Molecular Modelling In Structural Biology

PERGAMON Micron 33 (2002) 365±384 www.elsevier.com/locate/micron Review Molecular modelling in structural biology Ma...

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PERGAMON

Micron 33 (2002) 365±384

www.elsevier.com/locate/micron

Review

Molecular modelling in structural biology Mark J. Forster* Informatics Laboratory, National Institute for Biological Standards and Control, Blanche Lane, South Mimms, Hertfordshire EN6 3QG, UK Received 16 February 2001; revised 11 June 2001; accepted 12 June 2001

Abstract Molecular modelling is a powerful methodology for analysing the three dimensional structure of biological macromolecules. There are many ways in which molecular modelling methods have been used to address problems in structural biology. It is not widely appreciated that modelling methods are often an integral component of structure determination by NMR spectroscopy and X-ray crystallography. In this review we consider some of the numerous ways in which modelling can be used to interpret and rationalise experimental data and in constructing hypotheses that can be tested by experiment. Genome sequencing projects are producing a vast wealth of data describing the protein coding regions of the genome under study. However, only a minority of the protein sequences thus identi®ed will have a clear sequence homology to a known protein. In such cases valuable three-dimensional models of the protein coding sequence can be constructed by homology modelling methods. Threading methods, which used specialised schemes to relate protein sequences to a library of known structures, have been shown to be able to identify the likely protein fold even in cases where there is no clear sequence homology. The number of protein sequences that cannot be assigned to a structural class by homology or threading methods, simply because they belong to a previously unidenti®ed protein folding class, will decrease in the future as collaborative efforts in systematic structure determination begin to develop. For this reason, modelling methods are likely to become increasingly useful in the near future. The role of the blind prediction contests, such as the Critical Assessment of techniques for protein Structure Prediction (CASP), will be brie¯y discussed. Methods for modelling protein±ligand and protein±protein complexes are also described and examples of their applications given. Crown Copyright q 2002 Published by Elsevier Science Ltd. All rights reserved. Keywords: Molecular modelling; Three dimensional structure; Homology; Threading; Protein±ligand complexes; Protein±protein complexes

Contents 1. 2. 3.

4.

5.

Introduction to molecular modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. How to compute the molecular potential energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2. Exploring conformation space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Common modelling force®elds and packages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Macromolecular structure determination and databases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Nuclear Magnetic Resonance (NMR) methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. X-ray methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. The protein data bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Combining X-ray and electron microscopy data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Protein homology modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Why create protein homology models? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Outline of homology modelling schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. An example of automated homology modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Evaluating protein homology models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5. Databases of protein homology models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ThreadingÐcomparing protein sequence to structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Outline of threading methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Large scale application and testing of threading methods . . . . . . . . . . . . . . . . . . . . . . . . . . .

* Tel.: 144-1707-654-753; fax: 144-1707-646-730. E-mail address: [email protected] (M.J. Forster). 0968±4328/02/$ - see front matter Crown Copyright q 2002 Published by Elsevier Science Ltd. All rights reserved. PII: S 0968-432 8(01)00035-X

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6.

Modelling protein±ligand complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. The goals of protein±ligand docking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Docking methodology and programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. An example of protein±ligand docking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. Computational screening of small molecule databases by docking . . . . . . . . . . . . . . . . . . . . . 7. Modelling protein±protein complexes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1. Methods for modelling protein±protein interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2. Testing protein±protein docking methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3. Modelling protein±protein interactions in viruses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8. Summary and conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction to molecular modelling 1.1. How to compute the molecular potential energy There are many levels of theory at which computational models of three-dimensional molecular structure can be constructed. The overall aim of modelling methods will often be to try to relate biological activity to structure. An important step towards this goal is to be able to compute the potential energy of the molecule as a function of the positions of the constituent atoms. Quantum methods in which electronic structure is explicitly considered (Foresman and Frisch, 1996) are the most rigorous, but because of the computational demands involved, they can usually only be applied to smaller molecules (e.g. up to 100 atoms). A widely used approximation is to treat the molecule by a scheme known as molecular mechanics (Burkert and Allinger, 1982). In this approach there are energy terms that describe the deformation of bond lengths, bond angles and torsion angles away from their equilibrium values. In addition there are energy terms for non bonded pairs of atoms that describe the attractive and repulsive components of the van der Waals energy and a term for the coulombic interaction between charges. The molecular mechanics potential energy function can then be written as an expression of the form: V

1 1 S K b 2 b2 1 S angles Ku ueqm 2 u2 2 bonds b eqm 2 1

1 S K 1 1 cosnf 2 torsions u

1S non-bonded pairs i2j A=rij12 2 B=rij6 1 qi qj =Drij The equilibrium bond lengths (beqm), bond angles (u eqm), partial charge values (q), force constants (K) and van der Waals parameters (A, B) must be carefully determined. This is normally achieved by ®tting to experimental data and/or higher level quantum calculations. Such an expression treats the molecular system in a highly simpli®ed fashion, for example, the electrostatics of the system are assumed to be describable by a uniform dielectric constant (D) with

375 375 376 376 377 377 377 378 378 380 380 380

partial charges placed at atom centres. It should be understood that the dielectric constant is a macroscopic quantity and its application to atomic level simulations has no formal basis. Dielectric constants that vary with distance are sometimes used in simulations as a very approximate scheme to mimic the screening of electrostatic interactions by solvent. A more realistic treatment of solvent is to include explicit ions and solvent molecules in the molecular model, and use a dielectric constant of one. Fig. 1 illustrates the type of molecular model that is required for this kind of simulation. However modelling using explicit solvent and ions greatly increases the number of atoms in a model, leading to an increase in the time required to complete the calculation. Such calculations may also require knowledge of the salt concentration, ionisation state of particular residues etc. Other calculation schemes known as continuum electrostatic models (Antosiewicz et al., 1994) address the electrostatic effects of solvation, by treating the macromolecule as a region of low dielectric material surrounded by a continuous medium of high dielectric. The simple nature of the above molecular mechanics expression means that it can be rapidly evaluated and applied to molecular systems with many thousands of atoms. The selection of a given mathematical or functional form along with a chosen set of molecular mechanics parameters is usually referred to as a force®eld. Some force®elds also include additional terms designed to maintain non planarity of certain atom environments (e.g. N atoms in amine groups), or to explicitly model hydrogen bonding. Other force®elds allow for so called `cross terms' in which, for example, an energy term may arise for the product of a bond length and a bond angle deformation. In the ®eld of protein modelling there are many examples of using sets of known protein structures to derive `knowledge based' potential functions. These functions are fundamentally different from the molecular mechanics potential functions described above. The knowledge based potentials utilise a representative database of solved protein structures to provide a sampling of the types of interactions that occur in proteins. Interactions that occur more or less frequently than those expected on a statistical basis, are then parameterised to represent favourable and unfavourable terms in


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Fig. 1. Molecular model of a protein±protein complex and counter ions (space ®lling representation) along with water molecules (red and white line drawing representation) as used for a simulation that mimics aqueous solution. This shows that very complex models are required for such simulations. In this case the protein portion of the system consists of three copies of the monomer of the membrane associated (MA) protein of HIV-1, arranged so as to form inter-trimer interactions (Forster et al., 2000). The large purple and yellow/green spheres are sodium and chloride ions respectively, within the protein hydrogen, carbon, nitrogen and oxygen atoms are represented as white, green, blue and red spheres respectively. The box represents a periodic boundary condition whereby any particles leaving one face of the box are made to reappear at the opposite face; this prevents solvent etc. from drifting away during the simulation.

the scoring function respectively. Many of these potential functions are designed for use with a simpli®ed model of each amino acid in the protein. Applications of knowledge based potentials to protein homology model building, and to assessing protein sequence-structure compatibility, will be discussed. 1.2. Exploring conformation space Once a method for evaluation of the molecular potential energy is available, it is natural to try to ®nd an optimum molecular geometry by minimising the energy of the system. A number of distinct algorithms are available for seeking the values of adjustable parameters that minimise a mathematical scoring function, examples include the simplex method, steepest descent and conjugate gradient methods (Press et al., 1993). These algorithms differ in the way in which they use the gradient of the energy as well as in their robustness and search ef®ciency. In a biological macromolecule the potential energy surface is a complicated one, in which there are many local energy minima as well as a single overall global energy minimum. All of

the above energy minimisation algorithms have a marked tendency to locate only a local energy minimum that is close to the starting conformation. If a systematic search of the conformation space could be performed, e.g. by varying all available torsion angles through the allowed range of values, then identi®cation of the global minimum for a given force®eld would be guaranteed. For a biological macromolecule the number of conformations that must be searched rises exponentially with the size of the molecule, hence systematic searching is not a practical method for larger molecules. Molecular dynamics (MD) is a conformation space search procedure in which the atoms of the biological macromolecule are given an initial velocity, and are then allowed to evolve in time according to the laws of Newtonian mechanics (van Gunsteren and Berendsen, 1977). Depending upon the simulated temperature of the system, the macromolecule can then overcome barriers in the potential energy surface in a way that is not possible with a minimisation procedure. This scheme provides a picture of the molecular conformation that is a dynamic one, as opposed to the static picture provided by a minimisation procedure.

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One useful combination of molecular dynamics and minimisation schemes is a method known as simulated annealing. This method uses a molecular dynamics calculation in which the system temperature is raised to a high value, allowing for a widespread exploration of the available conformation space. Then the system temperature is gradually decreased as further dynamics is performed. Finally a minimisation phase may be used to select a minimum energy molecular conformation. The annealing scheme is typically run several times in order to create an ensemble of representative molecular conformations. The application of simulated annealing methods to structure determination will be discussed in a subsequent section. One of the most important applications of molecular modelling techniques in structural biology is the simulation of the docking of a ligand molecule to a receptor, such as a protein. If the structure of the receptor is known then the application is essentially one of structure based drug design. These methods have a number of related aims; they often seek to identify the location of the ligand binding site and perhaps the geometry of the ligand in the active site. Another goal is the correct ranking of a series of related ligands in terms of their af®nity, or to evaluate the absolute binding free energy as accurately as possible. A review of docking methodologies have been provided by Kuntz et al. (1994), and by Lengauer and Rarey (1996). 2. Common modelling force®elds and packages In order to select a force ®eld and modelling methodology for a given task it is important to appreciate the range of molecular systems to which it is applicable, and the types of simulations that can be performed. To this end, some of the better known force®eld/modelling software packages will be brie¯y discussed. One of the most widely used of these packages is AMBER (Assisted Model Building with Energy Re®nement). The AMBER force®eld (Weiner et al., 1984, 1986; Cornell et al., 1995) was originally developed with the intent of enabling the simulation of protein and nucleic acid molecules. After the initial publications, parameters that enable the simulation of carbohydrate systems have been reported (Homans, 1990; Woods et al., 1995). Thus the program is capable of simulating a wide range of biological macromolecules. However, when an unusual chemical moeity or functional group is present in the molecule, which can often occur for a drug like small molecule, then the parameters required for the evaluation of the molecular mechanics energy are not automatically available and these must be supplied by the user. Details of the AMBER force®eld and the software package can be obtained from the website located at http://www.amber.ucsf.edu/. In addition an internet accessible AMBER server has recently become available (http://nar®.compchem.ucsf.edu/), this allows a protein or nucleotide molecular structure to be

sent to the server in the form of a protein data bank (PDB) co-ordinate ®le. Once uploaded the structure is minimised and the energy terms reported when the minimisation is complete. This allows for easy access to some of the simpler capabilities of the AMBER package without the involved steps of purchasing, downloading, installing and testing the full software package. However, the server is only intended for small molecular systems (typically less than 20,000 atoms); for more demanding simulations use of the full package on your own system will naturally be required. The AMBER software allows simulations such as simple minimisation, molecular dynamics and simulated annealing as discussed above. In addition to this tools are available for structure generation and analysis using NMR data (Gippert et al., 1990; Case et al., 1994; Case, 2000) and for calculating relative binding af®nities in complexes of proteins and other molecules. (Radmer and Kollman, 1998; McCarrick and Kollman, 1999). A recent development in AMBER enables the use of a simulated continuum solvent (Cheatham et al., 1998; Kollman et al., 2000). There are other force®elds and molecular mechanics software packages that offer a broadly similar range of capabilities to AMBER. The CHARMM (Chemistry at HARvard Molecular Mechanics) force®eld/software (Brooks et al., 1983) is another widely used and highly capable package. The program was designed for simulations of proteins, nucleic acids and lipids. For internet accessible information on this program see the sites located at http://yuri.harvard. edu/ and http://www.scripps.edu/brooks/charmm_docs/ charmm.html. Both the AMBER and CHARMM software suites are available to academic users for a modest cost. The AMBER and CHARMM force®elds have also been implemented in a number of different software packages. As an example the TINKER (Ponder and Richards, 1987; Pappu et al., 1998) program implements both of these along with the MM2/MM3 force®elds (Allinger and Yan, 1993; Allinger and Durkin, 2000) and the OPLS force®eld (Jorgensen and Tirado-Rives, 1996). The TINKER program suite offers facilities to build initial nucleic acid and protein models from de®ned sequences. It also includes programs to perform energy minimisation, molecular dynamics and a number of other conformational search schemes. The TINKER software is available without charge from the website located at http://dasher.wustl.edu/tinker/. It is often the case that each force®eld has a particular area of application for which it is particularly suited, this arises because the force®eld parameters have been carefully optimised for a particular class of molecules. While AMBER and CHARMM are intended for biological macromolecules, the MM2/MM3 force®elds are often used for conformational energy calculations of small molecules. Similarly the OPLS force®eld was derived to reproduce liquid state or solution properties. The MMFF force®eld of Halgren (1996) is of interest because it is contains parameters for a wide variety of functional groups that arise in organic and medicinal chemistry. Commercially available modelling


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packages such as those from Molecular Simulations (http:// www.msi.com or http://www.accelrys.com) and Tripos (http://www.tripos.com) include several of the force®elds mentioned above, they often provide an integrated graphical environment for simulations that is reasonably easy for a novice user to use.

3. Macromolecular structure determination and databases 3.1. Nuclear Magnetic Resonance (NMR) methods The three dimensional structures of biological macromolecules can be determined by the methods of X-ray crystallography and by NMR spectroscopy. This brief review allows discussion of only a few selected aspects of these methods, and draws attention to the way in which structure determination is related to molecular modelling methods. Both NMR and X-ray methods have their own particular merits and drawbacks, but it is instructive to consider them as complementary methods of achieving the same goal (Brunger, 1997). One advantage of NMR methods is that they ®nd the structure of the molecule in aqueous solution. Structure determination projects based on NMR methods traditionally require experimental data known as proton±proton nuclear Overhauser effect (nOe) peaks and scalar coupling constants (Wuthrich, 1986). The former are typically observed for hydrogen atoms that have a spatial Ê or less. The latter arise from interactions separation of 5 A between atoms that are separated by a few bonds, these couplings can be used to obtain information on torsion angles within the macromolecule. NMR methods are also used for studying the conformational ¯uctuations of macromolecules in solution. This is often achieved by using macromolecules that are enriched with the isotopes 13C and/or 15N and by measuring nOes and spin relaxation times for these nuclei. This provides a detailed picture of local ¯exibility at many sites in the macromolecule (Ishima and Torchia, 2000). Newer methods of ®nding structural information by NMR are based upon achieving a partial alignment of the macromolecule in solution. This partial alignment leads to dipolar interactions between pair of atoms that could not normally be observed, because the interaction is averaged to zero in a normal isotropic solution. Distances and angles can be derived from the observed dipolar couplings, this provides geometric information complementing that obtained by nOe spectral peaks (Tjandra and Bax, 1997). The experimental data are then combined with (empirically determined) weighting factors to provide additional distance and/or torsional pseudo-energy terms, known as restraints. The restraints are incorporated into a molecular mechanics energy expression such as that described above, to provide a combined scoring function. A molecular dynamic simulated annealing scheme (Brunger et al., 1986; Nilges et al., 1988) can then be used to generate a set of structures that are

Fig. 2. An example of protein structure determination by NMR. The basic pancreatic trypsin inhibitor structure was obtained by a simulated annealing protocol using the Discover force ®eld (Molecular Simulations Inc., see http://www.accelrys.com). The dashed lines represent pairs of hydrogen atoms for which distance restraints, obtained from experimental NMR data, were used in determining the structure. Picture generated with insightII (MSI).

consistent with the force ®eld and the experimental data. A distance geometry calculation (Havel and Wuthrich, 1985) can also be used for generating sets of structures that best satisfy the experimentally derived constraints, while avoiding steric overlap between atoms in the model. Thus NMR spectroscopic structure determination relies heavily upon simulation methods normally associated with molecular modelling. Fig. 2 shows an example of a protein structure (basic pancreatic trypsin inhibitor) along with a representation of some of the NMR data used for the structure determination. One of the principal drawbacks of NMR structure determination methods is that they are limited in the size of the molecule that can be studied, molecules larger than 20 kDa usually require isotopic labelling with 13C and 15N isotopes (Clore and Gronenborn, 1998). 3.2. X-ray methods X-ray crystallography does not suffer from the limits on macromolecular size that affect NMR spectroscopy. In a

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crystallographic structure determination the data that are collected provide information on the amplitude of the scattered radiation but not on the phases. Since this phase information is required for reconstructing an image of the electron density of the macromolecule, it must be obtained by additional experiments or other means. One way in which phase information can be obtained is by a second experiment in which the macromolecule is doped with heavy atoms, a method known as isomorphous replacement. Another procedure, called molecular replacement (Rossmann and Henderson, 1982), uses a known homologous structure to provide estimates of the phases. Model structures obtained by a homology modelling scheme (see later section), if they are suf®ciently reliable, can be very useful in this regard. Phase information can also be obtained by a method known as multiple wavelength anomalous diffraction (MAD) (Hendrickson, 1991). This requires access to a tuneable radiation source such as a synchrotron, as well as data collection at several wavelengths. It also requires the presence of one or more anomalously diffracting atoms (heavy atoms such as metal ions) in the crystal being studied. Once an electron density map is obtained a preliminary atomic model can be ®tted to it. Recently developed computational procedures now allow this initial model building phase to be highly automated (Perrakis et al., 1999). The ®nal stage of structural re®nement often involves a molecular dynamics simulated annealing procedure (Brunger, 1987; Kuriyan et al., 1989) in which the X-ray data are used to form a pseudo-energetic restraint term similar to that already described for NMR methods. The computer program suite X-PLOR and latterly the crystallography and NMR system (CNS), are the packages that have most frequently been used for generating structures from NMR data, and for X-ray structure re®nement (Brunger, 1992; Brunger et al., 1998). The molecular mechanics component of these programs is derived from the CHARMM program described above. These programs can simultaneously utilise X-ray and NMR data, where appropriate. A sophisticated scripting language is available that allows the researcher to create customised re®nement protocols where these are needed. The range of features available for handling NMR and X-ray data is too large to be fully described here. Information on obtaining and using X-PLOR and CNS can be found at the web sites http:// xplor.csb.yale.edu/xplor-info/ and http://cns.csb.yale.edu/ v1.0/ respectively. The time consuming bottleneck of growing protein crystals is now being addressed by automated robotic methods designed to achieve high throughput protein crystallisation (Stevens, 2000). This will be an important component of a pipeline for automating the overall process of X-ray crystallography (Abola et al., 2000). For those interested in a thorough description of the computational approaches utilised in macromolecular structure determination, by both NMR and X-ray methods, a review article by Brunger and Nilges (1993) should be consulted.

Fig. 3. Total number of macromolecular structures in the protein data bank (PDB) for the years 1970±2000. The databank stores co-ordinates and other information on proteins, nucleic acids, carbohydrates etc. Both experimental structures found by X-ray crystallography and NMR methods, as well as some theoretical models, are included in the total.

3.3. The protein data bank Both NMR and X-ray methods of structure determination generate co-ordinate data that are usually deposited in the Protein Data Bank (or PDB) (Berman et al., 2000, web site http://www.rcsb.org/pdb/). The number of macromolecular structures in the database is growing rapidly; the year by year rise in total number of structures is illustrated in Fig. 3. Automating procedures for structure determination will accelerate this growth, and will have far reaching implications for our knowledge of protein folds and protein function. In the past the selection of proteins for structure determination by crystallography and NMR was decided by each individual research group, there was no co-ordinated effort. Many reported structures were simply variants of currently known protein folds rather than new protein architectures. A community wide effort to undertake a systematic approach to structure determination is now emerging (Burley, 2000). The aim will be to quickly obtain a more complete view of the set of all possible protein folds. The PDB is an extremely valuable resource for structural biology and for molecular modelling applications. Later sections of this review will describe how the data stored in the PDB can be exploited in computational modelling schemes designed to study protein±ligand and protein± protein interactions, as well as estimating the overall protein fold when only sequence information is available. 3.4. Combining X-ray and electron microscopy data There is now a growing number of reports in which the


molecular architecture of complex biological systems have been elucidated by an interdisciplinary approach, combining data from X-ray crystallography and electron microscopy. This promising approach brings together the high resolution detail of atomic coordinate data obtained by crystallography, with the broader scale but lower resolution overview provided by microscopy. Systems that have been studied by this approach include membrane bound annexin A5 trimers (Oling et al., 2000) and the 50S ribosomal subunit (Mueller et al., 2000). There are a number of reports describing the structure of virus particles and their interactions by these methods. Two groups have published detailed studies of the poliovirus interacting with its extracellular receptor (Belnap et al., 2000; He et al., 2000). The former group also report a structural study of human rhinoviruses in complex with soluble fragments of the cellular receptor (Kolatkar et al., 1999) and the structure of canine parvovirus complexed with the Fab fragment of a neutralising antibody (Wikoff et al., 1994). A study of the capsid protein (CP) subunits of the brome mosaic virus (BMV) has revealed the presence of two distinct capsid forms that contains 120 and 180 CP subunits (Krol et al., 1999). The latter form is indistinguishable from the form found in virus particles in natural infections. It was found that the capsid form obtained could be switched by packaging either natural genomic RNA or an engineered mRNA. Molecular modelling using the X-PLOR package (see above) was an integral part of this study. A review article covering the creation of pseudo-atomic resolution models of macromolecular complexes by combining crystallographic and EM data is also available (Baker and Johnson, 1996). A detailed description of some programs used for performing this type of computation can be found in the reports by Volkmann and Hanein (1999) and by Wriggers et al. (1999).

4. Protein homology modelling 4.1. Why create protein homology models? Protein and nucleic acid sequencing methods are now well advanced and available in many laboratories. As a result sequence databases such as the protein information resource (see http://www-nbrf.georgetown.edu/), SwissProt and TrEMBL (see http://www.expasy.ch/) have been growing rapidly in recent years. In contrast the determination of protein structure by NMR or X-ray crystallography has tended to proceed much more slowly. Hence there are many important proteins where the sequence is available but the three-dimensional structure is not yet known. One of the grand challenges of computational science is to be able to predict the overall fold of a protein purely from its sequence. This is commonly known as the protein folding problem. At the present time, some progress is being made (Lee et al., 1999; Osguthorpe, 2000), but in overall terms the problem remains one that is unsolved. Homology modelling

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or comparative modelling methods, ®rst reported by Browne et al. (1969), are able to predict the 3-D structure of a protein sequence by using information derived from an homologous protein of known structure (Sali and Blundell, 1993; Sanchez and Sali, 1997). The utility of homology methods is evident when considering the vast numbers of open reading frames (ORFs), which are potential protein coding sequences, produced as a result of genome sequencing projects. It has been estimated that of the order of 20±30% of these open reading frames can be assigned to a fold classi®cation derived from structures in the PDB protein structural databank (Gerstein and Levitt, 1997; Fischer and Eisenberg, 1999). If a three dimensional model of the protein of interest can be derived, it may be usable as the basis for a structure based drug design study. In addition such models can be a useful aid to the rational design of experiments such as site directed mutagenesis or in understanding protein stability and function. In short it may be easier to rationalise the behaviour of a protein if an experimental or model three-dimensional structure is available, than it is to do so solely on the basis of sequence information alone. 4.2. Outline of homology modelling schemes In order to construct a homology model for a query protein sequence, the query must ®rst be aligned with one or more homologous reference proteins of known structure. Experience of homology modelling shows that when the sequence identity between two proteins falls to 30% or less, then the alignment process becomes increasingly unreliable (Fig. 1 of Venclovas et al., 1999). The consequence of this will be regions of the protein model that are incorrectly folded in relation to the true structure. Methods for identifying likely misfolded regions of a protein model will be discussed later in this section. The full details of the methods used in each homology modelling program cannot be described here. However, the available programs tend to fall into one of two general types, and an outline of the procedures used will be given here. Fragment based homology modelling procedures use the alignment between the query sequence and the known protein(s) to identify a number of structurally conserved regions (SCRs). These tend to be sections of the protein structure where there are no insertions or deletions in the sequences, and to be regions of well de®ned secondary structure (i.e. helices or strands). These also tend to be regions where the level of sequence conservation is the highest. Regions of the protein sequences in between the structurally conserved regions are usually denoted as variable regions (VRs). The SCRs provide a consistent framework between the known and unknown proteins. Hence the coordinates of the protein backbone in the query protein can be copied from those in one of the known proteins. Variable regions in an alignment are most often protein loop regions where mutations, insertions and deletions are common. This makes them hard to model accurately. Typically the loops

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are modelled by searching a database of structures for regions of a suitable length and geometry at the interface with the SCRs, along with the requirement that they do not have steric clashes with the rest of the model structure. After a loop building stage a molecular mechanics minimisation procedure may then be required to reduce irregularities in the structure. There are many published homology modelling studies which use methods similar to the fragment based approach described here (Levitt, 1992; Unger et al., 1989; Blundell et al., 1987, 1988). Several commercially available homology modelling programs utilise a fragment based approach to model construction. These include the COMPOSER program (Blundell et al., 1987, 1988; Topham et al., 1990) which is incorporated into the SYBYL program suite (Tripos Inc., St Louis, http://www.tripos.com) and HOMOLOGY which is a component of insightII (MSI, San Diego, http://www.accelrys.com). Unlike fragment based methods, the restraint based homology modelling methods do not generally break the model building process into two distinct phases i.e. building conserved regions then ®nding variable loop regions. Instead the alignment is used to derive geometrical restraints, such as limits on distances between pairs of C a atoms, ranges of backbone and side chain dihedral angles etc. These restraints can then be combined together to ®nd an overall scoring function that de®nes how well the model structure matches the set of geometric criteria. A structure generation procedure, of which multiple types have been reported, is then used to create model structures which best satisfy the restraints. In the method reported by Havel and Snow (1991) a distance geometry structure generation procedure was tested on Kazal type trypsin inhibitors and used to predict the structure of the human pancreatic secretory trypsin inhibitor. Distance geometry (Crippen and Havel, 1988) is a method of deriving 3-D coordinates from distance values and was the method applied in the earliest determinations of protein structure by NMR (Havel and Wuthrich, 1985). In this approach the restraints are typically atom±atom distances derived from corresponding atoms in the known structure and compared to distances in the model protein. Restraint based molecular dynamics procedures for structure generation have been used in the MODELLER program (Sali and Blundell, 1993). Academic authors may obtain MODELLER from the author's web site (http://guitar.rockefeller.edu/modeller/ modeller.html). The MODELLER program is also available commercially as a component of insightII (see above for details). The restraint based scoring function used in this program is a complicated combination of distance, dihedral and other terms that cannot fully be described here. Generation of model structures that satisfy the restraints is performed by a combination of minimisation and molecular dynamics methods, similar to those discussed in the introduction. Once an alignment of the query sequence with the known protein structures is obtained, the homology model building process can proceed in a largely automated fashion.

Fig. 4. Experimental structure and a theoretical model of the basis ®broblast growth factor (bFGF). The experimental structure (pdb code 1BFC) is shown as a blue ribbon, while the theoretical model is shown as a red ribbon. The model was created using the publicly accessible SwissModel server. In overall terms the protein backbone of the model is very close to that of the experimental structure. The residues labelled are those in the model de®ning the two regions of greatest discrepancy between the model and experimental structures.

4.3. An example of automated homology modelling Increased automation of the homology model building process can make the bene®ts of modelling available to a wider audience of non-experts, although caution and expertise will always be required for a critical appreciation of the results. The Swiss-Model program suite (Peitsch, 1996; Guex et al., 1999) provides one level of operation (known as ®rst approach mode) that requires only a protein sequence as input. Details such as reference protein selection, alignment, model building and re®nement are largely hidden from the user. The method is also provided as a world wide web accessible server (http://www.expasy.ch/swissmod/SWISS-MODEL.html). This development allows simpli®ed access to homology modelling methods without the need to purchase specialised hardware and software. As an example of use of this server Fig. 4 shows an X-ray structure of the basic ®broblast growth factor (blue ribbon, PDB code 1BFC) superimposed on a predicted model structure (red ribbon). The model structure was obtained using a single known protein structure as a reference (rat keratinocyte growth factor FGF7, PDB code 1QQK chain B). The level of sequence identity between the two sequences is 40.5% (similarity 53.3%), and this represents a typical level at which a homology modelling exercise might be attempted. The protein backbones of the experimental and model structures are seen to be very similar, with most of


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the differences arising in a few loop regions. The predicted structure has an overall root mean squared deviation Ê for the backbone atoms. This exercise (RMSD) of 1.54 A shows that if basic FGF were a protein that had not been solved by crystallography or NMR methods, then homology modelling could provide a high quality model of the proteins three-dimensional structure. In turn this could be used for rationalising experimental data or guiding the design of new experiments. Another use of protein homology models, which will be further examined in this review, is that they can be used as input to a molecular docking procedure, which aims to ®nd the binding site for small molecule ligands. 4.4. Evaluating protein homology models As discussed above, dif®cult cases in homology modelling correspond to protein sequences that only possess distant homologues of known structure, where the level of sequence identity may be low. In such cases incorrect alignment can lead to regions of a model protein structures that have signi®cant structural errors. Tools that can predict the quality of model protein structures and identify erroneous regions are valuable for model selection and helping to identify alignment errors. Simple checks on the geometry of the model protein bonds, bond angles and torsions etc. can be performed using a program such as PROCHECK (Laskowski et al., 1993). Several other groups have designed knowledge-based force®elds that are designed to highlight residues that do not possess favourable environments or interactions (Sippl, 1993; Luthy et al., 1992; Melo and Feytmans, 1998). The latter two knowledge based potential functions have been made available as web servers (see http://www.doe-mbi.ucla.edu/verify3d.html and http:// guitar.rockefeller.edu/~fmelo/anolea/anolea.html, respectively). To use these a protein model can be uploaded using a web browser and an evaluation report is returned. As an example of the use of such a server, Fig. 5 illustrates a per-residue score analysis for the basic ®broblast growth factor model protein in Fig. 4, using the method of Melo and Feytmans (1998). High positive scores indicate possible misfolded regions in the model, or regions of poorer than expected structural environments. When the model protein is compared with the known structure (Fig. 4) the utility of this scoring scheme can be tested. In Fig. 5 the two regions with scores above a threshold of 5.0 (residues 60±63 and 90±94 in the model) were found to be the two regions where the model protein deviates most from the known structure. This shows that knowledge based scoring functions have real value in assessing the reliability of various regions of a model protein structure. The knowledge-based force®elds discussed above are closely similar to those used for recognising protein sequence-structure compatibility and these are discussed more fully in a following section of this review. The accuracy of model protein structures is most strongly limited by the accuracy of the protein loop regions.

Fig. 5. Application of the ANOLEA protein structure evaluation server (Melo and Feytmans, 1998) to the homology model of bFGF shown in Fig. 4. The two highest scoring, least favourable, regions identi®ed by the server correspond to the areas of greatest differences between the backbones of the model and experimental structures.

Attempts to re®ne this area of the protein models are an active area of research (Zheng et al., 1994; Rapp and Friesner, 1999; Fiser et al., 2000). Critical testing of protein structure modelling methods is essential if they are to be applied with any degree of con®dence. One of the most valuable scienti®c exercises in this ®eld is the series of blind prediction contests known as the Critical Assessment of Structure Prediction (CASP). These exercises have taken place once every two years since 1994 (Moult et al., 1995, 1997, 1999). The protein modelling exercises utilise the sequences of proteins that will soon be solved by X-ray or NMR methods, but are not yet available. Therefore all protein modelling predictions are performed blindÐwithout knowledge of the protein structure. Such an exercise is also valuable in that it allows a community wide suite of modelling methods to be compared on a common set of benchmark proteins. One of the conclusions of the CASP meetings (Venclovas et al., 1999) provides the following useful rule of thumb. If a known protein has a high level of identity with the query sequence (over 60%) then it should be feasible to produce a high quality model structure, in which the C a atom root Ê . While mean squared deviation (RMSD) is less than 1 A the quality of protein models tends to be reduced at lower levels of identity, it was concluded that the models can still be extremely useful for providing detailed hypotheses of ligand binding, enzyme catalysis etc. (Moult et al., 1999). 4.5. Databases of protein homology models. Large scale protein homology modelling, in which whole sequences databases or whole genomes are used as input into automated modelling algorithms, have been reported by several groups. By utilising powerful computer systems with multiple processors, these efforts have allowed the

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creation of large databases of homology models of proteins. These include those using the methodology of the SwissModel server (Schwede et al., 2000; Guex and Peitsch, 1997; Peitsch, 1997, http://www.expasy.ch/) and those utilising MODELLER (Marti-Renom et al., 2000; Sanchez and Sali, 1999; http://pipe.rockefeller.edu/modbase/). These databases can be accessed by any biological researcher with access to the internet. The main dif®culties in obtaining accurate models in these cases arise from recognising weak sequence-structure similarities as well as modelling movements of rigid sections of the protein, along with loops and side chains. However, it has proved possible to model signi®cant parts of the protein structure in at least one third of known protein sequences (Marti-Renom et al., 2000). From these projects it is becoming clear that homology modelling is an increasingly useful tool in structural biology and that it can be very valuable in annotating genome sequence information and in contributing to structural and functional genomics.

5. ThreadingÐcomparing protein sequence to structure 5.1. Outline of threading methods The prediction of protein three-dimensional structure has been found to be a valuable computational tool in structural biology. In addition there is an extensive literature on methods for the prediction of the compatibility of protein sequences with known protein structures. An early development in this ®eld was a method known as three-dimensional pro®les (Luthy et al., 1991; Bowie et al., 1991). There are a number of important problems to which this methodology can be applied. Firstly a protein sequence of interest can be used to search a database of protein structures, with the aim of ®nding the overall protein fold that the sequence is likely to adopt (Luthy et al., 1991). This application is therefore known as fold recognition. A related approach uses a known protein structure to search a database of protein sequences, to ®nd which structure is most likely to be adopted by the sequence of interest (Bowie et al., 1991). This approach is commonly known as inverse protein folding. The overall goal of assessing protein sequence-structure compatibility is typically known as protein threading. The pro®les-3-D methodology was an extension of the sequence based pro®le analysis method of Gribskov et al. (1987). In the pro®les-3D approach a scoring scheme is developed that describes the propensity of each of the 20 amino acid types for its structural environment. The structural environment is assessed in terms of the protein secondary structure type (helix/strand/ other) as well as the degree of solvent exposure and the polarity of the amino acid environment. Early applications of the pro®les-3-D methods were able to detect some structural similarity in the actins and 70 kDa heat shock proteins, even though they share no detectable level of sequence similarity (Bowie et al., 1991). In addition it was suggested

that the pro®les-3-D score could be used to ascertain whether a protein that undergoes oligomerisation is aggregated into its most stable oligomeric state (Eisenberg et al., 1992). The pro®les-3-D methodology also found uses as one of the ®rst tools to assess potentially misfolded regions in a protein model structure (Luthy et al., 1992). This is achieved simply by the assessment of the compatibility of the protein model structure with its own protein sequence. The pro®les-3-D scoring function considers the local structural environment of each amino acid in the protein in isolation; it does not explicitly consider pairwise interactions between amino acids as part of the scoring scheme. Hence it can be described as a one-body potential function. Methods that utilise pairwise interactions in the scoring scheme were reported by Jones et al. (1992) and also by Bryant and Lawrence (1993). Both methods obtain the potential function by performing a statistical analysis of known protein crystal structures and deriving pairwise contact energy terms as well as solvation and/or hydrophobic energy terms. In the application of their method Jones et al. (1992) were able to correctly identify that the sequence of C-phycocyanin adopts a globin fold. The most compatible known structure was that of sea hare myoglobin. Such an assignment could not have been obtained by traditional sequence alignment methods because the level of sequence identity was too low. The folds of the two proteins are compared in Fig. 6. Using their method Bryant and Lawrence (1993) were able to identify the correct protein models for the core folding motifs of hemerythrin and an immunoglobulin antibody domain. A further application of threading methods by this group was able to suggest that the obese gene product would be a protein with a helical cytokine structure, from the family that included interleukin-2 and growth hormone (Madej et al., 1995). Another approach to scoring protein-sequence compatibility was that suggested by Rost (1995). His method reduced protein structure to a one dimensional string encoding secondary structure and solvent accessibility. For each sequence, these parameters were also predicted using a neural network program (known as PHD, see web site http://www.embl-heidelberg.de/ predictprotein/submit_def.html). Alignment of the predicted and observed 1-D strings were used to detect remote threedimensional structural homologues of the sequence. Although the method is superior to normal similarity based sequence searches in ®nding remote homologues, only about 25% of the ®rst hits were correctly identi®ed, although a ®ltering procedure was able to improve this to 30%. It is clear that the threading procedures do have considerable value, in that they are sometimes able to correctly identify correct protein folds for sequences of interest even when the level of sequence similarity is low. 5.2. Large scale application and testing of threading methods One important application of these methods is in the mass screening of translated protein sequences obtained by


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Fig. 6. Protein folds of comparable regions of C-phycocyanin (left PDB code 1CPC) and sea hare myoglobin (right PDB code 2FAL). In this schematic diagram of protein structure helices are portrayed as red cylinders, turns as blue tubes and coil regions as green tubes. The structural similarity is seen to be high despite the lack of sequence similarity.

genome sequencing. When a fold recognition method was applied to the genome of Mycoplasma genitalium, it was found that 46% of the proteins derived from the predicted protein coding regions had a signi®cant relationship to a protein of known structure (Jones, 1999). As structure determination efforts proceed then the fraction of proteins that can be assigned to a known fold type will continue to rise. As well as prediction of protein fold, prediction of protein functional class is possible using methods related to protein threading, even when the level of sequence similarity is too low for global sequence alignment and local sequence motif identi®cation to work. One such method (Zhang et al., 1998) looks at the structural conservation and variation in the active site, for a set of known enzyme structures. This can then be used to derive a three dimensional motif that identi®es the essential requirements for the enzyme to function. A threading algorithm allows potential protein sequences to be aligned against the family of known enzyme structures and to be screened against the three dimensional motif. When applied to a set of 651 open reading frames (ORFs) from the genome of Escherichia coli, 17 ORFs were predicted to be members of the alpha/beta hydrolase family and the potential active site residues were identi®ed (Zhang et al., 1998). Most of these predictions were found to be in accord with experiments and/or other database search techniques. In addition some uncharacterised protein coding sequences were also suggested to be members of this enzyme family. The same group have also screened the E. coli genome to identify proteins having glutaredoxin/ thioredoxin and T1 ribonuclease activity (Fetrow et al., 1998; Fetrow and Skolnick, 1998). This method is known as the sequence-to-structure-to-function paradigm. As with the prediction of full protein three dimensional structure, threading methods have also been extensively

investigated as one of the categories of prediction studied in the Critical Assessment of Structure Prediction (CASP) meetings (Levitt, 1997; Murzin, 1999). The methods used in the CASP contest to generate protein models or assign a protein fold type often require an expert user in order to achieve the best results. A critical assessment of methods fully automated methods of structure prediction (known as CAFASP) has also been reported (Fischer et al., 1999). Although not a `blind' contest, this allows the performance of the computational methods to be evaluated in the absence of human intervention. The servers were evaluated only for the accuracy of their fold recognition accuracy; an assessment of the alignment accuracy was not performed.

6. Modelling protein±ligand complexes 6.1. The goals of protein±ligand docking One of the most important and useful areas of application of molecular modelling is the approach of ®tting together, or docking, a protein to a second molecule. Typically the latter is a small molecule ligand. This is of interest because it models the possible interactions between the protein and the ligand in the formation of a biologically important protein±ligand complex. Development of a novel pharmaceutical agent is a process that usually requires several years of effort and often a huge ®nancial investment. If computational docking can effectively model protein±ligand complexes, screening out non feasible or unfavourable ligands at an early stage, then the drug discovery process could be made more ef®cient. There are several desirable goals for such a docking procedure. First and foremost one would like to be able to identify the site of ligand-binding

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and the geometry of the complex. The ability to be able to predict the free energy of binding, and hence the binding af®nity would greatly add to the value of the procedure. For a series of distinct ligands we would like to be able to assess their relative binding af®nity and relate this to details of the structure. If the docking and other aspects of the calculation are suf®ciently rapid, then the ability to perform a computational screening of a library of model ligands against the selected protein, is essentially a computational approach to drug discovery. Several reviews exist which describe the basic methods utilised in this area (Kuntz et al., 1994; Lengauer and Rarey, 1996; Joseph-McCarthy, 1999). 6.2. Docking methodology and programs In order to perform a computational docking exercise, experimental or model three dimensional structures of both the protein and ligand molecules are required. In order to assess the electrostatic contribution to the protein±ligand interaction, estimates of the charge distribution for each molecule are required. For the protein component these are often available from standard molecular mechanics force ®elds in the form of atom centred partial atomic charges (see above). When a set of force ®eld charges are not available for the ligand molecule, then these must be derived before the docking exercise can be started. Such partial atomic charges can often be derived by using a quantum mechanics code, and by ®tting the charge values to the computed electron distribution at the molecular surface (Merz, 1992). If the ligand molecule is too large for a direct quantum calculation, then smaller model compounds are sometimes used and the charges thus derived are transferred to the ligand. It is clearly desirable to utilise experimental, NMR or X-ray crystallographic structures for the two molecular components in the docking exercise. However, sometimes an experimental protein structure may not yet be available. In this case the calculation can also be performed with a model protein structure and valuable insights into the protein±ligand docking may well be obtained. There are several software programs that are available for carrying out docking calculations, only some of which can be considered here. The DOCK program suite (Kuntz, 1992) is one of the best known. The algorithm used by DOCK has a number of steps. In the ®rst step a set of overlapping spheres are used to construct a negative image of a speci®ed site on the protein or other macromolecule. In the second step the negative image is matched against the structures of potential ligands. The matches can be scored by the quality of the geometric ®t, as well as by the molecular mechanics interaction energy (Meng et al., 1992). Applications of the DOCK program have led to a number of protein-binding ligands that have micromolar levels of binding af®nity (Kuntz et al., 1994). The program GRID (Goodford, 1985) utilises a three dimensional grid around the protein. At each grid point the program computes the molecular mechanics

interaction energy between proteins and a series of chemical functional groups (hydroxyl, alkyl, phosphate etc) known as probes. This allows the identi®cation of likely protein binding sites for ligands (Reynolds et al., 1989; Cruciani and Goodford, 1994). The concept of using a grid-based scheme for energies of individual atoms has been utilised by the Autodock program (Morris et al., 1996; web site http:// www.scripps.edu/pub/olson-web/doc/autodock/). The interaction energy of the protein±ligand complex can then be computed more rapidly as the interaction between the ligand and the grid. In AutoDock version 2.4 the likely ligand binding site is then identi®ed by a simulated annealing algorithm of the type described in the introduction section. Later versions of AutoDock (version 3.0) have found a genetic algorithm search procedure to be yet more ef®cient than the simulated annealing search scheme (Morris et al., 1998). Estimated binding free energies can also be produced by the program. When applied to a set of HIV-1 protease/inhibitor complexes a standard error of approximately 2 kcal/ mol was obtained (Morris et al., 1998). What this implies is that the program is discriminating enough to identify whether a given ligand will have millimolar, micromolar or nanomolar binding af®nity. In the small molecule docking section of the second CASP contest (Dixon 1997; web site http://predictioncenter.llnl.gov/casp2), seven small molecule ligand±protein targets were selected for prediction without knowledge of the structure of the complex. The results were considered to be good. At least one predicÊ for tion method found models with a RMSD within 3 A Ê for more than half the nearly all proteins and within 2 A proteins. However, no single docking procedure consistently produced the best results. In the summer of 2001 a novel meeting on the critical assessment of techniques for free energy evaluation (CATFEE) will take place (see web page http://uqbar.ncifcrf.gov/~catfee/). This will aim to assess existing methods for predicting biomolecular binding af®nities and not just the geometrical accuracy of the predicted complexes. 6.3. An example of protein±ligand docking Bitomsky and Wade (1999) have reported a comparison of the programs GRID, DOCK and AutoDock when applied to the task of docking heparin oligosaccharides to three proteins. The proteins studied were acidic and basic ®broblast growth factors (FGFs) along with antithrombin; these were the only proteins for which heparin±protein complex crystal structures were available at the time of the report. All three programs were able to correctly identify the heparinbinding site on the protein. Heparin oligosaccharides are important since they are model compounds for the sulphated, protein-binding regions of cell surface heparan sulphates, which in turn are involved in biological signal transduction (Guimond and Turnbull, 1999). In this laboratory we have also used AutoDock to evaluate the predicted binding site for model


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Fig. 7. Comparison of the experimental structure of the bFGF/heparin complex (right) with a model obtained by a docking calculation (left). This is a stern test for a docking exercise, since the protein structure used in docking is not an experimental structure, but is an homology model (Fig. 4). In addition the heparin probe molecule used for docking is a pentasaccharide in the model, compared to a hexasaccharide in the known structure of the complex. This illustrates that heparin binding sites on growth factors can be identi®ed using generic probe molecules and protein homology models.

heparin pentsaccharides and have compared this to the crystal structure of the basic-FGF heparin hexasaccharide complex (Mulloy and Forster, 2000). It should be emphasised that in this case the docking calculation is truly predictive, in the sense that the protein and/or ligand coordinates used are not derived from the reported structure of the complex. The protein coordinates used were obtained from a non complexed form of basic-FGF, while the ligand coordinates used are derived from the reported NMR structure of the isolated ligand (Mulloy et al., 1993). A further example of the value of computational docking is provided by Fig. 7. This ®gure shows the results of docking heparin model pentasaccharides to the homology model of basic-FGF (Fig. 4) generated by the Swiss-Model server. Despite the fact that the protein structure is a homology model, and the heparin probe is of a different length to that in the complex, the predicted heparin-binding site is still in the correct location. When multiple protein±ligand complex models obtained from the docking calculation are examined, we tend to ®nd that the residues involved in the heparin binding are reliably identi®ed, but that these models tend to have a variable orientation for the heparin in the binding site, sometimes differing by a 1808 rotation. In overall terms these calculations suggest that homology models do have value as model protein targets for computational docking and other areas of structure based drug design.

used for this task include the Cambridge Structural Database (Allen and Kennard, 1993; see web page http:// www.ccdc.cam.ac.uk/). This contains experimentally determined structural data for 220,000 organic and metal-organic compounds. In addition the Chemical Abstracts registry holds covalent structure information for over 28 million compounds (see web page located at http://www.cas.org/ casdb.html). Methods are available to convert the covalent structure information to three dimensional structure coordinate data required for docking calculations (Rusinko et al., 1989). Applications using docking calculations as a method of virtual ligand screening have been reported by Knegtel and Wagener (1999) and by Broughton (2000). In an interesting study Burkhard et al. (1998) developed a docking program known as SANDOCK and used this to screen a database for ligands that bind to the protein thrombin. The structure of one of the predicted complexes was then solved by X-ray crystallography and was found to have a root mean Ê from the predicted squared deviation (RMSD) of only 0.7 A structure. This further illustrates the value of predictive docking calculations as an aid to rationalising protein± ligand complexes.

7. Modelling protein±protein complexes 7.1. Methods for modelling protein±protein interactions

6.4. Computational screening of small molecule databases by docking It is now becoming possible to use docking codes to screen a large database of ligands. Databases that can be

There are many known examples where modelling methods have been used to study protein±protein complexes. This topic is of critical importance because it touches upon aspects of molecular recognition that affect many

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areas of biology. While there are now many thousands of crystal structures available for individual proteins, there are far fewer crystal structures of protein±protein complexes. Thus a reliable modelling method that could describe the nature of the protein±protein interactions would be highly valuable. In this brief review we will consider some of the basic concepts and programs involved in modelling such interactions. We will provide some examples of modelling applications in an area likely to be of interest in the ®eld of microscopy, namely that of virus protein±protein interactions. Many of the computational methods used for modelling protein±protein complexes are similar to those used to model protein±ligand complexes. Some of the computer codes available can be applied to both tasks. The DOCK program (Kuntz, 1992), which has already been discussed above, has been applied to problems in protein±protein docking (Shoichet and Kuntz, 1996). Due to the size of the computational task involved in docking two large protein structures, one approximation that is often invoked is to treat the two proteins as rigid bodies. Under these conditions a method based on Fourier transform procedures (Katchalski-Katzir et al., 1992) is able to greatly accelerate the search for the best geometric ®t between the two proteins, relative to a conventional scheme which searches all rotational and translational degrees of freedom. By using this Fourier transform procedure, and adding a method to determine electrostatic complementarity, Gabb et al. (1997) have developed a program (FTDOCK) that can exhaustively search for the optimum interactions between two rigid proteins. They tested the program on several systems including enzyme-inhibitor and antibody-antigen complexes. It was found that adding the electrostatic component improved the ability of the program to ®nd solutions similar to the known structure. This group extended their method to include protein sidechain ¯exibility and the effect of solvation (Jackson et al., 1998) and they have also reported tests of a pair potential function in screening docked complexes (Moont et al., 1999). The docking method of Vakser (1995, 1996) does not utilise a model with full atomic detail; instead a low resolution approach is used with simpli®ed atom±atom and residue±residue potential terms. This neglects small structural details on a Ê and smoothes out many of the local scale less than 7 A minima in the full atom representation. The search procedure is then more rapid than it would be utilising high resolution structures. One drawback of rigid body docking schemes is that they will not be able to identify changes in the conformations of the two proteins as the complex is formed. In a recent study (Betts and Sternberg, 1999) of protein pairs for which the structures were available in both bound and unbound forms, just over half the cases of complex formation led to some signi®cant degree of structural rearrangement. Flexible docking procedures are designed to accommodate such rearrangements by allowing for protein side-chain and/or backbone movement during

the computation. Development of such methods have been reported by a number of groups (Jackson et al., 1998; Sandak et al., 1998); in some cases these methods have identi®ed protein±antibody complexes with a backbone Ê from the crystal structure (Totrov RMSD of only 1.6 A and Abagyan, 1994). Several research groups have made use of the available crystal structure data to examine the nature of the residues and interactions involved at protein±protein interfaces. The ultimate aim of this type of analysis of crystallographic structures must be to be able to predict the sites of protein±protein interactions from the structures of the individual proteins. A question of interest is to examine whether residues of particular types occur more frequently at an interface than would be expected by chance. Thornton and co-workers have been particularly active in this area, they have recently reported detailed analyses of residue±residue interactions in homodimers (Valdar and Thornton, 2001) and oligomeric protein interfaces (Jones et al., 2000). This studies build on earlier work describing protein±protein interfaces in terms of protein surface patches (Jones and Thornton, 1997a,b). At present these methods do ®nd speci®c interactions to occur more frequently than expected by chance, but the statistical signi®cance of these is quite low. Nussinov and co-workers have reported an extensive study of the conservation of polar residues forming `hot spots' at protein±protein interfaces (Hu et al., 2000). While the overall binding regions tend to be hydrophobic they did ®nd conserved polar residues at speci®c locations in many types of protein±protein interface. These trends were compared to experimental observations from alanine-scanning mutagenesis and were found to be consistent with these data. Wang and Kollman (2000) have reported a study using the AMBER force®eld and modelling package, to estimate relative binding free energies between different dimers of the HIV-1 protease. They have developed a rapid screening method called virtual mutagenesis, this aims to identify mutations affecting binding af®nities in protein±ligand and protein±protein complexes. The rationale for identifying residues involved at protein±protein interfaces is that this information can sometimes be used to aid in the development of novel therapeutic agents. This has been illustrated by a recent report on the protein reverse transcriptase of HIV-1 (Morris et al., 1999). In this study a short peptide corresponding to the residues present at the dimer interface, was able to block dimerisation of the enzyme both in vitro and in infected cells. Thus methods which can identify and rationalise interactions in protein± protein complexes may contribute to our knowledge of molecular recognition events, and also help to develop vital new treatments. 7.2. Testing protein±protein docking methods The utility of blind prediction contests as a means of testing computational methods have already been discussed


in relation to protein homology modelling and protein threading. Similar contests have also been held to evaluate methods of protein±protein docking. These include the Alberta challenge (Strynadka et al., 1996). This constituted the ®rst community wide `blind' test of protein±protein docking methods. In this challenge a beta-lactamase protein complex with the relevant inhibitor were predicted prior to the release of the coordinates of the complex. Most groups submitted multiple predictions, but all six participating groups submitted at least one model with a C a atom Ê or less. This was considered to correctly RMSD of 2.5 A identify the general mode of association of the two proteins, but not to reliably indicate local structural details. Similarly the docking section of CASP2 1997; web site http:// predictioncenter.llnl.gov/casp2) evaluated methods for predicting an antibody-hemagglutinin complex. In this Ê ) were only case even the best predictions (RMSD 8.5 A able to correctly identify a fraction of the correct residue contacts in the complex. Combining biochemical or other experimental data with a computational docking scheme can assist in the dif®cult process of distinguishing the true complex structure from many hundreds or thousands of possibilities (Gabb et al., 1997). In a recent report, Clore (2000) has shown that NMR data can be utilised in a computational protein±protein docking procedure to ®nd the structure of the complex. Provided the structures of the unbound proteins are available this method can greatly reduce the time required to determine protein±protein complexes by NMR. 7.3. Modelling protein±protein interactions in viruses There are several examples where modelling methods have been used to study details of protein structures in viral capsids. Reddy et al. (1998) have computed dimer association energies for quasi-equivalent protein±protein interfaces in three viruses, namely human rhinovirus-14 (HRV), southern bean mosaic virus (SBMV) and black beetle virus (BBV). These studies utilised published crystal structures as the starting point for their calculations. Both BBV and SBMV have only a single coat protein, and the quasi-equivalent interfaces in these icosahedral particles arise from differing sets of conformations at the distinct interfaces. A number of assembly pathways were compared on the basis of their molecular mechanics energies. Horton and Lewis (1992) developed a method for estimating the free energy of association of two proteins in forming a complex. This method was then applied to intermediate structures produced in the process of viral assembly. Molecular dynamics simulations have been used to study the effect of an anti-viral drug on human rhinovirus 14 (Phelps et al., 1998; Phelps and Post, 1999). The drug-free and drugbound capsids exhibited differences in long range collective motions, but not in fast time scale local ¯uctuations. The simulations were used to rationalise the experimentally observed stabilisation of the ligated virus. Continuum elec-

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Fig. 8. Molecular model of the pentameric cap of an icosahedrally organised network of membrane associated (MA) proteins in HIV-1. The geometry parameters used to construct the cap were obtained from a docking exercise in which protein±protein interaction energies were computed as a function of distance and/or orientation. The MA protein trimers used as a building block for the model were determined by crystallography (pdb code 1HIW).

trostatic models have been fruitfully employed in studies of viral structures. Van Vlijmen et al. (1998) investigated the stability of the foot-and-mouth disease virus as a function of pH. Their calculation method reproduced the observed trends, whereby the capsid is less stable at acidic pH. In addition they were able to show that histidine residues close to the protein±protein interface were important to the observed stability. Another study (Warwicker, 1992) used similar methods of computing electrostatic effects to evaluate the stability of poliovirus and rhinovirus with respect to pH. Detailed models of conformational changes upon receptor binding were discussed. Molecular modelling methods have also been used to investigate possible networks of membrane associated (MA) proteins forming the sub-membrane shell of mature HIV particles (Forster et al., 2000). Previous EM studies (Nermut et al., 1998) had suggested a hexagonal organisation of HIV Gag proteins in forming prebudding assemblies and immature virus like particles. The AMBER molecular mechanics force®eld, implemented in the Tinker program, was used to identify feasible networks that were then evaluated by comparison to data from electron microscopy and X-ray crystallography. This force®eld was then used to ®nd geometry parameters for an icosahedrally organised model of the virus protein shell. This model was found to be consistent with the number of copies of MA in the protein shell and the distance separation of glycoprotein knobs. The model also provided a simple explanation for the observed size variation in a population of virus particles. Fig. 8 shows a pentameric

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cap constructed using planar arrays of MA trimers and geometric parameters derived from the modelling study. The existence of such a pentameric interface in HIV-1 has not yet been experimentally observed. Theoretical models describing the kinetics as well as the energetics of viral capsid assembly have been reported by Zlotnick and coworkers. In a study of a generalised icosahedral virus, they calculated the fractions of free sub-units, assembly intermediates and intact virus (Zlotnick, 1994). At equilibrium only traces of the intermediate species can be expected, while inter sub-unit energies will strongly affect the position of the equilibrium. Their model also suggested that a cascade of bimolecular reactions rather than a single higher order reaction is likely to take place. In a recent study (Zlotnick et al., 1999) they have used theoretical models to interpret experimental data (light scattering and size exclusion chromatography) for the assembly of the hepatitis B virus. These models were able to account for the concentration dependence of the assembly process and provide a powerful insight into the physical chemistry of viral assembly. These results suggest that protein interactions in viral assembly could become a target for anti-viral therapy. A `local rules' theory of protein±protein interactions in viral capsids has been reported (Berger et al., 1994). This suggests that the self assembly process is governed only by the local interaction of the protein sub-unit with it neighbours, rather than on a longer range interactions. At the molecular level these local rules arise from the ®nite number of ways in which the protein sub-units can ®nd favourable interactions. Computer simulations of a pseudo particle showed some types of assembly malformation that are seen experimentally. In a later study (Schwartz et al., 1998) they extended this work to develop a kinetic model of assembly. This allowed a molecular dynamics-like simulation of protein±protein interactions describing many features of the assembly process. Their model accounted for the dependence of growth and malformation rates on the energetics of sub-unit interactions and on sub-unit concentration. This approach has recently been applied to a study of polyomavirus assembly (Schwartz et al., 2000). Various assemblies such as icosahedral, dodecahedral, spiral and tubular structures are observed experimentally for the VP1 protein of this virus. The local rules were found to be consistent with with many of these polymorphic forms but could not explain all of those present. 8. Summary and conclusions From the range of applications reported here, it should be clear that molecular modelling is a very versatile technique and can be applied to many areas of macromolecular structural studies. Pure prediction in which no direct experimental data are used is still an area that must be approached cautiously; there are many dif®culties and pitfalls that await the unwary. Successful prediction methods are likely to

require the careful development of a model that is realistic and yet computationally tractable. In this regard the growing trend for holding prediction contests is very valuable. It allows numerous computational methods to be applied on a common set of problems, and for them to be evaluated in a common way. Prior to the emergence of such contests it was often dif®cult to evaluate the relative merits of methods from different laboratories, or variations in methods from within the same laboratory. The development of parameters for molecular mechanics simulations requires a high degree of skill and care. Knowledge of the limitations of a particular package is important for its effective use. There are still cases in the literature where a force®eld has been applied to a system for which it was not parameterised. The quality of results will then be unpredictable. Modelling type simulations are utilised in experimental structure determination methods, such as NMR, where the experimental data are incorporated into restraint terms in the force ®eld. Simulation schemes can incorporate data from a number of experimental disciplines, including EM, in this way. As computer systems become more powerful with time the utility of modelling and simulation methods can only increase. This will happen in two ways. Firstly, existing types of simulations will be able to be run for longer time periods, thus allowing better sampling of conformational space and property statistics. Secondly, more realistic but expensive computation schemes will be accessible in a reasonable time. The growth of structure databases such as PDB will make the application of methods such as protein homology modelling, threading and virtual docking applicable to a wider range of proteins. Molecular modelling methods have much to contribute to our understanding of structural biology. Acknowledgements The author wishes to thank Dr James Feeney, Dr Milan Nermut and Dr Barbara Mulloy for reading the manuscript and providing many helpful comments. References Abola, E., Kuhn, P., Earnest, T., Stevens, R.C., 2000. Automation of X-ray crystallography. Nature Structural Biology Suppl, 973±977. Allen, F.H., Kennard, O., 1993. 3-D search and research using the Cambridge structural database. Chemical Design Automation News 8, 31±37. Allinger, N.L., Durkin, K.A., 2000. Van der Waals effects between hydrogen and ®rst-row atoms in molecular mechanics (MM3/MM4). Journal of Computational Chemistry 21, 1229±1242. Allinger, N.L., Yan, Q.L., 1993. Molecular mechanics (MM3)Ðcalculations of vinyl ethers, and related-compounds. Journal of the American Chemical Society 115, 11918±11925. Antosiewicz, J., McCammon, J.A., Gilson, M.K., 1994. Prediction of pHdependent properties of proteins. Journal of Molecular Biology 238, 415±436. Baker, T.S., Johnson, J.E., 1996. Low resolution meets high: Towards a

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