Annual Reports on NMR Spectroscopy, Volume 32

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ANNUAL REPORTS ON

NMR SPECTROSCOPY

This Page Intentionally Left Blank

ANNUAL REPORTS ON

NMR SPECTROSCOPY Edited by

G. A. WEBB Department of Chemistry, University of Surrey, Guildford, Surrey, England

VOLUME 32

ACADEMIC PRESS Harcourt Brace & Company, Publishers

London San Diego New York Boston Sydney Q Tokyo 0 Toronto

ACADEMIC PRESS LIMITED 24-28 Oval Road, LONDON NW17DX

U.S. Edition published by ACADEMIC PRESS INC. San Diego, CA 92101

This book is printed on acid-free paper

Copyright

0 1996 ACADEMIC PRESS LIMITED

Ail Rights Reserved No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical including photocopying, recording, or any information storage and retrieval system without permission in writing from the publisher A catalogue record for this book is available from the British Library

ISBN 0-12-505332-0 ISSN 0066-4103

Phototypesetting by Keyset Composition, Colchester, Essex Printed in Great Britain by Hartnolls Limited, Bodmin, Cornwall

List of Contributors P. S. Belton, Institute of Food Research, Norwich Research Park, Colney, Norwich NR4 7 U A , UK. David J. Craik, Centre f o r Drug Design and Development, University of Queensland, Brisbane, 4072 Q L D , Australia. A, M . Gil, Department of Chemistry, University of Aveiro, Aveiro 3800, Portugal. Christopher J. Groombridge, Metropolitan Police Forensic Science Laboratory, 109 Lambeth Road, London SE1 7 L P , U K . Kerry A. Higgins, Department of Biochemistry, Monash University, Clayton, 3144 V1C, Australia. B. P. Hills, Institute of Food Research, Norwich Research Park, Colney, Norwich NR4 7 U A , UK. Katherine J. Nielson, Centre f o r Drug Design and Development, University of Queensland, Brisbane, 4072 Q L D , Australia. William S . Price, Water Research Institute, Sengen 2-1-6, Tsukuba, Ibaraki, 305 Japan.


Preface It is a veridical fact that NMR has found applications in all areas of modern science and that its appeal continues to expand apace. This year-1995sees the 50th anniversary of the discovery of NMR spectroscopy, and it is almost 30 years since the appearance of the first volume of Annual Reports on N M R Spectroscopy, during which time a large and diverse collection of topics have been covered. The contents of Volume 32 of this series are no exception, and consist of reviews covering four, clearly distinct, areas of science. It is my pleasure to be able to introduce the very interesting accounts on Applications of NMR to Food Science by Dr A. M. Gil, Professor P. S. Belton and Dr B . P. Hills; Gradient NMR by Dr W. S. Price; Pharmaceutical Applications of NMR by Professor D. Craik, Dr K. A. Higgins and Dr K. J. Nielsen; and NMR Specroscopy in Forensic Science by Dr C. J. Groombridge. Expressions of gratitude go to these reporters and to the production staff at Academic Press (London) for their generous cooperation in the creation of this volume. University of Surrey Guildford, Surrey England

G. A. WEBB June 1995


Contents List of Contributors . . . . . . . . . . . . . . . . . v Preface . . . . . . . . . . . . . . . . . . . . . vii

Applications of NMR to Food Science A . M . GIL. P . S . BELTON and B . P . HILLS

1. 2. 3. 4.

Introduction Water in foods Biopolymers Analysis . References .

. . . . . . . . .

. . . . .

. . . . .

. . . . .

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. . . . .

1

. . . . .

. . . . .

. . 2 . . 3 . . 12 . . 30 . . 43

Gradient NMR WILLIAM S . PRICE

1. 2. 3. 4. 5. 6. 7. 8. 9.

Introduction . . . . . . . . . . . Nuclear spins and gradients . . . . . . Diffusion measurements . . . . . . . Non-homogeneous gradients and other problems Pulse sequences for measuring diffusion . Applications to high-resolution NMR . . . Technical aspects of gradient production . . . Specific examples of gradient NMR . . . . Concluding remarks . . . . . . . . . . References . . . . . . . . . . . . .

51

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . .

. . . . . . . . . .

Pharmaceutical Applications of NMR D . J . CRAIK. K . J . NIELSEN and K . A . HIGGINS 1. 2. 3. 4.

Introduction . . . . . . . . . The role of NMR in drug development NMR techniques in drug design . . . . . . . Selected examples Acknowledgements . . . . . . References . . . . . . . . .

. . . . . . . . .

. 53 . 55 . 58 . 95 . 100 109 121 128 135 135

143

143

. . . . . . . . . 147 . . . . . . . . . 149 . . . . . . . . . . 162

. . . . . . . . . . 208 . . . . . . . . . . 208

X

CONTENTS

215

NMR Spectroscopy in Forensic Science CHRISTOPHER J . GROOMBRIDGE 1. Introduction . . . . . 2. Misused drugs . . . . 3. Toxicology, body fluids . . 4 . Other forensic analysis . . 5. Magnetic resonance imaging Acknowledgements . . . . References . . . . . .

Index

. . . . . . . . . . . . . 215

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. 219 . 282 . 284 . 286 . 288 . 288 299

Applications of NMR to Food Science A. M. GIL Department of Chemistry, University of Aveiro, Aveiro 3800, Portugal

P. S. BELTON and B. P. HILLS Institute of Food Research, Norwich Research Park, Colney, Norwich, NR4 7UA, U K 1. Introduction 2. Water in foods 2.1. Water in solute-biopolymer systems 2.2. Water in heterogeneous food materials 2.3. Water relaxation in cellular food material 2.4. Magnetic resonance imaging of foods 2.4.1. MRI and temperature mapping 2.4.2. One-dimensional imaging protocols 2.4.3. MRI studies of food surfaces 2.4.4. MRI and food quality 3. Biopolymers 3.1. Introduction 3.2. Proteins 3.3. Polysaccharides 3.3.1. Polysaccharides in solution 3.3.2. Solids, gels and heterogeneous systems 3.4. Plant cell walls 3.5. 2 spectroscopy and biopolymers 4. Analysis 4.1. Introduction 4.2. Developments in authentication 4.3. Process applications 4.4. RSC methods 4.5. MAS methods 4.6 Other applications 4.6.1. Tea, coffee and wine 4.6.2. Fruit and vegetables 4.6.3. Lipids 4.6.4. Spices and phytochemicals 4.6.5. Milk 4.6.6. Meat 4.6.7. Other studies References ANNUAL REPORTS ON N M R SPECTROSCOPY VOLlJME 32 ISBN 0-12-505332-0

2 3 3 5 8 9 10 11 11 12 12 12 12 15 15 17 24 29 30 30 31 31 32 34 36 36 37 37 40 41 41 42 43

Copyrighi 01996 Acudemrc Press LImrfed AN rights of reproducrion in any form reserved

2

A. M. GIL, P. S. BELTON AND B. P. HILLS

1. INTRODUCTION

In the first review on applications of nuclear magnetic resonance (NMR)to food science to appear in this series,' it was remarked that the rate of publication in the area was increasing. This trend has continued. The first international conference on the subject was held in 1992, and 1994 saw the second of what is now an established series. Three booksz4 have been published, and in addition several reviews have appeared. Reviews of a more general nature are listed in Table 1; more specific reviews are dealt with under the various subject headings. In this review we attempt to give a fairly comprehensive account of the activity in the area since 1992. This inevitably requires a degree of selectivity since much of food research uses N M R in a routine way and much N M R is relevant to food research. We have tried to focus only on those aspects where N M R plays a major rather than a peripheral role in research and where the main focus is food o r food-relevant systems. A feature of this review is an account of recent work on plant cell walls. This subject is one which is becoming of increasing interest to food scientists and has been benefited by the application of solid state N M R methods. In addition to applications in food science we also consider two new N M R methods which seem likely to prove to be of general usefulness. These are magic angle spinning for improved resolution in proton spectra, and the use of Z spectroscopy in which polarization is transferred from biopolymer protons to water protons to allow mapping of the biopolymer lineshape.

Table 1.

A list of reviews on the applications of NMR in food science.

Subject

Date ~

~

Ref. ~

General General articles on applications of NMR General review General review General review Applications to food and engineering General review

1992 1993 1993 1993 1994 1994

10

Water Protein hydration

1994

11

Imaging General review of imaging Imaging, diffusion and relaxometry

1994 1994

12 13

Biopolymers Protein NMR

1993

14

5 6 7 8 9

APPLICATIONS OF NMR TO FOOD SCIENCE

2. WATER

3

IN FOODS

2. I. Water in solute-biopolymer systems

The amount and dynamic state of water in food systems affects many important properties such as food texture, the rates of enzymatic and non-enzymatic reactions and microbiological activity. NMR water relaxation measurements can provide a powerful probe of the amount and mobility of water in foods, and a number of recent studies have taken advantage of this. Of the three NMR-active nuclei in water (namely protons, deuterium in D 2 0 and oxygen-17 in H2170), proton-decoupled oxygen-17 transverse relaxation measurements provide the most direct probe of water mobility since they are unaffected by the chemical exchange of protons (or deuterons) between solute and water which complicates the interpretation of water proton and deuterium relaxation studies.’ Table 2 summarizes some of the recent oxygen-17 relaxation studies in sugar-biopolymer systems. Most of these studies have attempted to interpret their water oxygen-17 relaxation data in a qualitative way in terms of changing “water mobility” related to various degrees of “water binding” by the solute or biopolymer. Few attempts have been made to interpret the relaxation data with the two-site fast exchange theory developed by Halle et ~ 1 and. extended ~ ~ to sugar solutions by Hills24 and Belton et ~ l . These ~ * theories show that the water at the solute or biopolymer interface reorients anisotropically and needs to be characterized by two reorientational correlation times and a local order parameter. In principle the slow reorientational correlation time can be determined uniquely by combining oxygen-17 relaxation data obtained at two or more spectrometer frequencies. This approach has been used to study the interaction of water and dimethyl sulfoxide (DMSO) with gelatine22 but not, so far, with sugar solutions or solute-starch systems. In addition to the intramolecular quadrupolar relaxation pathway, water deuterium relaxation has potential contributions from the fast chemical Table 2.

”0 relaxation studies of sugar and biopolymer systems.

System Potato starch suspensions Wheat starch-sucrose Starch-based fat replacers Skim milk and caseinate solutions Sugar-water systems Sucrose-containing food system Wheat starch-sugar Gelatine gels

Nucleus

Ref.

1 7 0 , 2 ~ ‘H ,

15

170

16 17

170

170,

IH

18

170

19

170

20 21 22

170

’H, ‘H

4


exchange of deuterons between water ( D 2 0 ) and exchangeable deuterons on the solute. Water proton relaxation in solute-biopolymer systems has contributions from both chemical exchange and intermolecular dipolar interactions between the hydration water and the solute or biopolymer.26 Some progress has been made in quantifying the relative contributions of these pathways, at least in potato starch suspensions by a combined multinuclear relaxation study. l5 The idea behind these experiments is that the ratio of transverse relaxation rates RIR, (where R is the observed relaxation rate and R, is that of pure water) should be independent of the nucleus, whether oxygen-17 or deuterium, provided that only the intramolecular quadrupolar relaxation mechanism contributes. Any difference in this ratio is presumed to arise from chemical exchange of deuterons with the solute. Similarly, in the short pulse spacing limit of the CMPG sequence, the ratio RIR, for protons and deuterons measured in the same system will differ because of the contribution of intermolecular dipole-dipole interactions between water and solute. It was found that both chemical exchange and dipolar interactions make significant contributions to water transverse relaxation in potato starch suspensions, especially at lower water concentrations, above -40% w/w starch. This approach has yet to be applied to other solute-biopolymer systems. observed a doublet splitting in It is interesting to note that Yakubu et ~71.'~ the deuterium spectrum and a triplet splitting of the oxygen-17 spectrum for water inside potato starch granules but that no such splitting has been observed for other cereal starches such as corn, wheat or pea starch. This could arise from the uniquely ordered hexagonal arrangement of amylose double helices in potato starch. The relationship between NMR water relaxation times and glass transitions in food materials remains to be elucidated. Many papers have used non-NMR techniques such as differential scanning calorimetry (DSC) and dynamical mechanical thermal analysis (DMTA) to measure glass transition temperatures in food ingredients such as casein,27 and amylopectin3' and their mixtures with sugars and to show how increasing water content lowers the glass transition temperature. However, very little NMR work has been done on the relationship between water and biopolymer mobility (as monitored by NMR relaxation times) and the glass ~ transi~ transition temperature. Early work by Kalichevsky et ~ 1 on . glass tions in gluten showed that the proton relaxation time characterizing the non-exchanging gluten protons remained constant below the glass transition temperature but increased above it. Corresponding changes in the water relaxation times were not reported. A detailed investigation of water dynamics in 10% maltose glasses3' using proton and deuterium NMR reported a similar increase in the maltose proton relaxation time above the glass transition temperature and, in addition, demonstrated the remarkable mobility of water in the glassy state of the 10% maltose glass. The water


5

relaxation data suggested a model of the glassy state in which water molecules undergo rapid rotational and translational motion inside more rigid “cages” or “channels” formed by maltose molecules.

2.2. Water in heterogeneous food materials

An aspect of relaxation theory that has been paid only scant attention in the food literature is the effect of food microstructure (and the microscopic air-water distribution) on water relaxation behaviour. Most work relating water proton relaxation behaviour to microstructure has been carried out on non-food materials such as water-saturated porous rocks, sandstones, chalks and cement pastes where the distribution of water proton relaxation times is used to determine pore size distributions in the porous matrix. This procedure succeeds because water in a pore relaxes by diffusion to the pore surface, which acts as a surface relaxation sink, so that larger pores are associated with longer relaxation times than smaller pores. An overview of the field has been published recently,32 and Table 3 lists a number of recent papers on water relaxation in heterogeneous non-food materials. From the morphological viewpoint there is little fundamental difference between a starch slurry and a cement paste, or between a bread loaf and a porous sandstone, but the more complex chemical composition of most real foods prevents a simple application of the pore size distribution concept to food relaxation behaviour. For this reason most reports on water relaxation in real foods are of a preliminary and empirical nature. The second part of Table 3 lists a number of typical water relaxation studies on food materials Table 3. Water relaxation measurements heterogeneous systems.

System

in

Ref.

Non-food materials Hydrating cement paste Hydrating sandstones Chalk Hydrating zeolite powder plugs Hydrating silica beds Hydrating Sephadex microspheres Glass microsphere beds

33,34 35 36, 37 38 39, 40 41-43 44

Food materials Staling of bread Cooking of cakes Frozen food gels Hydrating flour and starch pastes

45 46 47 48

6

A.

M.GIL, P. S . BELTON AND B . P. HILLS

reported at the 2nd International Conference on Applications of Magnetic Resonance in Food Science held at Aveiro, Portugal, in 1994. To try to place these real food studies on a less empirical basis and bridge the gap between the non-food and food literature, a number of systematic water proton relaxation studies have been made on model heterogeneous systems having a simpler morphology. These include randomly packed beds of Sephadex microspheres where both the microsphere radius and the internal dextran chain cross-linking density can be systematically ~ a r i e d , ~ ~ . ~ ~ randomly packed beds of glass microspheres4 and crushed silica of various mean particle diameter^.^',^^ In each of these systems the distribution of water proton relaxation times was measured as the water content was varied between the saturated bed and the almost dry powder. Because of their more clearly defined morphology it was possible to mathematically model the relaxation behaviour by numerically solving the Bloch-Torrey equations.49 When comparing theory and experiment on randomly packed beds of non-porous particles such as glass microspheres and s i l i ~ ait~ ~ , ~ ~ was found that the water proton relaxation behaviour depends not only on the pore size distribution as defined by the radius of the largest sphere that can be accommodated inside a pore but also on the pore geometry. This is an important distinction, because the former definition predicts a continuous distribution of pore sizes and of relaxation times in the glass microsphere beds, whereas the observed relaxation time distribution actually consists of four distinct peaks (Fig. 1). The longest relaxation time peak is thought to arise from water in distorted octahedral pores formed between six microspheres, the next longest relaxation time peak to water in distorted tetrahedral pores and the third longest peak to water in triangular pores or throats formed between three spheres. The assignment of the shortest relaxation time peak is uncertain; one possibility is that it corresponds to higher-order relaxation modes predicted by the Bloch-Torrey equations with restricted d i f f u ~ i o n . ~ 'A . ~ similar ~ four-peak distribution was observed in water-saturated beds of silica particles with mean diameters between 130 and 250 pm. By fitting the changing relaxation time distribution as the overall water content is lowered in the glass microsphere and silica beds from saturation to the almost dry powder it is possible to deduce the changes in the microscopic air-water distribution between the different pore categorie~.~' The results appear to conform reasonably well to the expectations of capillary suction theory, which predicts that air first penetrates the largest pores before entering successively smaller pores. A similar protocol has been followed with randomly packed beds of Sephadex microspheres with the difference that the Sephadex microspheres are porous so that water can diffuse freely between the compartments inside and outside the r n i c r o ~ p h e r e s . In ~~~ this ~ porous system, osmotic forces predict that lowering the water content of the bed should first remove all water outside


1.0

5.0 10.0

50.0 100.0

7

500.0

Relaxation time/ms

Fig. 1. The distribution of water proton transverse relaxation times in a water saturated randomly packed bed of monodisperse glass microspheres of radius 200 pm. The shaded peak is the distribution predicted when the pore size is defined as the radius of the largest sphere that can be fitted inside the pore. (Reproduced with permission from Hills and Snaar&).

the Sephadex microspheres, at which point the relaxation is necessarily single exponential with a value equal to the intrinsic relaxation time inside the fully swollen microsphere. Further removal of water causes the relaxation time to shorten as the microsphere shrinks. As with the non-porous silica and glass microsphere beds the concomitant changes in the water proton relaxation time distributions as the air-water distribution and microstructure changes can be modelled, at least semi-quantitatively, using numerical solutions of the Bloch-Torrey equations.4143 Ice has such a short transverse relaxation time (a few tens of microseconds) such that if water in a particular compartment of pore freezes, the relaxation time peak corresponding to that compartment or pore essentially disappears. This idea has been used to study the microscopic distribution of non-freezing water and ice in the packed Sephadex microsphere beds as they are taken through a freeze-thaw cycle.43 By fitting the relaxation time changes with the Bloch-Torrey equations it was then possible to derive a value for the surface relaxation strength of ice. The value for transverse relaxation at -2°C is 1.34 x lop3cm/s, which is sufficiently large to suggest that surface relaxation effects should significantly affect the relaxation time of non-freezing water in frozen foods. It would be interesting to extend these model relaxation studies to other

8

A. M. GIL, P. S . BELTON AND B. P. HILLS

nuclei such as water deuterium and oxygen-17 relaxation. This would help establish the relationship, if any, between the changing microscopic airwater-pore distribution and the oxygen-17 relaxation times that was discussed in the context of unsaturated packed beds of starch granules in the previous review.' It remains to be investigated whether the Bloch-Torrey equations can also be used to rationalize the effects of changing microstructure in more complex food materials such as doughs, breads, crumbles and food mixes. 2.3. Water relaxation in cellular food material

Water in plants is also compartmentalized on a variety of distance scales. On a macroscopic distance scale different types of tissue such as the vascular bundles or parenchyma tissue within the intact plant are distinguished by different cell types and sizes and are expected to be characterized by different water relaxation times or effective water diffusion coefficients. This is the origin of contrast in relaxation or diffusion-weighted magnetic resonance images of intact plant tissue which can be used to monitor the quality of fruit and vegetables. Table 4 lists a number of examples of this use of imaging. Much less work has been done on the more fundamental issue of interpreting the water relaxation and diffusion behaviour of particular tissue types in terms of cell structure and composition. At a microscopic distance scale, water in plant cells is compartmentalized in various membrane-bound subcellular organelles such as vacuoles, starch granules and the cytoplasm, and the water outside the plasmalemma membrane is associated with the plant cell wall. Each of these aqueous subcellular compartments is expected

Table 4.

Water relaxation measurements in plant materials.

Tissue Carrot, onion, apple Apple parenchyma tissue Apple parenchyma tissue Courgette Mango fruit Tomato Red raspberry fruits Bean hypocotyls Potato Carrot Zucchini squash MRI, magnetic resonance imaging.

NMR measurement Water relaxation Water relaxation and diffusion Water relaxation MRI relaxation contrast MRI MRI MRI 'H relaxation of cell walls Water relaxation Water relaxation MRI

Ref. 52

53 54

55 56 57 58

59 60 61 62


9

to be characterized by intrinsic water proton relaxation times determined by the chemical composition of solutes and biopolymers comprising the compartment. The observed distribution of water proton relaxation times arising from tissue of a homogeneous cell type therefore largely reflects the distribution of water between these subcellular compartments and, once again, the relaxation time distribution can be interpreted with numerical solutions of the Bloch-Torrey equations provided the compartment morphology, the membrane water permeabilities and the intrinsic compartment relaxation times are known. Cell morphology can be observed with light or electron microscopy, and the intrinsic compartment relaxation times estimated by separating the cell compartments such as starch granules or cell walls. Fitting the observed relaxation time distribution can then give information about the membrane water permeability coefficients. So far this quantitative approach to plant tissue relaxation has been applied only to a but further applications are expected. parenchyma apple Of particular interest to food manufacturers and distributors are the changes in the water/air/ice distribution in fruits and vegetables as they are ripened, dried, rehydrated, frozen and stored. Here again the changes in the distribution of water proton relaxation times during these ripening, processing and storage operations can, in principle, reveal the microscopic (sub-)cellular changes, though the only recent application of this approach concerns the freezing of potato tissue where the changing subcellular distribution of ice and non-freezing water at temperatures down to -20°C were monitored.60 This study established that even at -15°C there is still unfrozen water in the starch granules and cell wall compartments, an observation of potential significance in understanding shelf-lives in food cryopreservation.

2.4. Magnetic resonance imaging of foods

Mention has already been made of magnetic resonance imaging (MRI) studies of fruit and vegetable quality and of the need for a more fundamental understanding of the origin of tissue contrast in these foods. This highlights the recent trend in food imaging away from merely qualitative imaging of “static” food structure to quantitative imaging applications. Indeed, the true potential of MRI in food science undoubtedly lies not in static structure determination but in following, non-invasively, mass and heat transport in foods, in real time during processing and storage. Relevant food-processing operations include drying, rehydration, heating, blanching, frying, microwaving, extrusion, curing, mixing, drainage freezing and freeze drying. This lengthy, but far from exhaustive, list serves to emphasize that MRI has the potential for revolutionizing food-processing science, a point that has been made in a recent book on MRI of foods.’

10


Table 5. MRI studies in foods.

MRI study

System Carrot Potato Model food gels Peach Potato Sephadex Extruded pasta Potato Apple Glass bead beds Cod Peanut butterlbread Milk Barley seeds Alginate gels

Temperature mapping Temperature mapping Temperature mapping Freezing Freeze drying Radial imaging Rehydration, radial imaging Drying, one dimensional Drying, one dimensional Drying, one dimensional Texture Fat transport Cream separation Maltose distribution Spatial heterogeneity

Ref. 63 64 65 66 67 68 69 70 71 72 73 66 74 75 76

Table 5 lists a number of recent quantitative MRI studies of mass and heat transport in foods. For convenience these will be discussed under the following subheadings.

2.4.1. MRI and temperature mapping Temperature mapping is one of the most exciting recent developments in food imaging. It is based on the observation that water proton longitudinal and transverse relaxation times as well as water self-diffusion coefficients in food materials depend on temperature so that an image (or map) of the spatial dependence of any of these parameters can be converted into a temperature image provided a suitable calibration curve exists relating relaxation times or diffusion coefficients to temperature. This calibration curve can be determined separately from non-spatially resolved NMR measurements on uniform samples. Table 5 lists a number of recent publications based on this idea. By modelling the time course of the temperature profiles the thermal diffusivity and surface heat transfer coefficient can be deduced. At subzero temperatures MRI has potentially important contributions to make in the measurement of freezing times and of freeze-drying kinetics. Ice has such a short transverse relaxation time that it appears as a black region in the image. An unfrozen central region in a food therefore appears as a bright region. Whether this can be exploited in an “on-line” non-invasive technique for optimizing a food-freezing operation remains to be seen. An example of a qualitative MRI study of a freezing peach half is given by McCarthy and Kauten.66 Recently, MRI has been used to study the kinetics


11

of the freeze drying of potato cylinder^.^' In contrast to the previous application, the central core of unsublimed ice in the freeze drying potato appears as a bright region in the image. This apparent contradiction can be explained by the presence of the unfrozen water in the starch granules and cell walls referred to in the previous section. The time course of the shrinking central ice core permitted the kinetics of the freeze drying process to be m ~ d e l l e d . ~ '

2.4.2. One-dimensional imaging protocols A number of recent papers have pointed out the advantages of simple one-dimensional projection imaging when attempting to follow rapid changes in moisture, temperature or quality factors during food processes such as drying or rehydrati~n.'~.'~ One-dimensional projection imaging assumes that the food can be cut or moulded into cuboids or cylinders and then processed so that mass and heat transport occur only along one of the principal axes of the cuboid or, in the case of the cylinder, either along the axis or in a radial direction. In the latter case the radial profile can be obtained from the projection by an inverse Abel transformation.68 Such one-dimensional imaging is necessarily faster than two-dimensional imaging since no phase-encoding gradients are required. Moreover, since the whole sample cross-section is projected, sufficient signal is usually obtained in just one or two scans. A further advantage of this protocol is the comparative ease of theoretically modelling the profiles in one space variable. Table 5 lists a number of such one-dimensional imaging studies.

2.4.3. M R I studies of food surfaces Real-time MRI moisture and temperature images include the values at or near the food surface. These surface values are particularly significant because the efficiency of processing operations such as drying or baking depends on the magnitude of the heat and moisture surface transfer rates, which also vary during the processing as the chemical state, moisture content and temperature of the surface changes. It is therefore essential to monitor the changing conditions of the food surface during processing and storage. The potential of MRI surface studies has been demonstrated recently during the surface air drying of an initially water-saturated randomly packed bed of glass beads." Here it was found that the surface degree of saturation decreased almost exponentially with drying time, but it is unclear why this should be the case or to what extent this observation depends on the nature of the food matrix and drying conditions. The surface moisture content is also expected to influence the rate of growth of spoilage organisms and surface quality factors such as texture and colour.

12


2.4.4. MRI and food quality

A food-manufacturing operation has to be optimized by maximizing food quality while at the same time minimizing energy expenditure. MRI can assist in this process by providing not only spatial maps of moisture content and temperature but also of certain food quality factors such as lipid and solute concentrations. For example, MRI studies of whole fresh and frozen cod have been used to determine differences in water binding and its effect on the fish texture.73 This is an important storage problem because cod shows marked changes in texture due to protein aggregation during frozen storage, thereby rendering the fish unpalatable. Other recent examples of MRI quality monitoring include the transport of fat into bread from peanut butter66 and the separation of cream from milk over a 9 h period.74 MRI microimaging and localized spectroscopy have been used to image the production and spatial distribution of maltose and other metabolites in germinating barley seeds,75 which affects the quality of beers and spirits. The use of MRI to monitor bruising in fruits has already been discussed in the section on water in cellular food material and in the previous review.' More generally, it is known that water proton relaxation times depend on the degree of protein and polysaccharide aggregation as well as solute concentration, pH and solid-liquid ratios, so MRI should be capable of monitoring any food quality factor dependent on these factors. A recent example involves the T2-weighted imaging of spatial heterogeneity in calcium alginate gels,76 which is important in controlled release applications.

3. BIOPOLYMERS 3.1. Introduction

The area of research into food biopolymers continues to attract considerable interest. A notable feature of work over recent years is the growing activity in the investigation of plant cell walls by NMR. There have also been developments in methodology particularly in the exploitation of polarization transfer methods by the use of Z spectroscopy. 3.2. Proteins One of the most active areas in protein research has been in cereal proteins. This is largely due to the increased availability of pure protein fractions isolated from the cereal seeds or from gluten. Cysteine-rich basic proteins have been isolated from heat,^',^^ barley77 and maize.78 The larger (9 kDa) proteins are lipid transfer protein^^^,^'


13

which have a high affinity for lipid and unusual foam stabilization properties.80 High-resolution one-, two- and three-dimensional methods have been used to assign the sequence and characterize secondary The smaller (5 kDa) protein has had its three-dimensional solution structure defined using NOESY data and distance geometry methods followed by dynamical simulated annealing calculation^.^^ The roles of both these proteins in the cereals are unclear, but both may be used for defensive purpose^.'^^^^ There is now a general recognition that the high molecular weight subunits of gluten have a major role in the bread-making characteristics of flour." However, until quite recently these have not been available in sufficient quantities for examination by NMR. They are high molecular weight, insoluble proteins and are thus unsuitable for high-resolution solution state approaches. An interesting hypothesis exists that these proteins are analogous to the mammalian connective tissue protein elastin and that the elastic properties of the high molecular weight subunits derived from the same mechanism as elastin.82 The hypothesized mechanism was that, in analogy to elastin, the high molecular weight subunits had a p spiral structure which on extension behaved rather like a spring. The restoring force in elastin derives from its hydrophobic nature. Good evidence for this hydrophobic interaction has been obtained by pulsed NMR studies of *H20 in contact with e l a ~ t i n . 'When ~ 'H20 is in excess, heating causes contraction of the protein mass and expulsion of water. This is manifested in an increase in intensity of the slowly relaxing component of the 'H transverse relaxation. When the same experiment was carried out using high molecular weight subunits, behaviour the reverse of that in elastin was observed.84 As the temperature rises, the amount of the slowly relaxing component decreases. This is equivalent to the absorption of water by an expanding protein mass. Such behaviour is typical of a hydrophilic system and is therefore not consistent with a hypothesis which requires elastin-like behaviour. Simultaneously with the developments with the high molecular weight subunits, systematic studies of proton relaxation and lineshape in the barley protein C-hordein have been r e p ~ r t e d . ' ~The . ~ ~strategy was to hydrate the protein in 2H20 and then to use the 'H behaviour as an indication of the protein behaviour at different temperatures and levels of hydration. The results showed that the protein, although insoluble, is highly mobile. C-Hordein, like the high molecular weight subunits, has a high density of glutamine and proline residues. Comparison of relaxation when the sidechain amide contained 'H or 'H suggested that rotation of this group was primarily responsible for spin-lattice relaxation in the laboratory and rotating frames. Analysis of these results, as well as transverse relaxation behaviour, led to the idea that the insolubility of C-hordein was the result of the formation of interchain hydrogen bonds by glutamine side-chains.

14


60 40 20 0 -2040-60 6

60 40 20 0 -20-40-60

B

Fig. 2. Static (lower) and magic angle spinning (upper) spectra of hydrated C-hordein containing (A) 27% water and (B) 30% water. (Reproduced with

permission from Belton and Gi1.85)

Hydration resulted in the breaking of these bonds, but because of the high density of glutamine residues it was statistically very unlikely that all bonds could be simultaneously broken. The insoluble hydrated protein mass thus consisted of “loops” of hydrated protein together with “chains” of intermolecular hydrogen bonds.86 This idea has been extended, by analogy, to high molecular weight subunits, and forms a key part of a new hypothesis on the origins of the elasticity of these material^.'^ Not only have these studies contributed to the understanding of the behaviour of cereal proteins, they have also uncovered some rich NMR phenomena. The proton lineshape of hydrated C-hordein consists of a broad line with a narrow line superimposed on it.”@ This observation is fairly common in biopolymers. However, magic angle rotation causes the narrow component to narrow still further and lose fine structure. This is illustrated in Fig. 2. The origins of this effect lie in both chemical shift anisotropy and dipolar effects,85 and represent an interesting and unusual regime of be haviour .


15

Milk proteins continue to attract attention. Lamberlet and c o - ~ o r k e r s ~ ~ have evaluated the usefulness of low-resolution NMR in studying thermal effects of milk proteins. They found that the results were affected by ionic strength and the addition of caseinate or casein micelles. They propose that NMR can be used for determining either reversible or irreversible thermal denaturation of whey proteins in model systems. A multinuclear (25Mg, 31P and 43Ca) study of ion binding with p-casein has shown that there are at least two magnesium binding sites, one of which is unexpectedly strong.” Magnesium competes with calcium for binding sites, but sodium does not, under physiological conditions. The data for the dependence of the 43Ca chemical shifts required a five-site model but could not discriminate between the sites being identical and independent or operating with negative cooperativity .

3.3. Polysaceharides

3.3.1. Polysaccharides in solution The amylose content and degree of amylopectin branching were quantified in normal, high-amylose and waxy barley starches.” After enzymatic debranching treatment and gel permeation chromatography, ‘H NMR spectroscopy showed that amylopectin has longer chains in high-amylose starch (containing 40% amylose) than in the other types studied. The interactions of metal salts with amylodextrin were investigated by highresolution 13C NMR, using ethyl, isopropyl and t-butyl alcohols as model compounds.Y2Within the metal salts studied, potassium thiocyanate was an exception since, instead of causing up-field shifts on hydroxyl carbons on amylodextrin and in alcohols, it caused down-field shifts in C I and C4 of amylodextrin. This is similar to the effect observed for amylodextrin triiodide and other amylodextrin helical complexes, which suggests that a similar type of system may be formed in the presence of potassium thi~cyanate.~~ Carrageenans are an important class of sulfated polysaccharides used in food. Structural studies of various carrageenan oligosaccharides, at room temperature, have been carried out making use of high-resolution bidimensional ‘H and 13C NMR methods.93 Carrageenans may contain additional minor structural features that can, however, determine their functional properties. The set of 13C NMR absorptions produced by all diads potentially present in carrageenans have been either calculated or compiled from chemical shift data.94 Structural determination may be carried out by computer-aided matching of experimental data to the data bank reported. High-resolution ‘H NMR has helped to characterize carrageenans from Furcellaria lumbricalis and Eucheurna gelatinae, after degradation to

16


oligosa~charides.~~ P-Carrageenan has been recently obtained from the sun-dried seaweeds E. gelatinae, E. speciosa and E. r n ~ r i c a t u r nCharacter.~~ ized by chemical analysis, optical rotation and NMR, P-carrageenan was shown to be devoid of ester sulfate. Gelling was found to be ionindependent, and the structure of the resulting gel is suggested to be less restrictive relatively to agarose gel.96 13C NMR was also used to help characterize the cell wall polysaccharide of Australian Cutenella nipae, which was found to be a highly sulfated carrageenan type of polysaccharide. The same work established that the dominant component of the extract is i-~arrageenan.~~ ‘H NMR and I3C NMR spectral parameters of eight sulfated uronic acid-containing disaccharides were used to determine the conformational dependencies on the pattern of ~ulfation.’~ These studies help to understand the role of charged groups on the conformations of the major class of sulfated polysaccharides relevant in food science. The role of carboxylate groups and sulfate groups and their interaction with cations on the three-dimensional structure of the disaccharides was extrapolated to the polymeric chondroitin sulfates and related to the resulting rigidity and flexibility of some glycosidic linkages.98 Several gum arabic samples from Uganda were analysed, and structural comparisons carried out by 13C NMR.” Alginic acids are heteropolysaccharides that are composed of varying ratios of p-D-mannuronic (ManA) and a-L-guluronic (GulA) residues. The ability of alginate solutions to form cross-linked matrices upon interaction with calcium ions provides a range of rheological properties that has led to a variety of applications in food products as well as in other areas. In order to investigate the effects of calcium ion binding on the structure of alginic acid, the high-resolution ‘H NMR spectra of poly-GulA (low degree of polymerization (d.p.)), poly-ManA (low d.p.) D-mannuronic acid and D-guluronic acid were fully assigned via two-dimensional methods. loo Conformational changes of the polymers upon calcium titration were examined, and a binding model was proposed. Combined NMR and molecular modelling studies were used to characterize the conformation of methylated pectic disaccharide (4-0-a-Dgalactopyranurosyl-l-~-methy~-cY-D-galactopyranuronic 6,6’-dimethyl diester).”’ The extrapolation of such information to a regular polymer structure shows that different helical structures can result from small changes in conformation, without any drastic variation of the fibre repeat. Algal cellulose may be detected in solution by 13N NMR spectroscopy, using lithium chloride-N-N-dimethylacetamideas a suitable non-degrading mixture for dissolving underivatized cellulose. lo’ A method of rapid analysis of cellulose-like regions in cereal P-glucans has been devised by the use of high-performance anion exchange chromatography, followed by characterization by 13C NMR. lo3


17

Wheat bran has been widely used as a source of dietary fibre, having been found to have several desirable functions at the intestinal level. Wheat bran hernicellulose was digested with a commercial Aspergillus japonicus hernicellulase, and some resulting oligosaccharides were purified and characterized by I3C NMR. lo4 Wheat flour oligosaccharides have also been obtained by digestion of alkali-extractable arabinoxylan with Aspergillus awamori. These fractions were identified by 'H NMR, showing chains of (1--+4)-P-~-xylopyranosylsubstituted at 0 3 and/or 0 2 , 3 with arabinofuranosyl groups. 105~106The structure of water-soluble wheat arabinoxylans, as studied by high-resolution NMR, has been correlated with physical properties such as gelling capacity and thermal stability. lo' Some wheat arabinoxylans have also been identified and characterized after acid hydrolysis and methylation

3.3.2. Solids, gels and heterogeneous sjstems Ready access to the wealth of data on the physical properties of complex carbohydrates is of great interest to those involved in the study and manipulation of food carbohydrate structure and functionality. Such information is available in various databases, recently described," including an NMR spectroscopy database. A variety of studies have been carried out on the gelatinization and retrogradation processes of starch. On heating above about 70°C starch absorbs water and gelatinizes. The starch gel so formed is not stable and, on cooling, starch crystallization or retrogradation occurs. This latter process is the main cause for the staling of bread and has, therefore, inspired significant interest in the food science community. 13C cross-polarizationmagic angle spinning (CP-MAS) was used to characterize wheat starch and wheat starch gels. l 2 Separate subspectra for crystalline and amorphous regions were obtained by the "delayed contact" NMR method, which consists of taking combinations of spectra corresponding to moieties with different rotating frame relaxation times. The CP-MAS starch spectrum of the freshly cooled product after gelatinization showed significant changes such as a 65% loss of signal intensity, and a relative increase of the intensity of some peaks in the amorphous region. After a few days, the spectrum showed an increase in the peaks corresponding to the crystalline components of starch. These results suggest that a starch gel consists of at least three types of regions: a portion of liquid-like properties (in which the carbons do not cross-polarize), an amorphous region, practically unaltered by the gelation process, and a crystalline region in which the starch form is strongly dependent on the water content."* The loss of molecular and crystalline order occurring during starch gelatinization was investigated for various types of starch (maize, waxy maize, wheat, potato and tapioca), after defined thermal pretreatment~."~As a short-distance range probe, I3C

'

18


CP-MAS NMR spectra were used to quantify the "double-helix" content, whereas X ray diffraction was used to detect only the double helices that are packed regularly. Both levels of structure were shown to be disrupted during gelatinization. The corresponding gelatinization enthalpic values seem, however, to reflect primarily the loss of short-range order.ll3 The NMR method of Z spectroscopy or cross-relaxation was applied to the study of immobilized polymer in starch ~ a m p 1 e s .Spectra l ~ ~ of starch granules, freshly gelatinized and cooled starch and retrograded starch reflected different amounts and relative rigidities of immobilized starch chains, in each state. The use of wide-line 'H NMR with MAS confirmed the presence of immobilized starch as well as highly mobile starch fractions. The retrogradation process was shown to be accompanied by an increase in fraction of immobilized chains. Through cross-relaxation, the kinetics of ageing were expressed in terms of the changes in the amount and rigidity of solid-like components (see Fig. 4). The relative amounts of immobilized and mobile starch moieties were found to change with the ageing of gelatinized starch.' l 4 Molecular mobility and water organization in starch forms A and B were investigated recently through the application of the two-dimensional 'H-13C heteronuclear wideline separated (WISE) solid state NMR method. 'I5 From WISE spectra measured with a short mixing time it was estimated that 28% of the water present is bound to polysaccharide chains in forms A and B. It was also concluded that water is not preferably bound to particular sites of the glucose rings. Experiments at different mixing times revealed the existence of different water organizations between the starch forms. Spin diffusion studies showed that water mobility in form A is greater than in form B. This fact is related to the lower gelation temperature of the A form of starch. '15 The structural elements of starch gels may, in principle, be built either from macromolecules of single species (amylose or amylopectin) or develop owing to the interaction of different molecules. The roles of both types of polymers on starch structure formation have been investigated by a combination of T2 relaxation measurements, rheology and X ray diffraction,l16 as a function of temperature and relative quantities of the three components: amylose, amylopectin and water. Results showed that aggregates forming during starch gelatinization are composed of amylose and that the polymer amylopectin acts as a precipitating agent. It is suggested that the resulting gel consists of a polymeric network filled by amylopectin macromolecules. 'I6 31P NMR has also been extensively used in the study of starch and its constituents. The phosphate ester groups on potato starch contribute to its clarity and viscosity when it is cooked to a paste. Both the number and the location of phosphate groups determine those properties, and both factors have been studied by 31PNMR. An enzymatic method for the determination


19

of the amount of phosphate bound to glucose C6 atoms in potato starch has been established and applied to a number of potato plants. 31P NMR has been used on samples before and after the enzymatic treatment, showing that the major signal observed represents C6-bound phosphate. '17 The location of phosphates has been studied on a phosphorylated wheat starch, using some mono- and disaccharides as well as potato starch phosphodextrins as model compounds."' High-resolution 31P NMR spectra and 'H NMR spectra (particularly of the anomeric region) of all compounds enabled the assignment of the 31P peaks to mainly glucose C6-bound monophosphate esters and lower levels of C3-bound and CZbound monophosphates. 31P NMR has also been applied to the study of the structure of the starch granule and, particularly, to the location of amylose in the granule.'19 Native maize starch was cross-linked with P0Cl3 and separated in fractions soluble and insoluble in DMSO. The former contained amylose molecules of small size and the latter contained cross-linked amylopectin and larger amylose molecules. 31PNMR peaks at -1.0 and 1.0 ppm, corresponding to phosphate diester, were observed for the insoluble cross-linked fraction whereas peaks at 4.3 and 4.9ppm, registered for the soluble amylose fraction, denoted only a small amount of phosphate monoester. These results were interpreted as indicating that amylose molecules are randomly interspersed in the granule instead of being in bundles. '19 With the increasing interest in starch associated with the food and paper industries, textile manufacture, pharmacology, and biomedical and pharmaceutical research, impressive activities on the modification of natural starch to obtain polymer networks have been carried out. In order to characterize the networks formed, amylose is often used as a model. Amylose networks obtained by complexation of calcium and by covalent cross-linking with epichlorohydrin were studied by solid state 13C NMR and X ray diffraction.'*' The 13C CP-MAS spectral lines of the amylose network prepared by the calcium procedure were very narrow, and fine splitting was observed. The splitting in the C1 region was interpreted as indicating the formation of a short-range helical structure. The spectral lines of the network formed by reaction with epichlorohydrin were broad and almost structureless, indicating a highly disordered and amorphous system. These results were supported by X ray diffractograms.'*' The differences in structure were related to the relatively lower enzymatic degradation rate of the amylose network formed by addition of epichlorohydrin. Phase transitions associated with ordering/disordering processes have been extensively studied, and attention has recently turned to glass transitions. The glass transition of amylopectin was studied by recording the 'H NMR free induction decay (FID) after a 90" p u l ~ e . ~The ' fast decay (rigid) component, with T2R,corresponds to solid polysaccharide protons in the glassy or crystalline states whereas the slow (mobile) component, with

20

A. M.GIL, P. S. BELTON AND B . P. HILLS

T2M,reflects water protons and exchangeable protons. After the rigid lattice limit (RLL), the increase of T2, with temperature is attributed to the onset or increase in frequency of the motion of groups containing hydrogen. The RLL determined by NMR was found to be 20-30°C lower than the Tg measured by DSC. The thermal results also suggest an increase of Tg with crystallinity whereas NMR shows an initial difference between amorphous and 2% crystalline samples, but no difference between 2 and 4% crystalline samples. It is suggested that this is because NMR looks at short-range mobility which may not be detected by X ray diffraction, while DSC and DMTA look at larger-scale effects.30 The CP-MAS spectra of amylopectin were recorded as a function of water content and, at water contents higher than 17.5%, showed the disappearance of the 82 ppm peak, characteristic of amorphous amylopectin, whereas the C1 signal at 100 ppm shows a triplet multiplicity, characteristic of A-amylose. These changes indicate the occurrence of molecular reorganization. The water content at which these changes occur coincides with the one at which the RLL is observed by NMR.30 Potato starch maltodextrins are a special group of reversibly gelling polysaccharides. Pulsed low-resolution NMR, at a field strength of 20 MHz, was applied to follow the gelation process in different thermally reversible rnaltodextrin-water systems. 12' Results were expressed by the ratio of proton populations with high and low relaxation times following a 90" pulse. A linear relation between the solid-liquid ratio from NMR and X ray crystallinity suggested the formation of highly ordered domains as essential constituents of the gel network. The effect of the presence of amylopectin or acetylated maltodextrins on the gelation process was investigated. Part of the economic interest in carrageenan polysaccharides lies in the diversity of their rheological properties, from pure thickening ( A ) , to soft, elastic gels (1) to hard, brittle gels (K). A coil-helix transition is induced by lowering the temperature or adding salt.lz2 The salt effect has been interpreted as stabilization of the polymeric helices by screening out of the electrostatic interactions. In addition to this general salt effect, some ions specifically promote the formation of helices via site binding of the ions. Anion specificity is generally observed to follow the lyotropic series (C1- < Br- d NO3- < 1- < SCN-. However, the K-carrageenan and furcellaran (low-sulfated carrageenans) anion specificity is opposite to the one commonly observed since anions stabilize the helical conformation against the coil conformation. Further, some deviations from the lyotropic series are observed.'** Previous 12'1 NMR studies had shown a dramatic increase in line width with the coil-helix transition, indicating binding of I- to the K-carrageenan helices. The technical difficulties associated with the strong nuclear electric quadrupole of 1271 ( I = "2) have been tackled to some extent by a more recent study.12* The single-pulse excitation was replaced by a composite pulse where the phases of the constituents are cycled


21

producing spectra of improved signal-to-noise ratio. The 1271spectra of standard samples in the extreme narrowing regime were recorded and used as signal intensity references. Measurements of transverse relaxation, longitudinal relaxation and spectral signal intensity were registered as functions of temperature. Signal loss caused by motional correlation times outside the extreme narrowing regime made it difficult to analyse line widths. Longitudinal relaxation times, however, proved more suitable for a comprehensive study, enabling a lower limit of lO-'s to be set up for the residence time at the binding site. 122 The role of cations and of water in the gelation of K-carrageenan has been studied by 23Na, 87Rb and 133CsNMR.'23 The NMR intensity of gel-forming cations undergoes significant change in the vicinity of the sol-gel transition whereas the NMR intensities of the non-gel-forming cations, which coexist with the former, d o not change. This was interpreted as being evidence of selective cation interaction with the polysaccharide. Proton T2 relaxation times showed the existence of three populations of water molecules in the gel system: free bulk water, water strongly bound to polysaccharide and water weakly bound to the network.'23 The functional properties of mixed carrageenan gels have been little studied. Such knowledge should enable the detection of small quantities of a distinct carrageenan type in samples supposedly pure in one type of carrageenan. These small amounts may have a great impact on the rheology and apparent ion selectivity of the system. A rheological method has been devised so that as little as 2% of K-carrageenan may be detected in samples of 1-carrageenan.lZ4 Impurity levels measured rheologically were confirmed by measurements of I3C NMR spectra. Decreasing sodium content in processed foods is a primary concern today. A major problem is to make a low-sodium product with similar chemistry, stability, texture and sensory attributes to that of the full-sodium product. Some studies have investigated the effect of the nature of the hydrocolloid (ionic or non-ionic) on the interaction with sodium ions. 125 The ionic hydrocolloids xanthan and K-carrageenan and the non-ionic guar and locust bean gum were studied. After trace metal analysis of the samples, the 23Na transverse relaxation rates (R 2 ) (inverse seconds) were calculated from the line widths at half height, as a function of added sodium. A t low added Na+, R2 decreased rapidly and was larger for the ionic gums, denoting preferential binding to those than to the non-ionic gums (Fig. 3). At high added Na+, R2 values of ionic gums levelled off and approached the non-ionic gum values. A two-state model with fast exchange, between bound and free Na+, was used to interpret the relaxation behaviour in the ionic systems. A study of xanthan at very low Na+ concentrations suggested a possible competition process between Na+ and endogenous concentrations of K + and Ca2f.125 The polysaccharide xanthan is now widely used as a stabilizer of oilin-water emulsions in most salad dressings. Xanthan has also been found

22

A. M. GIL, P. S. BELTON AND B.

100

1

.

~

.

.

.

~

.

I

80 1

v)

. 9. . , , . . . . , . - - -

.

100

I

n

r

,

.

3

80

P. HILLS

-

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~

.

\

.

.

~

.

.

.

~ I *

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- 8- Kappa-carrageenan 8 - Xanlhan - - o Guar - x - Locust bean

-

'

I

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rh

~

'

~

I

-

\

K 60

5 z a

z

40

20 0

2 0 0 400 600 8 0 0 l O O O " 3 0 0 0 5000

Added NaCl (mg/lOOml) Fig. 3. 23Na NMR R2 for 100 mg/100 ml wcarrageenan, xanthan, guar and locust bean gums as a function of added NaCI, 20-5000 mg/100 ml (note break in x axis). The insert shows the 20-250mg added NaCl/lOOml range. (Reproduced with permission from Shirley and S~hmidt.''~)

to have the role of suppressing oil peroxidation by the inactivation of metal The property of Fe2+ binding to xanthan has been ions such as Fe2+.126 investigated, and results suggest that the metal binds through a pyruvate residue. This has been supported by the high-resolution 'H NMR spectra of xanthan before and after addition of Fe2+;the selective broadening and shift to low field of the pyruvate peak indicates its proximity to the paragmagnetic metal ion.'26 The gelation of pectins with a high degree of esterification (HDE), in the presence of different co-solutes, was investigated by measuring 'H and 23Na Tl and T2 relaxation times.127 Both proton transverse and longitudinal relaxation times decrease to a constant value, as pectin concentration increases. This has been interpreted as reflecting a progressive decrease in mobility due to the formation of higher number of junction zones, for higher concentrations. The effect of the co-solutes ethanol, t-butanol and dioxane on the relaxation behaviour helped to establish that the formation of junction zones in HDE pectins is largely dependent on hydrophobic interactions between methoxyl groups. Scleroglucan, a highly polar polymer, is soluble in water, and generally yields, at low concentration, highly viscous solutions which are used as


23

thickeners in the food industry. This polysaccharide is composed of repeating units of our D-glucopyranosyl residues; one of these is linked as a pendant sugar to the main p(1-3) chain.lZ8 Solid state and solution 13C NMR were used to follow the fixation of water molecules on anhydrous scleroglucan and the evolution of the complex from the solid state to the gel and solution state. Determination of chemical shifts and proton and carbon relaxation times show that hydration to 21% water leads to an increase in solid state order and in chain mobility. The gel state, containing 90% water, was shown to be of an amorphous nature and to be characterized by a triple-helix model of considerable molecular rigidity. 128 Konnyak is a gel of konjac glucomannan (KGM), which is frequently used in traditional Japanese dishes. In order to characterize the structure and behaviour of this gel, measurements of dielectric coefficient, elastic moduli and broad-line NMR were carried out in the temperature range -180 to 150°C. Mechanical and dielectric loss at - 100°C were attributed to rotational motion of hydroxymethyl groups. Decrease of the NMR second moment at 0 to -60°C suggested that such motion is hindered in KGM, to a larger extent than in other polysaccharides such as amylose, dextran or pullulan. Methyl and hydroxylpropylmethyl derivatives of cellulose have the unusual property of forming gels on heating and reverting to the solution state on cooling, with practical industrial applications, including in the food industry. 13" The thermogelation of methylcellulose was studied by 'H NMR, along with other techniques. The proton spectra of the system were obtained at different temperatures in the 3MO"C range. The integrating intensities below 4.2 ppm correspond to most cellulose non-exchangeable protons and to methyl substituents. The changes in proportion of visible NMR signal during heat-induced gelation and dissociation upon cooling were studied. The overall trend is towards higher intensity at lower temperatures, but the slight reduction in the visible NMR signal with decreasing temperature (at the bottom end of the range studied) suggests that in the sol state there is a substantial proportion of the polymer remaining conformationally immobile. 130 The proposed interpretation of these findings is that methylcellulose chains exist in solution as aggregated "bundles", held together by packing of unsubstituted regions of cellulose and by hydrophobic clustering of methyl groups in regions of denser substitution. 130 As the temperature is raised, the bundles come apart, exposing methyl groups to the aqueous environment and causing an increase in volume. At higher temperatures, a hydrophobically cross-linked network is formed. Due to the importance of water retention of dietary fibres in the colon, a variety of dietary fibres have been evaluated according to their hydration ability.131 Pulsed proton NMR was used and the shape of the relaxation curves studied as well as parameters such as the ratio of the different

24

A.

M.GIL, P. S. BELTON AND B. P. HILLS

relaxation components. The behaviours of water-soluble dietary fibres and water-insoluble fibres were compared. Taking into account the distribution and position of polar groups in the molecules, the 6-carboxylate group seemed to determine most of the hydration behaviour of the polysaccharides. Sodium salt forms showed a more pronounced hydration ability than corresponding protonated forms. 13’ The in vitro and in vivo digestion of insoluble dietary fibres was in~estigated.’~~ Proton NMR spectra of the arabinoxylans in digesta of chickens helped to confirm the in vivo studies, which indicated preferential enzymatic degradation of soluble monosubstituted xylose residues, relative to un- and disubstituted residues.’32 3.4. Plant cell walls Plant cell walls are of major importance in foods. They contribute to the texture of plant foods, and as a major source of dietary fibre have an important nutritional role. Much of the literature on plant cell walls has emphasized its phytochemical and botanical importance rather than its relevance to food. However, since much of the methodology developed is equally relevant to food applications the literature is reviewed here. Cell walls can be regarded as a heterogeneous polymer matrix, and one of the classical ways to apply NMR to such a system is to look at proton relaxation processes. Such an approach has been pioneered by Taylor and MacKay and co-workers. In an early paper133 they observed proton relaxation in cellulose, calcium and sodium pectate gels and bean cell walls. The polymers were immersed in 2H20 to avoid interference from water signals. The FIDs of all samples showed two components: a fast relaxing component described as “rigid”, and therefore, supposedly, Gaussian, and a more mobile fraction, presumably exponential or multi-exponential. In cell walls the rigid component represented 60% of the magnetization, and had a second moment intermediate between that of cellulose and pectate. This is consistent with a model in which the rigid component arises from cellulose (30% of cell wall material) and xyloglucans bound to cellulose. The rigid and mobile components also had different T I values. Dipolar relaxation (TD) was two component in the cell walls and was dependent on pD. The results were interpreted in terms of a speculative model in which increasing protonation weakened some intermolecular interactions allowing more motion to occur. A subsequent development to the approach described has been to extend the range of relaxation measurements to include TIP and the use of the 90,-~-90, sequence to measure interpair second moments. These methods have been applied to cellulose’34 and bean cell walls. 135-137 On the basis of these measurements a cell wall model was proposed which incorporated the


25

dynamic features of the biopolymers. Rigid cellulose microfibrils have an outer sheath of rigid hemicellulose molecules. Attached to these are pectic and other hemicellulose molecules which are loosely suspended in a large volume of water.13s In a subsequent study, 136 chemical fractionation was used. This showed results consistent with the proposed model but indicated that removal of the pectin resulted in the loosening of the less lightly bound hemicellulose and that removal of this in turn loosened the remaining hemicellulose. The indication of these results is that sequential chemical removal of cell wall polymers does not leave the remaining cell wall unchanged. This conclusion has also been supported by a combination of neutron scattering and magnetic resonance methods. 13* An alternative approach to cell walls is to employ solid state highresolution 13C NMR. The heterogeneity of the cell walls makes the use of the analysis of chemical shift anisotropy difficult, and most work has concentrated on reporting one-dimensional spectra under conditions of rapid rotation. Under the conditions of dipolar decoupling and/or crosspolarization, quantitative information is difficult to obtain. Polarization transfer rates for the uronic acids vary with the age of the tissue,139 and are likely to vary between different polysaccharide types. 139 Aromatic signals from lignified tissue cross-polarize very slowly and tend to have low intensity in the spectrum.14" This problem can be overcome by using a single-pulse excitation method,141 but even here care is required: spin-lattice relaxation in such a system can be very slow and rotation must be sufficiently rapid to spin out side-bands. The slowness of spin-lattice relaxation makes data acquisition very time-consuming; however, by optimizing contact times and using dipolar dephasing to eliminate unwanted carbohydrate signals14' good estimates of the bound phenolic substances in flax have been obtained using cross-polarization methods. The chemical shift of cell wall polysaccharides is dependent not only on chemical constitution but also on the physical state of the material, particularly conformation and packing.I4' Considerable progress has been made in the assignment of resonance^'^^^^^ and the effects of successive removal of polysaccharides in Vigna radiata have been examined14* in order to examine the contribution of the various polysaccharides to the overall spectrum. In order to carry this out, an assumption was made that removal of polymers did not affect the signals from the remaining polymers. This assumption may not be valid in the light of previously reported proton relaxation results,'36 and it would be interesting to carry out a combined proton and 13C study of a system to further investigate this problem. The nature of cellulose in the cell wall is likely to be of importance in the determination of the eating quality of fruits. A detailed CP-MAS study of cellulose in apple cell walls'46 has indicated that most of it is in crystalline form with crystallites containing about 23 polymer chains per crystallite. There are also disordered chains on the crystallite surfaces.

26

A.

Table 6.

M.GIL, P.S. BELTON AND B. P.HILLS I3C chemical shifts and assignments obtained from CP-MAS experiments on plant cell walls.

Chemical shift (PPm)

Origin

Carbon atom

Celery cell walls 175.3 174 171.7 105.1 101.5, 100.2 88.5, 86.9 81.8, 80.0 75.1, 72.2 68.3 64.7 61.6 53.5 21 17.6

Galacturon, non-esterified Acetyl Galacturon esterified Cellulose, P-galactan p-Glucosyl, a-xylopyranose, P-galacturon Cellulose I Morphous cellulose, xyloglucan P-glucosyl Hexoses and galacturonic acid Cellulose I P-Glucosyl, p-galactosyl Amorphous cellulose Acetyl Pectic methoxyl Rhamnose

C6 Carbox yl C6 c1 c1 c4 c4 c2, c3, c 5 C6 C6 C6 Methyl Methyl C6

Oil palm leaf cell walls 172.7 152.9 149.5 147 136 132.8 132.8 116 116 109.5 105.3 88.7 84.2 75.0, 72.8 64.7 64.7 63.3 56.5 32.6, 29.9 21

Acetyl Ether-linked syringyl Ether-linked guaiacyl Guaiacyl and syringyl not ether linked Syringyl Guaiacyl Syringyl Guaiacyl p-Hydroxyphenyl Arabinofuranosyl Cellulose, xylan Crystalline cellulose Amorphous cellulose, xylan Cellulose, xylan Crystalline cellulose Xylan Amorphous cellulose Aromatic Cutin Acetyl

Carboxyl c3, c 5 c3 c3, c 5 c1 c1 c4 c5 c3, c 5 c1 c1 c4 c4 c 2 , c3, c 5 C6 c5 C6 Methoxyl Methylene Methyl

Millet cell walls 170-180 154 140-148 140-148 140-148 130-140 11C130 11C130

Various carboxyl groups Ether-linked syringyl Guaiacyl Syringyl not ether linked Ether-linked syringyl Aromatic rings Guaiacyl p-Hydroxyphenyl

c3, c 5 c3, c 4 c3, c 4 , c 5 c4

c1

C2, C5, C6 c3, c 5


27

Table 6.-contd. ~

Chemical shift (PPm) 102-109 102-109 102-109 100-102(?) 89 84 78-80 72-75 72-75 64 64 62 56 29-33 21

Origin Cellulose or xylans Syringyl Fructans Free sugars Crystalline cellulose Amorphous cellulose Xylans Cellulose Xylans Crystalline cellulose Xylans Amorphous cellulose Aromatic Long-chain waxes and alcohols Acetyl

Carbon atom

c1 C2, C6 c2

c1

c4 c4 c4 c 2 , c 3 , c5 c2, c 3 C6 c5 C6 Methoxyl Methylene Methyl

Data compiled from refs 143-145 and 147.

CP-MAS spectra of rind, parenchyma and vascular bundle fractions of pearl millet have been reported and some assignments of resonances made.147 Treatment of the tissues with alkali resulted in the reduction of signals from aromatic residues. A partial list of resonance assignments is given in Table 6. The table needs to be used with some caution. Chemical shifts and lineshapes in polysaccharides can be very dependent on water content and a range of chemical shifts assigned to the same carbon atoms is to be expected. One of the great attractions of solid state carbon NMR is the ability to measure the relaxation parameters of specific chemical activities within the cell wall. This has been very extensively exploited in a study of the suberization of potato cell wall.15" Suberin is a polyester that grows in response to wounds, and its function is thought to be the prevention of tissue invasion by fungi and bacteria. 150 By careful examination of proton T1, as well as 13C T1and T I , using CP-MAS it was possible to show that the effect of suberization was to decrease motion of the cell wall polymers in the megahertz range and enhance them in the kilohertz range. This, in effect, may be regarded as a stiffening process resulting in hampering of local segmental motions. Presumably such a decrease in motion inhibits invasion. Interestingly, the related polyester material cutin enhances motion when in contact with wax chains in lime cuticle.'51 More recently, isolation and spectral characterization of cutin and suberin have been reported. 15'

28


3.5. Z spectroscopy and biopolymers Food mechanical and rheological properties often depend on the flexibility of macromolecular networks. In the food science context, it is important to characterize the structure and dynamics of coexisting structural components but, in many cases, relatively immobile or rigid regions may be present in small quantity, thus making them difficult to detect. A recently developed NMR method, denominated cross-relaxation or Z spectroscopy, enables the selective detection of solid-like domains and is sensitive to the dynamic characteristics of the solid components, over a wide range of mobilities."4 The cross-relaxation experiment probes the magnetic and dynamic properties of the solid components through the observation of the liquid signal. The sample is initially irradiated with a preparation pulse that is offresonance from the liquid signal to be measured. After the preparation pulse, an on-resonance 90" observation pulse measures the effect on the liquid magnetization. The principle of this technique is that due to the cross-relaxation process partial saturation of protons in solid components will transfer to water during the preparation period. The degree of saturation of the solid components depends on the irradiation frequency and on the relaxation rates in the solid moieties. The resonance intensity of the liquid, magnetically coupled to the solid, is plotted as a function of the off-resonance frequency of the preparation pulse producing a spectrum that reflects the solid NMR spectrum: the cross-relaxation spectrum. The cross-relaxation spectrum may be presented in the form of a plot of (1 - MAZ/MAZO)as a function of offset frequency, where MAZ is water intensity with a saturation pulse and MAZo is water intensity without saturation. The lineshape of the spectrum is dependent on the amount and relative rigidity of the solid component: the more solid component the sample contains and/or the more rigid the solid component is, the broader and more intense will be the resulting cross-relaxation spectrum. '14 One advantage of the use of the cross-relaxation NMR method is that it may, in principle, be executed on a low-field (5-20 MHz), low-resolution, singlefrequency ('H) spectrometer of relatively low cost. The Z spectroscopy method was applied to the study of immobilized polymer in starch samples. '14 Comparison of spectra of starch granules, freshly gelatinized and cooled starch and retrograded starch showed that they reflect the amount and relative rigidity of immobilized starch chains (Fig. 4). Spectral intensities for freshly gelatinized starch were significantly dependent on starch concentration, and retrogradation was shown to introduce a broad component in the spectrum. A wide variety of segmental mobilities is suggested, their distribution changing as gelatinized starch ages. The same method of cross-relaxation has been applied to detect and quantify solid components and to follow their changes during ripening of banana.153 The evolution of solid-like phases in banana during ripening was

el

APPLICATIONS OF NMR TO FOOD SCIENCE 1.0

-..

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.-. ...

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29

. *

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-60

-30

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-10

10

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, 30

I

1-60

-30 -10

10

30

60 -60

-30

-10

10

30

60

Offset Frequency (kH5) Fig. 4 ‘H cross-relaxation spectra of 10% waxy maize starch: (a) suspension of granules in 0.25% acqueous xanthan solution; (b) freshly gelatinized and cooled ( X ) , and DMSO solution (0); (c) retrograded gel (5°C for 30 days). (Reproduced with permission from wu et al.’ 4,

monitored. Cross-relaxation spectra show that during ripening there is a dramatic decrease in the area of the broad component (from 20 to 2% w/w). This is consistent with the fact that unripe banana is rich in starch and that ripening is accompanied by starch conversion to soluble sugars. Two superimposed spectral components are observed, a broad and a narrow one. The area of the former decreases with ripening whereas the area of the latter increases during the process. The nature of both broad and narrow components in the cross-relaxation spectrum is discussed in terms of the chemical composition of banana. The wide-line proton spectrum of banana was obtained with the solid echo pulse sequence and showed two components, the broader of which arising from starch.ls3 The results of the quantification of soluble sugars by high-resolution ‘H MAS NMR and of solid starch by the cross-relaxation method confirmed the hydrolytic conversion of starch to sugars during banana r i ~ e n i n g . ” ~

4. ANALYSIS

4.1. Introduction

Interest in NMR as an analytical method is continuing to develop, and the area has been reviewed.ls4 One of the interesting trends is the reexamination of the idea that NMR is an insensitive technique. As higher field strengths become available, very high sensitivities may be achieved. Even with the relatively modest (by current trends) proton frequency of 500MHz it has been shown’’5 that for benzene in water the detection limit is 35 ng/ml and for N-nitrosodimethylamine 510 ng/ml. Both these figures represent detection at the sub-parts per million level. Often in food systems straightforward high-resolution solution state methods are not suitable.

30


Lines may be broadened by motional effects, and thus require the use of wide-line or pulse methods, or they may be broadened by susceptibility effects. In the latter case, MAS can restore resolution. For at-line or in-line applications or routine quality control laboratories, cost is often a factor. In order to lower costs, low-field systems are required together with simple electronics. This need continues to drive exploration of low-field pulsed N M R methods and has renewed interest in rapid scan correlation (RSC)NMR. A continuing major application of N M R in food science is the use of isotopic and other methods for the authentication of foods and the detection of adulteration. As the market for foods with specific claims to geographic origin, particular forms of processing or “naturalness” grows, so apparently does the level of fraud. The various topics outlined above are reviewed in the following sections. 4.2. Developments in authentication The importance of authentication and the detection of adulteration by N M R is attested by the continuing output of reviews and reports on the subject. Many of these do not offer any new N M R approaches but reflect applications of standard methods to new areas. One new application is the use of very high-field NMR as a proximate analysis method.’56 The use of I3C N M R combined with discriminant analysis157 has been reported for identifying olive oils. It was shown that it was possible to distinguish different grades of oil by this method. Deuterium N M R is still finding new applications in the detection of adulteration. An example is the distribution of deuterium in the aromatic sites of ben~aldehyde;’~~ this has enabled the detection of synthetic benzaldehyde in bitter almond oil. The remaining publications in this area are listed in Table 7. 4.3. Process applications

N M R does not lend itself very easily to process applications; nevertheless, there continues to be interest in the field and progress is being made. Reade17’ has considered some of the problems involved in applying N M R on-line in the food industry. Among the most important applications of N M R are the determination of oil and water contents171 and the solids contents of fats. For the latter application a new low-field instrument has been devised. 172 The use of N M R to measure oil and moisture contents in seeds is valuable because the non-destructiveness of the technique allows measurement of seeds to be used in breeding programmes as well as in general quality


31

Table 7. Recent publications concerned with the authentication of foodstuffs. Subject

Ref.

Comments

Deuterium NMR of wines Preparation of musts Use of deuterium and carbon NMR Isotopic methods SNIF-NMR NMR for authentication and adulteration Authentication of essential oils SNIF-NMR for flavours and fragrances SNIF-NMR for fruit juices SNIF-NMR Authentication of decanolides

159 Refers to Lombardy wines 160 New method proposed 161 Review 162 Review 163 Review 164 Review 165 Use of GC, GC-MS and NMR 166 Review

167 Review 168 Review 169 Uses 2H NMR

GC, gas chromatography; MS, mass spectrometry; SNIF-NMR, site-specific natural isotope fractionation studied by NMR.

Where results are to be shared between laboratories, it is vital to ensure traceability, and certified reference materials need to be available. The Community Bureau of Reference (BCR) has developed these for rapeseed. 177 An unusual and interesting application of N M R is for the control of cake ~ o o k i n g . ' ~ 'The approach was to sample rapidly and slowly relaxing components of transverse relaxation to characterize the liquid-solid ratio in the material. The results were then analysed for an experimental design in which ingredients and cooking times were systematically varied. Transformation of the variables was performed using principal components analysis (PCA). It is clear that much work remains to be done, but this approach seems to suggest a route to the use of relatively simple N M R measurements in the control of complex processes. The non-destructive detection of fruit quality by relaxation time measurements has concentrated on the role of sugars in ripeness'79 and their estimation in intact fruits.'" However, 31P N M R may be used to examine the effects of low oxygen levels and p H changes in fruit ripening.''l 31PN M R has also been used to measure phospholipid contents in peas.'** 4.4. RSC methods

One of the problems of the food industry is that it is typically an industry where profit margins are low. This means that quality control instruments must be of low cost, otherwise they do not pay for themselves. Sophisticated high-field instrumentation is, notoriously, not low cost. If the advantages of N M R are to be brought to the food industries' quality control problems they

32


must come in a suitably low-cost form. One way of doing this is to revert to low-field methods and use the relatively cheap electronics associated with continuous wave methods. Experimentally this brings with it the difficulty of low signal-to-noise ratios and long scan times if distortion of the resonance lines is to be avoided. These problems can to a large extent be ameliorated by the use of RSC NMR.ls3>ls4In this technique the spectral range is scanned rapidly. This results in a spectrum which is strongly distorted by oscillations in intensity following each peak maximum. ls3 This is caused by the convolution of a residual component of transverse magnetization with the swept field. The origins of this are well understood, and the intensity can be described by the simple equation ~ ( t =) exp(-ib?) where b is the sweep rate in radians per second and f is the time after the peak maximum. Deconvolution may be achieved by reverse Fourier transformation of the spectrum, multiplication by the appropriate function in the Fourier domain. Forward transformation then recovers the spectrum. When this method is used for proton spectra on a 60 MHz machine, surprisingly good results can be obtained, an illustration of which is given in Fig. 5 . Ethanol could be

I

1

8.0

1

7.0

I

I

1

I

6.0 5.0 4.0 3.0 CHEMICAL SHIFT ppm

1

1

1

2.0

1.0

0.0

1

Fig. 5. An RSC proton NMR spectrum of a margarine sample. (P. S. Belton and B. J. Goodfellow, unpublished results.)


33

measured quantitatively in water to levels as low as 0.01%, and the technique compared favourably with gas chromatography and density methods for the analysis of the ethanol content of wines and beer.'83,184 Similarly, quantitative measurements of glucose and estimates of unsaturation in oil were made.184 In general, the technique seems to hold some promise as a low-cost, non-invasive, minimal preparation method of food analysis.

4.5. MAS methods

Observation of emulsion phases is important in studies of emulsion stability and capacity as well as in quantification. A 'H NMR method has been used to quantify the different phases in the multiple emulsion water in oil in water (W/O/W) whose dispersed oil drops contain even smaller droplets of a dispersed aqueous phase. 18' MAS was applied, showing that it greatly improves resolution by removing broadening due to magnetic susceptibility mismatch among phases. This result will enable more detailed studies of chemical and physical processes in emulsions. Addition of the shift reagent [DyEDTAI- to the external water phase, in combination with MAS, allows separation and quantification of external and internal water phases. 185 Selective observation of internal water was achieved by T2-selective application of the CPMG spin echo sequence, leading to elimination of external water resonance. MAS methods may be applied to study the liquid phase in fruit tissue, 153.186.187 N arrow peaks for water or metabolite nuclei are expected, since the primary line-broadening interactions should be suppressed by fast molecular reorientation. This enables the study of metabolism in intact plant tissue, and its application to foods has been previously reported. 18' High-resolution 13C NMR spectra of intact fruit tissues-grape, peach, persimmon, banana and apple-were obtained while spinning the sample at the magic angle to improve resolution (see Fig. 6). Only low speeds (of the order of a few hundred hertz) were required to reduce susceptibility broadening, which decreased as apple > banana > grape. 18' Fructose, glucose and sucrose resonances appeared with correct chemical shifts, thus permitting their identification and quantification. The most abundant anomers of fructose and glocose were observed. Scalar IH-I3C couplings were observable as multiplets in spectra taken without proton decoupling, thus aiding the assignment. Measured values of the nuclear Overhauser enhancement effect and longitudinal time T1 were consistent with rapid, effectively isotropic tumbling of sugar molecules, at rates very close to those observed in solutions of pure sugars. The method developed is capable of detecting sugar anomers in concentrations at least as low as 0.5%.'*' The relatively low sensitivity of 13C led to long acquisition times, and minor

34


~

110

"

'

l

100

"

'

l

90

"

'

l

m

'

'

70

'

~

'

Bo

Chemical Shift I ppm

Fig. 6. Proton scalar decoupled 50MHz I3C NMR spectra of intact fruit tissue (effect of MAS shown in lower spectra): (A) grape, (B) persimmon, (C)banana and (D) apple. The vertical scaling been adjusted for convenient display. (Reproduced with permission from Ni and Eads.Is6)


35

x1

Chemical Shift/ppm

Fig. 7. 'H NMR spectrum (200MHz) of intact banana fruit tissue: (A) non-MAS spectrum obtained in a conventional high-resolution probe with sample axis parallel to magnetic field; (B) MAS spectrum obtained without water peak suppression; (C) vertical expansion of (B); (D) MAS spectrum obtained with water peak suppression. The signal-to-noise ratios in spectra (C) and (D) are 55 and 1137, respectively. The MAS rate was 1.05 kHz. (Reproduced with permission from Ni and Eads.ls7).

components were not visible, which makes routine quantification rather difficult. Another method was advanced, consisting of the recording of the MAS 'H NMR spectra using water peak ~uppression'~'(Fig. 7). As indicated before, MAS reduced susceptibility broadening while water suppression increased the dynamic range, enabling the detection of liquid phase components with concentrations as low as 0.01%. Water, glucose, fructose, sucrose, organic acids (malic, citric, tartaric) and total fatty acyl lipids were quantified. Longitudinal relaxation times of non-exchangeable glucose protons were measured in situ in banana and found to be dominated by

36

A . M. GIL, P. S. BELTON A N D B. P. HILLS

intra- and intermolecular homonuclear dipolar interactions, as found for the in vitro situation. Apparently, rotational motions of the water and sugar molecules within the fruit are relatively ~ n h i n d e r e d . In ' ~ ~a separate study, the increase in soluble carbohydrate during ripening of banana was monitored by high-resolution proton NMR, using low-speed MAS and water peak suppression. 153 Resonances of water, sucrose, fructose, glucose, fatty acyl chains of mobile lipids, and organic acids were easily detected and their changes with ripening quantified.

4.6. Other applications

4.6.1. Tea, coffee and wine

Pu-erh tea is a kind of Chinese tea, manufactured in specific provinces, and which undergoes periods of postfermentation and piling processing longer than those for dark teas. '*' These differences in the processing are believed to have a determining effect on the production of the characteristic aroma and colour components of Pu-erh tea. 13C NMR studies, along with chromatographic techniques, showed that carbohydrates and amino acids as well as catechins are digested during the microbial fermentation process, the main constituents of made-tea being caffeine, gallic acid and 2 - 0 - p - ~ arabinopyranosyl-myo-inositol. The volatile components were identified by gas chromatography and gas chromatography-mass spectrometry. The film of tea scum which forms on the surface of tea brewed in hard water has been characterized by several techniques, including powder diffractometry , electron microscopy, Fourier transform infrared (FTIR) spectroscopy, mass spectrometry and solid state 13C NMR."" The presence of inorganic carbonate was confirmed by FTIR and 13C NMR, and the same techniques pointed to the presence of hydroxyl groups, carbonyl groups and some unsaturated organic linkages.'" Dry tea leaves are known to have a high fluorine content, but its chemical form, and hence its bioavailability, is unknown. "F NMR has been used to study several types of tea infusions showing that F- is the main fluorine form present.lgl To identify forms of accumulated aluminium in tea leaves, 27Al NMR was applied to the study of intact tea leaves and the detection of complexes such as aluminiumcatechin, aluminium-fluorine, aluminium-phenolic acid and aluminiumorganic acid. On the basis of the NMR results and leaf constitution, it was found that most of the aluminium present in intact leaves is in the form of catechin complexes while some portion is bound to phenolic and organic acid complexes."* The in vitro speciation of aluminium in black tea infusion was assessed in order to investigate the quantity of aluminium potentially available for absorption throughout the small bowel. This work included an in vivo study of the breakdown of tea-derived polyphenols to low molecular


37

weight phenols, which was measured by analysing ileostomy effluent through high-resolution 'H NMR.'93 At present, the output of coffee amounts to about 40 million tonnes, and almost the same amount of extraction residue of coffee is formed. However, most of the residue is disposed of as waste, and it is therefore of interest to find an effective method of reusing coffee residues. Some recent studies have used NMR to clarify the chemical structure of an unknown antimicrobial substance found in coffee residue in order to use it as an antibacterial substance for foods. 194 Following purification by high-performance liquid chromatography, and characterization using mass spectrometry and 'H and 13C NMR, the substance was found to be 3',4'-dihydroxyacetophenone. Solid state 13C NMR, using CP and MAS, has been applied to analyse insoluble deposits adhering to the inner glass surface of bottled red wine. 19' These deposits were found to be composed of a phenolic polymer of anthocyanins, procyanidins and protein. Some terpene disaccharides of wine have been characterized by a combination of mass spectrometry and high-resolution 'H NMR'96 4.6.2. Fruit and vegetables

Chilling injury (CI) is a disorder associated with a number of fruits and vegetables that occurs when they are stored at low but non-freezing temperatures (S12"C) for periods specific to the species. Brown pits or stains appear on grapefruit peel when the fruit is stored at 5°C for 3 weeks. One of the triterpenone components found to have a direct relationship with CI effects, friedelin, was identified by 'H and 13C NMR.19' A 10MHz 'H NMR technique has been developed to estimate the sugar content of intact fruits.lg8 Proton T2 relaxation times have been calculated for intact grapes and sweet cherries. The results were then interpreted taking into account the chemical exchange process between sugar and water in the fruit. NMR has been used to analyse pesticide residues in field-grown carrots. These were grown in trifluralin-treated soil and sampled regularly. The pesticide residue was measured by 19F NMR and chromatographic methods. The two methods were found to be in agreement, although the latter proved more adequate for the measurement of low concentration^.'^^ 4.6.3. Lipids In contrast to some of the previous sections much of the work on lipids relies on the application of conventional high-resolution methods. These have been used to explore the chemical composition of lipids in foods, and result in experiments which generally give less ambiguous results than those described elsewhere.

38


A recent work has reviewed the use of high-resolution 13C methods for the study of lipid structure and composition.200The I3C NMR spectra of Vernoniu galurnensis seed oil and of epoxidized palm super olein, soybean oil and linseed oil have been recorded and interpreted.201 Both natural epoxy oils and epoxidized oils are of commercial interest, and the spectroscopic procedure provides a semi-quantitative method of analysing oils that contain epoxy acids. I3C NMR has also been used to quantify castor oil in various edible oils, such as coconut oil, palm oil, groundnut oil and mustard oil. The C10, C9, C12, C13 and C11 peaks of the main component of castor oil, ricinoleic acid, have been used for quantification down to 2.0 and 3.0%, respectively, for qualitative and quantitative analysis.202 Oil chemical changes during the various stages of plant flowering and fruiting may be studied by making use of 'H and I3C NMR spectroscopic methods, as demonstrated in a recent study of Tugetes minutu Determination of the content of saturated fatty acids in positions 1,3 and 2 of triacylglycerols of olive oil has been carried out by high-resolution 13C NMR methods.204 This work was the basis for the development of an analytical method to detect synthetic esterified oils in mixtures of virgin olive oils. Pure fractions of olive oil highly esterified sucrose polyesters have been produced and subsequently identified by infrared and NMR spectroscopy.205In a separate study, high-resolution I3C NMR spectroscopy was used to characterize the composition of the unsaponifiable matter of 20 olive oils and pomace oils.2o6 Based on the identification of characteristic peaks corresponding to molecular substructures, rather than to individual constituents, it was possible to distinguish between different grades of olive oils. There are some indications that high levels of certain fatty acids of fish oils may be related to a lower incidence of heart disease. Most abundant fish fatty acids contain a double bond in the 0-3 position. The w-3 fatty acid distribution in lipid e ~ t r a c t ~ ' ' ,and ~ ~ ~white muscle208 from the Atlantic salmon (Salmo salur) has been quantified by high-resolution IH and I3C NMR. The effect of storage at below freezing temperatures was discussed.207A structure-specific 'H NMR method for quantification of w-3 fatty acids in fish oils has been ~ u g g e s t e d . ~This " ~ method relies on the different chemical shift observed for the methyl resonance of w-3 fatty acids (6 = 0.95 ppm) relative to that of other fatty acids (6 = 0.86 ppm). Oils from 24 samples of raw, cooked and canned albacore tuna (Thunnus ululunga) were quantified and compared.209 This approach is also useful to obtain structural knowledge about fatty acids and related compounds concerned with by-products or bioreactions of w-3 acid formation. A variety of high-resolution 'H and 13C NMR techniques have enabled the elucidation of the structure of cis-5,8,11,14,17eicosapentaenoic acid ethyl ester (EPA-EE) and cis-4,7,10,13,16,19docosahexaenoic acid ethyl ester (DHA-EE).210The distribution of the two corresponding acids, EPA and DHA, between the a- and P-glycerol chains


39

have been determined by high-resolution 13C NMR, for various fish oils. This study showed that DHA is concentrated in the /3 position whereas EPA is randomly distributed between the (Y and /3 positions.211 Oxidative deterioration of vegetable and of salted dried fish oils214,215 was investigated using NMR spectroscopy. The ratios of olefinic protons and divinylmethylene protons to aliphatic protons were determined by NMR and shown to decrease during ~ t o r a g e . ~ *Comparison ~*~'~ with corresponding peroxide values and acid values showed that the ratios of olefinic protons to aliphatic protons may serve as an index of oxidative deterioration. A recent study demonstrated the uses of high-field proton NMR in characterizing the products of the oxidative deterioration of polyunsaturated fatty acids.213 Thermal stressing of culinary oils, rich in those acids, generated high levels of some n-alkanals, trans-2-alkenals, alka-2,4-dienals and 4-hydroxy-rrans-n-alkanals.Yields were compared between different types of cooking oils. The same work discusses the dietary, physiological and toxicological implications of the process. The extent of lipase-catalysed esterification reactions has been studied non-invasively.216 Ratios of ester:alcohol signals were measured and shown to be reproducible and suitable for the study of varying conditions and nature of fatty acid and alcohol substrates on the extent of the reaction. In order to investigate intermediates and products due to chemical transformation of cholesterol during storage and heating of foodstuffs, quantitative analysis of cholesterol oxides in egg powder was carried out by high-resolution 'H NMR.217 Quantified cholesterol derivatives ranged from 4.9 to 9.1 ppm with a detection limit of 0.3 ppm. Pigments responsible for colour formation during blanching and deodorization of canola oils (rapeseed oil) were analysed by 'H and 13C resonance, proving to be trace glycerides. Both the bleaching agent and the deodorization treatment were shown to affect the distribution and concentration of the chromophores.218The essential oil liguloxide, responsible for the tomato ketchup characteristic odorific note, has been characterized by 'H and 13C NMR methods.219 High-resolution I3C spectra of butter, two vegetable fats, four baking fats, seven spreading fats and an infant formula were obtained.220 Peak assignment enabled the identification and semi-quantification of constituents such as butterfat, lauric oils, partially hydrogenated fat, linoleic acid or linolenic acid. The low-resolution pulsed methods to determine solid fat contents have been standardized for animal and vegetable oils and fats, with specification The existing of sample preparation and conditions of experimental techniques for the study of solid-liquid fat ratios, fat structure and polymorphism and fat crystallization have been complemented by the Table 8 summarizes application of imaging and localized the variety of recent NMR studies of fats and oils.

40


Table 8. Recent NMR studies of lipids. System/nucleus

Ref. ~

High-resolution methods Vario~s/'~C and 'H Vegetable epoxidized ~ i l s / ' ~ C Castor 0ii/l3c Minuta oiVl3C and 'H Olive 0ii/l3c Pomace 0i1s/'~C Fish o i l ~ / ' ~and C 'H Oxidative deterioration of oils/'H Cholesterol oxides Canula o i l ~ / ' ~and C 'H

200, 216, 219 201 202 203 204-206 206 207-211, 214, 215 213 217 218

Low-resolution methods Animal and vegetable oils and fats/'H Tripalmatin/2H Cocoa masses/'H Various oilseeds/'H Milkfat ~ h e e s e / ' ~ C / ~ ' P Palm oil/'H Review of methods and sample preparation

221-224 225 226 227, 228 229, 230 231 232

Lipid polymorphism and crystallization have also been studied by 'H solid state NMR.'" The molecular dynamics in three crystalline forms of tripalmitin were investigated, as well as the motional consequences of certain thermally induced structural transitions, in the solid state. Below the melting point, at 20°C, molecular motions were found to be more restricted in the p form than in the a and p' forms. On the other hand, spin-lattice relaxation measurements have shown that the motion of methylene groups is dynamically heterogeneous and faster in the a and p' forms than in the p form. The transition between the a and p forms was followed by lineshape studies of the deuterium spectra, which showed the occurrence of immobilization. Other tripalmitin transitions were studied on the basis of deuterium NMR spectra and relaxation times.225 4.6.4. Spices and phytochemicals Antioxidants are used in processed foods to minimize the undesirable effects of lipid oxidation, and natural compounds have been increasingly needed to replace the conventional agents butylated hydroxytoluene (BHT) and butylated hydroxyanisole (BHA). 'H NMR has helped to characterize six major compounds purified from oleoresin of sage (Salvia oficinalis) .233 They were quantified in sage and in four commercial rosemary extracts and their antioxidative activity measured with an accelerated test. Mushrooms


41

contain reducing substances with chemical properties similar to those of ascorbic acid. Four types of these ascorbic acid analogues have been purified from different varieties of mushrooms and their structures characterized by NMR methods.234Capsaicin is a pungent principle of the hot pepper, and its study has more recently focused on its nutritional benefits and physiological functions. However, the use of capsaicin as a food ingredient has been limited because of its strong pungency and low The corresponding glucoside was obtained and characterized completely by 'H NMR; additional tests showed that glucosylation of the phenolic hydroxyl group resulted in loss of pungency and increase in water 4.6.5. Milk

Thermal denaturation, aggregation and gelation of P-lactoglobulin in solutions either with no added salts or with some added mono- or divalent ions were investigated by 'H and '"Cd NMR spectroscopy.236 The aggregatiodgelation kinetics were studied at 70°C, by 'H NMR, showing that the protein folded form unfolds under all salt conditions and is followed by aggregation and gel formation. Binding divalent ions seemed to stabilize the unfolded conformation. "'Cd NMR line widths indicate that Cd2+ ions interact predominantly with carboxylate oxygen sites and are not tightly bound. The physical properties of milk fat and its fractions, blends of milk fat with other fats and mixtures of milk fat with liquid oils have been investigated using methods such as differential scanning calorimetry and NMR.230

4.6.6. Meat Collagen is an important component of meat protein and has, therefore, been in the past a subject of extensive work, including the use of spectroscopic techniques such as NMR. More recently, a proton NMR study of different cross-linked collagens was performed as a function of water and temperature237 in order to obtain information about the different processes of water-collagen interaction. Collagens from the connective tissues of the calf, steer and cow with different numbers of non-reducible cross-links were analysed. Transverse and cross-relaxation times of water protons were accounted by two processes: proton exchange at higher temperatures and dipole-dipole interactions prevailing at lower temperatures. All the relaxation parameters showed specific behaviour for the 0.44 water activity, for every tissue. In addition, the NMR parameters obtained for calf collagen tissue behaved differently from the other tissues. This should relate to the relatively lower number of cross-links and higher solubility of this tissue.237 Ar present, heart muscle is not considered to be a useful by-product of the meat industry, thus justifying the very few studies dedicated to this system.

42

A.

M. GIL, P. S. BELTON AND B. P. HILLS

However, heart muscle is a potential source of protein and a functional ingredient in the food industry of new products such as beef heart surimi analogues. The behaviour of heart muscle from chicken, pork and beef relative to composition and processing conditions has been studied through 'H NMR relaxation methods.238 The transverse magnetization decay was found to best fit a three exponential component model, which should correspond to three proton populations of average T2 values in the range 2 m s to 0.7s. Heating the system to 6 5 T , during 30min, produced significant increase in the longest T2, in all cases providing a rapid and accurate method to monitor water release and, hence, meat quality.23s Phosphorous NMR has also been found useful to monitor changes in ATP, creatine phosphate and pH in order to help assessing halothane (bromochlorotrifluoroethane) sensitivity and meat quality in pigs.239 Halothane sensitivity is a metabolic defect that produces the well-known condition termed pale soft exudative (PSE) meat, which is of low organoleptic quality and yield. Further research on PSE as well as on dark firm dry meat (DFD) was carried out by 31P NMR.240 Comparison of the phosphorous spectra of several different pig breeds and muscles showed that normal, PSE and DFD meats correspond to clearly distinct compositions in phosphorylated compounds, under 30 min post-mortem conditions.

4.6.7. Other studies The molecular motion of sucrose in water-ethanol-sucrose-casein solutions These was studied by 13C NMR spin-lattice relaxation studied are relevant to the investigation of colloidal stability of cream liqueurs. Results suggest that the sucrose conformation is not affected by concentration, temperature or the presence of alcohol or casein, there being no evidence of interaction between sucrose with either alcohol or protein. 2H NMR has helped the study of baker's yeast fermentation.242 Experiments in deuterated water showed that yeast fermenting on D-mannose, D-glucose or D-fructose yielded trideuterated (R)S-benzylthioglycerate. The extent and stereochemistry of labelling was shown, by 2H NMR studies, to depend on the carbohydrate precursor. The Maillard reaction of model compounds for peptide-bound lysine with reducing sugars was investigated under both stringent and mild condition^.^^' The structure of a new reaction product was determined by a combination of chromatography and NMR methods. One should be cautious of automatically regarding a high dietary fibre level as beneficial. One component of bran, phytic acid, is a potent complexer of divalent cations, being often implicated in calcium and zinc deficiency diseases. Phytate and trace elements of the daily diet of healthy subjects in Taiwan were determined by 31P NMR and by instrumental neutron activation analysis, r e s p e c t i v e ~ y . ~ ~ ~ The volatile components of salak fruit have been isolated, and over 40

APPLICATIONS OF NMR T O FOOD SCIENCE

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compounds have been identified by a combination of techniques, including 'H NMR.245The conformational preferences of some L-aspartyldipeptide methyl esters to elicit tastes such as sweet and bitter have been investigated by conformational free energy calculations and conformational studies by 'H NMR.246 The presence of the ~-aspartylgroup proved to be a necessary factor for sweet dipeptides whereas the orientation of hydrophobic moiety relative to the structural system AH/B was confirmed to be determinant.

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A. M. GIL, P. S. BELTON AND B. P. HILLS M. A. Murcia and J . Villalain, J . Sci. Food Agric., 1993, 61, 345. H . Barjat, P. S. Belton and B. J. Goodfellow, Analyst, 1993, 118, 73. H. Barjat, P. S. Belton and B. J. Goodfellow, Food Chem., 1993, 48, 307. T. M. Eads, R. K. Weiler and A. G . Gaonkar, J . Coll. Interface Sci., 1991, 145,466. Q. W. Ni and T. M. Eads, J . Agric. Food Chem., 1992, 40, 1507. Q. W. Ni and T. M. Eads, J . Agric. Food Chem., 1993, 41, 1026. T. M. Eads, Frontiers in Carbohydrate Research-2 (ed. R. Chandrasekara). Elsevier, New York, 1992. 2. Gong, Biosci. Biotech. Biochem., 1993, 57, 1745. M. Spiro and D. Jaganyi, Food Chem., 1994, 49, 351. H. Horie, T. Nagata, T. Mukai and T. Goto, Biosci. Biotech. Biochem., 1992, 56, 1474. T. Nagata, M. Hayatsu and N. Kosuge, Phytochemistry, 1992, 31, 1215. J. J. Powell, S. M. Greenfield, J . K. Nicholson and R. P. H. Thompson, Food Chem. Toxicol., 1993, 31, 449. A. Nishina, Biosci. Biotech. Biochem., 1994, 58, 293. E. J. Waters, Z . Peng, K. F. Pocock, G. P. Jones, P. Clarke and P. J . Williams, J . Agric. Food Chem., 1994,42, 1761. V. A. Marinos, M. E. Tate and P. J . Williams, J . Agric. Food Chem., 1994,42, 2486. H. J . Nordby and R. E. McDonald, J . Agric. Food Chem., 1994, 42, 708. S . I. Cho, R. L. Stroshine, I. C . Baianu and G. W. Krutz, Trans. ASAE, 1993, 36, 1217. R. D . Mortimer, D. B. Black and B. A. Dawson, J . Agric. Food Chem., 1994, 42, 1713. F. D. Gunstone, Progr. Lipid Res., 1994, 40, 1215. F. D. Gunstone, J . A m . Oil Chem. Soc., 1993, 70, 1139. H . Sajid, K. Mohd, G. S. R. Sastry and N. P. Raju, J . A m . Oil Chem. SOC.,1993, 70, 1251. R. K. Thappa, S. G . Agarwal, N. K. Kalia and R. Kapoor, J . Essent. Oil Res., 1993, 5, 375. R. Sacchi, F. Addeo, I. Giudicianni and L. Paolillo, Ital. J . Food Sci, 1992, 4, 117. J. J. Rios, M. C. Perez-Carmino, G . Marquez-Rui and M. C. Dobarganes, J . A m . Oil Chem. SOC., 1994, 71, 385. R. Zamora, J. L. Navarro and F. J. Hidalgo, J. Am. Oil Chem. SOC., 1994, 71, 361. M. Aursand, J. R. Rainuzzo and H. Grasdalen, Proceedings of the Qualify Assurance of the Fish Industry, Ministry of Fisheries, Denmark, 1992. M. Aursand, J . R. Rainuzzo and H. Grasdalen, J . Am. Oil Chem. SOC., 1993, 70, 971. R. Sacchi, I. Medina, S. P. Aubourg, F. Addeo and L. Paolillo, J . Am. Oil Chem. Soc., 1993, 70, 225. C. A. H. Hegg, 17th Nordic Lipid Symposium Proceedings, (eds Y. Maikki and G. Lambertsen) Scand. Forum Lipid Res. Technol., Bergen, Norway, 1993, p. 240. F. D. Gunstone and S . Seth, Chem. Phys. Lipids, 1994, 72, 119. U . N. Wanasundara and F. Shahidi, J . Food Lipids, 1993, 1, 15. A. W. D. Claxson, G. E. Hawkes, D. P. Richardson, D. P. Naughton, R. M. Haywood, C. L. Chander, M. Atherton, E. J. Lynch and M. C. Grootveld, FEBS Lett., 1994, 355, 81. H. Saitb and M. Udagawa, J . Am. Oil Chem. SOC.,1992, 69, 1157. H. SaitB and M. Udagawa, Biosci. Biotech. Biochem., 1992, 56, 831. C. J. O’Connor, S. F. Petricevic, J. M. Coddington and R. A. Stanley, J . A m . Oil Chem. SOC.,1992. 69, 295. A. Fontana, F. Antoniazzi, G. Cimino, G. Mazza, E. Trivellone and B . Zanone, J . Food Sci., 1992, 57, 869. D. M. Chapman, E. A. Pfannkoch and R. J. Kupper, J . Am. Oil Chem. SOC., 1994, 71, 401. C. Dragar, V. A. Dragar and R. C. Menary, J . Essent Oil Res., 1993, 5, 507.

APPLICATIONS O F NMR T O FOOD SCIENCE 220. 221. 222. 223. 224. 225. 226. 227. 228. 229. 230. 231. 232. 233. 234. 235. 236. 237. 238. 239. 240. 241. 242. 243. 244. 245. 246.

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F. D. Gunstone, J . A m . Oil Chem. SOC., 1993, 70, 361. British Standards Institution, British Standard, 1992. BS 684, Section 2.22. M. C. M. Gribnau, Trends Food Sci. Technol., 1992, 3, 186. C. Simoneau, M. J. McCarthy, D. S. Reid and J. B. German, Trends Food Sci. Technol., 1992, 3 , 208. S. Oezilgen, C. Simoneau, J. B. German, M. J. McCarthy and D. S. Reid, J . Sci. Food Agric., 1993, 6 , 101. D. Precht and E. Frede, Fett. Wiss. Technol., 1994, 96, 324. C. V. Hernandez and D. N. Rutledge. Food Chem., 1994, 49, 83. G. Rubel, 1. A m . Oil Chem. SOC., 1994. 71, 1057. P. N. Gambhir, Trends Food Sci. Technol., 1992, 3, 191. L. T. Kakalis. T. F. Kumosinski and H. M. Farrell, J . Dairy Sci., 1994, 7 7 , p. 667. W. L. Ng and C. H. 0 h . J . Am. Oil Chem. SOC., 1994,71, 1135. T. M. Eads, A . E. Blaurock, R. G . Bryant, D. J . Roy and W. R. Croasmun, J . A m . Oil Chem. Soc., 1992, 69, 1057. M. C. M. Gribnau, Trends Food Sci. Technol., 1992, 3, 186. A.-E. Cuvelier, C. Berse and H. Richard, J . Agric. Food Chem., 1994, 42, 665. M. Okamura, J . Nutr. Sci. Vitaminol., 1994, 40, 81. T. Kometani, H . Tanimoto. T. Nishimura, I. Kanbara and S. Okada, Biosci. Biotech. Biochem., 1993, 57, 2192. H. Li, C. C . Hardin and E. A. Foegeding, J . Agric. Food Chem., 1994, 42, 2411. J . P. Renou, M. Bonnet, G . Bielicki, A. Rochdi and P. Gatellier, Biopolymers, 1994, 34, 1615. J . R . Lee, I . C. Baianu and P. J. Bechtel, J . Agric. Food Chem., 1992, 40, 2350. R. Lahucky, J. Mojto, J . Poltasky, A. Miri, J. P. Renou, A . Talmant and G . Monin, Meat Sci., 1993, 33, 373. A. Miri, A. Talmant, J. P. Renou and G. Minin. Meat Sci., 1992, 31, 165. D. G . Cornell, R. L. Dudley, R . F. Joubran and N . Parris, Food Hydrocoll., 1994,8, 19. G. Fronza. C. Fuganti, A. Mele, G. Pedrocchi-Fantoni and S. Servi, Tetrahedron, 1994, 50, 857. R. Tessl, G . Wondrak, R. Kesrten and D . Rewicki, J . Agric. Food Chenz., 1994,42, 2692. C. F. Wang, S. M. Tsay, C. Y. Lee, S. M. Liu and N. K. Aras, J . Agric. Food Chem., 1992, 40, 1030. K . C. Wong and D. Y . Tie, Flavour Fragrance J . , 1993, 8, 321. Y.J. Kim, S. J. Han, S. C. Kim and Y . K. Kang, Biopolymers, 1994, 34, 1037.


Gradient NMR WILLIAM S. PRICE National Institute of Materials and Chemical Research, Tsukuba, Ibaraki 305, Japan 1. Introduction 2. Nuclear spins and gradients 2.1. Introduction 2.2. BO versus B1 gradients 2.3. BOand B 1 gradient geometries 3. Diffusion measurements 3.1. Introduction 3.2. Free and restricted diffusion 3.3. Correlating the signal attenuation with diffusion 3.3.1. Macroscopic description 3.3.2. GPD approximation 3.3.3. SGP approximation 3.3.4. Numerical methods 3.4. “Diffusive diffraction” and imaging molecular motion 3.5. Simple geometries 3.5.1. Flow 3.5.2. Reflecting boundaries 3.5.3. Absorbing boundaries 3.5.4. Fractals and anomalous diffusion 3.5.5. Anisotropic diffusion 3.6. Validity of the SGP and GPD approximations 3.7. More complicated boundary conditions 3.7.1. Introduction 3.7.2. Polydispersity, polymers and macromolecular systems 3.7.3. Size distributions of the restricting geometry 3.7.4. Obstruction 3.7.5. Exchange and many body effects 3.7.6. Porous media 4. Non-homogeneous gradients and other problems 4.1. Introduction 4.2. Imperfect gradient pulses and sample movement 4.3. Eddy currents and perturbation of Bo 4.4. Internal gradients and relaxation time distributions 5. Pulse sequences for measuring diffusion 5.1. Introduction 5.2. BOsequences 5.2.1. Basic sequences 5.2.2. Reduction of the effects of background gradients 5.2.3. Reduction of eddy current and phase distortion effects ANNUAL REPORTS ON NMR SPECTROSCOPY VOLUME 32 ISBN 0-12-505332-0

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Copyrighl 019% Academic Press Limited All right5 of reproduction in any form reserved

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5.2.4. Steady gradient 5.2.5. Fringe (or stray) field methods 5.2.6. Zero and multiple quantum 5.2.7. Multiple spin echoes 5.2.8. Miscellaneous 5.3. B1 sequences 6. Applications to high-resolution NMR 6.1. Introduction 6.2. Coherence selection and quadrature detection 6.3. Spectral selectivity and editing 6.4. Solvent suppression 6.4.1. Introduction 6.4.2. Coherence selection 6.4.3. Diffusion 6.4.4. Selective excitation 6.4.5. Watergate 6.4.6. B1 solvent suppression methods 6.5. Spectral simplification according to mobility 6.5.1. Introduction 6.5.2. Diffusion-ordered two-dimensional experiments 6.5.3. Electrophoretic mobility 7. Technical aspects of gradient production 7.1. Introduction 7.2. Gradient coil design 7.2.1. Bo gradient coils 7.2.2. B 1 gradient coils 7.3, Power supplies 7.4. Gradient calibration 7.4.1, Bo gradients 7.4.2. B 1 gradients 7.5. Sample shimming and field frequency locking 7.6. Temperature control 8. Specific examples of gradient NMR 8.1. Introduction 8.2. Diffusion-based studies 8.2.1. Diffusion measurements 8.2.2. Restricted diffusion and obstruction 8.2.3. Binding and transport 8.2.4. Liquid crystals and surfactants 8.2.5. Porous media 8.2.6. Polymers and macromolecules 8.3. High-resolution NMR applications 8.3.1. Applications of DOSY and electrophoretic NMR 8.3.2. Coherence selection, phase cycling and solvent suppression 9. Concluding remarks References

104 105 105 107 107 108 109 109 110 112 114 114 114 115 115 115 117 118 118 119 119 121 121 122 122 124 124 125 125 125 126 127 128 128 128 128 128 130 130 131 131 133 133 134 135 135

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1. INTRODUCTION

In the last decade there has been a tremendous increase in the use of both magnetic (Bo), and to a lesser extent, radiofrequency (rf or B,) field gradients in nuclear magnetic resonance (NMR). Not too long ago a gradient was something to be avoided since it would lead t o poor resolution and complicate the analysis of relaxation experiments in the case of Bo gradients or cause uneven excitation in the case of B1 gradients. However, as is often the case in NMR, phenomena that at first sight seem to be only the cause of artifacts are later found to have practical applications. Gradients now pervade almost all areas of NMR ranging from coherence selection in high-resolution NMR to inputting spatial dependencies into NMR imaging (also known as magnetic resonance imaging or MRI) and NMR microscopy. The increased use has occurred concomitantly with the widespread commercial availability of NMR gradient probes and gradient drivers. In fact, most modern spectrometers now come equipped with gradient probes and amplifiers as standard, sufficient for high-resolution applications. This also provides at least limited scope for performing diffusion measurements. The use of gradient NMR allows diffusion to be added to the standard NMR observables of chemical shifts and relaxation times (i.e. longitudinal or T I ;transverse or T,; and in the rotating frame or Tip). The applications of gradients can be roughly separated into two broad areas; k and q space.' k space involves the spatial spectrum of nuclear spin positions and q space involves the spatial spectrum of nuclear spin displacements. These notions will be further explained below. This chapter is concerned with the theory, applications and technical aspects of diffusion measurements and high-resolution applications of gradients. Since the field is now so large, this chapter will not concern itself with predominantly &-based k space applications such as MR12 and NMR microscopy.= Although, it should be noted that microscopy and imaging are now within the realms of B1 gradient^.^,^ It is not possible to cleanly divide the literature between k space and q space as some studies contain elements of b ~ t h . ~ *Some ~ - ' ~mention will be made regarding homogeneous and inhomogeneous static gradients. A number of reviews on gradient NMR have already appeared in the literature including ones of a general nature'"-16 and also of specific areas of interest such as heterogeneous systemsi7 such as zeolites and porous system^,'^+*^^^ surf act ant^,'^ liquid crystals and membranes,26 and high-resolution application^.^^.'^ The monograph by Callaghan on the closely related field of NMR microscopy covers much of the theory and technical aspects of gradient NMR.4 In this review I have attempted to give a rather general coverage of the field, but with special emphasis on the field of diffusion and transport in restricted geometries and in biological systems. As mentioned above, gradients are now established parts of many areas of

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NMR methodology. Using steady gradients and, more particularly, in the guise of pulsed field gradient (PFG) NMR, gradients afford a powerful tool for not only studying molecular diffusion (under favourable circumstances down to less than m2/s) but also for providing structural information in the range 0.1-10 p m when the diffusion is restricted on the NMR time-scale. In PFG experiments, the ‘tuneable’ parameter is termed q ( = ( 2 r ) - l y S g ; where y is the gyromagnetic ratio, S is the duration of the gradient pulse and g is the gradient magnitude; NB-some authors use k = ySg) and it is analogous to the scattering wave vector in neutron diffraction .29 Neutron scattering, however, is confined to making measurements on the scale of only a few nanometres and thus is usually confined to single scattering events. Hence for observation on the micrometre scale, PFG is a unique method and its measurements may correspond to multiple scattering events. This interesting new area of PFG NMR has given rise to “diffusive diffraction experiments” and q space imaging (see Section 3.4).1,30,31 While in k space imaging the resolution is limited by the signal-to-noise ratio as the voxel size decreases, q space imaging is limited only by the size of the applied gradient and artifacts such as gradient pulse mismatch and sample motion. This is an important distinction. Due to its non-invasive nature, it is especially suited to probing the molecular dynamics and structural details of biological system^.^^,^^ Since PFG NMR does not perturb the system or require labelled probe molecules, it provides an excellent tool for investigating such molecular dynamics by examining the underlying diffusive processes directly. Importantly, it allows measurements to be performed under physical conditions, such as high pressure34 and temperature, where other methods may be precluded. Recently, a report of measuring self-diffusion in the earth’s magnetic field has even appeared.35 Because of the length scale in which PFG NMR is sensitive, it is especially suited to studying the physics of restricted diffusion in materials. Restricted diffusion influences fluid penetration in ceramics and plastics, transport in polymers and biological systems, and sorption and reaction in catalysts. PFG NMR is complementary to NMR relaxation-based molecular dynamic studies in that it studies macroscopic happenings which occur on the time-scale of milliseconds to seconds. Relaxation studies, however, tend to be microscopic in nature since relaxation is sensitive to occurrences on the time-scale of the reorientational correlation time of the species ( T ~ ) Further, . it allows diffusion to be measured directly without the assumptions needed to relate T~ to diffusion and v i s ~ o s i t y . ~ ~ , ~ ~ , ~ However, the diffusion measured on the time-scale of a PFG measurement is normally subject to restriction. To obtain the true diffusion coefficient, D ,as opposed to an “apparent” diffusion coefficient, Dapp,an appropriate model must be used to account for the effects of restricted diffusion. At present anything but the simplest restricted system is beyond the reach of analytical solutions. To study transport and exchange between two domains, the domains must

GRADIENT NMR

55

be able to be distinguished by some measurable property. Traditional NMR methods for studying transport and exchange have relied upon either a difference in chemical shift o r a difference in relaxation rate. However, using PFG NMR a difference in the diffusion coefficient between the domains may be used to separate the two regions even if the chemical shift of the probe species in both domains is the same. Thus, PFG provides the basis of a new method for measuring transport and exchange. There are now numerous gradient applications in high-resolution NMR, including: (1) solvent suppression, (2) coherence selection, ( 3 ) induction of quadrature detection and (4) separation of complicated mixtures in twodimensional experiments based on their diffusion and electrophoretic mobilities. These new methods not only allow multidimensional experiments to be collected in a fraction of the time normally taken, but also allow for significantly improved solvent suppression with the ability of observing resonances which resonate close to the solvent frequency. Bo and B1 gradients have some similarities and yet many differences both theoretically and technically. One of the largest technical problems in pulsed Bo gradient NMR is the effect of eddy currents generated by the rapid rise and fall of the gradient pulses. Much research has been done to overcome these eddy current problems (see Section 4). These problems, however, do not apply when B1 gradients are used. On the theoretical side, B1 gradients are inherently more complicated than Bo gradients since the normally separate steps of coherence transformation and gradient evolution occur simultaneously. This review will first characterize the differences between Bo and B1 gradients and their effects on nuclear spins. It will then discuss the basis of diffusion measurements by gradient NMR including the effects of restriction, exchange, relaxation and problems that confront such measurements. Next, the applications to high-resolution NMR and technical aspects of gradient production and use will be discussed. Finally, the last section will give a brief introduction to a few selected applications. 2. NUCLEAR SPINS AND GRADIENTS 2.1. Introduction

In this section we review relevant theory concerning NMR and Bo and B1 gradients. Since most of the work done so far pertains to Bo gradients, the discussion and theory will be oriented to Bo gradients. Generally the theory for Bo and B , gradients is analogous, and the points at which they differ will be noted. All of the NMR theory pertaining to Bo gradients in the following sections has the Larmor equation as the origin:

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WILLIAM S. PRICE

where w is the Larmor frequency and Bo is the strength of the static magnetic field and we have neglected the small effect of the shielding constant. Since Bo is spatially homogeneous, o is the same throughout the sample. Equation (1) holds for a single quantum coherence (i.e. n = 1). However, if in addition to Bo there is a spatially dependent magnetic field Bo(r), and accounting for the possibility of more than single-quantum coherence, then w becomes spatially dependent,

The important point is that if a homogeneous gradient of known magnitude is imposed through the sample, the Larmor frequency becomes a spatial label. Thus, in PFG measurements the NMR signal is phase encoded according to the molecular displacements over a well-defined time interval, whereas in NMR imaging the signal is phase encoded according to molecular position.38 Equation (2) also shows that successively higher quantum transitions are more sensitive to the effects of the gradient whereas zero-quantum transitions are unaffected by the presence of the gradient. Counsel1 et u I . ~first ~ demonstrated that it is possible to use the natural inhomogeneity of the B1 field produced in a normal NMR probe to mimic Bo gradient pulses. They showed that the sequence (also known as a is equivalent to generatcomposite z pulse) (d2),+,{spin 10~k}~+,/~(7~/2), ing an inhomogeneous rotation about the z axis, which is just the effect of a Bo gradient pulse. The “sign” of the gradient is changed by changing the phase of the spin lock pulse or of either of the d 2 pulses.

2.2. Bo versus B1 gradients

B1 gradients are inherently more complex than Bo gradients. Apart from purely technical considerations, there are three main differences between Bo and B1gradients4’ (1) A Bo field couples only into the spin system along the z axis, thus the effective gradient tensor is always truncated into an effective vector. Rf fields, however, couple into the spin system, from any orientation within the transverse plane. As a result the B1 gradient generally retains its tensor form when it couples into the spin system. (2) When the same rf coil is used for both excitation and detection, any phase variation is cancelled during the measurement. But when an experiment involves two rf fields at the same frequency this cancellation no longer occurs, and phase variations need to be considered. This spatial dependence of the phase difference between the two rf fields presents an additional complication (or opportunity).

GRADIENT NMR

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(3) The third difference is that B1 fields are non-secular and so do not commute with internal Hamiltonians. Thus, unlike a Bo gradient, a B1 gradient cannot be treated additively with respect to internal Hamiltonians. A formalism has recently been introduced for describing the spin dynamics of B1gradient experiment^.^' Importantly, the steps of coherence transformation and gradient evolution are clearly separated in this formalism. In &-based experiments only the gradient strength is varied spatially. In B1 experiments there are two mechanisms that lead to spatially varying spin dynamics: the amplitude variation of the gradient rf field and the phase difference between the gradient and homogeneous rf fields. The amplitude variation is most directly analogous to Bo experiments. The phase variation arises from the symmetry of the rf field and current flow through the coils. A number of technical problems arise in the generation of Bo gradients and also as side-effects of their generation. It is difficult to obtain gradient pulses with very rapid rise times, and the imposition of the gradient pulse generates eddy currents in the surrounding metal parts of the probe. These eddy currents have deleterious effects on the spectral acquisition and resolution. The gradient pulse also perturbs the field-frequency lock system. As will be discussed in Section 4, much effort has gone into finding ways to lessen these problems including special pulse sequences, shielded gradient probes and pre-emphasis of the gradient pulses. At a technical level, B1 gradients have some significant advantages over their Bo counterparts. The main advantages are:42 (1) the switching times are much shorter, (2) the lock channel is unaffected, (3) there is no need for pre-emphasis, (4) the lineshape is not distorted, ( 5 ) no eddy currents are induced and so there is no need for shield coils, etc., and (6) the gradient is frequency selective. However, at present, the absolute strength of B1 gradients (-0.2 T/m) is still far less than that available with Bo gradients (-80T/m). And because B1 gradients generally preserve their tensor form when they couple into a spin system, the design of truly planar rf gradient fields is difficult.

2.3. Bo and B1 gradient geometries The technical aspects of Bo and B1 gradient production will be reviewed in Section 7.2. Here we examine the geometries and consequences of Bo and, in particular, B1 gradients and how B1 gradients can be introduced into pulse sequences so as to behave like Bo gradient pulses. Bo gradients are ideally linear (i.e. planar) along one axis (generally the z axis). Additional gradient coils may be added to provide gradients oriented along other directions. Two types of B1 gradients can be employed depending on the coil geometry: planar or radial (i.e. quadrupolar). The

58

WILLIAM S. PRICE

amplitude of a planar field (i.e. dBJdx) increases along one axis in the laboratory frame, while the amplitude of a radial field (i.e. dB,/dr, -dB,,ldy) increases along two orthogonal axes. The dephasing due to a planar gradient occurs in a plane perpendicular to the rotating frame axis along which the rf gradient field is applied. For a radial gradient, however, the dephasing, being the result of both an amplitude and phase variation has the effect of scattering the magnetization over the surface of a sphere. Hence, when trying to dephase longitudinal magnetization, a radial gradient is more efficient than a planar gradient. Also because of the radial phase distribution, the gradient phase does not have to be adjusted to the phase of the homogeneous rf coil. A planar gradient can be formed from a radial gradient by inserting T pulses into the gradient evolution. This refocuses the evolution perpendicular to the phase of the T pulses and leaves only gradient evolution along the direction dictated by the phase of the T pulses. An example of such a where g , is a B1 gradient sequence is (gl)~-T,-(gl)8-(gl)e-T~-(gl)~, pulse.42 The effect of this sequence can be evaluated by examining the average H a m i l t ~ n i a n , ~ ~

{ (y) i, (y) i,,} cos

- sin

where u and v are the transverse axes of the laboratory frame. If the phases C$ and 8 of the gradient pulses are the same, then the average Hamiltonian is proportional to i, and represents a planar gradient. An exact analogue of a Bo gradient pulse can be formed if this sequence is sandwiched between two homogeneous ~ / pulses 2 of opposite phase (i.e. composite z pulse); the effect of this sequence is a composite z rotation in which the rotation angle is a function of position in the transverse plane. 3. DIFFUSION MEASUREMENTS 3.1. Introduction

In this section we discuss how the diffusion and flow of spin-bearing species in homogeneous and heterogeneous systems are related to the observable NMR signal. To better understand the mechanism of how diffusion is measured with gradients, we must first review some relevant aspects of diffusion. Next we discuss how diffusion and the boundary conditions are related to the observable NMR signal. An analogy between diffraction and

GRADIENT NMR

59

PFG diffusion studies will be made. We will then present the results for some simple restricting geometries (e.g. cylinders, planes and spheres), followed by more complicated models such as those which include exchange. Finally we will discuss PFG NMR from the viewpoint of being a probe for studying porous media. 3.2. Free and restricted diffusion

For the case of diffusion in an isotropic and homogeneous medium, the conditional probability, P(ro, r, t ) , of finding a particle initially at position ro, at a position r after a time t is equal to

(

‘)

P(ro, r, t) = ( 4 ~ D t ) - ~ ” e x p - (r 4Dt - ro>

(3)

Thus the radial distribution function of the spins in an infinitely large system with regard to an arbitrary reference time is Gaussian. From equation (3) it can be deduced that the root mean square displacement for diffusion in three dimensions is given by

((r - r,J2) = 6Dt

(4)

o r for diffusion along one direction ((x - X”)2) = 2Dt

(5)

Equation (4) provides an alternative definition of the diffusion coefficient and is equivalent to Fick’s first and second laws. Naturally, the probability given in equation (3) is determined by solving the diffusion equation

where D represents the (rank two) diffusion tensor, subject to the initial condition

P(ro,r, 0) = S(ro - r)

(7)

and the boundary condition P-0 as r+m. In the case of isotropic diffusion, which we shall consider first below, the tensor D is replaced by the diffusion coefficient D ,and equation (6) simplifies to

60

WILLIAM S. PRICE

7

I

7

I

Acquisition

A

'VVV"' 0 tl

I

71

A

"

1

V

tl + A

71

72

I

Acquisition

B

0'

tl

tl + A

Fig. 1. (A) The Stejskal and Tanner PFG sequence.52This is a Hahn spin echo pulse sequence with a "rectangular" gradient pulse of duration S and magnitude g inserted into each 7 period. The separation between the leading edges of the gradient pulses is denoted by A. The applied gradient is enerally along the L axis (the direction of the static field). (B) The STE ~equence.~"

The solution of this equation becomes much more complicated when the diffusion of the particle is affected by its boundaries, although the solutions of equation (8) for many cases of interest can be found in the l i t e r a t ~ r e . ~ ~ ? ~ ~ Any echo sequence is susceptible to the effects of diffusion. Diffusion measurements are generally performed with some variation of the Hahn spin echo or stimulated echo pulse (STE) sequences incorporating field gradient pulses (i.e. the PFG experiment; Fig. 1). Steady gradient experiments also exist but due to the greater usage and applicability we will concentrate on the PFG approach. In our discussion we will refer to the

GRADIENT NMR

61

simplest possible PFG sequence, namely a Hahn spin echo pulse sequence with a gradient pulse inserted into each T period. The second half of the echo is used as the free induction decay (FID). This is commonly known as the “Stejksal and Tanner” sequence (see Fig. l(A)). The main magnetic field is taken to be in the z direction, and the gradient pulses are also applied along the z direction. Normally, the experiment is started with the spins being at thermal equilibrium (i.e. equilibrium magnetization along the z axis). In the absence of magnetic field gradient pulses, the application of the d 2 pulse rotates this magnetization into the x-y plane. The spins then dephase during the first 7 period. At a time 7,a T pulse is applied which reverses the dephasing process so that an echo is formed at time 27. The T pulse also has the effect of refocusing chemical shift effects and frequency dispersion due to residual Bo inhomogeneity. The first applied magnetic field gradient pulse spatially ‘‘labels’’ the spins with respect to their position along the z axis. The spins then continue to diffuse during the time A, at which point they are subject to a second gradient pulse of equal but negative magnitude (NB-the T pulse has the effect of changing the sign of the gradient). If the spins have not moved with respect to the z axis the effect of the two applied gradient pulses cancel, but if the spins have moved, the degree of dephasing due to the applied gradient is proportional to the displacement in the direction of the gradient (i.e. the z direction) moved in the period A. Any dephasing will result in a diminished echo signal, M ( q , t ) , at time 27, and thus the effect of diffusion is monitored by the attenuation of the echo signal. In correlating the signal attenuation to diffusion, the spin echo signal is generally normalized by dividing the echo signal obtained in the absence of field gradients, M ( q = 0, t). Thus we define the attenuation, E ( q , t ) (or E ) , of the echo signal as

The experiment is performed by varying one of the experimental variables (i.e. 6, A or g). 7 is generally kept constant, and thus by using the normalized signal attenuation and not the echo, bulk relaxation effects are factored This “factorization ansatz” will be further considered in Section 3.7.6. The degree of dephasing is determined by the “area” of the gradient pulses (i.e. 6g) and the displacement of the spin along the z-axis. We need to equate the attenuation ( E ) of the echo signal to the experimental variables, the diffusion coefficient and the available diffusion space. At this point it is appropriate to introduce the concept of restricted diffusion. We define R as being the characteristic distance of a restricting geometry (e.g. the radius of a sphere or cylinder, or half the separation between planes), we also define the dimensionless variable, 6 = DA/R2, which is useful in characterizing restricted diffusion. Consider a case where we have two particles diffusing at the same rate, one is freely diffusing (i.e.

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m

Fig. 2. The effects of restricted diffusion are schematically presented for the three relevant A time-scales for a particle diffusing within a sphere of radius R : (1) 6 (=DAlR2)< 1 (the short time limit); the particle does not diffuse far enough in the time A to feel the effects of restriction. Measurements performed within this time-scale lead to the true diffusion coefficient (i.e. 0). (2) 6-1; some of the particles feel the effects of restriction, and the diffusion coefficient measured with this time-scale will be apparent (i.e. D,,,) and be a function of A. (3) 6> 1 (the long time limit); all particles feel the effects of restriction. In this time-scale the displacement of the particle is independent of A and depends only on R .

an isotropic homogeneous system) while the other is confined to a reflecting sphere (Fig. 2). Assume that we measure the motion of a particle by taking a measurement at time t = 0 and a second measurement at time t = A. In the case of freely diffusing particles the diffusion coefficient determined will be independent of A for any value of A. However, for particles confined to the sphere the situation is entirely different. For short values of A such that the diffusing particle does not “feel” the effect of the boundary (i.e. [< 1)

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63

the measured diffusion coefficient (i.e. D,,,) will be the same as that observed for the freely diffusing species. As A becomes larger such that 6 - 1, the particle will begin to feel the effects of the boundary, and the diffusion coefficient determined will be dependent on A. At very long A, the maximum distance that the confined particle can travel is limited by the boundaries, and thus the measured diffusion coefficient again becomes independent of A. A further complication arises if the restricting geometry is not symmetric with respect to the gradient (e.g. a cylinder). In this case the diffusion becomes anisotropic, and the measured diffusion coefficient will depend on the direction of measurement. In free solution, averaging makes the measurement isotropic (i.e. independent of the field direction).

3.3. Correlating the signal attenuation with diffusion We will now discuss the mathematical formulations necessary to relate the signal attenuation to the diffusion coefficient and boundary conditions in the PFG experiment. We will not pursue the analysis for steady gradient diffusion experiment^.^^ Both macroscopic and quantum mechanical (i.e. density matrix) formulations exist. The quantum mechanical basis of the spin echo experiment is well known’3’15,49and will not be presented here. The theory used to interpret B1 gradient experiments is essentially the same as that for Bo gradient^.^" We will first give an outline of the macroscopic approach, which is necessary to understand later discussions on gradient pulse shapes. The macroscopic approach allows for the finite length of the gradient pulse. However, in the case of restricted diffusion the macroscopic and density matrix approaches become mathematically intractable. Thus, in the general case one is forced to use different approximations to find formulae relating E to the diffusion coefficient, boundary and experimental conditions. There are two common approximations, the first is the Gaussian phase distribution (GPD) approximation and the second is known as the short gradient pulse approximation (SGP). It is found that even using these approximations, analytic solutions are generally not possible and numerical methods must be used. Some solutions using the GPD and SGP approximations are presented in Section 3.5, and the validity of the SGP and GPD approximations is discussed in Section 3.6. Finally, some solutions and discussion are made for more complicated systems, such as porous media and those including transport.

3.3.1. Macroscopic description The macroscopic treatment is based upon the “magnetization fluid” approach of Torrey.’l In the following discussion we consider only the case

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WILLIAM S. PRICE

of isotropic diffusion. The more general case where the diffusion coefficient scalar D is replaced by the tensor D has been considered elsewhere52 and in the presence of gradients in more than one direction.53754The magnetization, M(r, t) is considered to be both a time- and space-dependent function. By combining the Bloch equations with Fick's second law, we obtain, for isotropic diffusion,

where Mo is the equilibrium magnetization, Mx,y,z are the components of local magnetization along the directions of the respective unit vectors ex,y,z. Further, it is assumed that the static magnetic field is oriented along the z axis such that B = (0, 0, BO).Thus, only the z component of the time dependent external magnetic field must be considered,

.

BZ(r,t) = Bo

+g. r

(11)

where g is defined by g=-

a& e y + -e, aB* dBz e x + aY az ax

The transverse magnetization can now be defined as

V

= (Mx

+ iMy)exp( -iwot + t/T2)

Inserting equation (13) into equation (10) we get

Setting

(1')

"(r, t ) = T(t)exp - iyr

and inserting this into equation (14) leads to

which has the solution

g(t')dt'

(13)

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This can then be rewritten as

As noted above, the effect of a 72 pulse is to change the sign of the gradient. Further, the effective gradient is zero for longitudinal magnetization. Replacing g with the effective gradient, g e f f , allows the attenuation due to diffusion to be calculated for any pulse sequence (including steady gradients). In the simplest PFG sequence as shown in Fig. l(A), including a background gradient, go, equation (18) becomes”

+ r ’ g * g o D 8 [ ~ + ~ + 8 ( t , + t 2+2/382-2?] ) \

v

g. gocross-terms

The direction in which the diffusion is measured is the same as the direction of the gradient. Generally the condition g > > g o holds, and thus the g-go cross-terms can be neglected in equation (19). The (A - 813) factor in the go = 0 term reduces to A when A > > 6 , which corresponds to the solution found using the SGP approximation. It must be noted, however, that equation (19) only holds for free diffusion. In fact, analytical solutions only exist for free diffusion and for free diffusion superimposed upon flow.4

3.3.2. GPD approximation The Gaussian phase approximation results from the method of phase accumulation, which was originally suggested by Douglass and McCa1LS6In this scheme the phase of the ith spin at the end of the PFG sequence is given by

1,

ti+A+ 8

flf8

4ii(q,A) = yg(

zi(t)dt -

Zi(t) /,+A

1

dt

(20)

where zi(t) is the spin position in the direction of the field gradient and the time c1 is defined in Fig. 1. The echo intensity is proportional to the resultant magnetic moment, which is given by ?j

(21)

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WILLIAM S. PRICE

where P(4, A) is the relative phase distribution accumulation function. If, as in the case of free diffusion, it is assumed that the phases have a Gaussian distribution then the echo attenuation is given by57

3.3.3. SGP approximation In this approximation, motion during the gradient pulse is ignored (rigorously, one assumes that 6+ 0 and lg(+ while their product remains finite). Operationally this condition is approximated by keeping S > 1 and S 1 holds, and only the lowest

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0

5000

10000

15000

0

5000

10000

15000

1

0.1 r?

Q CY

G 0.01

0.001

I

Fig. 5. Plot of E ( q , A) versus q for a PFG experiment of pentane diffusing in a capillary stack (2R = 100pm) for different values of A ( 0 , 200ms; a, 300ms; 0 , 700 ms; m, 900 ms). The theoretical lines represent regressions of equation (40) on to the experimental data. In the upper graph H was fixed according to the known relaxation time, and R and D allowed to float. In the lower graph a distribution of R was allowed. (Reproduced with permission from Coy and C a l l a g h a r ~ . ~ ~ )

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eigenvalue a = aoo is important. Thus, from equation (43), a satisfies the following equation:

In this long-time limit the normalized echo amplitude is independent of and is given by

(

a2 (hh a’- (27rqR)’

sin (2rrqR) 2rrqR

6,

+ cos(2rrqR)

In the limit of weak permeability (i.e. h-0, reflecting boundary), the lowest positive solution of equation (44) is a2 = 3h, and equation (45) transforms into

which is, of course, the same as equation (38). In the limit of infinite permeability (i.e. h+w, perfectly absorbing boundary), we have

The approximate equalities in equations (46) and (47) are obtained for 2rrqR 1, in agreement with the predictions by N e ~ m a n . ~The ' SGP equation described the data well for large values of 5 and small gradient strengths. The results showed that at 5- 1 the long-time limit of the SGP equation (i.e. the attenuation has become independent of A) is already applicable. In the GPD approximation the problem of finite gradient pulses is treated by writing an expression for the phase of the

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WILLIAM S. PRICE

magnetization in terms of an integral over particle displacements. However, a severe approximation must be made when this approach is adapted to treat restricted diffusion, and the Gaussian phase condition is enforced and the phase factor is calculated from the mean squared phase deviation. This approach therefore does not yield interference effects.69 Blees6' extended the finite difference approach of Zientara and Freed6' to obtain solutions for diffusion between two planes using gradient pulses of finite duration, and compared this to the SGP result (see equation (31)). Blees focused on the effects of the gradient pulse duration on the diffraction peaks that occur at high q values. He found that as the gradient pulse duration increased, the diffraction peaks shifted toward higher values of q (i.e. making the pore size appear smaller than the actual size); further, the higher-order minima were more greatly affected (see Fig. 8). Recently, it has been shown that at finite gradient pulse lengths, the echo amplitude is the spatial Fourier transform of a "centre of mass" p r ~ p a g a t o r .As ~~ expected, as b 0 , the centre of mass propagator reduces to the usual diffusion propagator.

3.7. More complicated boundary conditions

3.7.1. Introduction Above we have considered only simple systems, where species diffusing within a restricting geometry do not interact with other restricting geometries. In real systems (e.g. biological cells or porous systems) though, it may be necessary to consider the effects of (a combination of) exchange, obstruction and polydispersity in addition to surface and bulk relaxation. The case of exchange rapidly becomes very complicated since the spins in each domain may have different diffusion coefficients and relaxation rates as well as being subject to restricted diffusion. 3.7.2. Polydispersity, polymers and macromolecular systems Since a number of reviews (e.g. see refs 13, 19 and 98) have been concerned with the application of gradient NMR for determining the diffusion coefficients and other related physical parameters of polymers, we will only touch upon this topic briefly. A major problem in using PFG to study polymers is their p ~ l y d i s p e r s i t y . ~Apart ~ " ~ from the distribution of diffusion coefficients, the different molecular weights and molecular mobility of polydisperse species lead to different relaxation rates (see Section 4.4), and, hence, the observed echo signal is not weighted by the respective concentrations alone. STEbased experiments are less influenced by this relaxation problem. Analysis

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0

-1

-2

-3

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Fig. 8. Failure of the SGP approximation. The effect of the finite duration of the gradient pulse on the spin echo attenuation is shown. The numbers given in the key are the ratio 6/A. The calculations were performed setting ( 2 R ) * / 2 0 A= 1. (Reproduced with permission from Blees.61)

of the data from polydisperse samples is considerably simplified if one is able to assume a particular diffusion coefficient di~tribution.''~Recently a new, gradient based method, called DOSY (diffusion ordered spectroscopy) (see Section 6.5.2) provides another alternative for tackling polydisperse systems. By directly measuring the polymer diffusion coefficient at high dilution, it is possible to obtain the effective hydrodynamic (or Stokes) radius, r,, of the polymer using the Stokes-Einstein equation,

where T is temperature and 7 is the solvent viscosity. However, as the polymer concentration increases, the interaction between polymer chains causes the diffusion to become concentration dependent. Thus, the concentration dependence of the polymer and solvent diffusion coefficients provide information about the shape of the polymer. In polymer melts and in

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WILLIAM S. PRICE

solutions with high polymer concentrations, the dependence of the diffusion coefficient on concentration and molar mass provides information about entanglement of the polymer chains. In some polymer gel systems the diffusion is described by the particles diffusing in an isotropic medium while being harmonically bound to an attractive For small values of A, the observed displacement may be smaller than the end-to-end distance of the polymer chain. Hence, a polymer system can be considered as being heterogeneous at short A values. The diffusion of the polymer molecules is restricted by instantaneous tubes formed by the bulk phase of the surrounding molecules. The reptation time, tr, is defined as the time required for a polymer molecule to cover a curvilinear diffusion path of the order of its contour length. For A > & , the confining tube will be completely uncorrelated with the previous tube and the observed diffusion coefficient will appear to be constant (i.e. it will not scale with time; see Section 3.5.4). Conversely, for A < tr, the motion of the polymer segments is subject to a correlated confinement. Accordingly, the apparent diffusion coefficient will decrease with increasing A. This model of molecular "reptation" in polymers has been confirmed with PFG NMR for both polymer melts'05-107 and solutions. 108~109 Polymeric microgels are quite distinct from polymers. They are semi-rigid and are unable to penetrate each other. While, similar to polymers, their diffusivity is determined by mutual interactions, their transport properties are quite different from polymer chains. In a study with cross-linked polystyrene beads, it was noted that with increasing concentration a large decrease in mobility is observed and the deviation from ordinary diffusion increased.'" This indicated that the individual microgels are in a cage formed by their neighbours. However, as the cages are not perfectly confining at large A, the motion of the microgels appears to occur via normal diffusion.

3.7.3. Size distributions of the restricting geometry A related problem to polydispersity is where spins diffuse inside a polydisperse set of restricting geometries. With an appropriate model, PFG data can be analysed to give the size distribution. As an example, we consider the attenuation of the NMR signal resulting from spins diffusing inside a polydisperse set of spheres (e.g. an emulsion). The possibility of exchange between the two domains is neglected. Taking into account the distribution of the sphere radii, P(R), the attenuation is given by"' io

[

dR R3P(R)E(q, A)

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83

where E ( q , A) is given by equation (37). Often P ( R ) is taken to be a log-normal function. Callaghan et a1.'l2 developed a similar method using another size distribution. An improvement based on the recognition that the echo attenuation data obtained in the long-time limit contains all the necessary information on the radii distribution has been presented.' l 3 More recently, Fourel et al. 'I4 supplemented equation (59) by adding an unrestricted diffusion component. The unrestricted component is either to account for the case where the distribution of radii is not perfectly log-normal or to account for a freely diffusing component.

3.7.4. Obstruction

Obstruction occurs when a small molecule, for example in a colloidal system, is excluded from a fraction of the total volume by the colloidal particles. This causes a lengthening of the diffusion paths which results in an effective diffusion coefficient, Deff.The description of self-diffusion in such systems is mathematically very difficult since the diffusion path of the molecule can be very complicated; also, the colloidal particles are not distributed in space in a totally ordered way nor in a totally random way. Using a cell model, Jonsson et ul."' derived the obstruction effect for a system containing spherical monodisperse particles; neglecting binding effects, the effective diffusion coefficient is given by

Hence, it can be seen that in the case of obstruction by spheres the limiting value of Deff is 2D/3. They also considered the cases of obstruction by spheroidal particles and by polydisperse systems. Since the degree of obstruction is dependent on the shapes of the obstructing particles, it provides an additional source of structural information. Recently, Blees and Leyte'I6 derived a model for the effective translational diffusion coefficient of particles diffusing within colloidal crystals modelled as a lattice of immobile spheres. The centres of the spheres are located on the lattice points of a cubic array (either simple cubic, body-centred cubic or face-centred cubic lattices). In their model, the diffusing particle has dimensions much smaller than those of the colloidal particles and is able to move freely inside both the colloidal particles and the continuous phase. The diffusing molecule is characterized by both a diffusion coefficient and a concentration in the continuous phase, and a diffusion coefficient and concentration inside the colloidal particles. They found that for low volume fractions of the obstructing particle ( 4 < 0.3), the calculated self-diffusion coefficient is independent of the lattice type and is in agreement with the simple cell model of Jonsson et ~ l . ~ ' '

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WILLIAM S. PRICE

3.7.5. Exchange and many body effects The simplest case of exchange that we consider is that between two freely diffusing regions, with each region being characterized by a different diffusion coefficient. Ignoring relaxation time differences between the two compartments, the echo attenuation is given by a superposition of exponentia~s,’~J~’

E ( q , A) = P1 exp[ - ( 2 ~ q ) ~A]D +, P2 exp[ - ( 2 ~ q ) ~ D ~ A l(61) where D 1and D2 are the apparent self-diffusion coefficients defined below, and P1 and P2 are the population fractions (relative signal intensities) given by

D1(2)=

‘i 2

D,+Di+

1 ~

(2Tq)2(

-+ie

ii

)

and

where D, and Di are the diffusion coefficients in the two domains. Similarly P, and Pi are the relative populations, and T, and T~ are the mean residence lifetime in each domain. The above equation is based on the assumptions that the exchange rates are much faster than the transverse relaxation rates of the species in question. This approach involves a serious approximation, transport between different subregions is introduced through the mean residence times and conditional hopping probabilities, by combining Fick’s second law with the Chapman-Kolmogorov equations.” Thus, the space coordinate is applied in a macroscopic sense, leaving the space unit much larger than the diameters of the individual subregions. However, this approximation considerably simplifies the solution of the underlying diffusion problem. If the exchange is in the slow or fast exchange limit, equation (61) can be further ~imp1ified.l~ In biological systems such as red blood cell suspensions, transport occurs between a restricted and an unrestricted (or perhaps obstructed) domain. In the present discussion we will assume that the restricted domain is constituted by a sphere. In this case the solution to equation (8) becomes very complicated. A means of making the system more mathematically tractable is to achieve the “partially absorbing wall” condition (see Section

GRADIENT NMR

85

3.5.3 and Fig. 4). In this case a two-site system is modelled by a one-site system, implying infinitely fast relaxation in the other domain (see equation ( 4 2 ) ) . In cell or vesicle systems the partially absorbing wall experiment is, at least in principle, possible as the relaxation properties of the exterior medium may be manipulated by addition of relaxation agents. However, in practice it is experimentally difficult to attain the instant quenching condition,86~"8and the spins in the exterior medium contribute considerably to the observed echo signal. Further, even if the true partially absorbing boundary condition is achieved, this model is only weakly sensitive to t r a n ~ p o r t . ~An ~ , ' extension ~ of the partially absorbing wall condition for the experimentally more realizable model where the spins that transport through the interface are rapidly relaxed but not instantly quenched has been developed.86 In this formulation, the finite lifetime of the spins in both domains is included. Accordingly, the diffusion equation (i.e. equation (8)) must be complemented with a decay term and is given by

T2 and D are different in each domain and are denoted below by the subscripts i and e, corresponding to the interior and the exterior, respectively. The boundary conditions for the Green's function are given by Di--/ a Pi ar

r=R

De$( r=R

and

Equation (65) describes the flux continuity over the interface, while equation (66) states that the flux is proportional to the concentration difference between the domains weighted by the appropriate permeability coefficients. At equilibrium, there is no flux across the interface, and [Pi/P,leq = He/Hi. The contribution to the echo signal from the spins found at time A inside the sphere is found to be r

E i ( q , ~= ) 6 C (2n + l)exp(-tiaL)fn(anm) n,m

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WILLIAM S. PRICE

where anmare the positive real roots of the equation a n m j n + 1 ( a n m ) [PnmKn+3/2(Pnm)- ( n - he) Kn+l/~(Pnm)l

= jn(anm)[(n+ hi)PnmKn+3/2(Pnm)- n ( n + h i - he)Kn+l/2(Pnm)] (68)

Pnm = (&-I with E = DeT2,IR2 and 5 = DiiD,; hi = H i R / D i , he = H e R / D e , K is the modified Bessel function of the third kind, and fn(anm) is a constant and is further considered below. It is assumed that at least one root exists; this requires small Tze and sufficiently small permeability. The latter condition is normally fulfilled experimentally for most systems of interest. As the lifetime in the outer domain is decreased (i.e. T Z e + 0 ) , Pam tends to infinity, and the inner component of the echo reduces to equation (42) as expected. The contribution to the echo signal from the spins found at time A outside the sphere iss6 m

Ee(q, A) = 6hil

C (2n + 1)exp(-tia;m) n,m

f

The roots are defined as above. For n = 0, the functions f and are related via

The outer component vanishes as T2, tends to zero, as expected. In the long-time limit, only the lowest eigenvalue a = am is important, which, from equation (68), satisfies the following equation:

where P = Poo. The corresponding constant fo(a) in equation (67) is given by

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87

The overall normalized long-time echo amplitude is again independent of A. The components are given by

and

[&p2 +

a

(2~q)~R~ (74)

where h = hi/[l + hJ(1 + p)]. The amplitude of the echo signal for a typical set of experimental pararneters1l8 is plotted in Fig. 9 as a function of (qR)2 for a range of permeability values. It is assumed that the permeability coefficient and hence the equilibrium spin concentrations are equal in both domains. In contrast to the partially absorbing wall case, finite relaxation rates in the external medium lead to an increase in the apparent diffusion coefficient given by the initial slope as the permeability increases. This is what was experimentally observed in a study of bicarbonate ions diffusing through red blood cell membranes into an Mn2+-doped extracellular medium. Even though the external relaxation rate is very fast (but not infinite), a small population of spins survive at the end of the PFG experiment and result in a considerable enhancement in the observed apparent diffusion coefficient. Typically, two stages are observed, a rapid initial attenuation due to the external component followed by a slower attenuation due to the internal component. When the ratio of the internal and external diffusion coefficients is very small (i.e. [> T2 because it causes the information on spin phases to be stored along the applied field direction for a time interval between the gradient pulses. Thus, in the STE sequence A is limited by T I ,whereas in the Stejskal and Tanner sequence it is limited by T2.

5.2.2. Reduction of the effects of background gradients The basis of most sequences for the removal of background gradients is to add additional 7r pulses to the PFG sequence to refocus the dephasing

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101

effects of go in a way analogous to the Carr-Purcell-Meiboom-Gill sequence. In 1980, Karlicek and L ~ w e proposed ' ~ ~ the use of alternating (bipolar) pulsed field gradients in a modified Carr-Purcell sequence (Fig. 16(A)) to eliminate the contribution of the g.go cross-terms. In the case of the Karlicek and Low sequence, the echo attenuation can be shown to be

E ( g , 2n.r)

= e~p{-~/3?Dd[n&

+ ( n - 1)3g2]}

(85)

where the integer n is defined in Fig. 16(A). Systematic errors due to the cross-term can also be eliminated in a Carr-Purcell sequence that only uses pulses of one polarity,155 but this sequence is not as efficient as that of Karlicek and Lowe, especially when T2< T l . The Karlicek and Lowe sequence154is limited by T2, and thus it is desirable to have STE-based pulse sequences. Cotts and c o - ~ o r k e r s presented '~~ three modified STE sequences incorporating alternating pulsed field gradients (Fig. 16(B)) which greatly reduce the effects of the background gradients. Latour et al.148have recently proposed a pulse sequence that combines features of the Karlicek and Lowe and Cotts pulse sequences in which the gradient pulses in the normal STE echo pulse sequence are replaced by a series of short gradient pulses of alternating sign (Fig. 16(C)). Lian and c o - w o r k e r ~have ' ~ ~ demonstrated that an image of D or (Dgz) can be obtained without the corrupting g-goterms by appending a standard imaging sequence to an alternating pulsed field gradient sequence154or a Carr-Purcell sequence.

5.2.3. Reduction of eddy current and phase distortion effects Griffiths et a1.15' proposed an experiment in which a train of 7~ rf pulses is used to refocus the stimulated echo so as to delay the acquisition until after the eddy currents have subsided. However, since the magnetization is transverse during this period it is susceptible to transverse relaxation, J modulation and phase distortions from the eddy currents. Gibbs and co-workers have proposed the LED (longitudinal eddy current delay) pulse sequence (Fig. 17(A)).158This is a modified STE experiment, and is useful when the Tl values of the species in question are longer than the lifetime of the eddy current transients. However, the LED sequence does not solve the problem of the eddy current tail extending from the first gradient pulse into the second transverse evolution period. A partial solution is to precede the sequence by a train of identical gradient pulses with the same separation as Another problem common to both the that used in the LED LED sequence and to the STE sequences is that extensive phase cycling is required. For the LED sequence at least 64 steps are required. The phase cycling requirements of both sequences can be greatly reduced if a homospoil pulse is included after the second rf pulse.

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WILLIAM S . PRICE

n/2 n

.. , . . ...

A

0

n/2

z

(8n+ 1 ) ~

32 n

...-

0

C

2

(A

4It...... kl.. ....

Fig. 16. Sequences for removal of background gradients. (A) The Karlicek and and (C) the Lowe sequence,'54 (B) the nine-pulse sequence of Cotts et improved stimulated echo sequence of Latour et ~ 1 . ' ~ '

Wider et al. have recently proposed self-compensating magnetic field gradient pulses (Fig. 17(B)). In the method, a gradient pulse is replaced by two pulses of half the duration with a n- rf pulse in between the two gradient pulses. The two gradient pulses are of opposite sign. In this way the two gradient pulses in quick succession but opposite sign attempt to cancel out imperfections of the individual pulses. Using this sequence the signal

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103

A

x/2

x

B

Fig. 17. Sequences for removal of eddy current effects. (A) The LED pulse ~equence.'~'Ideally the delay T, is of a duration sufficient for the eddy currents to have dissipated before acquisition begins. A common addition to the sequence is to prefix a series of gradient pulses separated by a duration A, to allow the eddy current effects to reach a steady state. Homospoil pulses are commonly employed in the period 7, to reduce the phase c cling requirements. (B) The self-compensating gradient sequence of Wider et al. I X

attenuation due to diffusion is related by the following equation (the time periods are defined in Fig. 17(B)):

The MASSEY sequence has been developed by Cal1aghanlz9for minimizing phase instability in very high-gradient NMR spectroscopy (Fig. 18). This method incorporates a read gradient (i.e. k space), G, into the standard Stejskal and Tanner sequence. The addition of G allows for the restoration of spatially dependent phase shifts such as caused by a mismatch in the ( q

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WILLIAM S. PRICE

I

z

z

I

Fig. 18. The sequence used in the MASSEY technique for removing phase in~tability.”~ The sequence is a combination of the Stejskal and Tanner sequence with a read gradient, G.

space) gradient pulses. The restoration of the phase occurs at t = -A27rq/ yG with respect to the centre of the echo. The phase twist caused by the pulse mismatch is resolved by Fourier transformation of the whole echo with respect to 27rq. Finally, the effects of the phase twist together with any net phase twist due to sample movement is removed by subsequent modulus calculation. 5.2.4. Steady gradient

Steady gradient methods have a number of inherent problems: (1) because the rf pulses are imposed in the presence of the gradient, it may be difficult or even impossible to evenly excite the whole spectrum; (2) measurements are normally limited to samples containing a single component since the resonances are greatly broadened by the gradient; (3) it can be difficult to separate relaxation and diffusion effects; and (4) the time over which diffusion is measured is not so well defined. However, they do have one large advantage compared to the pulsed gradient sequences-no eddy current problems. Norwood and Quilter16* have developed a constant time, pulse and gradient amplitude diffusion experiment (CTPG) which circumvents a number of problems associated with steady gradient experiments. Subsequently, N o r ~ o o d ’has ~ ~considered several new sequences for measuring diffusion, some of which can be used to measure restricted diffusion and species having coupled spins and short T2.

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105

5.2.5. Fringe (or stray) field methods Kimmich et al.i64 have recently considered the use of steady gradient methods in the fringe field of superconducting magnets. The enormous gradient so provided (10-180 T/m)'65 has the potential for measuring very small diffusion coefficients. However, the inherent properties of using the fringe field are a major drawback. Because of the large field inhomogeneity, only a thin layer of the sample is on-resonance, and the signal-to-noise ratio is dramatically reduced. Further, multicomponent and spatially resolved diffusion coefficients are not possible. The large gradient also means that the echo will become very sharp, and so it may be difficult to digitize the echo properly. Later studies have extended the fringe field approach to allow the production of relaxation-independent diffusion decays, multislice experiments, experiments using shaped rf pulses and two-dimensional variants. More recently, Demco et al. '61 have developed constant relaxation methods using a pulse sequence based on a stimulated echo and Carr-Purcell mixed echo pulse sequences. 5.2.6. Zero and multiple quantum It is often desirable to work with heteronuclei, especially when measuring the diffusion coefficient of nuclei in a complex mixture such as a biological fluid. However, heteronuclei generally have a sensitivity far beneath that of protons. Further, because of the low magnetogyric ratios of heteronuclei, larger gradients must be used. The most straightforward means of alleviating the signal-to-noise problem is through the use of specifically labelled/ enriched probe molecules. Large gains in sensitivity can be made through using pulse sequences to generate polarization transfer from protons to the heteronuclei. This approach has the advantage of generating multiplequantum transitions. If the attenuation of the multiple-quantum coherence can be studied (instead of the single-quantum coherence), the same degree of attenuation can be achieved but with smaller gradients and therefore smaller eddy current problems. In multiple quantum experiments, it is the effective sum of the y values of the nuclei involved in the coherence which is relevant to the attenuation. Thus, for the Stejskal and Tanner pulse sequence in the case of the free diffusion and neglecting the effects of background gradients, the formula relating echo signal attenuation to diffusion can be written as

For the normal (i.e. single-quantum) experiment f(y) = -$. For homonuclear multiple-quantum experiments f ( y ) = For heteronuclear multiple-quantum experiments the definition of f(y) is not SO straight-

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WILLIAM S. PRICE

I

'I:

I

4

,

'I:

4

Fig. 19. A pulse sequence for detecting homonuclear zero-quantum coherence in an

inhomogeneous magnetic field (phase cycling not shown). The first 7 delay corresponds to the preparation period, the evolution period is denoted by tl and the second r delay corresponds to the detection period. forward. For Z spin-detected heteronuclear double-quantum experiments with an I-S spin system, f(y) = [(y, + y ~ ) / y ~ ] * y , . ~ ~ ~ The use of heteronuclear inverse distortionless enhancement by polarization transfer (DEPT)-based sequences (i.e. inverse detection) and inverse heteronuclear correlation spectroscopy (1HETCOR)-based sequThe DEPT-based sequence has significant ences has been investigated, 168~16y advantages for working with low y nuclei due to the polarization transfer from the I spin (usually 'H) to the S spin. However, the IHETCOR pulse sequence is more suited to the observation of protons as the unfavourable polarization transfer from the less abundant heteronuclear population to the proton population. Coherence order selection may be incorporated into the diffusion experiment to provide solvent suppression. Multiple-quantum steady gradient experiments have also been devised, and Norwood has recently presented a multiple-quantum version of his CTPG e~perirnent.'~' Hall and N o r ~ o o d ' ~ have ' pioneered the use of zero-quantum spectra for measuring diffusion. Zero-quantum spectra are unaffected by magnetic field gradients. Since zero-quantum coherences are "spin forbidden", they can only be excited and observed indirectly. A zero-quantum coherence can only be formed in a spin system consisting of at least two coupled spins, and its precession frequency will be the difference in chemical shifts of the contributing spins. A typical pulse sequence used for observing zeroquantum coherences is shown in Fig. 19. Diffusion will be encoded with respect to t,. The signal attenuation is given by14,52

GRADIENT NMR

107

where TFQc is the transverse relaxation time of the zero-quantum coherence which evolves during t l . Hence the decay of the tl FID signal due to relaxation and diffusion is given by

Thus the amplitude and linewidths of zero-quantum coherences are diffusion dependent. Assuming a Lorentzian lineshape, the linewidth of a zeroquantum coherence at half peak height due to relaxation and diffusion will be

The diffusion-dependent part can be separated by acquiring a zero-quantum coherence using a sequence not containing an echo, for example by adding a n- pulse to the middle of each 7 period of the sequence given in Fig. 19. The difference in the measured linewidths will be determined solely by diffusion. There are two major problems with this method: first, high F1 resolution is required and, second, the signal-to-noise ratio decreases as g increases. Although this is a steady gradient experiment, it does allow separate measurements of individual components.

5.2.7. Multiple spin echoes There have now been a number of reports of multiple spin echoes (MSE) for spin I = Y2 nuclei occurring after a sequence of only two pulses. It has been shown that these MSE are generated by the dipolar demagnetizing field. 172~173The stimulated echo sequence, 9W1-t1-9OoX-t2-9Vx, is particularly favourable for generating MSE. If t2 = ntl for integer n , it is likely that one of the MSE will interfere with the stimulated echo. The amplitude of the MSE has been related to the pulse separations, magnetic field gradient and the diffusion coefficient.

5.2.8. Miscellaneous A “single-shot” method based on a Carr-Purcell-like sequence with incremented gradient pulses in each 7 period has been proposed.’74 While the method is susceptible to the effects of imperfect n- pulses, it does, under ideal conditions, offer a means of determining the diffusion coefficient in the one experiment. It was noted that two possible applications of this method are for measuring macroscopic incoherent motions and also, if gradient pulses are applied alternatively along three orthogonal directions,

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anisotropic diffusion effects. Van Gelderen and c o - ~ o r k e r s ’have ~ ~ proposed another single-shot diffusion method based on a series of gradientrecalled echoes. The method offers improved time resolution and reduced sensitivity to bulk motion. The method consists of a spin echo experiment during which a series of echoes are created by alternating pulsed gradients. Since subsequent echoes are attenuated by additional gradient pairs, the total diffusion curve can be acquired within a single experiment. In the presence of a static field gradient (i.e. Bo inhomogeneity), neglecting go2 terms, the signal attenuation for the nth echo is given by

En = exp{ - 2 ? L l [ 2 r ~ 6 ~ / 3- g o * g ( d 2- ns3)]} for n odd

(91)

En = exp[ - 2 y D ( g 2 n S 3 / 3 - go-gnS3)] for n even

(92)

and

Thus, the difference in dependence of the even and odd echoes on the go-g terms may be used to estimate static local gradients. The phase induced by bulk motion is

Thus, if the motion can be considered as constant within a time interval 46, the even echoes will be motion compensated. Diffusion can be determined from the experiment in two ways. In the first method the experiment is performed twice, changing only the gradient strength. The ratios of the corresponding echoes can then be compared to extract the diffusion constant. In the second approach, just one experimental data set is acquired, and the ratio of the peaks symmetric in time to the echo maximum are recorded. However the second method does not account for T2 effects. 17’ Li and S ~ t a k have ’ ~ ~ described a pulse sequence that combines both a stimulated echo and a spin echo component. It is noted that this sequence has potential for measuring anisotropic and restricted diffusion since the two echoes can be used to observe diffusion in different directions and over different time-scales. It should be mentioned that “multiple wave vector” sequences are also now being developed which contain more than two gradient pulses but in different directions.”

5.3. B1 sequences B1 gradients can also be used for diffusion measurement^,^^ combined with water upp press ion'^^ or a sequence for measuring the longitudinal relaxation

GRADIENT N M R

109

t, + A

A Fig. 20. B1 Gradient pulse sequences for diff~sion.~'This sequence is the B1 analogue of the Stejskal and Tanner sequence. The B1 gradient pulses are represented as grey rectangles.

along the gradient axis.'78 The B1 analogue of the Stejskal and Tanner sequence is given in Fig. 20. As noted by Canet and co-workers, this experiment is merely a transposition in the z-y plane of the rotating frame of the conventional Stejskal and Tanner sequence which is performed in the x-y plane. 6. APPLICATIONS TO HIGH-RESOLUTION NMR

6.1. Introduction In this section, we briefly review the recent applications of both Bo and B1 gradients to high-resolution NMR. The effects of diffusion as discussed in the preceding sections may play a part in the mechanism of a particular technique, but determination of the diffusion coefficient is not the aim. Gradients have long been used in high-resolution NMR as a homospoil, and here we consider applications such as coherence selection, quadrature detection, spectral selectivity and solvent suppression. Also included in this section are diffusion-ordered experiments and electrophoretic NMR. These latter two techniques are difficult to classify into a particular experimental category. For example, the diffusion-ordered experiment can be thought of as a method for measuring diffusion but, and certainly more importantly, it can be thought of as a means of spectral simplification of complex mixtures. A similar argument can be made for electrophoretic NMR. Caution should be used when comparing the efficiency of gradient and non-gradient methods, and also when comparing different gradient methods, since in most cases, inherent effects such as relaxation have not been

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considered. Some recent reviews have also considered gradients in highresolution NMR. 28*179 6.2. Coherence selection and quadrature detection Often a single scan gives a sufficient signal-to-noise ratio, and thus phase cycling results in an inefficient use of spectrometer time. Field gradients can be used instead of phase cycling for selecting a particular order coherence'" and also for inducing quadrature detection. 181-183 Through the incorporation of field gradients at appropriate times into the pulse sequences, desired coherences can be selectively rephased, while dephasing those that do not follow the desired coherence pathway.180y181 We can imagine that during a gradient pulse of duration 6, a spin of coherence order n will acquire a complex phase factor (see equation (2))

If an rf pulse transfers the coherence from n to n' and then a second gradient pulse of equal duration and magnitude but opposite sign is applied, the spin will acquire an additional phase of

Clearly, if n6 = n'6, then the dephasing effects of the two pulses cancel and the resonance is refocused. Coherences which do not fulfil this requirement will acquire spatially dependent net phases, and thus the effects of the two gradient pulses will not cancel. Thus, in the general case only those coherences are observed for which the cumulative phase factor is zero. In the case of heteronuclear coherences, a composite coherence order is defined, thereby allowing the inclusion of the gyromagnetic ratios. Thus, a particular coherence transfer pathway can be selected according to the ratios of the gradient pulses used. Assuming a sufficiently strong sample, multidimensional experiments can be acquired with one scan per increment. Further since the coherence selection does not rely on subtraction, there is a large reduction in f 1 noise. An example of a phase-cycled COSY (correlation spectroscopy) sequence and its gradient counterpart are given in Fig. 21. The gradients in the COSY sequence in Fig. 21(B) can perform either N- or P-type selection in a single acquisition depending on the sign of the gradient. Gradients of the same sign result in N-type selection and produce quadrature detection in w l . If we assume an AX spin system, the observable signal, in terms of product operator^,'^^'^^ is lS3 */2 USycos (dfl) exp ( - iws tl)

GRADIENT NMR

+;

-1

111

;

+;

-1

._\__I___

Fig. 21. Schematic diagrams of (A) phase-cycled and (B) gradient COSY sequences. The pulses P I P2 must be cycled in the phase-cycled sequence in an appropriate manner to effect N- or P-type selection.

where US, is the initial coherence of the X spin and w, is the Larmor frequency of the X spin. A disadvantage in using gradients for coherence selection in this sequence is that the gradient pulses can only refocus one of the two possible coherence pathways (see Fig. 21(B)). An absorption mode spectrum can be obtained by recording separate P- and N-type data sets. An example of a double-quantum COSY sequence which uses gradients for coherence selection is depicted in Fig. 22.18’ A formalism for representing coherence transfer by pulsed field gradients has recently been presented. lg6 Since gradients select only one of two possible coherence pathways, there is at least a V? loss in sensitivity compared to the equivalent phase-cycled

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w2

:

0 -1 -2

Fig. 22. Schematic diagram of a gradient-selected double-quantum filtered COSY

sequence. experiment. The sensitivity of experiments which use gradient pulses for coherence pathway selection has recently been investigated. lX7 However, if gradients are used simply to purge unwanted coherences rather than to select coherences, there is no loss of signal intensity compared to nongradient-based methods. To minimize intensity losses due to diffusion effects, the strength and duration of the gradient pulses should be kept as small as possible. Similarly, the duration between gradient pulse pairs should be kept as short as possible. B1 gradients as well as Bo gradients can be used for coherence selection and phase cycling. In the case of B1 gradients, if the geometry of the rf coil is such that the amplitude and/or the phase of the B1 field is a function of space, then this heterogeneity can be used to distinguish between different coherence p a t h ~ a y s An . ~example ~ ~ ~of ~a heteronuclear ~ ~ ~ ~ ~ single~ ~ ~ ~ ~ quantum correlation (HSQC) experiment that incorporates B1 gradients is given in Fig. 23. 6.3. Spectral selectivity and editing Spectral editing is normally based on subtraction, but such methods are limited by dynamic range difficulties and the precision of the subtraction. It

GRADIENT NMR

113

0

0

9

9 0

65

70

75

3 30

15

I0

0

I PP.

0

15 IDn

I

-

"

'

I

-

5.0

'

.

'

41s

1

4 .O

"

"

I

"

"

3.5

I

Fig. 23. A 400 MHz 'H-13C HSQC experiment of sucrose in 'HzO observed using an rf sequence incorporating planar B1 gradient pulses. (Reproduced with permission from Maas and Cory.30')

can be shown that both zero-quantum and two-spin order (correlated z order) are unaffected by a Bo gradient whereas single- and double-quantum transitions are dephased.'" This can be used as the basis for editing procedure^.'^^ However, with zero-quantum filtering, since only part of the coherence is converted into observable signal, there is a factor of 4 loss of signal. The situation is better with z-order filters.''' Selection of a particular frequency domain can be achieved by either (1) frequency, phase and amplitude modulated soft rf or (2) DANTE (delays alternating with nutations for tailored excitation)-like sequences which employ a train of hard pulses of appropriate duration and phase. Canet et UZ.~'have ~ developed sequences relying on trains of B1 gradient pulses to

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WILLIAM S. PRICE

achieve such selectivity. Due to the greater technical problems involved, a Bo gradient equivalent is not possible.

6.4. Solvent suppression

6.4.1. Introduction

Large solvent resonances (e .g. the water resonance in biological samples) present formidable challenges to proper acquisition of NMR spectra. They prevent optimal use of the available dynamic range of the analogue-todigital converter of the spectrometer and, perhaps more seriously, obscure peaks near the solvent resonance. Additional problems arise depending on the method used to suppress the solvent resonance. Methods of solvent suppression have recently been reviewed. Here we will review the gradient-based methods of solvent suppression and contrast them with the more traditional NMR methods. Solvent suppression methods fall into two general categories: (1) magnetization destruction prior to excitation of the remaining spectrum and (2) non-excitation. Traditionally, selective irradiation of the solvent peak (i.e. a magnetization destruction method) has been the most common method since it is both simple and easily incorporated into multidimensional experiments. However, it suffers from the disadvantages that signals close to the solvent signal are also saturated, species that are in exchange with the solvent are difficult to observe, and in the case of water as the solvent, it is impossible to observe hydration water. Selective excitation (i.e. a nonexcitation method) has the advantage that exchangeable protons can be observed. Its disadvantages are that it does not provide such a large degree of water suppression and the resulting spectrum suffers from intensity, phase and baseline distortions. Gradients offer far superior methods of water suppression. There are three ways in which gradients may be used to effect solvent suppression: (1) through coherence selection, (2) by differential diffusion between the solvent and solute or (3) by selective excitation of the water and subsequent destruction of the magnetization. 1937194

6.4.2. Coherence selection

In this method, gradients are used to select multiple-quantum coherence and thereby suppress the water resonance. However, problems arise since either large gradients or small gradients but with longer durations must be used. Thus, there are solute signal losses due to diffusion and, especially when using longer gradient pulses, due to relaxation. Hurd and co-workers have shown that coherence selection alone is insufficient to fully remove the H 2 0 signal from a multiple-quantum filtered COSY.19’

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115

6.4.3. Diffusion In the differential diffusion m e t h ~ d ' ~ (DRYCLEAN ~.'~~ (diffusion-reduced water signals in spectroscopy of molecules slower than water); i.e. magnetization destruction) the faster diffusion of the solvent compared to the solute forms the basis of the water suppression. For example, at 298K, water has a diffusion coefficient of about 2.3 x m2/s and a large protein has a diffusion coefficient nearly two orders of magnitude smaller (see Table 3). Thus, the solvent resonance will be greatly attenuated compared to the protein resonance if a pulse sequence is used that incorporates some form of gradient spin echo sequence (e.g. see Fig. 1). Clearly this method requires there to be a large difference between the diffusion coefficient of the solute and solvent molecules to work efficiently, and it also entails the use of large gradients. 6.4.4. Selective excitation In this method, depicted schematically in Fig. 24(A), a selective pulse is used to excite the solvent signal to become a transverse coherence. This transverse coherence is then dephased by a gradient pulse. A hard 7d2 pulse may then be used as the final excitation pulse, resulting in uniform Thus, this technique is excitation with minimal phase distortion. both frequency and lineshape independent. Conversely, excellent lineshape is not a prerequisite to obtaining good solvent suppression. A one rf pulse/gradient pulse combination is extremely sensitive to any mis-setting of the ad2 pulse. The solvent suppression can be improved by using further applications of the selective rf pulse/gradient combination before the excitation pulse, although the subsequent gradients should be, ideally, in a different direction to avoid creating echoes. The negative aspects of this method are that a highly selective rr/2 pulse is required and that if the solvent TI is very short and on the order of the time for the dephasing procedure then some (unwanted) z-magnetization will be re-established prior to the excitation pulse. One method of circumventing the problems imposed by a short solvent T I is to follow the dephasing gradient by a weak gradient to broaden the solvent signal to approx. 180Hz. A noise pulse is then applied and thus, following gradient collapse, the remaining solvent magnetization is randomized and no coherence is read by the final excitation pulse. 197 191,1953197

6.4.5. Watergate Watergate198*199o r water suppression by gradient-tailored excitation is a combination of selective excitation with pulsed field gradients. The basis of the method, schematically represented in Fig. 24(B), consists of a gradient

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selective TG

B

XI2

selective TC

Fig. 24. Solvent suppression by Bo gradients. (A) Selective excitation and then dephasing. (B) the Watergate sequence. (C) An example of a two-dimensional sequence incorporating a Watergate unit (i.e. a Watergate TOCSY (total correlation spectroscopy)).

pulse, a selective 7~ pulse and then a second gradient pulse. All coherences that are dephased by the first gradient pulse can only be rephased if they are subject to a 7~ pulse. Ideally, the coherences of interest are rotated by 180" while the net rotation of the water in near 0". Providing the echo interval is kept short to minimize J modulation, T2 relaxation and molecular diffusion effects, the desired resonances are retained in the spectrum with full intensity while the water peak should be suppressed by a factor of at least lo4. In one-dimensional usage a 90" non-selective excitation pulse can be applied before the Watergate sequence. In cases where it is desired to observe exchangeable protons, a selective 90"-, pulse (selective of the water

GRADIENT NMR

117

resonance) can precede the non-selective 90". Watergate can be incorporated into two- and higher-dimensional experiments (Fig. 24(C)).

6.4.6. BI solvent suppression methods The residual inhomogeneity of (supposedly) homogeneous rf coils have been used to suppress water. 2oo,201 In these experiments the spins of interest were spin locked while the water magnetization, which was previously placed perpendicular to the spin-locking direction, was dephased. Maas and Cory202 have developed a water suppression technique based on the formation of B1 gradient spin echoes or B1 gradient recalled echoes (i.e. rotary echoes). The method is in effect the B1 gradient analogue of the Watergate sequence. The B1 gradient sequence can be used to selectively suppress a resonance by preventing the formation of an echo for a specific resonance while allowing the other resonances to refocus. Maas and Cory202 note that a radial (i.e. quadrupolar) B 1 gradient is more efficient for dephasing longitudinal magnetization than a planar gradient since it has a spatially dependent phase variation in addition to the amplitude variation. Their El solvent suppression technique is reasonably insensitive to artifacts such as J modulation, off-resonance excitation, radiation damping and, chemical shift evolution, and will allow the observation of exchangeable protons. The B1 gradient suppression sequences of Maas and Cory differ from the Bo gradient Watergate sequence in that the magnetization to be observed rotates in a plane perpendicular to the applied rf field and the relaxation is given by an effective TI defined by 1

Tleff

zjl+k) 1 1

=

whereas in the Watergate sequence the relaxation of the observed spins depends on T2. In a preliminary study, Canet and c o - ~ o r k e r s ~have ' ~ shown that a DANTE train of B1 gradient pulses may be used to selectively suppress water. The DEBOG (DANTE elimination by B-one gradient) sequence may be written as

where (gl)xis an rf gradient pulse of duration 7,7' is the precession interval which governs the selectivity process and (d2),, is a homogeneous read pulse. They remark that while it is desirable to have the B1 gradient as strong as possible, the natural B1 gradient in normal saddle coils may be sufficient for most cases. An example of a COSY incorporating E l gradient water suppression is given in Fig. 25.

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WILLIAM S . PRICE

Fig. 25. A B , gradient COSY experiment incorporating water suppression of a sample of 0.9 M glucose in H 2 0 recorded at 200 MHz using a sequence involving the DEBOG suppression scheme203and the equivalent of a double-quantum filter. The B , gradient stren th was about 0.03T/m. (Reproduced with permission from Mutzenhardt et al. 8 4)

6.5. Spectral simplification according to mobility 6.5.1. Introduction

Diffusion and electrophoretic mobility provide a criterion by which to separate mixtures of species according to their size and charge, respectively, Schulze and Stilbs204 have described a method which uses the complete spectral bandshape to extract the individual component contributions. Below we will discuss two, more elaborated, methods: diffusion-ordered spectroscopy and electrophoretic NMR.

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119

6.5.2. Diffusion-ordered two-dimensional experiments

Recently a two-dimensional diffusion experiment (or DOSY), has been proposed for separating species according to their diffusion coefficient^.^^^-^^^ In the SGP limit, the acquired FID is transformed with respect to t2 (the acquisition time) to obtain an NMR spectrum of the form N.

An(v) is the one-dimensional spectrum of the nth species ( q = 0), including the effects of transverse and longitudinal relaxation, Dn is the diffusion coefficient, and NA is the number of components. Here q is incremented to obtain data for the second dimension. The analysis consists of inverting the q dimension to obtain the spectrum of diffusion coefficients. Generally the inversion is mathematically ill-conditioned, and thus additional information must be supplied. For example, whether the distribution of diffusion coefficients is discrete or continuous, which corresponds to whether the components are monodisperse or polydisperse. When there is a discrete number of components the inversion programs DISCRETE209 and SPLMOD210 can be used. Alternatively, if there is a distribution the program CONTIN211 can be used. An example of a DOSY spectrum is given in Fig. 26. Recently, Johnson207 has investigated the effects of chemical exchange in DOSY spectra.

6.5.3. Electrophoretic mobility Electrophoretic NMR (ENMR) resolves the NMR spectra according to the electrophoretic mobility of ionic species. The NMR method has a number of advantages over traditional methods, including needing only a relatively short drift period and not requiring labelled ions. Johnson and He212 have recently reviewed the theory and applications of ENMR. Early ENMR experiments were based on the Stejskal and Tanner sequence and used a U-tube electrophoresis chamber.2123213The ionic drift velocities were determined from the co-sinusoidal dependence of signal intensity on the electric field in the sample. The method was subsequently extended to two dimensions through Fourier transformation of the NMR intensities with respect to either the duration or the amplitude of the electric field Morris and Johnson217 have reported an improvement called mobility ordered two-dimensional NMR (or MOSY: mobility ordered spectroscopy) which achieves resolutions of approximately 1 part per 100 in the mobility dimensions for ions in mixtures and permits the display of both positive and negative mobility. In this method, the LED pulse sequence is used and the

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lo-*

1

D (m2s-')

8.0

7.0 6.0

5.0

4.0

3.0

2.0

1.0

0.0

lo-''

6 (PPm) Fig. 26. DOSY contour plot for a solution containing BSA (bovine serum albumin) (2 g/dl), SDS (sodium dodecyl sulfate) (2 g/dl) and P-mercaptoethanol (0.01 M) in phosphate buffer. The unlabelled line represents the reaction p o d u c t , HOCH2CH2SSCH2CH20H.(Reproduced with permission from Chen ef af. 84)

U-tube electrophoresis chamber is replaced with a cylindrical cell allowing observation of unidirectional flow. Agarose gels are used to stabilize the samples when higher currents are needed. For ENMR collected with the LED sequence (see Fig. 17(A)) the complex data set is given by k

~

x

=y

2 ~xPc~(P~(oI./~(T~, 727 7,)

j=O

where

and

(97)

GRADIENT NMR

121

k is the number of species, A = T] + T~ is the electrophoretic drift time, I is the current, A is the cross-sectional area of the electrophoresis cell and K is the conductivity of the solution. Dl and pJ are the diffusion coefficient and the electrophoretic mobility of the jth species, respectively. M,j is the equilibrium magnetization, and T< and T2I are the spin-lattice and transverse relaxation times, respectively, of the jth species. The drift velocity of the jth species is given by uJ = p,Edc, where Edc = IIAK is the electric field in solution. The real and imaginary parts must be acquired in separate experiments. The mobility spectra (i.e. the second dimension) are obtained by transforming with respect to A or I (depending on what was incremented in the experiment). Incrementing I is preferable since it excludes diffusional broadening. Transformation with respect to I gives, for ions with mobility pl,peaks at u, = qpJA/AK in the mobility dimension. If a cylindrical electrophoresis chamber is used and two FIDs are acquired using the LED sequence at each current value (i.e. one FID for each polarity), the resulting phase-modulated NMR spectra, S , is given by k

where the subscripts "+" and "-"denote the polarity, and uJ(o)and dj(w) are the absorption and dispersion lineshapes for the jth species. From appropriate linear combinations of these spectra, two data sets of absorption mode spectra, one modulated by cos(2~quA)and the second modulated by sin(2rquA), are obtained. These data sets can then be analysed by means of Fourier transformation or linear prediction to yield a MOSY spectrum with pure absorption mode peaks in both dimensions.

7. TECHNICAL ASPECTS OF GRADIENT PRODUCTION 7.1. Introduction

The technical aspects of pulsed field gradient NMR have been discussed by a number of authors (e.g. see refs 4, 14, 15, 104 and 218). Most of the following discussion will be relevant to Bo gradients. The design of a Bo gradient probe is essentially similar to that of a microscopy probe (e.g. see refs 4 and 219) except that the gradients used for the BOgradient probe are larger and normally in one direction only. To perform gradient NMR, it is necessary to have a coil to produce the gradient, a power supply to drive the coil and to have the switching (and perhaps the magnitude) of the gradient under software control (i.e. in appropriate synchronization with the rf pulse sequence).

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7.2. Gradient coil design 7.2.1. Bo gradient coils

Ideally the gradient coils should produce a perfectly linear gradient, but it has been found in practice that a reasonable deviation from perfect linearity is allowable for many experiments.220Many other types of gradient coil are possible (see ref. 218), and typically quadrupolar (for g, and gz) and planar array (for g y ) coils are used in electromagnet-based systems, whilst saddle coils (for g, and g y ) or Maxwell pair coils (i.e. anti-Helmholtz) for g , are used in superconducting geometries. In fact, a design suitable for use in a magic angle spinning probe has recently been presented.221 Since most recent experiments have been performed in superconducting magnets using a shielded Maxwell pair, our discussion will be based upon on this geometry. The magnetic field strength at any point can be estimated from the Biot-Savart law ,2227223

where

u=

J

4pr2

(p

+ r2)2 + z2

K and E are the elliptic integrals of the first and second kinds, respectively. r2 is the radius of the point at which the gradient is calculated, p is the radius of the gradient coil and z is the displacement along the z axis from the coil. Equation (100) may be used as a starting point for determining how many turns are necessary in the primary gradient coil. However, shield gradient coils need to be introduced into the design such that the desired gradient is imposed over the sample volume but a greatly reduced (ideally nothing) gradient is generated outside the coils (see Fig. 27). In this way no (or at least greatly reduced) eddy currents are generated. The idea of shielded gradient coils was originally proposed by Mansfield, Chapman and B o ~ l e y The . ~ theoretical ~ ~ ~ ~ ~aspects of shielded gradient coils have recently been summarized by Callaghar~,~ and will not be discussed here. Numerical optimization procedures for designing coils have been It should be noted that the shield coils decrease the strength and linearity of the gradient that would be produced if the primary et al.232 discussed techniques to gradient coil were u n ~ h i e l d e d . ’ Carlson ~~ design shielded gradient coil systems; specifically, they considered the design compromises between gradient homogeneity, construction complexity, accessible bore and coil efficiency. Although PFG experiments are generally performed with a gradient in

GRADIENT NMR

123

Insert glass

rf coil Shield Coil

1

I-.-

.. .. .. ..

..

.. ...... .. ......

Coil

.... .. ........ .. .... .. .. ..

..... ...... ..... ...... ..... ..... ..... .. .. .. .. .. ...... . .. .. .. .. .....

Thermocouple

Fig. 27. Shielded gradient coils. Schematic diagram of a probe head containing shielded gradient coils.

one dimension only, it is now increasingly common, especially with the advent of imaging and microscopy probes, to perform diffusion experiments in three dimensions so as to obtain the diffusion tensor. Basser and co-workersS3 have proposed that measured diffusion anisotropy in anisotropic media can be used as a basis for calibrating and aligning magnetic field gradients. It is important to account for “cross-terms’’ between gradients, otherwise they will lead to incorrect estimates of the diffusion coefficient .54,233

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The gradient coils can have a strong mutual inductance with the rf coils. This has two deleterious effects, first the Q of the rf coil(s) is diminished, and secondly the gradient coils can have the effect of coupling in external radio sources since the current leads act as antennae.

7.2.2. B, gradient coils Various B1 gradient coil geometries have been proposed. Counsel1 et aZ.39 used the residual inhomogeneity of a conventional transmitter coil to produce a planar gradient. As only the one rf coil is used, both the gradient and homogeneous field are exactly in phase, and thus only the amplitude variation of the fields needs to be considered. The disadvantage of this design is that the gradient is very weak. Canet and c o - w ~ r k e r sused ~~ a remote single-turn coil to create an approximately planar B1 gradient. This design delivers a modest gradient of 0.02-0.03 T/m.234 More recently, Maas and have used an inverted Helmholtz coil which creates a radial gradient. This configuration gives a much higher gradient strength of about 0.1-0.2Tim. In their NMR probe design, the gradient coil is placed on the outside of a conventional homogeneous inner coil. Both coils are driven by the same transmitter, and therefore the response of a spin system to rf from either coil is coherent. This gradient coil design is useful in that it generates two orthogonal gradients and the resulting rf field has cylindrical symmetry. This symmetry obviates the need to know the phase angle between the homogeneous and the gradient rf coils, which would otherwise need to be known for a planar gradient. In using a radial gradient to form a planar gradient (see Section 2.3) this phase angle is variable through the phases of the gradient pulses. This setup, however, requires an odd sample geometry (i.e. an annulus).

7.3. Power supplies Two factors limit the maximum current switching speed; the first is that the power supply voltage must equal RI L dlldt, where L and R are the load (i.e. gradient coils + leads) inductance and resistance, respectively, and the second is the “slew rate” of the power supply. Since the current through a gradient coil induces heating, this causes the coil resistance to change; a constant current power supply is generally preferred so that the gradient pulses are more reproducible. A number of power supply designs have recently been discussed. 128,236 The design by Boerner and Woodward’28 is interesting in that the driver regulates the total charge delivered to the gradient coil independent of the coil inductance or resistance. The design by Saarinen and W ~ o d w a r dincludes ~ ~ ~ provision for electrophoresis pulse generation.

+

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125

7.4. Gradient calibration 7.4.I . Bo gradients The different Bo gradient calibration methods have recently been reviewed by Holz and Weingartner.237 In theory the applied gradient could be calculated from the known dimensions, geometry and the number of turns of wire in the coil and the current applied. In practice, this method should give an estimate with an error of S10%, the major reason being interaction with nearby metal in the probe. Thus, other methods are needed to get accurate gradient calibrations. The simplest way of calibrating a gradient is to use a "standard sample" of known diffusion coefficient. Ideally, a reference compound should have a diffusion coefficient and T2 that are not strongly temperature-dependent. Further, caution should be used with standards containing coupled spins to avoid artifacts arising from J modulation. Some suitable standard samples and their diffusion coefficients are listed in Table 2. Apart from sample-dependent problems, the effects of eddy currents and/or mechanical vibrations will result in this method giving only an apparent calibration. Further, because eddy current effects increase with gradient strength, a calibration at one current value cannot be used to determine the gradient strength at another value of the applied current. This method of gradient calibration is further limited by the need to have a compound containing a nucleus that can be observed with the probe at hand and with a similar diffusion coefficient. For lower diffusion coefficients, suitable reference compounds become more scarce. Glycerol has often been used as a reference, but its diffusion coefficient is greatly affected by water

Table 2. Some selected reference compounds and their diffusion coefficients at 298 K useful for calibrating PFG experiments. A more comprehensive listing can be found in the paper by Holz and W e i r ~ g a r t n e r . ~ ~ ~ Observed nucleus

'H 2H ' ~ i 13C 'YF *'Ne 23Na 31P 129~e 133cs

Compound H20

'HzO LiCI (0.25 M) in H 2 0 C6H6 C6H6F

Ne (4 MPa) in 2H20 NaCl (2 M) in H 2 0 (C6HM' (3 M) in C6D6 Xe (3 MPa) in H 2 0 CsCl(2 M) in H 2 0

Diffusion coefficient (m2/s) 2.30 x 1.87 x 9.60 x 2.21 x 2.40 x 4.18 x 1.14 x 3.65 X 1.90 x 1.90 x

10-9 10-9 lo-'' 10-9 10-9 10-9 10-9 lo-'" 10-9 10-9

Ref. 302 303 237 304 237 245 305 237 244 237

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WILLIAM S. PRICE

content as well as having a highly temperature-dependent diffusion coefficient and T2.14,237 Hrovat and Wade132,160*238 have suggested using the time displacement of the echo maximum caused by the intentional mismatch of gradient pulses. It is possible to calculate the gradient strength using the echo shape from a sample of known geometry, such as a ~ y l i n d e ? or ~ ~other geometries.’60 However, this method is prone to a number of systematic errors. Another possibility, although limited by the spectrometer bandwidth, is a onedimensional image.2”2.240One procedure for calibrating the gradient with a one-dimensional image is to use a sample of known length in the direction of the gradient (a bulb is typically used). The FID is recorded in the presence of the gradient for a number of different applied currents, and then by plotting the width of the spectrum versus the current the gradient strength can be calibrated.222 This method requires that the length of the samplecontaining cell be known accurately, and the final calibration will have an error of around 5 % . The virtue of this method is that the calibration can be performed without any knowledge of the sample diffusion coefficient. If confronted with an uncalibrated coil, a realistic calibration procedure is to first perform a theoretical calculation of what gradient the coil should produce for a given current. A one-dimensional image should then be used for experimental verification. Finally, if a suitable reference compound exists, this should be used for “fine tuning” of the calibration.

7.4.2. BI gradients As for Bo gradients, B1 gradients can be calibrated using reference compounds. However, B1 gradients can also be calibrated, for example, by determining the 360” pulse for a substance inside a capillary at different locations in the sample. One complication, though, is that since gl is directly proportional to the rf field strength, the gradient is proportional to the pulsewidth (and therefore probe tuning). Canet et ~ 1 . ~have ’ shown that after calibration of a B , gradient coil, on changing the sample (and therefore the tuning) the gradient can be determined for the new sample by comparing the 360” pulse width at the centre of the sample relative to that found in the calibration.

7.5. Sample shimming and field frequency locking The sample should be firmly held inside the linear region of the gradient coils, and thus the sample is normally contained in a volume not more than 1 cm high or 1cm in diameter. Such a sample, though, has large changes in magnetic susceptibility close to the rf coils. Accordingly, it is very difficult to achieve good resolution. A solution is depicted in Fig. 28, This method,

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127

Sample

I

Solvent

2/

Fig. 28. A possible sample configuration for gradient NMR measurements in a 10 mm NMR probe. The sample (0.5 ml) is placed in the 8 mm i.d. flat-bottomed NMR tube which is coaxially supported in a 10mm tube. The space beneath the flat-bottomed tube is filled with water, and the sample capped with a Teflon vortex plug to minimize susceptibility differences between the sample and its adjacent

environment, and thus allow the sample to be more readily shimmed. (Adapted from Price .222) compared to just coaxially inserting a bulb into an NMR tube, has the advantage in that it is easy to clean the sample tube or to work with viscous substances. With the use of increasingly higher gradients and the desire to measure ever smaller diffusion coefficients, the rigidity of the sample is of great concern. A sample spinner suitable for use in PFG experiments has been developed that allows for the spinning to be arrested during the motion-sensitive part of the experiment and yet spun, to achieve higher resolution, during acquisition.241 The normal 2H lock is coupled to the Z shim coil to counteract the natural drift of the magnet. A Bo gradient pulse will obviously affect this mechanism. The simptest solution, in the case of low-resolution experiments, is simply to turn the lock off. A better solution is just to gate the lock off for the duration of the gradient pulse.

7.6. Temperature control

Since the temperature regulation in NMR probes is by heated (or cooled) air (or gas, e.g. nitrogen) through the base of the probe, it is possible for

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temperature gradients to be produced along the long axis of the sample. If the temperature gradient is large enough, convective flow may be induced, resulting in an overestimate of the diffusion coefficient. Goux et al.242 studied the effects of thermal convection in PFG experiments. They concluded that, while the best solution is improved temperature control, the effects of convective flow can be minimized by using narrower sample tubes, decreasing the sample height, or increasing the sample viscosity.

8. SPECIFIC EXAMPLES OF GRADIENT NMR 8.1. Introduction

It is beyond the scope of this chapter to provide a comprehensive survey of the literature related to gradient NMR. Instead, this section is intended to give an introduction to the types of systems that have been studied, and the information obtained, and also to discuss some of the novel applications of gradient NMR. 8.2. Diffusion-based studies

8.2.1. Diffusion measurements

A list of diffusion coefficients for interesting species is given in Table 3. Recently, measurements of the self-diffusion coefficients of H2,243the noble gases Xe244 and Ne245 in water, and of Cm in b e n ~ e n e - dhave ~ ~ ~been ~ reported. 23Na PFG NMR has been used in conjunction with TI measurements to study the relationship between the diffusion coefficient, conductivity and T~ of sodium ions in water-glycerol solutions.33 Gibbs and Johnson have studied polyammonium cation diffusion in aqueous solutions of DNA.247 Even the diffusion behaviour of sodium monofluorophosphate (MFP2-), Na+, H20 have been studied in toothpaste-like pastes based on aqueous silica dispersions.248 B1 gradients have been used to measure the self-diffusion coefficient of hydroxyquinoline in aqueous solutions of micellized sodium dodecyl sulfate, and also to determine its partition coefficient as a function of

8.2.2. Restricted diffusion and obstruction have used 13C PFG NMR to study the diffusion coefficient of Price et glycine inside human red blood cells. Glycine transports across the red cell membrane slowly on the NMR time-scale. It was found that the intracellular glycine diffusion coefficient was one-third that of the free solution value.

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Table 3. Selected diffusion coefficients of species of biological and chemical significance. The species in parentheses denote the solvent, where applicable.

Observed nucleus 'H

l3C 31P

Species Ovalbumin 2H (H20) c 6 0 (l mM) (c6D6) [2-13C]Glycine(H20) H 13C03- (H20) H2P02-(H20)

Diffusion coefficient (m2/s)

Temperature (K)

Ref.

7.92 X lo-'' 4 x 10-9 8.3 x lo-'" 1.18 x 10-9 1.26 x lo-]" 1.60 X lo-'

Ambient 296

276 243

298

246 32 118 118

310 310 310

PFG NMR has been used to measure water diffusion and pore volume in wood pulp cellulose fibre^.^^',^'^ Two components were observed: one with a self-diffusion coefficient independent of time and the other with a time-dependent "apparent" diffusion coefficient. The two components were attributed to the bulk water between the cellulose fibres and water within the fibres, respectively. Van Gelderen and co-workersX1studied the diffusion of phosphocreatine in the cylindrically shaped fibres of rabbit skeletal muscle. By using diffusion measurements in three orthogonal directions, they were able to determine the trace of the diffusion tensor with time. This allowed them to evaluate the diameter of the cylindrical cells and the unrestricted diffusion coefficient. They found the radius of the cells to be in the range of 8-9pm, and the phosphocreatine diffusion coefficient to be in the range 7 x 10-l' to 9 x 10-" m2/s. Obstruction effects are quite common in both chemical and biochemical systems. Kuchel et measured the diffusion coefficients of H2 and H 2 0 in H 2 0 and in an H 2 0 solution of bovine serum albumin. They found that in H 2 0 the diffusion coefficients of H2 and H 2 0 were 4.0X and 2.1 x lo-' m2/s, respectively, at 296 K. However in the protein solution the diffusion coefficients were reduced to 1.0 x lo-' and 1.8 x m2/s, respectively. The larger reduction in the diffusion coefficient of H2 than H 2 0 was attributed to the greater obstruction felt by the faster diffusing H2. Latour et ~ 1 studied . ~the ~time-dependent ~ water diffusion coefficient in packed erythrocytes. They found that the long-time diffusion coefficient, Deff, was very sensitive to the extracellular volume fraction. Using an effective medium formula, they were able to estimate the erythrocyte membrane permeability. From the short-time behaviour of the diffusion coefficient, they estimated the surface-to-volume ratio of the cells to be approximately (0.72 p n - ' . Blees and L e ~ t e studied ' ~ ~ the self-diffusion of organic solvents in water and in a colloidal dispersion of poly(butylacry1ate) in water. They found

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WILLIAM S. PRICE

that, for the colloidal systems with A = 45ms, the self-diffusion was dominated by exchange effects amongst the colloidal particles. The diffusion coefficient was also found to depend strongly on the volume fraction of the colloidal particles. They noted that the partition of the organic solvent between the water and the colloid particle could be determined from the experiment. PFG has found great application in the measurement of droplet sizes and distributions. Systems that have been studied include emulsions stabilized by anionic, cationic and non-ionic surf act ant^."^^"^^^^^ In a study of water-inoil emulsions, it was noted that as the temperature changed the standard deviation of the droplet size remained constant, but there was a large decrease in the mean diameter of the dist~ibution.''~It was surmised that the most likely explanation of this effect was water interdroplet diffusion. Thus, there must be a significant probability for water molecules to move from droplet to droplet in aggregates as observed in oil-in-water emulsions255or by random coalescence and break-up providing additional distances for motion.256 Diffraction-like effects have been observed in a highly concentrated water-in-oil emulsion.257From the experiment the mean droplet size of the emulsion was able to be determined.

8.2.3. Binding and transport Hydration numbers may be determined from the concentration dependence of the water self-diffusion coefficients.2589259 31P PFG NMR has been used to measure the diffusion coefficient of 2,3-bisphosphoglycerate (DPG) in haemoglobin solutions in both free solution and in intact erythrocytes.260 The dependence of the measured diffusion coefficients on the amount of DPG bound to haemoglobin was used to estimate the dissociation constants for DPG complexed to carbon-monoxygenated, oxygenated and deoxygenated haemoglobin. An example of using PFG NMR to study the transport of hypophosphite and bicarbonate ions in human red blood cells"* has already been discussed in Section 3.7.5. More recently, Waldeck et aZ.261used PFG NMR to study the ionophore-mediated transmembrane exchange of Li+ in liposomes. They applied the two-region approximation approach of Karger (i.e. equation (61)) and found good agreement between the transmembrane exchange rates obtained from the PFG measurements and those using traditional NMR methods.

8.2.4. Liquid crystals and surfactants Extensive reviews on the application of gradient NMR to liquid crystal and result surfactant systems have recently been p r e ~ e n t e d .As ~ ~a, ~ ~ we will not spend any time reviewing this area apart from mentioning that gradient

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NMR provides a superb tool for such systems and has produced useful results in systems such as water self-diffusion in polycrystalline lamellar systems,262 hexagonal mesophases," smectic liquid crystals,263 and surfactan t systems. 264-267 As would be expected for restricting geometries, strong diffusional anisotropy effects have been noted in studies of biological cells. 150,151 In fact, the observation of the anisotropy has been noted as being a useful clinical probe of demyelinating disorders, white matter infarcts, neoplasms and neonatal brain and spinal cord development.1so Schoeniger et a1,268 studied water diffusion in neurons. They noted that water in the nucleus has different diffusion properties than that in the cytoplasm. Similarly, LeBihan and c o - w o r k e r ~have ~ ~ ~proposed that measurements of diffusion coefficients have clinical applications including functional assessment, tissue characterization and treatment monitoring.

8.2.5. Porous media Zeolites and rocks are well-known examples of porous media that have been studied by gradient NMR. PFG measurements can unambiguously discriminate between the limiting cases of (1) intracrystalline diffusion, (2) restricted self-diffusion and (33 long-range self-diffusion. The information that can be obtained about zeolite beds via PFG NMR has recently been summarized by K a r g e ~ - Consequently, .~~ we will just review some of the more recent applications. 'H NMR imaging has been combined with PFG NMR to study sorption in zeolites.270 Figure 29(A) contains an example of 'H NMR spectra of n-hexane in a bed of zeolite NaX after the onset of adsorption through the upper right face (right-hand side of the spectra) of the zeolite bed in the NMR sample. The data show that the observed diffusivities are a function of the local sorbate concentration (Fig. 29(B)). PFG NMR has also been used to study catalytic reactions271and the molecular diffusion of CH4, CO, C 0 2 , n-hexane and Xe in zeolite^.^^".^^^,^^' It has also been noted that the geometrical information factor F , which can be determined from PFG measurements, is important for transport phenomena in porous systems such as fluid flow, electrical conductivity, and fourth sound.'22 PFG NMR has also been used to study the pore size and to determine the surface-areato-volume ratio and surface relaxivity in 8.2.6. Polymers and macromolecules

Gradient NMR provides a convenient means for studying the physical chemistry of proteins. Gibbs and co-workers have used 'H PFG NMR to study ovalbumin intradiffusion coefficients as a function of protein concentration in free solution .276 They noted that PFG measurements in

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WILLIAM S. PRICE

m-0 m-2 In-4

m-2

m-6

m=9

L

a

B

\ 0

50

100

150

200

Fig. 29. Applications of PFG N M R to zeolite systems. (A) ‘H N M R resonances of n-hexane in a bed of zeolite NaX, (a) 50min and (b) 150min after the onset of adsorption with restricted adsorbate supply for different field gradient pulse widths 6 = 0.4 v m ms. The curve with m = 0 represents the concentration profiles. (B) Apparent self-diffusion coefficients of intracrystalline n-hexane observed by timeand space-resolved ‘H PFG N M R in zeolite NaX with restricted (a) and unrestricted ( 0 ) sorbate supply. The open symbols represent the true diffusivities. The solid line with error bars indicates the range of intracrystalline diffusivities as observed in previous PFG N M R studies. (Reproduced with permission from Karger et al.270)

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combination with the macroscopic boundary relaxation technique and independent measures of the protein activity coefficient offer a means of comparing the magnitudes of the frictional coefficients for mutual diffusion and intradiffusion. Later, using both 'H and 19FNMR, they extended their studies to the diffusion of ovalbumin in porous gel filtration chromatography media.277 PFG can provide an enormous amount of information about polymers both in solution and in polymer melts. For example, PFG NMR has recently been used to measure the critical overlap concentration for polystyrene in t e t r a c h l ~ r o m e t h a n e .Callaghan ~~~ and Coy,1o8 using very large values of q(27rq (13.0 nrn)-'), have obtained evidence for reptational motion of high molar mass polystyrene in semidilute solution using 'H PFG measurements. In a related study, Appel et dio7 used the fringe field of a superconducting magnet to measure the self-diffusion of poly(dimethylsi1oxane) , polybutadiene and polyisoprene for times smaller than the reptation time. A time-dependent apparent self-diffusion coefficient was observed. Solutions of block copolymers are interesting systems for the study of self-organization since, due to hydrophobic and hydrophilic moieties, the polymer molecules may form micelles over a certain temperature interval. As a result, the diffusion of some polymers can have strange temperature dependencies, such as has been observed with the triblock copolymer PEO-PPO-PEO in 2H20.279Interestingly, it was observed that even for the case of A = 3 ms the attenuation of the echo signal was single exponential. Thus, the exchange time of the polymer molecules between the micelles and unimers must be much shorter than the observation time. PFG also provides a means for studying ion motions in conducting polymers. For example, 7Li PFG NMR has been used to study lithium diffusion in polymer electrolytes. 280

-

8.3. High-resolution NMR applications

8.3.1 Applications of DOSY and electrophoretic N M R The DOSY experiment has opened up new possibilities for analysing spectra from samples containing more than one component. Apart from the examples presented in Section 6.5.2, it has been applied to the analysis of polydisperse systems,2o8 and for studying equilibria involving binding, absorption and partitioning in surfactant systems.281 The DOSY experiment has been used to study the non-Newtonian to Newtonian transition in a hexadecyltrimethylammonium bromide (CTAB)sodium salicylate-water viscoelastic micellar system induced by the addition of a soluble yet slightly hydrophobic polymer.282 It is shown that the diffusion coefficient of the different species provides information on the

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binding and aggregation processes in the system. Hinton and have used sucrose trapped inside vesicles as a marker to measure the diffusion coefficients of vesicles in a DOSY experiment. Since the size of the vesicles is much larger than the solvent, the Stokes-Einstein equation (equation (58)) can be used to relate the diffusion coefficient to the size of the vesicles. The method also allowed the determination of the trapped and free fractions of sucrose. In a later study, the DOSY experiment (see Fig. 26) was used to determine the binding isotherm and size of the bovine serum albumin-sodium dodecyl sulfate complex.284 Electrophoretic NMR has been used to study the tetramethylammonium ion, N , N , N ’,N’-tetramethylenediamine and tetrahexylammonium ion in polyacrylamide gels285and surfactant 8.3.2. Coherence selection, phase cycling and solvent suppression Since this area has only just been reviewed28we will not dwell on it greatly, but it is of note that gradient-enhanced multidimensional experiments have now become common place. A big advantage of gradient-enhanced multidimensional NMR experiments is that the gradients can also be used for water signal suppression. Thus, the one protein sample dissolved in H 2 0 , can be used for experiments which detect the amide chemical shifts during acquisition and experiments where the alpha protons are recorded (e.g. see ref. 288). Further, gradient-enhanced versions of many sequences are now in common use, for example: the selective one-dimensional COSY experiment,289 heteronuclear multiple-quantum correlation (HMQC),290 I5N-’H HSQC,291 triple-resonance three-dimensional NMR experim e n t ~and ~ three-dimensional ~ ~ , ~ ~ ~ homonuclear J COSY experiments.294A PFG-based method for determining the excitation profile of a shaped rf pulse has been presented.295 Kriwacki and c o - ~ o r k e r shave ~ ~ ~ studied water molecule binding to macromolecules. They employed modified nuclear Overhauser effect spectroscopy (N0ESY)-HMQC, rotating frame Overhauser enhancement spectroscopy (R0ESY)-HMQC and total correlation spectroscopy (T0CSY)HMQC sequences which incorporated a PFG “diffusion filter”. These modified sequences allowed them to select only those peaks arising from slowly diffusing species. Absorption mode phase-sensitive zero-quantum coherence has been developed by N o r ~ o o d This . ~ ~work ~ is interesting in the light of allowing acquisition of high-resolution spectra from samples containing strong internal magnetic gradients. B1 gradients have been used to improve the resolution and sensitivity in NOE and ROE experiments with water.298The B1 gradients were used to suppress radiation damping effects.

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9. CONCLUDING REMARKS In this chapter, I have endeavoured to summarize the main features of gradients in NMR. I have tried to emphasize that gradients in NMR can be a problem if unaccounted for, a probe of porous media if understood, and panacea for the high-resolution spectroscopist. Gradient NMR allows a very convenient means of non-invasively measuring diffusion and transport in biological and chemical systems. q space imaging opens up the possibility of being able to image porous materials at higher resolution than that available with conventional k space imaging. With improving technology (i.e. pulse sequences, shielded gradient coils and fringe fields) larger values of q become possible. Although diffraction effects only become visible at large attenuations, with increasingly higher static magnetic fields and probe technology the use of diffraction effects may become a generally useful method for many systems and not just specific model systems. Further extensions to “multiple wave vector” experiments have potential for providing increased information. Gradient methods that separate species according to their mobility and diffusion coefficient such as electrophoretic NMR and the DOSY experiment have enormous potential in the analysis of complex mixtures containing many species such as biological In high-resolution NMR, gradients allow many experiments to be achieved in a fraction of the time taken by their non-gradient counterparts. This has made the higherdimensional experiments much more practicable. Although Bo gradients are currently more popular than B1 gradients, it is expected that the application of B 1 gradients to high resolution NMR will increase due to their technical simplicity.

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Pharmaceutical Applications of NMR D. J. CRAIK and K. J. NIELSEN Centre for Drug Design and Development, University of Queensland, Brkbane, 4072, Q L D , Australia

K. A. HIGGINS Department of Biochemistry, Monash University, Clayton, 3144, VZC,Australia

1. Introduction 1.1. Instrumentation 1.2. Methodology 2. The role of NMR in drug development 3. NMR techniques in drug design 3.1. Drug conformations 3.2. Protein structure determination 3.3. Protein-ligand complexes 3.3.1. NMR titrations of complexes 3.3.2. NOESY analysis of complexes 3.3.3. Isotope editing 3.3.4. Transferred NOES 4. Selected examples 4.1. Endothelins 4.1.1. 3D structure of ET-1 and related peptides 4.1.2. Comparison of NMR and X ray structures of ET-1 4.1.3. 3D structure of cyclic pentapeptide ET antagonists 4.2. Conotoxins 4.2.1. 3D structure of w-conotoxin GVIA 4.2.2. Structure-activity relationships 4.2.3. Structurally related peptides 4.3. Insulin 4.3.1. 'H NMR studies 4.3.2. I3C NMR studies 4.3.3. Summary Acknowledgements References

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1. INTRODUCTION Since its discovery, nuclear magnetic resonance (NMR) spectroscopy has played an important role in the pharmaceutical sciences. An early application of NMR was to assist in the identification and characterization of A N N U A L REPORTS O N NMR SPECTROSCOPY VOLUME 32 ISBN 0-12-505332-0

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chemically synthesized drugs or biologically active molecules derived from a variety of natural sources which formed the basis of pharmaceutical products. The role of NMR as essentially an analytical tool has now been supplemented by a more fundamental application-providing information to be used in the design of new drugs. This application has become possible because of the significant advances in NMR instrumentation and methods that have occurred in recent years. This review will focus primarily on applications in drug design, rather than analytical or other applications of NMR in the pharmaceutical industry. The importance of NMR in drug design is demonstrated by the recent publication of several books and reviews on the topic,14 and related articles on protein-ligand interaction^.^.^ Applications of NMR to drug design had their origins in the 1960s and 1970s, with the determination of structures and conformations of biologically important organic molecules, typically with molecular masses of up to 1000 Da. These studies were done initially on 60-100 MHz spectrometers, where the conformational information was derived from chemical shifts, coupling constants, and nuclear Overhauser enhancement (NOE) measurements. Such studies proved useful in defining solution conformations; however, these did not necessarily reflect the biologically active form at the receptor site. Nevertheless, for cases where the molecules of interest are relatively rigid, a determination of their solution conformations is valuable. The increasing availability of higher-field (200-500 MHz) spectrometers in the late 1970s and early 1980s dramatically increased the complexity of molecules that could be studied. In parallel with these developments, the availability of wide-bore magnets made it possible to examine intact organs and even whole animals using surface coil technology. This allowed, for example, the study of the effects of drugs on metabolism.’ Further advances in high-resolution NMR have occurred since the mid-l980s, with the increasing availability of 500, 600 and now 750 MHz spectrometers, and new NMR methods. In particular, the development of methodology for assigning and determining the structures of peptides and proteins by two-dimensional (2D) NMR’ has enabled a wide range of new applications in the field of drug design. These arise because of the importance of biologically active peptides as potential targets in analoguebased drug design, and proteins in receptor-based drug design. Initially, the new technology provided the capability to extend the molecular weight range and allow the study of small proteins (

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