYCAC E S D KCNL
II IIilllilllf
....... GCFTPRGDMPGPYC40 50
(PLATELET
AGGREGATION
ACTIVATI
20 30 40 50 60 CYKNIWRNCTFGNCCR/~CRFGTKPRGCRTPRGDMPGPYCACESDKCNL
:i
:I
I[i
:I:I
GKECDCS S P ENPCCDAATCKLRPGAQCGEGLCCEQCKFSRAGKI X I0 20 30 40
:: il illlll
lllllIll
CESDKCNL 60
I
I
X
I
CR I PRGDMPDDRCTGQSADCPRYH 50 60 X
Fig. 1 Alignment of two proteins with the query protein sequence of NEWMBB. Search was conducted on the SWISS PROT database using the program IFIND (IntelliGenetics Inc.). 1, Alignment of TXS5$DENJA (short snake toxin) and NEWMBB; 9, alignment of DISI$AGKRH (distintegrin kistrin) and NEWMBB. Identity is noted by "1" and conservative substitution is noted by ":" Amino acids said to be "similar" are grouped according to Dayhoff: Hydrophilic: (small-A,P,G); (hydroxyl-S,T); (acidic-D,E); (acid amide-N,Q). Basic: (R,K,H). Hydrophobic: (aliphatic-I,L,M,V); (aromatic-F,Y,W).
still have significant homology (45% homology). The following is a rule of t h u m b for determining the significance of homology matches from this type of search. Score Z-value: Z > 3 possibly significant; Z > 6 probably significant; Z > 10 significant. So far these results tell us that the new protein is highly related to the snake toxins, probably will not be very toxic, and might be involved in functions of the RGD class of disintegrin molecules that are able to inhibit platelet aggregation. This is a lot of information for such a small investment in computer time.
2. Sensitive Searching Methods More recent advances in searching algorithms have addressed the need to find sequences that are more distantly related to the query sequence. These methods are valuable w h e n questions of evolutionary relationships are being asked, but they are of less value w h e n a highly homologous sequence with a k n o w n 3D structure is being sought. The most c o m m o n method of expanding the sequence search to include more distantly related sequences involves the use of conservative amino acid substitutions and the use of amino acid similarity matrices that are derived from an analysis of the frequency of evolutionary amino acid mutations for protein superfamilies. Dayhoff developed such a similarity matrix (PAM250) that is widely used in conjunction with the searching algorithm described above (Schwartz and Dayhoff, 1978). Sensitive search methods take advantage of the fact that amino acid replacements occur far more frequently than insertions or deletions. In the PAM250 matrix, matching k-tuples that contain rare amino acids (such as cysteine and tryptophan) receive higher scores than matches a m o n g more c o m m o n amino acids (such as serine and alanine). Also, replacements that have occurred frequently in evolution (such as methionine ---* leucine) receive positive scores. However, unlikely substitutions (such as cysteine ~ tryptophan) receive negative scores. As one might expect, sensitivity is greater w h e n a k-tuple value of I
Chapter 9 MacromolecularStructural Analysis
445
is used. When the Dayhoff matrix does not match the type of search required by the researcher, the matrix can be edited to suit the type of matches that are desired. A similarity matrix based on the genetic code (GCM) reflects the maximum numbers of nucleotides that the codons for two amino acids may have in common. For example, a score of + 3 is assigned to amino acid pairs that are identical, + 2 for pairs whose codons must differ by at least one nucleotide, + 1 for those whose codons must differ by two nucleotides, and 0 for those whose codons cannot have any nucleotides in common. In like fashion, similarity matrices can be based on any property of amino acids that can be expressed numerically (George et al., 1990). In addition to using a similarity matrix approach, the searching programs FASTA (Pearson and Lipman, 1988) and FASTDB (Brutlag et al., 1990) perform a check to see whether several of the diagonal elements can be joined to form a longer homologous region. To accommodate for this in comparing a query sequence to the database sequences, an additional parameter call the joining penalty (analogous to a gap penalty) is used. In this fashion, sequences that have an optimal set of diagonals that can be joined to form a single alignment attain higher scores than those sequences that have similar regions with large gaps. These methods provide improved sensitivity with a small loss of selectivity and a negligible decrease in speed. Many other programs based on variants of this method have been developed. One variant, called LFASTA, is used to find local matching regions within a single protein (Pearson and Lipman, 1988). These local similarity searches can detect the results of gene duplication or repeated structural features. Table II is a listing of the output from FASTDB (Intelligenetics) applied to the search for matches to Seq. S1. By using a sensitive searching algorithm (FASTDB) based on the Dayhoff protein similarity matrix, sequences that are more distantly related to the snake toxins were found. In addition to a number of disintegrins and short neurotoxins, hemorrhagic protein HRIB (Fig. 2) was found, with only limited homology (26% of NEWMBB sequences matched and only 4% of the hemorrhagic protein residues matched). The hemorrhagic protein is a zinc protease (416 amino acids) from Trimeresurus flavoviridis (Habu) that is not related in function to our NEWMBB hypothetical protein (Takeya et al., 1990). Interestingly, the hemorrhagic protein retains many of the cysteine residues of the snake toxins and the disintegrins and most likely folds in a similar manner in this region of the protein. The tertiary structure of the disintegrins is determined predominantly by the pattern of disulfide bonds formed between adjacent cysteine residues in the proteins. Later in this chapter, we will investigate methods for developing a three-dimensional model of our new protein based on homology with the disintegrins. Besides the SWISS PROT protein database, other types of databases are available. Table III lists some of the most accessible sequence and 3D structure databases. Both public domain and commercial programs are available for searching these databases, which are most conveniently accessible by using a Gopher program or E-mail service on the Internet (Hahn and Stout, 1994). For example, one can search the SWISS PROT database using a sensitive search method, by submitting an appropriately formatted E-mail query to
[email protected]. BLITZ is a completely automated searching program that runs with-
446
Michael B. Bolger Table II Results of Application of FASTDB (Intelligenetics) to the Search for Proteins Similar to Seq. $1 Similarity matrix PAM-150 T h r e s h o l d l e v e l of sim. 16% Mismatch penalty 1 Gap penalty 4.00 Gap size penalty 0.05 Cutoff score 1 Randomization group 0 I n i t i a l s c o r e s to save 20 O p t i m i z e d s c o r e s to s a v e 20 Scores:
Mean 26
Times:
K-tuple Joining penalty Window size
A l i g n m e n t s to save Display context
SEARCH STATISTICS Median 28
CPU 00:01:03.94
N u m b e r of r e s i d u e s : N u m b e r of s e q u e n c e s o p t i m i z e d : Randomization group 0
10 32
Standard 1.19
20 0 Deviation
Total Elapsed 00:01:04.00 1633010 3908
T h e s c o r e s b e l o w are s o r t e d b y o p t i m i z e d score. S i g n i f i c a n c e is c a l c u l a t e d b a s e d on o p t i m i z e d score. A 100% The
identical
list of b e s t
Sequence
Name
1. T X S 5 $ D E N J A 2.
DISI$AGKRH
3. 4. 5. 6.
DIST$TRIFL DISF$TRIFL DISI$TRIEL DISI$BOTAT
7. DISI$AGKIIA 8. D I S I $ B I T A R 9. D I S B $ T R I G A i0. ii.
DISA$TRIGA DISG$TRIGA
12. H R I B S T R I F L 13. V D E L S B P P 4 14. 15. 16. 17. 18. 19. 20.
CYC$TROMA ODP2$BACSU CYC$CUCMA NXSISDENPO K2CA$BOVIN NXS2$AIPLA NXSI$DENVI
sequence scores
to the q u e r y
s e q u e n c e w a s not
is:
Description
Length
found. Init. Opt. Score Score
**** 15 s t a n d a r d d e v i a t i o n s a b o v e m e a n S H O R T T O X I N $5CI. 61 **** II s t a n d a r d d e v i a t i o n s a b o v e m e a n DISINTEGRIN KISTRIN (PLATELET 68 **** I0 s t a n d a r d d e v i a t i o n s a b o v e m e a n D I S I N T E G R I N T R I F L A V I N (RGD-CO 70 D I S I N T E G R I N F L A V O R I D I N (RGD-C 70 D I S I N T E G R I N E L E G A N T I N (PLATEL 73 D I S I N T E G R I N B A T R O X O S T A T I N (PL 71 **** 9 standard deviations above mean DISINTEGRIN HALYSIN (PLATELET 71 DISINTEGRIN BITAN (PLATELET A 83 D I S I N T E G R I N T R I G R A M I N B E T A (P 73 **** 8 standard deviations above mean DISINTEGRIN TRIGRAMINALPIIA ( 72 DISINTEGRIN TRIGRAMINGAMMA ( 73 **** 7 standard deviations above mean H E M O R R H A G I C P R O T E I N IIRIB (EC 416 **** 6 standard deviations above mean T R A N S A C T I V A T I O N P R O T E I N (GENE 166 **** 4 standard deviations above mean CYTOCIIROME C. III DIHYDROLIPOAMIDE ACETYLTRANSF 441 CYTOCIIROME C. iii SHORT NEUROTOXIN 1 (NEUROTOXI 60 K E R A T I N , T Y P E II C Y T O S K E L E T A L 182 SHORT NEUROTOXIN B PRECURSOR. 81 SHORT NEUROTOXIN 1 (NEUROTOXI 60
**** 28 **** 15 **** 24 23 23 14 **** 23 28 22 **** ii 19 **** 18 **** ii **** 9 7 9 I0 12 9 9
Sig.
Frame
4,3
15.29
0
39
11.47
0
38 38 38 38
10.51 10.51 10.51 10.51
0 0 0 0
37 37 37
9.55 9.55 9.55
36 36
8.60 8.60
35
7.64
34
6.69
32 32 32 32 32 32 32
4.78 4.78 4.78 4.78 4.78 4.78 4.78
Chapter 9 Macromolecular Structural Analysis 12.
NEWMBB (1-65) HRIB$TRIFL HEMORRHAGIC
Initial Residue Gaps
Score Identity
= = =
18 26% 15
X I0 RICYNHLPTT-
:I I I
447 PROTEIN
HRIB
(EC
3.4.24.1).
Optimized Score = 35 Matches = 21 Conservative Substitutions
Significance Mismatches
= = =
7.64 42 2
20 30 40 50 ECTQEDSCYKNIWRNCTFGNCCRNCRFGTKPRGCRTPRGDMPGP-
I
II
I
I
I II
III I
II
PVCGNELLEAGEECDCGS PENCQYQCCDAASCKLHSWVKCESGECCDQCRFRTAGTECRAAESECDI X 220 230 240 250 260 270
9
I
YCA
I
PESCT 280
60 X CESDKCNL
I
I
GQSADCPT 290
Fig. 2 Alignmentof HRIB$TRIFL(hemorrhagic protein) and NEWMBB.Search was conducted on the SWISS PROT database using the sensitive searching program, FASTDB (IntelliGenetics, Inc.). Identity is noted by "1" and conservative substitution is noted by .....
out h u m a n intervention on a very fast computer. For example, a search for proteins that are homologous to Seq. S1 NEWMBB through the SWISS PROT database (33,329 sequences, 11,484,420 residues, using k = 2, PAM200) on the MasPar computer required just 22.20 sec at the European Molecular Biology Laboratory (Heidelberg, Germany). In a similar fashion, the search methods of Lipman and Pearson, as implemented in the p r o g r a m FASTA, can be used to search the GenBank, EMBL, or SWISS PROT by sending E-mail to
[email protected]. The search results from both of these programs are returned by E-mail within a few hours. For additional information about h o w to use these programs send E-mail to either of the addresses above with a single word, "HELP" located in the b o d y of the message. A complete d o c u m e n t describing h o w to use the programs will be returned automatically by E-mail on the Internet (depending on the a m o u n t of Internet traffic, the t u r n a r o u n d time on this varies from 5 min to several hours). If faster results are required, several companies provide custom " h a s h e d " versions of the databases and proprietary software (Intelligenetics Suite, PCGene, etc.). In most cases the proprietary software is based on the searching algorithms that have been described here. The National Center for Biotechnol-
Table III Public Databases of Sequences and 3D Data Database name
Type
Availability
GenBank SWISS PROT PIR EMBL Brookhaven Cambridge Crystallographic
Nucleic acid Protein Protein Nucleic acid 3D-protein 3D-smallmolecule
CD-ROM, Internet CD-ROM, Internet CD-ROM, Internet CD-ROM, Internet CD-ROM, Internet Private
448
Michael B. Bolger ogy Information (NCBI) of the NIH provides free software [by FTP on the Internet from "ncbi.nlm.nih.gov" (see Table XVII, later in chapter, for FTP sites)] and access to the latest versions of the databases described in Table III.
3. Additional Information for Researchers GenBank (release 80.0) contains 164 megabases of sequence and is doubling in size every 21 months. The SWISS PROT protein database currently has more than 43,000 sequences. A number of advanced issues regarding sequence searching methods, including choice of scoring systems, the statistical significance of alignments, the masking of uninformative or potentially confounding sequence regions, the nature and extent of sequence redundancy in the databases, and network access to similarity search services, are presented in a review by Altschul et al. (1994). A technique using pattern-matching discriminators allows for sequence alignment of protein families showing low sequence homology, such as the for G-protein-linked receptors (Attwood et al., 1991).
B. PROSITE Protein Motif Searching The use of protein sequence patterns (or motifs) to determine the function(s) of proteins is very rapidly becoming one of the essential tools of sequence analysis. Having isolated and purified a new protein, or having a derived amino acid sequence of a new protein, a search for short sequences that are diagnostic of certain binding properties or active sites can provide valuable information about the structure and function of the unknown protein. In some cases, the structure and function of an unknown protein which is too distantly related to any protein of known structure to detect its affinity by overall sequence alignment may be identified by its possession of a particular cluster of residue types classified as a motif. The motifs, or templates, or fingerprints, arise because of particular requirements of binding sites that impose very tight constraint on the evolution of portions of a protein sequence [Lesk, 1988].
PROSITE is a compilation of sites and patterns found in protein sequences (Bairoch, 1991; 1993). As of February 1994, PROSITE contained 715 documentation entries that described 926 different patterns. When our new protein is compared to the dictionary of PROSITE sequence motifs, the sites shown in Fig. 3 are identified. The most significant site found by PROSITE for the peptide NEWMBB is the signature for disintegrins: Consensus pattern: C-x(2)-G-x-C-C-x-[NQRS]-C-x-[FM]-x(6)-C-[RK] These patterns are interpreted using the single-letter code for amino acids. Residues in brackets [NQRS] indicate a variable selection of one of the listed amino acids at that position. A sequence of any amino acid type is represented by x(I), where (I) is the number of amino acids in that variable stretch. The PROSITE on-line documentation contains additional information about each type of signature. The PROSITE schematic representation of the structure of a
Chapter 9 Macromolecular Structural Analysis " DETECTION
OF S I T E S
Done
on
sequence
DE OS
DISINTEGRIN AGKISTRODON
AND
SIGNATURES
449 IN A P R O T E I N
SEQUENCE
*
NEWMBB. NEWMBB (PLATELET AGGREGATION HALYS BLOMHOFFI (MAMUSHI).
ACTIVATION
INHIBITOR).
T o t a l n u m b e r of r e s i d u e s is: 65. A n a l y s i s done on the c o m p l e t e s e q u e n c e . W a r n i n g : all the sites, r e g i o n s and s i g n a t u r e s d e t e c t e d b y this p r o g r a m are o n l y P O T E N T I A L L Y b i o l o g i c a l l y s i g n i f i c a n t . P l e a s e use the 'textbook' o p t i o n to l e a r n m o r e a b o u t the v a l i d i t y of w h a t was f o u n d in y o u r s e q u e n c e . .......................................
N-glycosylation ___ --Found
at 25
site.
: edscykniwr
N ctfgnccrnc
Protein kinase C phosphorylation . . . .
site.
Number ( i) ( 2)
of p o t e n t i a l s i t e s found: 2 46 : r f g t k p r g c f T p r g d m p g p y c 60 : d m p g p y c a c e S d k c n l
Casein --
kinase
site. ._==
Found
at
13
: cynhlpttec
Disintegrins Found Cell =
II p h o s p h o r y l a t i o n
signature
at 26 to 45 attachment
T qedscykniw
sequence. =======
: edscykniwr
CtfGnCCrNCrFgtkprgCR
tprgdmpgpy
sequence. ....
F o u n d at 48 to 50 : g t k p r g c f t p RGD m p g p y c a c e s ....................................... Sites ==~
annotated
on the
sequence (P)
l
1 Arg-Ile-Cys-Tyr-Asn-His-Leu-Pro-Thr-Thr-Glu-Cys-Thr-Gln-GluCho
Disintegrin
I ................... 16 A s p - S e r - C y s - T y r - L y s - A s n - I l e - T r p - A r g - A s n - C y s - T h r - P h e - G l y - A s n -
D i s i n t e g r i n cont. ........................................................... 31 C y s - C y s - A r g - A s n - C y s - A r g - P h e - G 1 y - T h r - L y s - P r o - A r g - G l y - C y s - A r g (P)
I
Cell
adhes.
...........
(P)
46 T h r - P r o - A r g - G l y - A s p - M e t - P r o - G l y - P r o - T y r - C y s - A l a - C y s - G l u - S e r -
I
61 A s p - L y s - C y s - A s n - L e u Abbreviations: Cho (P)
: stands : stands
for a c a r b o h y d r a t e group. for a p h o s p h a t e group. ===PC/GENE===
Fig. 3 Detection of PROSITE signatures in the protein NEWMBB. The PROSITE program (IntelliGenetics, PCGene) was used to find protein sequence motifs. The types of sequence motifs found include N-glycosylation, protein kinase C, casein kinase II, disintegrin, and cell attachment motifs.
450
Michael B. Bolger
typical disintegrin is shown below: +---+
T ........
"I . . . .
T
I' -
'
J
*I
xxxxxCxCxxxxxxCCxxxxCxxxxxxxCxxxxCCxxCxxxxxxxxCxxxRGDxxxxxCxxxxxxCxxxxxxx
1
I
+ ....... +
I
~
...... I........... I* +
+
I
+
Here C is the conserved cysteine involved in a disulfide bond and the asterisks (*) indicate the position of the pattern. In addition to this type of documentation, PROSITE provides a database file that can be used by software developers to provide the raw data for each type of PROSITE motif signature. Table IV shows the database listing for disintegrins. Each line of Table IV is preceded by a two-letter code representing the type of information in that line. For example, ID is identification, AC is accession number, and PA is the PROSITE pattern. Two of the most important lines are DR (cross-reference to SWISS PROT database) and 3D (cross-reference to the Brookhaven Protein Data Bank). By using these cross-references, one can locate the amino acid sequence information for related proteins, and three-dimensional structures if they are available for that type of protein motif. In this case, we are very fortunate to find two PDB files for the disintegrin molecules kistrin and echistatin. It so happens that these PDB files are based on three-dimensional structures determined by NMR (Adler et al., 1991, 1993; Saudek et al., 1991). These structures can be used to build a three-dimensional homology model of our new protein and will be studied in Section IV. The PROSITE documentation and database can be obtained on the Internet by anonymous FTP (see Table XVII, later in chapter, for FTP sites) from the following organization: National Center for Biotechnology Information (NCBI) Address ncbi.nlm.nih.gov (or 130.14.20.1)
Table IV Database Listing from PROSITE for Disintegrins ID DT DE PA NR
NR
NR CC CC CC DR DR DR DR DR DR DR DR DR DR 3D
DISINTEGRINS; PATTERN. PS00427; NOV-1990 (CREATED); DEC-1992 (DATA UPDATE); OCT-1993 (INFO UPDATE). D i s i n t e g r i n s signature. C-x (2) -G-x-C-C-x- [NQRS] -C-x- [FM] -x (6 ) -C- [RK]. /RELEASE=26, 33329; /TOTAL=29(29) ; /POSITIVE=29(29) ; /UNKNOWN=0(0) ; /FALSE_POS=0(0) ; / FALSE_NEG= 0 (0 ) ; / T A X O - R A N G E = ? ?E ? ?; /MAX-REPEAT= 1; /SITE=l,disulfide; /SITE=5,disulfide; /SITE=6,disulfide; /SITE=9, disulfide; /SITE=I3, disulfide; P16338, DISI_AGKPI, T; P21858, DISI_AGKIIA, T; P17494, DISI_AGKRH, T; P30403, DISR_AGKRI[, T; P18618, DISI_BOTAT, T; P31988, DISI_BOTCO, T; P31989, DISI_BOTJA, T; P31980, DISI_CROAT, T; P31981, DISI CROBA, T; P31982, DISI_CROCC, T; P31984, DISI_CROMM, T; P31985, DISI CROVE, T; P31986, DISI_CROVL, T; P31987, DISI_CROVV, T; P17347, DISI_ECHCA, T; P22826, DISI_ERIMA, T; P15503, DISA_TRIGA, T; P30431, DISJ_BOTJA, T; P17495, DISB_TRIGA, T; P17496, DISG_TRIGA, T; P31990, DISI_LACMU, T; P17497, DISI_BITAR, T; P22827, DISI SISBA, T; P22828, DISI_SISTE, T; P17349, DISI_TRIEL, T; P18619, DISF_TRIFL, T; P21859, DIST_TRIFL, T; P23323, DISC_TRIFL, T; P20164, HRIB_TRIFL, T; IKST; IECH; DO PDOC00351;
Chapter 9 Macromolecular
Structural Analysis
Login Directory
451
User Anonymous Password Your e-mail address / repository / PROSITE
The final analysis of our new protein that is based on sequence homology is the pattern of disulfide bond formation. Because we have located a threedimensional structure that is closely related to our new protein and we suspect that the new protein is a new member of the disintegrin family, we can compare the known disulfide bonding pattern of kistrin to the new protein and decide how the new protein might be bonded. Figure 4 shows an alignment and disulfide bonding pattern for NEWMBB compared to kistrin. The only difference is the lack of two cysteines in NEWMBB at positions 5 and 13, preventing formation of the sixth disulfide bond.
Ill. Secondary Structure Predictions of Proteins As discussed above, primary structure refers to the linear sequence of nucleotides or amino acids in a DNA, RNA, or polypeptide molecule. Secondary structure refers to the regular conformation of biopolymers that is produced by the dihedral rotation around certain bonds in nucleic acids and polypeptides. A description and examples of secondary structure are found Chapter 1. A.
Predictions
Based
on
Frequency
Analysis
Secondary structure predictions have been performed by various methods, and some of the modern methods are able to predict secondary structure at better than 70% accuracy (Rost and Sander, 1993). The newer methods rely on neural networks and some information about the protein family to which the new sequence most likely belongs. Secondary structure prediction methods can be divided into two categories: (1) algorithms that predict regions of secondary
Disintegrin
-Consensus pattern: C-x(2)-G-x-C-C-x-[NQ]-C-x-F-x(6)-C-[RK] Found from 26 to 45 in NEWMBB and from 27 to 46 in DISISAGKRH (Kistrin). 3
I I
NEW~4BB -
12 I
I
18
I I
i
I
31
26
I
I 3s 132 I
ii
I
56
I I
44
i
~3
i
I
RI CYNHLPTTECTQEDS CYKNIWRNCTFGNCCRNCRFGTKPRGCRTPRGDMPGPYCACES DKCNL
9 I
i
I
:i
:l
i ii : i ' i
:" il l l l i i l
i
i
I
D I S I $AGKRH- GKECDCSSPENPCCDAATCKLRPGAQCGEGLCCEQCKFSRAGKICRI PRGDMPDDRCTGQSADCPRYH
i l~li I 6 1~4 I ~3
4 Identity
Similarity:
: 22 7
i I I
19
i__il I 2~ i33_1 I _36
i 4s
32
64
57
(33.8%)
(10.7%)
(conservative substitutions are represented by o f gaps inserted i n D I S I S N E W M B : 0 Number o f gaps inserted i n D I S I $ A G K R H : 0 Number
i~i I I
':')
Fig. 4 Disulfidebonding pattern comparison for NEWMBBand DISI$AGKRH (disintegrin kistrin). Identity is noted by " l " and conservative substitution is noted by ":"
452
Michael B. Bolger structure in a protein by the amino acid content of the regions and the statistical frequency with which given amino acids tend to occur in particular conformations, as determined from X-ray crystallographic data of known proteins, and (2) algorithms that rely on the identification of patterns of hydrophobicity and hydrophilicity, which are favorable for the formation of certain protein conformations. The C h o u - F a s m a n and Garnier methods are representative of algorithms that are based on statistical frequency (Chou and Fasman, 1974; Garnier et al., 1978). Each algorithm is fairly accurate when predicting secondary structures of proteins that were included in the original data set for that algorithm. When new globular proteins of known structure are analyzed by these algorithms, however, prediction accuracy (measured as the percentage of amino acids predicted in the correct conformation) drops to about 56% for the Garnier algorithm, and about 50% for the popular algorithm of Chou and Fasman. It is well known that all secondary structure prediction algorithms fail to predict very hydrophobic and transmembrane regions as helical, and therefore underestimate the helical content of a membrane protein with helical transmembrane domains. This failure is due to the fact that the data sets of three-dimensional structures used by the algorithms were obtained from analysis of soluble proteins. If probable transmembrane segments are excluded from the secondary structure prediction, the accuracy of predicting the conformation of the remaining regions of the protein may approach the success rate for globular proteins.
1. Chou and F a s m a n M e t h o d The Chou and Fasman method relies on the probability of given amino acids to occur in certain conformations, and the probability that a tetrapeptide sequence can cause "nucleation" of a certain conformational structure. Because this method is guided by many rules and caveats, the results of the computerized algorithm may vary depending on the skill of the programmer and the ability of the user to interpret the results. Chou and Fasman (1977, 1978, 1979) have also developed a reliable and widely used statistical method for predicting tight ]3-turns. The probability of a ]3-turn occurrence at residue i is equal to
p(t) = f ( i ) . f ( i + 1) 9f(i + 2) 9f(i + 3),
(2)
where f(i) to f(i + 3) are the frequencies of occurrence of the first, second, third, and fourth residues in a ]3-turn. Probable ]3-turn positions are those with a p(t) value above 0.75 • 10 4 (which is approximately equal to 1.5 times the average probability of any tetrapeptide to be in the ]3-turn conformation). The list of probable ]3-turns is then reduced by eliminating tetrapeptide(s) that have either
(Pt) < 1.00
or
(Pt) < (Pa)
or
(Pt) < (P~)
where (Pt), (Pa), and (P/3) are the average conformational potentials for the tetrapeptide to be, respectively, in the ]3-turn, a-helix, and ]3-sheet conformations. Finally, directly adjacent probable tetrapeptides are considered pairwise and the tetrapeptide with the lowest p(t) value is eliminated. Table V lists the
Chapter 9 Macromolecular Structural Analysis
453
Table V Chou and Fasman Method for Turn Prediction Applied to NEWMBB PC/GENE===
************************************************* *
POSITION AND SEQUENCE OF PREDICTED BETA-TURNS * *************************************************
Done on sequence DE DISINTEGRIN OS AGKISTRODON
NEWMBB. NEWMBB (PLATELET AGGREGATION H A L Y S B L O M H O F F I (MAMUSHI).
ACTIVATION
INHIBITOR).
T o t a l n u m b e r of r e s i d u e s is: 65 Analysis done on the complete sequence. The
symbols
used
in the f o l l o w i n g
two t a b l e s
are:
p(t) : the p r o b a b i l i t y of b e n d o c c u r r e n c e [ p ( t ) = f ( 1 ) * f ( 2 ) * f ( 3 ) * f ( 4 ) ]. , <Pa> & : the a v e r a g e c o n f o r m a t i o n a l p o t e n t i a l for the t e t r a p e p t i d e to r e s p e c t i v e l y b e in t h e b e t a - t u r n , a l p h a - h e l i x a n d b e t a - s h e e t c o n f o r m a t i o n . 10
2O
i
i
3O
I
4O
I
50
60
i
I
RICYNHLPTTECTQEDSCYKNIWRNCTFGNCCRNCRFGTKPRGCRTPRGDMPGPYCACESDKCNL TTTT TTTT TTTT TTTTTTTTTT TTTT TTTT TTTTTT TTTTTT Table Nb 1 2 3 4 5
6 7 8 9
i0 Ii 12
of p r e d i c t e d From 31623293235414651535961-
beta-turns.
To
Tetrapeptide
6 19 26 32 35 38 44 49 54 56 62 64
Cys-Tyr-Asn-His Asp-Ser-Cys-Tyr Trp-Arg-Asn-Cys Gly-Asn-Cys-Cys Cys-Arg-Asn-Cys Cys-Arg-Phe-Gly Pro-Arg-Gly-Cys Thr-Pro-Arg-Gly Met-Pro-Gly-Pro Gly-Pro-Tyr-Cys Glu-Ser-Asp-Lys Asp-Lys-Cys-Asn
p(t)*10^4 1.00 2.99 2.00 1.27 3.86 1.56 2.63 3.90 2.64 4.48 1.32 1.80
<Pa>
1.210 1.305 1.165 1.375 1.222 1.075 1.305 1.248 1.300 1.352 1.160 1.305
0.765 0.792 0.858 0.66 0.762 0.845 0.705 0.738 0.79 0.632 1.112 0.885
1.105 0.988 1.095 1.005 1.05 1.062 0.855 0.855 0.725 0.99 0.6 0.84 PC/GENE===
results of the Chou and Fasman method of turn prediction applied to our hypothetical disintegrin NEWMBB. It is clear that the Chou and Fasman method predicts a high percentage of turn for the disintegrin peptide. This is not too surprising, considering the number of disulfide bonds and the short overall length of this peptide. It should be noted that one of highest regions of turn potential lies near the location of the RGD peptide.
2. Gamier M e t h o d The Garnier method also relies on the probability of amino acid i to occur in a certain conformation, and in addition considers short- and medium-range interactions between amino acids, from i - 8 to i + 8, along the sequence. This method is easier to translate into a computer algorithm, and the analysis results are usually consistent among different computerized versions. Table VI de-
454
Michael B. B01ger Table VI Secondary Structure Prediction by Garnier Method --PC/GENE=== ******************************************************************* * PROTEIN SECOI~R.Y S T R U C T U R E P R E D I C T I O N BY THE METHOD O F ~ I . N I E R ******************************************************************* Done
on
sequence
DE OS
DISINTEGRIN AGKISTRODON
*
NEWMBB. NEWMBB (PLATELET AGGREGATION HALYS BLOMHOFFI (MAMUSHI).
ACTIVATION
INHIBITOR).
T o t a l n u m b e r o f residues is: 65. Analysis d o n e o n t h e c o m p l e t e sequence. In Helical In Extended In Turn In Coil
(H) (E) (T) (C)
Semi-graphical
Symbols Helical Turn 3
I I I
used
conformation conformation conformation conformation
[DC [DC [DC [DC
= = = =
-75 -88 0 0
CNAT CNAT CNAT CNAT
] : ] : ] : ] :
9 14 37 5
AA AA AA AA
=> => => =>
13.896 21.5~ 56.9~ 07.6~
output. i n the
semi-graphical
conformation: conformation: 18
12__1 I I I I
representation:
Extended Coil
X
>
31
I
26__132 I II
3s I I
conformation: conformation:
* 56
44 I
I 1~63 I
I
RICYNHLPTTECTQEDSCYKNIWRNCTFGNCCRNCRFGTKPRGCRTPRGDMPGPYCACESDKCNL --->>**>>>--XXX>>>>>>>-->>>>>>>>>>>>>>>*>>>>-->>>>*>* ..... XX>XXXX "PC/GENE===
scribes the results of the Garnier method applied to our hypothetical disintegrin protein. The Garnier method predicts more than half of NEWMBB to be in the turn conformation and slightly less than 25% to be in extended chain conformation. By combining our knowledge of the disulfide bonding pattern, the location of predicted ]3-turns, and extended chain, we can create a proposed schematic model of the secondary structure for this new disintegrin molecule (Fig. 5). This model illustrates an important secondary structural feature that is common to all of the disintegrin molecules. Notice that the important RGD sequence (amino acids 48-50) is located in a region of high ]3-turn potential and is in the middle of two regions of extended chain. These two extended chains most likely form a loop with the RGD peptide at the tip of the loop, where it can participate in binding to the gp-IIb-IIIa complex.
B. H y d r o p a t h y A n a l y s i s and Superfamilies One of the first methods for predicting secondary structure based on regions of hydrophobic and hydrophilic amino acids required analysis of a very complex
455
Chapter 9 Macromolecular Structural Analysis
65-Leu 63-Cy~ s~
P
56-Cys M
I
S
S"
c s/s- ( ' 7
, 18-Gys '~-, s - - s -
3-Cys
26-Cy
1-Arg Fig. 5 Schematicmodel of secondary structure for NEWMBB. The two-dimensional schematic model was constructed from known disulfide bonding patterns.
set of heuristic rules (Lim, 1974). Due to its complexity and poor predictive ability, this method has not been widely adopted. One of the simplest and most important techniques for analysis and prediction of protein structure was developed by Jack Kyte and Russell Doolittle (1982). Their method identifies hydrophilic and hydrophobic regions of protein by sequentially determining the average polarity or hydropathy (H) of an n residue span of amino acids at each residue i of the span, i + [ 1 / 2 ( n - 1)]
Hi
=
(l/n)
~, i-[1/2(n-1)]
hi,
(3)
where h is an estimate of polarity (i.e., free-energy of transfer from a hydrophilic to a hydrophobic environment) for individual amino acids. Table VII lists the hydropathy values for the common amino acids and provides a brief description of their physicochemical properties at pH 7.0. The calculation of average hydropathy is done for all windows of span n along the protein sequence. In order to discern membrane-spanning regions from hydrophobic regions buried in the interior of globular proteins, a span of 19 residues is typically chosen for the value of n, because hydrophobic transmembrane segments are usually greater in length than hydrophobic segments buried in the interior of a globular protein. It has been determined that a segment of 18-22 amino acids with an average polarity value greater than 1.6 could be predicted with high probability as a transmembrane segment when using a window of 19 residues. The most hydrophobic protein segment from any protein studied by Kyte and Doolittle, however, was in the soluble dogfish lactate dehydrogenase. In addition, hydropathy analysis using the Kyte and Doolittle data set failed to predict any transmembrane segments for porin, an integral membrane protein. Although exclusive consideration of local interactions of a protein with lipid may be insufficient to detect all membrane-spanning sequences, hydropathy analysis is a reasonable first approximation algorithm for identification of transmembrane segments.
456
Michael B. Bolger Table VII Hydropathy Scale Amino acid side chain
Hydropathy index
Isoleucine Valine Leucine Phenylalanine Cysteine/cystine Methionine Alanine Glycine Threonine Tryptophan Serine Tyrosine Proline Histidine Glutamic acid Glutamine Aspartic acid Asparagine Lysine Arginine "At
Side-chain propertiesa Neutral, aliphatic Neutral, aliphatic Neutral, aliphatic Neutral, aromatic Neutral, raSH, H bond, disulfide Neutral, raSH, H bond Small, neutral, aliphatic Smallest, neutral Neutral, --OH, H bond Neutral, aromatic indole Neutral, --OH, H bond Neutral, aromatic --OH, H bond Neutral, cyclic, induces turns 9% positive charge, aromatic, H bond 100% negative charge, aliphatic acid Neutral, polar amide, H bond 100% negative charge, aliphatic acid Neutral, polar amide, H bond 100% positive charge, aliphatic amine 100% positive charge, aliphatic guanidine
4.5 4.2 3.8 2.8 2.5 1.9 1.8 0.4 0.7 0.9 0.8 1.3 1.6 3.2 3.5 3.5 3.5 3.5 3.9 4.5
-
pH 7.
H y d r o p a t h y a n a l y s i s h a s p r o v i d e d us w i t h o n e of t h e m o s t u s e f u l tools for r a p i d d e t e r m i n a t i o n of m e m b e r s h i p in a s u p e r f a m i l y of p h a r m a c o l o g i c a l receptors. F i g u r e 6 i l l u s t r a t e s the u n i q u e h y d r o p a t h y profile for t h e l i g a n d - g a t e d i o n c h a n n e l class of p h a r m a c o l o g i c a l r e c e p t o r s . T h e a c e t y l c h o l i n e r e c e p t o r (AchR) is c o m p o s e d of five s u b u n i t s a n d is a m e m b e r of the l i g a n d - g a t e d ion c h a n n e l s u p e r f a m i l y . T h e p r o t e i n c h a i n of each s u b u n i t s p a n s t h e n e u r o n a l m e m b r a n e f o u r times. Each s e c t i o n of p r o t e i n t h a t is f o u n d to be in c o n t a c t w i t h m e m b r a n e lipids is c o m p o s e d of a m i n o acids t h a t h a v e h i g h h y d r o p a t h y
,o t 3.0
m
2.0
>
1.o
t>-, ~I (D. 0
0.0 -1.0
">., 0
-3.0
"1"
-4.0
-2.0
---I
0
50
.......
T
. . . . . .
1O0
T
150
. . . .
T
200
......
I
250
I
300
. . . .
~
350
]
400
-
-
I
450
. . . .
50{
Residue Number
Fig. 6 Hydropathy plot for a human acetylcholine receptor a-1 subunit. Hydropathy was calculated using the method of Kyte and Doolittle.
Chapter 9 Macromolecular Structural Analysis
457
values. This produces four characteristic peaks in the hydropathy plot. The horizontal line at - 0 . 4 represents the grand average hydropathy (GRAVY) of all residues present in 84 randomly selected soluble enzymes. Peaks of hydropathy greater than the horizontal line at 1.6 are considered to have a high probability of being membrane-spanning sequences. One can see that there are four peaks of hydropathy that represent membrane-spanning helixes in the AchR c~ subunit. In addition, Fig. 6 shows a reasonably high peak at the N terminus. This short section of protein represents the hydrophobic membrane insertion signal peptide and is thought to be removed after the receptor is embedded into the neuronal membrane. Other members of this family include ,/-aminobutyric acid, glutamate, glycine, and NMDA (N-methyl-D-aspartate) receptors. When the 3D structure of one member of a superfamily of proteins is determined, then the structures of other members of the family can usually be inferred by "homology modeling." In contrast to the hydropathy plots for the ligand-gated ion channel receptors, the hydropathy plot for G-protein-coupled receptors such as the acetylcholine muscarinic receptor is quite distinct. Figure 7 shows the hydropathy profile for the Ach muscarinic receptor, with a characteristic profile of seven peaks of hydropathy. These represent the seven transmembrane-spanning domains of the G-protein-coupled receptors. The program PCGene contains a number of routines that allow the user to determine membrane-spanning regions of a protein (Eisenberg et al., 1984). The output of one such program applied to the Ach M2 receptor is shown in Table VIII. This program predicts and assigns the seven hydrophobic membranespanning regions of the muscarinic acetylcholine receptor. Notice that the first five membrane-spanning regions occur between the N terminus and residue 205, and the final two regions are predicted to be between residue 389 and the C terminus. Notice that membrane-spanning regions 3 and 7 do not cross the line of average hydropathy at 1.6 and would not be counted by using the Kyte and Doolittle method. These hydrophobic regions are known to be membranespanning domains from other types of biochemical experiments, and this profile is common to a number of other G-protein-coupled receptors.
,0 I 3.0
:::3 > ~', ~
2.0 1.0
0.0 -1.0
0 t._ ">,, 0
-2.0
=r
-4.o
-. /
-3.0 r
0
50
t .......
1O0
] ----
150
9 ....
200
~
250
r
300
I
350
-~ ......
400
t ......
450
500
Residue Number
Fig. 7 Hydropathy plot for a human acetylcholine muscarinic (M2) receptor. Hydropathy was calculated using the method of Kyte and Doolittle.
458
Michael B. Bolger Table VIII Output of Prediction for Membrane-Spanning Regions = = = 2 8 - A P R - 1 9 9 4 .........
====PC/GENE===
*********************************************
* PREDICTION
OF
MEMBRANE
ASSOCIATED
*********************************************
Done
on
DE OS
HUMAN M2 MUSCARINIC ACETYLCHOLINE HOMO SAPIENS (HUMAN)
Total
sequence
number
Analysis
done
The method stands
Number
(1~)
(I)
(9) (3) (4) (5) (6) (7)
of
of
on
used here
: : : : : : :
.79 .6 .62 .83 .74 .82 .51
*
PACHM2$HUM.
residues
is:
RECEPTOR
GENE.
466.
the complete sequence. i s t h a t of E i s e n b e r g , Schwarz,
for
membrane
:
HELICES
the
average
associated
helices
to to to to to to to
44 80 102 162 205 409 431
on
predicted
Segment
24 60 82 142 185 389 411
Komarony
hydrophobicity
a
by
21
and Wall.
residue
the program
segment.
is:
7.
Sequence -> -> -> -> -> -> ->
VFIVLVAGSLSLVTIIGNILV YFLFSLACADLIIGVFSMNLY LYTVIGYWPLGPWCDLWLAL MMIAAAWVLSFILWAPAILFW AVTFGTAIAAFYLPVIIMTVL ILAILLAFIITWAPYNVMVLI TFCAPCIPNTVWTIGYWLCYI
