Atomic solvation parameters in the analysis of protein-protein docking results

The Early Phase of β2m Aggregation: An Integrative Computational Study Framed on the D76N Mutant and the ΔN6 Variant

Human β2-microglobulin (b2m) protein is classically associated with dialysis-related amyloidosis (DRA). Recently, the single point mutant D76N was identified as the causative agent of a hereditary systemic amyloidosis affecting visceral organs. To get insight into the early stage of the β2m aggregation mechanism, we used molecular simulations to perform an in depth comparative analysis of the dimerization phase of the D76N mutant and the ΔN6 variant, a cleaved form lacking the first six N-terminal residues, which is a major component of ex vivo amyloid plaques from DRA patients. We also provide first glimpses into the tetramerization phase of D76N at physiological pH. Results from extensive protein–protein docking simulations predict an essential role of the C- and N-terminal regions (both variants), as well as of the BC-loop (ΔN6 variant), DE-loop (both variants) and EF-loop (D76N mutant) in dimerization. The terminal regions are more relevant under acidic conditions while the BC-, DE- and EF-loops gain importance at physiological pH. Our results recapitulate experimental evidence according to which Tyr10 (A-strand), Phe30 and His31 (BC-loop), Trp60 and Phe62 (DE-loop) and Arg97 (C-terminus) act as dimerization hot-spots, and further predict the occurrence of novel residues with the ability to nucleate dimerization, namely Lys-75 (EF-loop) and Trp-95 (C-terminus). We propose that D76N tetramerization is mainly driven by the self-association of dimers via the N-terminus and DE-loop, and identify Arg3 (N-terminus), Tyr10, Phe56 (D-strand) and Trp60 as potential tetramerization hot-spots.

A THEORETICAL INVESTIGATION OF MECHANISM OF THE ADENOSINE DEAMINASE MODIFICATION: REACTION OF GLUTAMATE RESIDUE WITH WOODWARD REAGENT K

The kinetics and mechanism of the modification of adenosine deaminase with N-ethyl-5-phenyl isoxazoliom-3′-sulfonate (WR-K) are investigated using molecular dynamics simulations, QM and QM/MM minimization methods. Two methodological algorithms are employed. In the first algorithm, a glutamate residue is dissected from ADA and its reaction with WR-K is studied by employing minimization and frequency calculations under the B3LYP method. Results obtained show that ketoketenimine is produced from the interaction of WR-K with OH-in an exergonic two-step reaction. In this process, an intermediate is consumed in the rate-determining step. Next, the dissected residue is modified using ketoketenimine in a three-step reaction. This reaction is accompanied by the production of two intermediates, with the first intermediate produced in the rate-determining step.

For the second algorithm, modification of glutamate residue in the presence of water molecules and ions is investigated using conformational sampling, MM and QM/MM minimization. Stability of species in the reaction is evaluated using a combination of the B3LYP method and the WASA model. It is proved that the stability of an intermediate which is initially produced in the reaction of glutamate residue with ketoketenimine must be considered crucial when the reactivity of the different residues is compared. Results obtained indicate that these reactions have energetic features qualitatively similar to the glutamate-dissected case. It is also clear that protein structure plays a basic role in the formation of the product that arises from the reaction of ADA with ketoketenimine.

Efficient molecular mechanics simulations of the folding, orientation, and assembly of peptides in lipid bilayers using an implicit atomic solvation model

Membrane proteins comprise a significant fraction of the proteomes of sequenced organisms and are the targets of approximately half of marketed drugs. However, in spite of their prevalence and biomedical importance, relatively few experimental structures are available due to technical challenges. Computational simulations can potentially address this deficit by providing structural models of membrane proteins. Solvation within the spatially heterogeneous membrane/solvent environment provides a major component of the energetics driving protein folding and association within the membrane. We have developed an implicit solvation model for membranes that is both computationally efficient and accurate enough to enable molecular mechanics predictions for the folding and association of peptides within the membrane. We derived the new atomic solvation model parameters using an unbiased fitting procedure to experimental data and have applied it to diverse problems in order to test its accuracy and to gain insight into membrane protein folding. First, we predicted the positions and orientations of peptides and complexes within the lipid bilayer and compared the simulation results with solid-state NMR structures. Additionally, we performed folding simulations for a series of host-guest peptides with varying propensities to form alpha helices in a hydrophobic environment and compared the structures with experimental measurements. We were also able to successfully predict the structures of amphipathic peptides as well as the structures for dimeric complexes of short hexapeptides that have experimentally characterized propensities to form beta sheets within the membrane. Finally, we compared calculated relative transfer energies with data from experiments measuring the effects of mutations on the free energies of translocon-mediated insertion of proteins into lipid bilayers and of combined folding and membrane insertion of a beta barrel protein.

A theoretical elucidation of glucose interaction with HSA's domains

The interaction of different domains belonging to Human Serum Albumin (HSA) with open form of glucose have been investigated using molecular dynamics simulation methods. Applying docking, primary structures involving interaction of some residues with glucose have been obtained. Subsequently, equilibrium geometries at 300 K and minimum geometries have been determined for each of aforementioned structures by employing MD simulation and simulated annealing. The stability of species has been evaluated using a SAWSA v2.0 model. Ultimately, NBO analysis has been carried out to specify possible hydrogen bonding regarding the HSA interaction with glucose. Results obtained show that glucose can interact with Lys195, Lys199, and Glu153. In these interactions, each lysine forms an H-bonding with glucose. The H-bonding is obtained by stretching of N-H bond belonging to NH(3)(+) group of lysine along an oxygen atom of glucose. In addition, the above mentioned lysines are protonated, and there is an electrostatic interaction between glucose with Lys195 or Lys199. In addition, an H-bonding is formed between O atom of -COO group belonging to Glu153 and H atom of OH group belonging to glucose. Because, the N-H group of Lys195 interacts with the O atom of latter OH group, reaction of Lys195 is more desirable than that of Lys199. In fact, glucose is placed in the vicinity of Lys195 along with electrostatic interaction and H-bonding to Lys195 and Lys199 as well as H-bonding with Glu153, which subsequently reacts with Lys195. Thus, Lys195 is the primary site in reaction of glucose with HSA.

Computer applications for prediction of protein-protein interactions and rational drug design

In recent years, protein-protein interactions are becoming the object of increasing attention in many different fields, such as structural biology, molecular biology, systems biology, and drug discovery. From a structural biology perspective, it would be desirable to integrate current efforts into the structural proteomics programs. Given that experimental determination of many protein-protein complex structures is highly challenging, and in the context of current high-performance computational capabilities, different computer tools are being developed to help in this task. Among them, computational docking aims to predict the structure of a protein-protein complex starting from the atomic coordinates of its individual components, and in recent years, a growing number of docking approaches are being reported with increased predictive capabilities. The improvement of speed and accuracy of these docking methods, together with the modeling of the interaction networks that regulate the most critical processes in a living organism, will be essential for computational proteomics. The ultimate goal is the rational design of drugs capable of specifically inhibiting or modifying protein-protein interactions of therapeutic significance. While rational design of protein-protein interaction inhibitors is at its very early stage, the first results are promising.

Thermodynamics of Protein–Ligand Interactions: History, Presence, and Future Aspects

The understanding of molecular recognition processes of small ligands and biological macromolecules requires a complete characterization of the binding energetics and correlation of thermodynamic data with interacting structures involved. A quantitative description of the forces that govern molecular associations requires determination of changes of all thermodynamic parameters, including free energy of binding (deltaG), enthalpy (deltaH), and entropy (deltaS) of binding and the heat capacity change (deltaCp). A close insight into the binding process is of significant and practical interest, since it provides the fundamental know-how for development of structure-based molecular design-strategies. The only direct method to measure the heat change during complex formation at constant temperature is provided by isothermal titration calorimetry (ITC). With this method one binding partner is titrated into a solution containing the interaction partner, thereby generating or absorbing heat. This heat is the direct observable that can be quantified by the calorimeter. The use of ITC has been limited due to the lack of sensitivity, but recent developments in instrument design permit to measure heat effects generated by nanomol (typically 10-100) amounts of reactants. ITC has emerged as the primary tool for characterizing interactions in terms of thermodynamic parameters. Because heat changes occur in almost all chemical and biochemical processes, ITC can be used for numerous applications, e.g., binding studies of antibody-antigen, protein-peptide, protein-protein, enzyme-inhibitor or enzyme-substrate, carbohydrate-protein, DNA-protein (and many more) interactions as well as enzyme kinetics. Under appropriate conditions data analysis from a single experiment yields deltaH, K(B), the stoichiometry (n), deltaG and deltaS of binding. Moreover, ITC experiments performed at different temperatures yield the heat capacity change (deltaCp). The informational content of thermodynamic data is large, and it has been shown that it plays an important role in the elucidation of binding mechanisms and, through the link to structural data, also in rational drug design. In this review we will present a comprehensive overview to ITC by giving some historical background to calorimetry, outline some critical experimental and data analysis aspects, discuss the latest developments, and give three recent examples of studies published with respect to macromolecule-ligand interactions that have utilized ITC technology.

CUSA and CUDE: GPU-accelerated methods for estimating solvent accessible surface area and desolvation

It is well-established that a linear correlation exists between accessible surface areas and experimentally measured solvation energies. Combining this knowledge with an analytic formula for calculation of solvent accessible surfaces, we derive a simple model of desolvation energy as a differentiable function of atomic positions. Additionally, we find that this algorithm is particularly well suited for hardware acceleration on graphics processing units (GPUs), outperforming the CPU by up to two orders of magnitude. We explore the scaling of this desolvation algorithm and provide implementation details applicable to general pairwise algorithms.

Absolute binding free energy calculations using molecular dynamics simulations with restraining potentials

The absolute (standard) binding free energy of eight FK506-related ligands to FKBP12 is calculated using free energy perturbation molecular dynamics (FEP/MD) simulations with explicit solvent. A number of features are implemented to improve the accuracy and enhance the convergence of the calculations. First, the absolute binding free energy is decomposed into sequential steps during which the ligand-surrounding interactions as well as various biasing potentials restraining the translation, orientation, and conformation of the ligand are turned "on" and "off." Second, sampling of the ligand conformation is enforced by a restraining potential based on the root mean-square deviation relative to the bound state conformation. The effect of all the restraining potentials is rigorously unbiased, and it is shown explicitly that the final results are independent of all artificial restraints. Third, the repulsive and dispersive free energy contribution arising from the Lennard-Jones interactions of the ligand with its surrounding (protein and solvent) is calculated using the Weeks-Chandler-Andersen separation. This separation also improves convergence of the FEP/MD calculations. Fourth, to decrease the computational cost, only a small number of atoms in the vicinity of the binding site are simulated explicitly, while all the influence of the remaining atoms is incorporated implicitly using the generalized solvent boundary potential (GSBP) method. With GSBP, the size of the simulated FKBP12/ligand systems is significantly reduced, from approximately 25,000 to 2500. The computations are very efficient and the statistical error is small ( approximately 1 kcal/mol). The calculated binding free energies are generally in good agreement with available experimental data and previous calculations (within approximately 2 kcal/mol). The present results indicate that a strategy based on FEP/MD simulations of a reduced GSBP atomic model sampled with conformational, translational, and orientational restraining potentials can be computationally inexpensive and accurate.

Comparison of automated docking programs as virtual screening tools

The performance of several commercially available docking programs is compared in the context of virtual screening. Five different protein targets are used, each with several known ligands. The simulated screening deck comprised 1000 molecules from a cleansed version of the MDL drug data report and 49 known ligands. For many of the known ligands, crystal structures of the relevant protein-ligand complexes were available. We attempted to run experiments with each docking method that were as similar as possible. For a given docking method, hit rates were improved versus what would be expected for random selection for most protein targets. However, the ability to prioritize known ligands on the basis of docking poses that resemble known crystal structures is both method- and target-dependent.

Importance of solvent accessibility and contact surfaces in modeling side-chain conformations in proteins

Contact surface area and chemical properties of atoms are used to concurrently predict conformations of multiple amino acid side chains on a fixed protein backbone. The combination of surface complementarity and solvent-accessible surface accounts for van der Waals forces and solvation free energy. The scoring function is particularly suitable for modeling partially buried side chains. Both iterative and stochastic searching approaches are used. Our programs (Sccomp-I and Sccomp-S), with relatively fast execution times, correctly predict chi1 angles for 92-93% of buried residues and 82-84% for all residues, with an RMSD of approximately 1.7 A for side chain heavy atoms. We find that the differential between the atomic solvation parameters and the contact surface parameters (including those between noncomplementary atoms) is positive; i.e., most protein atoms prefer surface contact with other protein atoms rather than with the solvent. This might correspond to the driving force for maximizing packing of the protein. The influence of the crystal packing, completeness of rotamer library and precise positioning of Cbeta atoms on the accuracy of side-chain prediction are examined. The Sccomp-S and Sccomp-I programs can be accessed through the Web (http://sgedg.weizmann.ac.il/sccomp.html) and are available for several platforms.

MIAX: a new paradigm for modeling biomacromolecular interactions and complex formation in condensed phases

A new paradigm is proposed for modeling biomacromolecular interactions and complex formation in solution (protein-protein interactions so far in this report) that constitutes the scaffold of the automatic system MIAX (acronym for Macromolecular Interaction Assessment X). It combines in a rational way a series of computational methodologies, the goal being the prediction of the most native-like protein complex that may be formed when two isolated (unbound) protein monomers interact in a liquid environment. The overall strategy consists of first inferring putative precomplex structures by identification of binding sites or epitopes on the proteins surfaces and a simultaneous rigid-body docking process using geometric instances alone. Precomplex configurations are defined here as all those decoys the interfaces of which comply substantially with the inferred binding sites and whose free energy values are lower. Retaining all those precomplex configurations with low energies leads to a reasonable number of decoys for which a flexible treatment is amenable. A novel algorithm is introduced here for automatically inferring binding sites in proteins given their 3-D structure. The procedure combines an unsupervised learning algorithm based on the self-organizing map or Kohonen network with a 2-D Fourier spectral analysis. To model interaction, the potential function proposed here plays a central role in the system and is constituted by empirical terms expressing well-characterized factors influencing biomacromolecular interaction processes, essentially electrostatic, van der Waals, and hydrophobic. Each of these procedures is validated by comparing results with observed instances. Finally, the more demanding process of flexible docking is performed in MIAX embedding the potential function in a simulated annealing optimization procedure. Whereas search of the entire configuration hyperspace is a major factor precluding hitherto systems from efficiently modeling macromolecular interaction modes and complex structures, the paradigm presented here may constitute a step forward in the field because it is shown that a rational treatment of the information available from the 3-D structure of the interacting monomers combined with conveniently selected computational techniques can assist to elude search of regions of low probability in configuration space and indeed lead to a highly efficient system oriented to solve this intriguing and fundamental biologic problem.

Principles of docking: An overview of search algorithms and a guide to scoring functions

The docking field has come of age. The time is ripe to present the principles of docking, reviewing the current state of the field. Two reasons are largely responsible for the maturity of the computational docking area. First, the early optimism that the very presence of the "correct" native conformation within the list of predicted docked conformations signals a near solution to the docking problem, has been replaced by the stark realization of the extreme difficulty of the next scoring/ranking step. Second, in the last couple of years more realistic approaches to handling molecular flexibility in docking schemes have emerged. As in folding, these derive from concepts abstracted from statistical mechanics, namely, populations. Docking and folding are interrelated. From the purely physical standpoint, binding and folding are analogous processes, with similar underlying principles. Computationally, the tools developed for docking will be tremendously useful for folding. For large, multidomain proteins, domain docking is probably the only rational way, mimicking the hierarchical nature of protein folding. The complexity of the problem is huge. Here we divide the computational docking problem into its two separate components. As in folding, solving the docking problem involves efficient search (and matching) algorithms, which cover the relevant conformational space, and selective scoring functions, which are both efficient and effectively discriminate between native and non-native solutions. It is universally recognized that docking of drugs is immensely important. However, protein-protein docking is equally so, relating to recognition, cellular pathways, and macromolecular assemblies. Proteins function when they are bound to other molecules. Consequently, we present the review from both the computational and the biological points of view. Although large, it covers only partially the extensive body of literature, relating to small (drug) and to large protein-protein molecule docking, to rigid and to flexible. Unfortunately, when reviewing these, a major difficulty in assessing the results is the non-uniformity in the formats in which they are presented in the literature. Consequently, we further propose a way to rectify it here.

Soft protein-protein docking in internal coordinates

The association of two biological macromolecules is a fundamental biological phenomenon and an unsolved theoretical problem. Docking methods for ab initio prediction of association of two independently determined protein structures usually fail when they are applied to a large set of complexes, mostly because of inaccuracies in the scoring function and/or difficulties on simulating the rearrangement of the interface residues on binding. In this work we present an efficient pseudo-Brownian rigid-body docking procedure followed by Biased Probability Monte Carlo Minimization of the ligand interacting side-chains. The use of a soft interaction energy function precalculated on a grid, instead of the explicit energy, drastically increased the speed of the procedure. The method was tested on a benchmark of 24 protein-protein complexes in which the three-dimensional structures of their subunits (bound and free) were available. The rank of the near-native conformation in a list of candidate docking solutions was <20 in 85% of complexes with no major backbone motion on binding. Among them, as many as 7 out of 11 (64%) protease-inhibitor complexes can be successfully predicted as the highest rank conformations. The presented method can be further refined to include the binding site predictions and applied to the structures generated by the structural proteomics projects. All scripts are available on the Web.

Structure-based thermodynamic analysis of the dissociation of protein phosphatase-1 catalytic subunit and microcystin-LR docked complexes

The relationship between the structure of a free ligand in solution and the structure of its bound form in a complex is of great importance to the understanding of the energetics and mechanism of molecular recognition and complex formation. In this study, we use a structure-based thermodynamic approach to study the dissociation of the complex between the toxin microcystin-LR (MLR) and the catalytic domain of protein phosphatase-1 (PP-1c) for which the crystal structure of the complex is known. We have calculated the thermodynamic parameters (enthalpy, entropy, heat capacity, and free energy) for the dissociation of the complex from its X-ray structure and found the calculated dissociation constant (4.0 x 10(-11)) to be in excellent agreement with the reported inhibitory constant (3.9 x 10(-11)). We have also calculated the thermodynamic parameters for the dissociation of 47 PP-1c:MLR complexes generated by docking an ensemble of NMR solution structures of MLR onto the crystal structure of PP-1c. In general, we observe that the lower the root-mean-square deviation (RMSD) of the docked complex (compared to the X-ray complex) the closer its free energy of dissociation (deltaGd(o)) is to that calculated from the X-ray complex. On the other hand, we note a significant scatter between the deltaGd(o) and the RMSD of the docked complexes. We have identified a group of seven docked complexes with deltaGd(o) values very close to the one calculated from the X-ray complex but with significantly dissimilar structures. The analysis of the corresponding enthalpy and entropy of dissociation shows a compensation effect suggesting that MLR molecules with significant structural variability can bind PP-1c and that substantial conformational flexibility in the PP-1c:MLR complex may exist in solution.

A solvent model for simulations of peptides in bilayers. I. Membrane-promoting alpha-helix formation

We describe an efficient solvation model for proteins. In this model atomic solvation parameters imitating the hydrocarbon core of a membrane, water, and weak polar solvent (octanol) were developed. An optimal number of solvation parameters was chosen based on analysis of atomic hydrophobicities and fitting experimental free energies of gas-cyclohexane, gas-water, and octanol-water transfer for amino acids. The solvation energy term incorporated into the ECEPP/2 potential energy function was tested in Monte Carlo simulations of a number of small peptides with known energies of bilayer-water and octanol-water transfer. The calculated properties were shown to agree reasonably well with the experimental data. Furthermore, the solvation model was used to assess membrane-promoting alpha-helix formation. To accomplish this, all-atom models of 20-residue homopolypeptides-poly-Leu, poly-Val, poly-Ile, and poly-Gly in initial random coil conformation-were subjected to nonrestrained Monte Carlo conformational search in vacuo and with the solvation terms mimicking the water and hydrophobic parts of the bilayer. All the peptides demonstrated their largest helix-forming tendencies in a nonpolar environment, where the lowest-energy conformers of poly-Leu, Val, Ile revealed 100, 95, and 80% of alpha-helical content, respectively. Energetic and conformational properties of Gly in all environments were shown to be different from those observed for residues with hydrophobic side chains. Applications of the solvation model to simulations of peptides and proteins in the presence of membrane, along with limitations of the approach, are discussed.

Folding-unfolding energy change of a simple sphere model protein and an energy landscape of the folding process

We have calculated the free energy of a spherical model of a protein or part of a protein generated in the way of protein folding. Two spherical models are examined; one is a homogeneous model consisting of only one residue type--hydrophobic. The other is a heterogeneous model consisting of two residue types--strong hydrophobic and weak hydrophobic. Both models show a folding transition state, and the latter model reproduces the trend of the experimental folded-unfolded energy change. The heterogeneous model suggests that in the folding process of a protein of more than 70 residues, a specific region of the protein folds first to form a stable region, then the other residues follow the folding process. The energy landscape of folding of a small protein is approximately a funnel model, whereas a flatter energy landscape is suggested for larger proteins of more than 55-70 residues.

Predicting structural effects in HIV-1 protease mutant complexes with flexible ligand docking and protein side-chain optimization

We present a computational approach for predicting structures of ligand-protein complexes and analyzing binding energy landscapes that combines Monte Carlo simulated annealing technique to determine the ligand bound conformation with the dead-end elimination algorithm for side-chain optimization of the protein active site residues. Flexible ligand docking and optimization of mobile protein side-chains have been performed to predict structural effects in the V32I/I47V/V82I HIV-1 protease mutant bound with the SB203386 ligand and in the V82A HIV-1 protease mutant bound with the A77003 ligand. The computational structure predictions are consistent with the crystal structures of these ligand-protein complexes. The emerging relationships between ligand docking and side-chain optimization of the active site residues are rationalized based on the analysis of the ligand-protein binding energy landscape.

Prediction of binding energetics from structure using empirical parameterization

We have presented an empirical method that can be used to predict the binding energetics for protein-protein or protein-peptide interactions from three-dimensional structures. The approach differs from other empirical methods in yielding a thermodynamic description of the binding process, including delta Cp, delta H degree, and delta S degree, rather than predicting delta G degree alone. These thermodynamic terms can provide a wealth of detail about the nature of the interaction, and, if sufficient experimental data are available for comparison, a greater assessment of the accuracy of the calculations. A recurring theme throughout this article is the need for more complete thermodynamic and structural characterizations of protein-ligand interactions. This includes not only characterization of the binding delta H degree, delta S degree, and delta Cp, but a thorough investigation into equilibria linked to binding, such as protonation, ion binding, and conformational changes. Sufficient data will allow parameterization on binding data rather than protein unfolding data. Further inclusion of information obtained from unfolding studies is not likely to generate significant improvement in the accuracy of the calculations. As additional binding data become available, the parameterization can be further extended to include relationships derived from analyses of these data. Not only will this increase accuracy and thus confidence, but allow extension of the method of additional types of interactions.

Predictive docking of protein-protein and protein-DNA complexes

Recent developments in algorithms to predict the docking of two proteins have considered both the initial rigid-body global search and subsequent screening and refinement. The result of two blind trials of protein docking are encouraging--for complexes that are not too large and do not undergo sizeable conformational change upon association, the algorithms are now able to suggest reasonably accurate models.

Rapid refinement of protein interfaces incorporating solvation: application to the docking problem

A computationally tractable strategy has been developed to refine protein-protein interfaces that models the effects of side-chain conformational change, solvation and limited rigid-body movement of the subunits. The proteins are described at the atomic level by a multiple copy representation of side-chains modelled according to a rotamer library on a fixed peptide backbone. The surrounding solvent environment is described by "soft" sphere Langevin dipoles for water that interact with the protein via electrostatic, van der Waals and field-dependent hydrophobic terms. Energy refinement is based on a two-step process in which (1) a probability-based conformational matrix of the protein side-chains is refined iteratively by a mean field method. A side-chain interacts with the protein backbone and the probability-weighted average of the surrounding protein side-chains and solvent molecules. The resultant protein conformations then undergo (2) rigid-body energy minimization to relax the protein interface. Steps (1) and (2) are repeated until convergence of the interaction energy. The influence of refinement on side-chain conformation starting from unbound conformations found improvement in the RMSD of side-chains in the interface of protease-inhibitor complexes, and shows that the method leads to an improvement in interface geometry. In terms of discriminating between docked structures, the refinement was applied to two classes of protein-protein complex: five protease-protein inhibitor and four antibody-antigen complexes. A large number of putative docked complexes have already been generated for the test systems using our rigid-body docking program, FTDOCK. They include geometries that closely resemble the crystal complex, and therefore act as a test for the refinement procedure. In the protease-inhibitors, geometries that resemble the crystal complex are ranked in the top four solutions for four out of five systems when solvation is included in the energy function, against a background of between 26 and 364 complexes in the data set. The results for the antibody-antigen complexes are not as encouraging, with only two of the four systems showing discrimination. It would appear that these results reflect the somewhat different binding mechanism dominant in the two types of protein-protein complex. Binding in the protease-inhibitors appears to be "lock and key" in nature. The fixed backbone and mobile side-chain representation provide a good model for binding. Movements in the backbone geometry of antigens on binding represent an "induced-fit" and provides more of a challenge for the model. Given the limitations of the conformational sampling, the ability of the energy function to discriminate between native and non-native states is encouraging. Development of the approach to include greater conformational sampling could lead to a more general solution to the protein docking problem.

Towards structural models of molecular recognition in olfactory receptors

The G protein coupled receptors (GPCR) are an important class of proteins that act as signal transducers through the cytoplasmic membrane. Understanding the structure and activation mechanism of these proteins is crucial for understanding many different aspects of cellular signalling. The olfactory receptors correspond to the largest family of GPCRs. Very little is known about how the structures of the receptors govern the specificity of interaction which enables identification of particular odorant molecules. In this paper, we review recent developments in two areas of molecular modelling: methods for modelling the configuration of trans-membrane helices and methods for automatic docking of ligands into receptor structures. We then show how a subset of these methods can be combined to construct a model of a rat odorant receptor interacting with lyral for which experimental data are available. This modelling can help us make progress towards elucidating the specificity of interactions between receptors and odorant molecules.

Empirical free energy calculation: comparison to calorimetric data

An effective free energy potential, developed originally for binding free energy calculation, is compared to calorimetric data on protein unfolding, described by a linear combination of changes in polar and nonpolar surface areas. The potential consists of a molecular mechanics energy term calculated for a reference medium (vapor or nonpolar liquid), and empirical terms representing solvation and entropic effects. It is shown that, under suitable conditions, the free energy function agrees well with the calorimetric expression. An additional result of the comparison is an independent estimate of the side-chain entropy loss, which is shown to agree with a structure-based entropy scale. These findings confirm that simple functions can be used to estimate the free energy change in complex systems, and that a binding free energy evaluation model can describe the thermodynamics of protein unfolding correctly. Furthermore, it is shown that folding and binding leave the sum of solute-solute and solute-solvent van der Waals interactions nearly invariant and, due to this invariance, it may be advantageous to use a nonpolar liquid rather than vacuum as the reference medium.

Atomic solvation parameters for proteins in a membrane environment. Application to transmembrane alpha-helices

Several sets of atomic solvation parameters imitating: (i) nonpolar environment of hydrocarbon core of a membrane, (ii) aqueous solution, and (iii) weakly-polar solvents have been developed. The parameters have been incorporated into the ECEPP/2 and CHARMM force fields and employed in non-restrained Monte Carlo and molecular dynamics simulations of membrane-spanning alpha-helical peptides (segment A of bacteriorhodopsin, melittin). Through these simulations, the structure and energetics of the helices have been examined as a function of the solvation term in the potential energy function. For the peptides under study, the set (i) of atomic solvation parameters reveals good retention of the alpha-helical conformation. By contrast, the simulations in vacuum or with the parameters imitating a polar solvent (sets (ii) or (iii)) show fast helix destabilization and tight packing of the structure accompanied by significant decreasing of the surface area accessible to solvent. Increased helical propensity for amino acid residues, population of side-chain rotamers as well as hydrogen-bonding pattern in nonpolar membrane-like environment agree well with available experimental and computational data. The problems related to further applications of the membrane-mimicking sets of atomic solvation parameters to simulations of membrane proteins and peptides are addressed.

Hydrophobicity regained

A widespread practice is to use free energies of transfer between organic solvents and water (delta G0transfer to define hydrophobicity scales for the amino acid side chains. A comparison of four delta G0transfer scales reveals that the values for hydrogen-bonding side chains are highly dependent on the non-aqueous environment. This property of polar side chains violates the assumptions underlying the paradigm of equating delta G0transfer with hydrophobicity or even with a generic solvation energy that is directly relevant to protein stability and ligand binding energetics. This simple regaining of the original concept of hydrophobicity reveals a flaw in approaches that use delta G0transfer values to derive generic estimates of the energetics of the burial of polar groups, and allows the introduction of a "pure" hydrophobicity scale for the amino acid residues.

Empirical potentials and functions for protein folding and binding

Simplified models and empirical potentials are being increasingly used for the analysis of proteins, frequently augmenting or replacing molecular mechanics approaches. Recent folding simulations have employed potentials that, in addition to terms assuring proper polypeptide geometry, include only two noncovalent effects-hydrogen bonding and hydrophobicity, with extremely simple approximations to the latter. The potentials that have been used in the free-energy ranking of protein-ligand complexes have generally been more involved. These potentials have more detailed solvation models and account for both local (hydrophobic and polar) solute-solvent phenomena and long range electrostatic solvation effects. The models of solvation that have been used most frequently are surface area related atomic parameters, knowledge-based models extracted from protein-structure data, and continum electrostatics with an additional area-related parameter. The knowledge-based approaches to solvation, although convenient and accurate enough, are suspect of double counting certain free-energy terms.

Modeling protein-ligand complexes

Increasing the rate at which new biologically active compounds are found is a major goal in pharmaceutical chemistry. Recently, several computational methods have been proposed with this intent. For some time, algorithms have been used to direct ligand evolution on the basis of complementarity to the three-dimensional structure of a selected protein. Current research focuses on enhancements to methods for searching chemical databases, proposing sensible modifications to known active compounds, and construction of novel ligands from theoretical principles.