Docking by least-squares fitting of molecular surface patterns

From face to interface recognition: a differential geometric approach to distinguish DNA from RNA binding surfaces

Protein nucleic acid interactions play a critical role in all steps of the gene expression pathway. Nucleic acid (NA) binding proteins interact with their partners, DNA or RNA, via distinct regions on their surface that are characterized by an ensemble of chemical, physical and geometrical properties. In this study, we introduce a novel methodology based on differential geometry, commonly used in face recognition, to characterize and predict NA binding surfaces on proteins. Applying the method on experimentally solved three-dimensional structures of proteins we successfully classify double-stranded DNA (dsDNA) from single-stranded RNA (ssRNA) binding proteins, with 83% accuracy. We show that the method is insensitive to conformational changes that occur upon binding and can be applicable for de novo protein-function prediction. Remarkably, when concentrating on the zinc finger motif, we distinguish successfully between RNA and DNA binding interfaces possessing the same binding motif even within the same protein, as demonstrated for the RNA polymerase transcription-factor, TFIIIA. In conclusion, we present a novel methodology to characterize protein surfaces, which can accurately tell apart dsDNA from an ssRNA binding interfaces. The strength of our method in recognizing fine-tuned differences on NA binding interfaces make it applicable for many other molecular recognition problems, with potential implications for drug design.

F2Dock: fast Fourier protein-protein docking

The functions of proteins are often realized through their mutual interactions. Determining a relative transformation for a pair of proteins and their conformations which form a stable complex, reproducible in nature, is known as docking. It is an important step in drug design, structure determination, and understanding function and structure relationships. In this paper, we extend our nonuniform fast Fourier transform-based docking algorithm to include an adaptive search phase (both translational and rotational) and thereby speed up its execution. We have also implemented a multithreaded version of the adaptive docking algorithm for even faster execution on multicore machines. We call this protein-protein docking code F2Dock (F2 = Fast Fourier). We have calibrated F2Dock based on an extensive experimental study on a list of benchmark complexes and conclude that F2Dock works very well in practice. Though all docking results reported in this paper use shape complementarity and Coulombic-potential-based scores only, F2Dock is structured to incorporate Lennard-Jones potential and reranking docking solutions based on desolvation energy .

Assessing the role of polarization in docking

We describe a strategy for including ligand and protein polarization in docking that is based on the conversion of induced dipoles to induced charges. Induced charges have a distinct advantage in that they are readily implemented into a number of different computer programs, including many docking programs and hybrid QM/MM programs; induced charges are also more readily interpreted. In this study, the ligand was treated quantum mechanically to avoid parametrization issues and was polarized by the target protein, which was treated as a set of point charges. The induced dipole at a given target atom, due to polarization by the ligand and neighboring residues, was reformulated as induced charges at the given atom and its bonded neighbors, and these were allowed to repolarize the ligand in an iterative manner. The final set of polarized charges was evaluated in docking using AutoDock 4.0 on 12 protein-ligand systems against the default empirical Gasteiger charges, and against nonpolarized and partially polarized potential-derived charges. One advantage of AutoDock is that the best rmsd structure can be identified not only from the lowest energy pose but also from the largest cluster of poses. Inclusion of polarization does not always lead to the lowest energy pose having a lower rmsd, because docking is designed by necessity to be rapid rather than accurate. However, whenever an improvement in methodology, corresponding to a more thorough treatment of polarization, resulted in an increased cluster size, then there was also a corresponding decrease in the rmsd. The options for implementing polarization within a purely classical docking framework are discussed.

Fully automated molecular mechanics based induced fit protein-ligand docking method

We describe a method for docking a ligand into a protein receptor while allowing flexibility of the protein binding site. The method employs a multistep procedure that begins with the generation of protein and ligand conformations. An initial placement of the ligand is then performed by computing binding site hotspots. This initial placement is followed by a protein side-chain refinement stage that models protein flexibility. The final step of the process is an energy minimization of the ligand pose in the presence of the rigid receptor. Thus the algorithm models flexibility of the protein at two stages, before and after ligand placement. We validated this method by performing docking and cross docking studies of eight protein systems for which crystal structures were available for at least two bound ligands. The resulting rmsd values of the 21 docked protein-ligand complexes showed values of 2 A or less for all but one of the systems examined. The method has two critical benefits for high throughput virtual screening studies. First, no user intervention is required in the docking once the initial binding site selection has been made in the protein. Second, the initial protein conformation generation needs to be performed only once for a given binding region. Also, the method may be customized in various ways depending on the particular scenario in which dockings are being performed. Each of the individual steps of the method is fully independent making it straightforward to explore different variants of the high level workflow to further improve accuracy and performance.

Specificity in lipases: a computational study of transesterification of sucrose

Computational conformational searches of putative transition states of the reaction of sucrose with vinyl laurate catalyzed by lipases from Candida antarctica B and Thermomyces lanuginosus have been carried out. The dielectric of the media have been varied to understand the role of protein plasticity in modulating the observed regioselective transesterification. The binding pocket of lipase from Candida adapts to the conformational variability of the various substates of the substrates by small, local adjustments within the binding pocket. In contrast, the more constrained pocket of the lipase from Thermomyces adapts by adjusting through concerted global motions between subdomains. This leads to the identification of one large pocket in Candida that accommodates both the sucrose and the lauroyl moieties of the transition state, whereas in Thermomyces the binding pocket is smaller, leading to the localization of the two moieties in two distinct pockets; this partly rationalizes the broader specificity of the former relative to the latter. Mutations have been suggested to exploit the differences towards changing the observed selectivities.

Predicting peptide binding to MHC pockets via molecular modeling, implicit solvation, and global optimization

Development of a computational prediction method based on molecular modeling, global optimization, and implicit solvation has produced accurate structure and relative binding affinity predictions for peptide amino acids binding to five pockets of the MHC molecule HLA-DRB1*0101. Because peptide binding to MHC molecules is essential to many immune responses, development of such a method for understanding and predicting the forces that drive binding is crucial for pharmaceutical design and disease treatment. Underlying the development of this prediction method are two hypotheses. The first is that pockets formed by the peptide binding groove of MHC molecules are independent, separating the prediction of peptide amino acids that bind within individual pockets from those that bind between pockets. The second hypothesis is that the native state of a system composed of an amino acid bound to a protein pocket corresponds to the system's lowest free energy. The prediction method developed from these hypotheses uses atomistic-level modeling, deterministic global optimization, and three methods of implicit solvation: solvent-accessible area, solvent-accessible volume, and Poisson-Boltzmann electrostatics. The method predicts relative binding affinities of peptide amino acids for pockets of HLA-DRB1*0101 by determining computationally an amino acid's global minimum energy conformation. Prediction results from the method are in agreement with X-ray crystallography data and experimental binding assays.

New fuzzy logic strategies for bio-molecular recognition

The concepts of molecular similarity and molecular complementarity, playing important roles in the broad field of molecular recognition, are chemical problems, in which the eyeball technique used by a human observer is very successful but which are very hard to code into a computer algorithm. Based on the model of molecular surfaces, our new approach defines overlapping surface patches with similar molecular properties. These patches are used to represent local features of the molecule in a way, which is beyond the atomistic resolution but can nevertheless be applied in partial similarity as well as complementarity analyses in a very general sense. It is shown that this molecular description can be used as the first step in a docking algorithm for complexes, where the structures of both molecules are known, as well as for the identification of possible active sites without the knowledge of specific molecules binding to this site.

A combinatorial approach to protein docking with flexible side chains

Rigid-body docking approaches are not sufficient to predict the structure of a protein complex from the unbound (native) structures of the two proteins. Accounting for side chain flexibility is an important step towards fully flexible protein docking. This work describes an approach that allows conformational flexibility for the side chains while keeping the protein backbone rigid. Starting from candidates created by a rigid-docking algorithm, we demangle the side chains of the docking site, thus creating reasonable approximations of the true complex structure. These structures are ranked with respect to the binding free energy. We present two new techniques for side chain demangling. Both approaches are based on a discrete representation of the side chain conformational space by the use of a rotamer library. This leads to a combinatorial optimization problem. For the solution of this problem, we propose a fast heuristic approach and an exact, albeit slower, method that uses branch-and-cut techniques. As a test set, we use the unbound structures of three proteases and the corresponding protein inhibitors. For each of the examples, the highest-ranking conformation produced was a good approximation of the true complex structure.

LigandFit: a novel method for the shape-directed rapid docking of ligands to protein active sites

We present a new shape-based method, LigandFit, for accurately docking ligands into protein active sites. The method employs a cavity detection algorithm for detecting invaginations in the protein as candidate active site regions. A shape comparison filter is combined with a Monte Carlo conformational search for generating ligand poses consistent with the active site shape. Candidate poses are minimized in the context of the active site using a grid-based method for evaluating protein-ligand interaction energies. Errors arising from grid interpolation are dramatically reduced using a new non-linear interpolation scheme. Results are presented for 19 diverse protein-ligand complexes. The method appears quite promising, reproducing the X-ray structure ligand pose within an RMS of 2A in 14 out of the 19 complexes. A high-throughput screening study applied to the thymidine kinase receptor is also presented in which LigandFit, when combined with LigScore, an internally developed scoring function, yields very good hit rates for a ligand pool seeded with known actives.

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.

A novel approach for identifying the surface atoms of macromolecules

A significant number of atoms lie buried beneath the "molecular surface" of proteins and other biologic macromolecules. Interactions between ligands and these macromolecules are dominated by interactions with the "surface atoms". Although interactions with the "buried" or interior atoms of the macromolecule certainly contribute to the total intermolecular interaction energy, many computer-assisted drug design (CADD) strategies can benefit from the identification of those atoms "on the surface" of proteins and other macromolecules. We have developed a simple, yet novel method to distinguish the surface atoms of macromolecules from the interior atoms which is based on computing the atomic contributions to the solvent-accessible surface (SAS) area. This report describes that method and demonstrates that it compares very favorably with four alternative methods.

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.

Electrostatic contributions to protein-protein interactions: fast energetic filters for docking and their physical basis

The methods of continuum electrostatics are used to calculate the binding free energies of a set of protein-protein complexes including experimentally determined structures as well as other orientations generated by a fast docking algorithm. In the native structures, charged groups that are deeply buried were often found to favor complex formation (relative to isosteric nonpolar groups), whereas in nonnative complexes generated by a geometric docking algorithm, they were equally likely to be stabilizing as destabilizing. These observations were used to design a new filter for screening docked conformations that was applied, in conjunction with a number of geometric filters that assess shape complementarity, to 15 antibody-antigen complexes and 14 enzyme-inhibitor complexes. For the bound docking problem, which is the major focus of this paper, native and near-native solutions were ranked first or second in all but two enzyme-inhibitor complexes. Less success was encountered for antibody-antigen complexes, but in all cases studied, the more complete free energy evaluation was able to identify native and near-native structures. A filter based on the enrichment of tyrosines and tryptophans in antibody binding sites was applied to the antibody-antigen complexes and resulted in a native and near-native solution being ranked first and second in all cases. A clear improvement over previously reported results was obtained for the unbound antibody-antigen examples as well. The algorithm and various filters used in this work are quite efficient and are able to reduce the number of plausible docking orientations to a size small enough so that a final more complete free energy evaluation on the reduced set becomes computationally feasible.

A novel approach for assessing macromolecular complexes combining soft-docking calculations with NMR data

We present a novel and efficient approach for assessing protein-protein complex formation, which combines ab initio docking calculations performed with the protein docking algorithm BiGGER and chemical shift perturbation data collected with heteronuclear single quantum coherence (HSQC) or TROSY nuclear magnetic resonance (NMR) spectroscopy. This method, termed "restrained soft-docking," is validated for several known protein complexes. These data demonstrate that restrained soft-docking extends the size limitations of NMR spectroscopy and provides an alternative method for investigating macromolecular protein complexes that requires less experimental time, effort, and resources. The potential utility of this novel NMR and simulated docking approach in current structural genomic initiatives is discussed.

Protein ligand docking based on empirical method for binding affinity estimation

An empirical protein-ligand binding affinity estimation method, SCORE, was incorporated into a popular docking program, DOCK4. The combined program, ScoreDock, was used to reconstruct the 200 protein-ligand complex structures and found to give good results for the complexes with high binding affinities. A quality assessment method for docking results from ScoreDock was developed based on the whole test set and tested by additionally selected complexes. The method significantly improves the docking accuracy and was shown to be reliable in docking quality assessment. As a docking tool in structural based drug design, ScoreDock can screen out final hits directly based on the predicted negative logarithms of dissociation equilibrium constants of protein-ligand complexes, and can explicitly deal with structure water molecules, as well as metal atoms.

Scoring docked conformations generated by rigid-body protein-protein docking

Rigid-body methods, particularly Fourier correlation techniques, are very efficient for docking bound (co-crystallized) protein conformations using measures of surface complementarity as the target function. However, when docking unbound (separately crystallized) conformations, the method generally yields hundreds of false positive structures with good scores but high root mean square deviations (RMSDs). This paper describes a two-step scoring algorithm that can discriminate near-native conformations (with less than 5 A RMSD) from other structures. The first step includes two rigid-body filters that use the desolvation free energy and the electrostatic energy to select a manageable number of conformations for further processing, but are unable to eliminate all false positives. Complete discrimination is achieved in the second step that minimizes the molecular mechanics energy of the retained structures, and re-ranks them with a combined free-energy function which includes electrostatic, solvation, and van der Waals energy terms. After minimization, the improved fit in near-native complex conformations provides the free-energy gap required for discrimination. The algorithm has been developed and tested using docking decoys, i.e., docked conformations generated by Fourier correlation techniques. The decoy sets are available on the web for testing other discrimination procedures. Proteins 2000;40:525-537.

Automated docking of ligands to antibodies: methods and applications

Many approaches to studying protein-ligand interactions by computational docking are currently available. Given the structures of a protein and a ligand, the ultimate goal of all docking methods is to predict the structure of the resulting complex. This requires a suitable representation of molecular structures and properties, search algorithms to efficiently scan the configuration space for favorable interaction geometries, and accurate scoring functions to evaluate and rank the generated orientations. For many of the available methods, tests on experimentally known antibody-antigen or antibody-hapten complexes have appeared in the literature. In addition, some of them have been used in predictive studies on antibody-ligand interactions to provide structural insights where adequate experimental information is missing. The AutoDock program is presented as example of a method for flexibly docking ligands to antibodies. Applying parameters of the second-generation AMBER force field, three antibody-hapten complexes (AN02, DB3, NC6.8) are used as new test cases to analyze the ability of the method to reproduce experimental findings. The X-ray structures could be reconstituted and the corresponding solutions were ranked with best energy score in all cases. Docking to the free instead of the complexed NC6.8 structure indicated the limits of the rigid protein treatment, although fairly good guesses about the location of the binding site and the contact residues could still be obtained if conformational flexibility was allowed at least in the ligand.

Analysis of structural and physico-chemical parameters involved in the specificity of binding between alpha-amylases and their inhibitors

Enzyme-inhibitor specificity was studied for alpha-amylases and their inhibitors. We purified and cloned the cDNAs of two different alpha-amylase inhibitors from the common bean (Phaseolus vulgaris) and have recently cloned the cDNA of an alpha-amylase of the Mexican bean weevil (Zabrotes subfasciatus), which is inhibited by alpha-amylase inhibitor 2 but not by alpha-amylase inhibitor 1. The crystal structure of AI-1 complexed with pancreatic porcine alpha-amylase allowed us to model the structure of AI-2. The structure of Zabrotes subfasciatus alpha-amylase was modeled based on the crystal structure of Tenebrio molitor alpha-amylase. Pairwise AI-1 and AI-2 with PPA and ZSA complexes were modeled. For these complexes we first identified the interface forming residues. In addition, we identified the hydrogen bonds, ionic interactions and loss of hydrophobic surface area resulting from complex formation. The parameters we studied provide insight into the general scheme of binding, but fall short of explaining the specificity of the inhibition. We also introduce three new tools-software packages STING, HORNET and STINGPaint-which efficiently determine the interface forming residues and the ionic interaction data, the hydrogen bond net as well as aid in interpretation of multiple sequence alignment, respectively.

Graph-theoretic techniques for macromolecular docking

We propose a solution to the problem of docking two macromolecules. We represent each of two proteins as a set of potential hydrogen bond donors and acceptors and use a clique-detection algorithm to find maximally complementary sets of donor/acceptor pairs. Preliminary results are presented which demonstrate the feasibility of the method.

VRDD: applying virtual reality visualization to protein docking and design

We have developed an interactive docking program called VRDD. It offers various modes of displaying molecules in an immersive, three-dimensional virtual reality (VR) environment. It allows a user to interactively perform molecular docking aided by automatic docking and side chain conformational search. Binding free energies are computed in real time, and the program enables the user to explore only clash-free orientations of a ligand. VRDD also supplies visual and auditory feedback during docking and side chain search, indicating the levels of atomic overlap and interaction energy. The stunning VR graphics immerse users in the scene and can maximally stimulate their design intuition. We have tested VRDD on three cases with increasing complexity: a nine-residue-long peptide bound to a major histocompatibility complex (MHC) molecule, barstar bound to barnase, and an antibody bound to a hemagglutinin. Without prior knowledge, combinations of hand-docking and automatic refinement led to accurate complex structures for the first two complexes. The third case, for which all automatic docking algorithms failed to identify the correct complex in a previous blind test, also failed for VRDD. Our results show that the combination of VR docking and automatic docking can make unique contributions to molecular modeling.

Three-dimensional profiles: a new tool to identify protein surface similarities

We report a procedure for the description and comparison of protein surfaces, which is based on a three-dimensional (3D) transposition of the profile method for sensitive protein homology sequence searches. Although the principle of the method can be applied to detect similarities to a single protein surface, the possibility of extending this approach to protein families displaying common structural and/or functional properties, makes it a more powerful tool. In analogy to profiles derived from the multiple alignment of protein sequences, we derive a 3D surface profile from a protein structure or from a multiple structure alignment of several proteins. The 3D profile is used to screen the protein structure database, searching for similar protein surfaces. The application of the procedure to SH2 and SH3 binding pockets and to the nucleotide binding pocket associated with the p-loop structural motif is described. The SH2 and SH3 3D profiles can identify all the SH2 and SH3 binding regions present in the test dataset; the p-loop 3D profile is able to recognize all the p-loop-containing proteins present in the test dataset. Analysis of the p-loop 3D profile allowed the identification of a positive charge whose position is conserved in space but not in sequence. The best ranking non-p-loop-containing protein is an ADP-forming succinyl coenzyme A synthetase, whose nucleotide-binding region has not yet been identified.

Reaching the global minimum in docking simulations: a Monte Carlo energy minimization approach using Bezier splines

The docking problem faces two major challenges: the global optimization of a multivariable function, such as the energy, and the ability to discriminate between true and false positive results, i.e., native from nonnative structures based on the input energy function. Among all energy evaluation tools, only a local energy-minimization method using an accurate enough potential function is able to discriminate between native and nonnative structures. To meet these requirements, a Monte Carlo with energy-minimization method has been incorporated into a new ECEPP/3 docking program. The efficiency of the simulation results from the use of an energy-grid technique based on Bezier splines and from a simplification of the receptor by switching on the energy of only important residues of the active site. Simulations of a thrombin-inhibitor complex show that the global minimum of the energy function was reached in every independent run within less than 3 min of time on an IBM RX 6000 computer. For comparison, 10 standard independent Monte Carlo simulations with 10(6) steps in each were carried out. Only three of them led to a conformation close to the x-ray structure. The latter simulations required an average of 24 min and about 10 hr with and without the grid, respectively. Another important result is that the Bezier spline technique not only speeds up the calculation by reducing the number of operations during the energy evaluation but also helps in reaching the global minimum by smoothing out the potential energy surface.

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.

Extent and nature of contacts between protein molecules in crystal lattices and between subunits of protein oligomers

A survey was compiled of several characteristics of the intersubunit contacts in 58 oligomeric proteins, and of the intermolecular contracts in the lattice for 223 protein crystal structures. The total number of atoms in contact and the secondary structure elements involved are similar in the two types of interfaces. Crystal contact patches are frequently smaller than patches involved in oligomer interfaces. Crystal contacts result from more numerous interactions by polar residues, compared with a tendency toward nonpolar amino acids at oligomer interfaces. Arginine is the only amino acid prominent in both types of interfaces. Potentials of mean force for residue-residue contacts at both crystal and oligomer interfaces were derived from comparison of the number of observed residue-residue interactions with the number expected by mass action. They show that hydrophobic interactions at oligomer interfaces favor aromatic amino acids and methionine over aliphatic amino acids; and that crystal contacts form in such a way as to avoid inclusion of hydrophobic interactions. They also suggest that complex salt bridges with certain amino acid compositions might be important in oligomer formation. For a protein that is recalcitrant to crystallization, substitution of lysine residues with arginine or glutamine is a recommended strategy.

Molecular docking to ensembles of protein structures

Until recently, applications of molecular docking assumed that the macromolecular receptor exists in a single, rigid conformation. However, structural studies involving different ligands bound to the same target biomolecule frequently reveal modest but significant conformational changes in the target. In this paper, two related methods for molecular docking are described that utilize information on conformational variability from ensembles of experimental receptor structures. One method combines the information into an "energy-weighted average" of the interaction energy between a ligand and each receptor structure. The other method performs the averaging on a structural level, producing a "geometry-weighted average" of the inter-molecular force field score used in DOCK 3.5. Both methods have been applied in docking small molecules to ensembles of crystal and solution structures, and we show that experimentally determined binding orientations and computed energies of known ligands can be reproduced accurately. The use of composite grids, when conformationally different protein structures are available, yields an improvement in computational speed for database searches in proportion to the number of structures.

Analytically defined surfaces to analyze molecular interaction properties

Molecular surfaces are widely used for characterizing molecules and displaying and quantifying their interaction properties. Here we consider molecular surfaces defined as isocontours of a function (a sum of exponential functions centered on each atom) that approximately represents electron density. The smoothness is advantageous for surface mapping of molecular properties (e.g., electrostatic potential). By varying parameters, these surfaces can be constructed to represent the van der Waals or solvent-accessible surface of a molecular with any accuracy. We describe numerical algorithms to operate on the analytically defined surfaces. Two applications are considered: (1) We define and locate extremal points of molecular properties on the surfaces. The extremal points provide a compact representation of a property on a surface, obviating the necessity to compute values of the property on an array of surface points as is usually done; (2) a molecular surface patch or interface is projected onto a flat surface (by introducing curvilinear coordinates) with approximate conservation of area for analysis purposes. Applications to studies of protein-protein interactions are described.

Molecular docking using surface complementarity

A method is described to dock a ligand into a binding site in a protein on the basis of the complementarity of the intermolecular atomic contacts. Docking is performed by maximization of a complementarity function that is dependent on atomic contact surface area and the chemical properties of the contacting atoms. The generality and simplicity of the complementarity function ensure that a wide range of chemical structures can be handled. The ligand and the protein are treated as rigid bodies, but displacement of a small number of residues lining the ligand binding site can be taken into account. The method can assist in the design of improved ligands by indicating what changes in complementarity may occur as a result of the substitution of an atom in the ligand. The capabilities of the method are demonstrated by application to 14 protein-ligand complexes of known crystal structure.

Molecular recognition via face center representation of a molecular surface

While docking methodologies are now frequently being developed, a careful examination of the molecular surface representation, which necessarily is employed by them, is largely overlooked. There are two important aspects here that need to be addressed: how the surface representation quantifies surface complementarity, and whether a minimal representation is employed. Although complementarity is an accepted concept regarding molecular recognition, its quantification for computation is not trivial, and requires verification. A minimal representation is important because docking searches a conformation space whose extent and/or dimensionality grows quickly with the size of surface representation, making it especially costly with big molecules, imperfect interfaces, and changes of conformation that occur in binding. It is essential for a methodology to establish that it employs an accurate, concise molecular surface representation. Here we employ the face center representation of molecular surface, developed by Lin et al., to investigate the complementarity of molecular interface. We study a wide variety of complexes: protein/small ligand, oligomeric chain-chain interfaces, proteinase/protein inhibitors, antibody/antigen, NMR structures, and complexes built from unbound, separately solved structures. The complementarity is examined at different levels of reduction, and hence roughness, of the surface representation, from one that describes subatomic details to a very sparse one that captures only the prominent features on the surface. Our simulation of molecular recognition indicates that in all cases, quality interface complementarity is obtained. We show that the representation is powerful in monitoring the complementarity either in its entirety, or in selected subsets that maintain a fraction of the face centers, and is capable of supporting molecular docking at high fidelity and efficiency. Furthermore, we also demonstrate that the presence of explicit hydrogens in molecular structures may not benefit docking, and that the different classes of protein complexes may hold slightly different degrees of interface complementarity.

Prediction of protein complexes using empirical free energy functions

A long sought goal in the physical chemistry of macromolecular structure, and one directly relevant to understanding the molecular basis of biological recognition, is predicting the geometry of bimolecular complexes from the geometries of their free monomers. Even when the monomers remain relatively unchanged by complex formation, prediction has been difficult because the free energies of alternative conformations of the complex have been difficult to evaluate quickly and accurately. This has forced the use of incomplete target functions, which typically do no better than to provide tens of possible complexes with no way of choosing between them. Here we present a general framework for empirical free energy evaluation and report calculations, based on a relatively complete and easily executable free energy function, that indicate that the structures of complexes can be predicted accurately from the structures of monomers, including close sequence homologues. The calculations also suggest that the binding free energies themselves may be predicted with reasonable accuracy. The method is compared to an alternative formulation that has also been applied recently to the same data set. Both approaches promise to open new opportunities in macromolecular design and specificity modification.

Molecular docking towards drug discovery

Fueled by advances in molecular structure determination, tools for structure-based drug design are proliferating rapidly. Lead discovery through searching of ligand databases with molecular docking techniques represents an attractive alternative to high-throughout random screening. The size of commercial databases imposes severe computational constraints on molecular docking, compromising the level of calculational detail permitted for each putative ligand. We describe alternative philosophies for docking which effectively address this challenge. With respect to the dynamic aspects of molecular recognition, these strategies lie along a spectrum of models bounded by the Lock-and-Key and Induced-Fit theories for ligand binding. We explore the potential of a rigid model in exploiting species specificity and of a tolerant model in predicting absolute ligand binding affinity. Current molecular docking methods are limited primarily by their ability to rank docked complexes; we therefore place particular emphasis on this aspect of the problem throughout our validation of docking strategies.

Predicting the structure of protein complexes: a step in the right direction

In a blind test of protein-docking algorithms, six groups used different methods to predict the structure of a protein complex. All six predicted structures were close enough to the experimental complex to be useful; nevertheless, several important details of the experimental complex were missed or only partially predicted.

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

Several sets of amino acid surface areas and transfer free energies were used to derive a total of nine sets of atomic solvation parameters (ASPs). We tested the accuracy of each of these sets of parameters in predicting the experimentally determined transfer free energies of the amino acid derivatives from which the parameters were derived. In all cases, the calculated and experimental values correlated well. We then chose three parameter sets and examined the effect of adding an energetic correction for desolvation based on these three parameter sets to the simple potential function used in our multiple start Monte Carlo docking method. A variety of protein-protein interactions and docking results were examined. In the docking simulations studied, the desolvation correction was only applied during the final energy calculation of each simulation. For most of the docking results we analyzed, the use of an octanol-water-based ASP set marginally improved the energetic ranking of the low-energy dockings, whereas the other ASP sets we tested disturbed the ranking of the low-energy dockings in many of the same systems. We also examined the correlation between the experimental free energies of association and our calculated interaction energies for a series of proteinase-inhibitor complexes. Again, the octanol-water-based ASP set was compatible with our standard potential function, whereas ASP sets derived from other solvent systems were not.

BUILDER v.2: improving the chemistry of a de novo design strategy

Significant improvements have been made to the de novo drug design program BUILDER. The BUILDER strategy is to find molecule templates that bind tightly to 'hot spots' in the target receptor, and then generate bridges to join these templates. In this paper, the bridging algorithm has been further developed to improve the chemical sense and diversity of the bridges, as well as the robustness of the technique. The improved algorithm is then applied to rebuild known bridges in methotrexate and HIV protease. Finally, the entire BUILDER approach is tested by rebuilding methotrexate de novo.

Monte Carlo docking with ubiquitin

The development of general strategies for the performance of docking simulations is prerequisite to the exploitation of this powerful computational method. Comprehensive strategies can only be derived from docking experiences with a diverse array of biological systems, and we have chosen the ubiquitin/diubiquitin system as a learning tool for this process. Using our multiple-start Monte Carlo docking method, we have reconstructed the known structure of diubiquitin from its two halves as well as from two copies of the uncomplexed monomer. For both of these cases, our relatively simple potential function ranked the correct solution among the lowest energy configurations. In the experiments involving the ubiquitin monomer, various structural modifications were made to compensate for the lack of flexibility and for the lack of a covalent bond in the modeled interaction. Potentially flexible regions could be identified using available biochemical and structural information. A systematic conformational search ruled out the possibility that the required covalent bond could be formed in one family of low-energy configurations, which was distant from the observed dimer configuration. A variety of analyses was performed on the low-energy dockings obtained in the experiment involving structurally modified ubiquitin. Characterization of the size and chemical nature of the interface surfaces was a powerful adjunct to our potential function, enabling us to distinguish more accurately between correct and incorrect dockings. Calculations with the structure of tetraubiquitin indicated that the dimer configuration in this molecule is much less favorable than that observed in the diubiquitin structure, for a simple monomer-monomer pair. Based on the analysis of our results, we draw conclusions regarding some of the approximations involved in our simulations, the use of diverse chemical and biochemical information in experimental design and the analysis of docking results, as well as possible modifications to our docking protocol.

A geometry-based suite of molecular docking processes

We have developed a geometry-based suite of processes for molecular docking. The suite consists of a molecular surface representation, a docking algorithm, and a surface inter-penetration and contact filter. The surface representation is composed of a sparse set of critical points (with their associated normals) positioned at the face centers of the molecular surface, providing a concise yet representative set. The docking algorithm is based on the Geometric Hashing technique, which indexes the critical points with their normals in a transformation invariant fashion preserving the multi-element geometric constraints. The inter-penetration and surface contact filter features a three-layer scoring system, through which docked models with high contact area and low clashes are funneled. This suite of processes enables a pipelined operation of molecular docking with high efficacy. Accurate and fast docking has been achieved with a rich collection of complexes and unbound molecules, including protein-protein and protein-small molecule associations. An energy evaluation routine assesses the intermolecular interactions of the funneled models obtained from the docking of the bound molecules by pairwise van der Waals and Coulombic potentials. Applications of this routine demonstrate the goodness of the high scoring, geometrically docked conformations of the bound crystal complexes.

Flexible ligand docking using a genetic algorithm

Two computational techniques have been developed to explore the orientational and conformational space of a flexible ligand within an enzyme. Both methods use the Genetic Algorithm (GA) to generate conformationally flexible ligands in conjunction with algorithms from the DOCK suite of programs to characterize the receptor site. The methods are applied to three enzyme-ligand complexes: dihydrofolate reductase-methotrexate, thymidylate synthase-phenolpthalein and HIV protease-thioketal haloperidol. Conformations and orientations close to the crystallographically determined structures are obtained, as well as alternative structures with low energy. The potential for the GA method to screen a database of compounds is also examined. A collection of ligands is evaluated simultaneously, rather than docking the ligands individually into the enzyme.

Prediction of the binding sites of huperzine A in acetylcholinesterase by docking studies

We have performed docking studies with the SYSDOC program on acetylcholinesterase (AChE) to predict the binding sites in AChE of huperzine A (HA), which is a potent and selective, reversible inhibitor of AChE. The unique aspects of our docking studies include the following: (i) Molecular flexibility of the guest and the host is taken into account, which permits both to change their conformations upon binding. (ii) The binding energy is evaluated by a sum of energies of steric, electrostatic and hydrogen bonding interactions. In the energy calculation no grid approximation is used, and all hydrogen atoms of the system are treated explicitly. (iii) The energy of cation-pi interactions between the guest and the host, which is important in the binding of AChE, is included in the calculated binding energy. (iv) Docking is performed in all regions of the host's binding cavity. Based on our docking studies and the pharmacological results reported for HA and its analogs, we predict that HA binds to the bottom of the binding cavity of AChE (the gorge) with its ammonium group interacting with Trp84, Phe330, Glu199 and Asp72 (catalytic site) and to the opening of the gorge with its ammonium group partially interacting with Trp279 (peripheral site). At the catalytic site, three partially overlapping subsites of HA were identified which might provide a dynamic view of binding of HA to the catalytic site.

Cavities and packing at protein interfaces

An analysis of internal packing defects or "cavities" (both empty and water-containing) within protein structures has been undertaken and includes 3 cavity classes: within domains, between domains, and between protein subunits. We confirm several basic features common to all cavity types but also find a number of new characteristics, including those that distinguish the classes. The total cavity volume remains only a small fraction of the total protein volume and yet increases with protein size. Water-filled "cavities" possess a more polar surface and are typically larger. Their constituent waters are necessary to satisfy the local hydrogen bonding potential. Cavity-surrounding atoms are observed to be, on average, less flexible than their environments. Intersubunit and interdomain cavities are on average larger than the intradomain cavities, occupy a larger fraction of their resident surfaces, and are more frequently water-filled. We observe increased cavity volume at domain-domain interfaces involved with shear type domain motions. The significance of interfacial cavities upon subunit and domain shape complementarity and the protein docking problem, as well as in their structural and functional role in oligomeric proteins, will be discussed. The results concerning cavity size, polarity, solvation, general abundance, and residue type constituency should provide useful guidelines for protein modeling and design.