A combinatorial approach to protein docking with flexible side chains

BetaSCPWeb: side-chain prediction for protein structures using Voronoi diagrams and geometry prioritization

Many applications, such as protein design, homology modeling, flexible docking, etc. require the prediction of a protein's optimal side-chain conformations from just its amino acid sequence and backbone structure. Side-chain prediction (SCP) is an NP-hard energy minimization problem. Here, we present BetaSCPWeb which efficiently computes a conformation close to optimal using a geometry-prioritization method based on the Voronoi diagram of spherical atoms. Its outputs are visual, textual and PDB file format. The web server is free and open to all users at http://voronoi.hanyang.ac.kr/betascpweb with no login requirement.

Fast search algorithms for computational protein design

One of the main challenges in computational protein design (CPD) is the huge size of the protein sequence and conformational space that has to be computationally explored. Recently, we showed that state-of-the-art combinatorial optimization technologies based on Cost Function Network (CFN) processing allow speeding up provable rigid backbone protein design methods by several orders of magnitudes. Building up on this, we improved and injected CFN technology into the well-established CPD package Osprey to allow all Osprey CPD algorithms to benefit from associated speedups. Because Osprey fundamentally relies on the ability of A* to produce conformations in increasing order of energy, we defined new A* strategies combining CFN lower bounds, with new side-chain positioning-based branching scheme. Beyond the speedups obtained in the new A*-CFN combination, this novel branching scheme enables a much faster enumeration of suboptimal sequences, far beyond what is reachable without it. Together with the immediate and important speedups provided by CFN technology, these developments directly benefit to all the algorithms that previously relied on the DEE/ A* combination inside Osprey* and make it possible to solve larger CPD problems with provable algorithms.

Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics

Investigation of macromolecular structure and dynamics is fundamental to understanding how macromolecules carry out their functions in the cell. Significant advances have been made toward this end in silico, with a growing number of computational methods proposed yearly to study and simulate various aspects of macromolecular structure and dynamics. This review aims to provide an overview of recent advances, focusing primarily on methods proposed for exploring the structure space of macromolecules in isolation and in assemblies for the purpose of characterizing equilibrium structure and dynamics. In addition to surveying recent applications that showcase current capabilities of computational methods, this review highlights state-of-the-art algorithmic techniques proposed to overcome challenges posed in silico by the disparate spatial and time scales accessed by dynamic macromolecules. This review is not meant to be exhaustive, as such an endeavor is impossible, but rather aims to balance breadth and depth of strategies for modeling macromolecular structure and dynamics for a broad audience of novices and experts.

Fast gap-free enumeration of conformations and sequences for protein design

Despite significant successes in structure-based computational protein design in recent years, protein design algorithms must be improved to increase the biological accuracy of new designs. Protein design algorithms search through an exponential number of protein conformations, protein ensembles, and amino acid sequences in an attempt to find globally optimal structures with a desired biological function. To improve the biological accuracy of protein designs, it is necessary to increase both the amount of protein flexibility allowed during the search and the overall size of the design, while guaranteeing that the lowest-energy structures and sequences are found. DEE/A*-based algorithms are the most prevalent provable algorithms in the field of protein design and can provably enumerate a gap-free list of low-energy protein conformations, which is necessary for ensemble-based algorithms that predict protein binding. We present two classes of algorithmic improvements to the A* algorithm that greatly increase the efficiency of A*. First, we analyze the effect of ordering the expansion of mutable residue positions within the A* tree and present a dynamic residue ordering that reduces the number of A* nodes that must be visited during the search. Second, we propose new methods to improve the conformational bounds used to estimate the energies of partial conformations during the A* search. The residue ordering techniques and improved bounds can be combined for additional increases in A* efficiency. Our enhancements enable all A*-based methods to more fully search protein conformation space, which will ultimately improve the accuracy of complex biomedically relevant designs.

The impact of side-chain packing on protein docking refinement

We study the impact of optimizing the side-chain positions in the interface region between two proteins during the process of binding. Mathematically, the problem is similar to side-chain prediction, which has been extensively explored in the process of protein structure prediction. The protein-protein docking application, however, has a number of characteristics that necessitate different algorithmic and implementation choices. In this work, we implement a distributed approximate algorithm that can be implemented on multiprocessor architectures and enables a trade-off between accuracy and running speed. We report computational results on benchmarks of enzyme-inhibitor and other types of complexes, establishing that the side-chain flexibility our algorithm introduces substantially improves the performance of docking protocols. Furthermore, we establish that the inclusion of unbound side-chain conformers in the side-chain positioning problem is critical in these performance improvements. The code is available to the community under open source license.

An efficient parallel algorithm for accelerating computational protein design

Motivation: Structure-based computational protein design (SCPR) is an important topic in protein engineering. Under the assumption of a rigid backbone and a finite set of discrete conformations of side-chains, various methods have been proposed to address this problem. A popular method is to combine the dead-end elimination (DEE) and A* tree search algorithms, which provably finds the global minimum energy conformation (GMEC) solution.

Results: In this article, we improve the efficiency of computing A* heuristic functions for protein design and propose a variant of A* algorithm in which the search process can be performed on a single GPU in a massively parallel fashion. In addition, we make some efforts to address the memory exceeding problem in A* search. As a result, our enhancements can achieve a significant speedup of the A*-based protein design algorithm by four orders of magnitude on large-scale test data through pre-computation and parallelization, while still maintaining an acceptable memory overhead. We also show that our parallel A* search algorithm could be successfully combined with iMinDEE, a state-of-the-art DEE criterion, for rotamer pruning to further improve SCPR with the consideration of continuous side-chain flexibility.

Availability: Our software is available and distributed open-source under the GNU Lesser General License Version 2.1 (GNU, February 1999). The source code can be downloaded from http://www.cs.duke.edu/donaldlab/osprey.php or http://iiis.tsinghua.edu.cn/∼compbio/software.html.

Contact:zengjy321@tsinghua.edu.cn

Supplementary information:Supplementary data are available at Bioinformatics online.

Image Geo-Localization Based on Multiple Nearest Neighbor Feature Matching Using Generalized Graphs

In this paper, we present a new framework for geo-locating an image utilizing a novel multiple nearest neighbor feature matching method using Generalized Minimum Clique Graphs (GMCP). First, we extract local features (e.g., SIFT) from the query image and retrieve a number of nearest neighbors for each query feature from the reference data set. Next, we apply our GMCP-based feature matching to select a single nearest neighbor for each query feature such that all matches are globally consistent. Our approach to feature matching is based on the proposition that the first nearest neighbors are not necessarily the best choices for finding correspondences in image matching. Therefore, the proposed method considers multiple reference nearest neighbors as potential matches and selects the correct ones by enforcing consistency among their global features (e.g., GIST) using GMCP. In this context, we argue that using a robust distance function for finding the similarity between the global features is essential for the cases where the query matches multiple reference images with dissimilar global features. Towards this end, we propose a robust distance function based on the Gaussian Radial Basis Function (G-RBF). We evaluated the proposed framework on a new data set of 102k street view images; the experiments show it outperforms the state of the art by 10 percent.

Protein flexibility in virtual screening: the BACE-1 case study

Simulating protein flexibility is a major issue in the docking-based drug-design process for which a single methodological solution does not exist. In our search of new anti-Alzheimer ligands, we were faced with the challenge of including receptor plasticity in a virtual screening campaign aimed at finding new β-secretase inhibitors. To this aim, we incorporated protein flexibility in our simulations by using an ensemble of static X-ray enzyme structures to screen the National Cancer Institute database. A unified description of the protein motion was also generated by computing and combining a set of grid maps using an energy weighting scheme. Such a description was used in an energy-weighted virtual screening experiment on the same molecular database. Assessment of the enrichment factors from these two virtual screening approaches demonstrated comparable predictive powers, with the energy-weighted method being faster than the ensemble method. The in vitro evaluation demonstrated that out of the 32 tested ligands, 17 featured the predicted enzyme inhibiting property. Such an impressive success rate (53.1%) demonstrates the enhanced power of the two methodologies and suggests that energy-weighted virtual screening is a more than valid alternative to ensemble virtual screening given its reduced computational demands and comparable performance.

Computational design of a PDZ domain peptide inhibitor that rescues CFTR activity

The cystic fibrosis transmembrane conductance regulator (CFTR) is an epithelial chloride channel mutated in patients with cystic fibrosis (CF). The most prevalent CFTR mutation, ΔF508, blocks folding in the endoplasmic reticulum. Recent work has shown that some ΔF508-CFTR channel activity can be recovered by pharmaceutical modulators (“potentiators” and “correctors”), but ΔF508-CFTR can still be rapidly degraded via a lysosomal pathway involving the CFTR-associated ligand (CAL), which binds CFTR via a PDZ interaction domain. We present a study that goes from theory, to new structure-based computational design algorithms, to computational predictions, to biochemical testing and ultimately to epithelial-cell validation of novel, effective CAL PDZ inhibitors (called “stabilizers”) that rescue ΔF508-CFTR activity. To design the “stabilizers”, we extended our structural ensemble-based computational protein redesign algorithm to encompass protein-protein and protein-peptide interactions. The computational predictions achieved high accuracy: all of the top-predicted peptide inhibitors bound well to CAL. Furthermore, when compared to state-of-the-art CAL inhibitors, our design methodology achieved higher affinity and increased binding efficiency. The designed inhibitor with the highest affinity for CAL (kCAL01) binds six-fold more tightly than the previous best hexamer (iCAL35), and 170-fold more tightly than the CFTR C-terminus. We show that kCAL01 has physiological activity and can rescue chloride efflux in CF patient-derived airway epithelial cells. Since stabilizers address a different cellular CF defect from potentiators and correctors, our inhibitors provide an additional therapeutic pathway that can be used in conjunction with current methods.

Cystic fibrosis (CF) is an inherited disease that causes the body to produce thick mucus that clogs the lungs and obstructs the breakdown and absorption of food. The cystic fibrosis transmembrane conductance regulator (CFTR) is mutated in CF patients, and the most common mutation causes three defects in CFTR: misfolding, decreased function, and rapid degradation. Drugs are currently being studied to correct the first two CFTR defects, but the problem of rapid degradation remains. Recently, key protein-protein interactions have been discovered that implicate the protein CAL in CFTR degradation. Here we have developed new computational protein design algorithms and used them to successfully predict peptide inhibitors of the CAL-CFTR interface. Our algorithm uses a structural ensemble-based evaluation of protein sequences and conformations to calculate accurate predictions of protein-peptide binding affinities. The algorithm is general and can be applied to a wide variety of protein-protein interface designs. All of our designed inhibitors bound CAL with high affinity. We tested our top binding peptide and observed that the inhibitor could successfully rescue CFTR function in CF patient-derived epithelial cells. Our designed inhibitors provide a novel therapeutic path which could be used in combination with existing CF therapeutics for additive benefit.

Predicting protein ligand binding motions with the conformation explorer

BACKGROUND

Knowledge of the structure of proteins bound to known or potential ligands is crucial for biological understanding and drug design. Often the 3D structure of the protein is available in some conformation, but binding the ligand of interest may involve a large scale conformational change which is difficult to predict with existing methods.

RESULTS

We describe how to generate ligand binding conformations of proteins that move by hinge bending, the largest class of motions. First, we predict the location of the hinge between domains. Second, we apply an Euler rotation to one of the domains about the hinge point. Third, we compute a short-time dynamical trajectory using Molecular Dynamics to equilibrate the protein and ligand and correct unnatural atomic positions. Fourth, we score the generated structures using a novel fitness function which favors closed or holo structures. By iterating the second through fourth steps we systematically minimize the fitness function, thus predicting the conformational change required for small ligand binding for five well studied proteins.

CONCLUSIONS

We demonstrate that the method in most cases successfully predicts the holo conformation given only an apo structure.

Automated bond order assignment as an optimization problem

MOTIVATION

Numerous applications in Computational Biology process molecular structures and hence strongly rely not only on correct atomic coordinates but also on correct bond order information. For proteins and nucleic acids, bond orders can be easily deduced but this does not hold for other types of molecules like ligands. For ligands, bond order information is not always provided in molecular databases and thus a variety of approaches tackling this problem have been developed. In this work, we extend an ansatz proposed by Wang et al. that assigns connectivity-based penalty scores and tries to heuristically approximate its optimum. In this work, we present three efficient and exact solvers for the problem replacing the heuristic approximation scheme of the original approach: an A*, an ILP and an fixed-parameter approach (FPT) approach.

RESULTS

We implemented and evaluated the original implementation, our A*, ILP and FPT formulation on the MMFF94 validation suite and the KEGG Drug database. We show the benefit of computing exact solutions of the penalty minimization problem and the additional gain when computing all optimal (or even suboptimal) solutions. We close with a detailed comparison of our methods.

AVAILABILITY

The A* and ILP solution are integrated into the open-source C++ LGPL library BALL and the molecular visualization and modelling tool BALLView and can be downloaded from our homepage www.ball-project.org. The FPT implementation can be downloaded from http://bio.informatik.uni-jena.de/software/.

Mining flexible-receptor docking experiments to select promising protein receptor snapshots

Background

Molecular docking simulation is the Rational Drug Design (RDD) step that investigates the affinity between protein receptors and ligands. Typically, molecular docking algorithms consider receptors as rigid bodies. Receptors are, however, intrinsically flexible in the cellular environment. The use of a time series of receptor conformations is an approach to explore its flexibility in molecular docking computer simulations, but it is extensively time-consuming. Hence, selection of the most promising conformations can accelerate docking experiments and, consequently, the RDD efforts.

Results

We previously docked four ligands (NADH, TCL, PIF and ETH) to 3,100 conformations of the InhA receptor from M. tuberculosis. Based on the receptor residues-ligand distances we preprocessed all docking results to generate appropriate input to mine data. Data preprocessing was done by calculating the shortest interatomic distances between the ligand and the receptor’s residues for each docking result. They were the predictive attributes. The target attribute was the estimated free-energy of binding (FEB) value calculated by the AutodDock3.0.5 software. The mining inputs were submitted to the M5P model tree algorithm. It resulted in short and understandable trees. On the basis of the correlation values, for NADH, TCL and PIF we obtained more than 95% correlation while for ETH, only about 60%. Post processing the generated model trees for each of its linear models (LMs), we calculated the average FEB for their associated instances. From these values we considered a LM as representative if its average FEB was smaller than or equal the average FEB of the test set. The instances in the selected LMs were considered the most promising snapshots. It totalized 1,521, 1,780, 2,085 and 902 snapshots, for NADH, TCL, PIF and ETH respectively.

Conclusions

By post processing the generated model trees we were able to propose a criterion of selection of linear models which, in turn, is capable of selecting a set of promising receptor conformations. As future work we intend to go further and use these results to elaborate a strategy to preprocess the receptors 3-D spatial conformation in order to predict FEB values. Besides, we intend to select other compounds, among the million catalogued, that may be promising as new drug candidates for our particular protein receptor target.

Optimization techniques in molecular structure and function elucidation

This paper discusses recent optimization approaches to the protein side-chain prediction problem, protein structural alignment, and molecular structure determination from X-ray diffraction measurements. The machinery employed to solve these problems has included algorithms from linear programming, dynamic programming, combinatorial optimization, and mixed-integer nonlinear programming. Many of these problems are purely continuous in nature. Yet, to this date, they have been approached mostly via combinatorial optimization algorithms that are applied to discrete approximations. The main purpose of the paper is to offer an introduction and motivate further systems approaches to these problems.

Rotamer optimization for protein design through MAP estimation and problem-size reduction

The search for the global minimum energy conformation (GMEC) of protein side chains is an important computational challenge in protein structure prediction and design. Using rotamer models, the problem is formulated as a NP-hard optimization problem. Dead-end elimination (DEE) methods combined with systematic A* search (DEE/A*) has proven useful, but may not be strong enough as we attempt to solve protein design problems where a large number of similar rotamers is eligible and the network of interactions between residues is dense. In this work, we present an exact solution method, named BroMAP (branch-and-bound rotamer optimization using MAP estimation), for such protein design problems. The design goal of BroMAP is to be able to expand smaller search trees than conventional branch-and-bound methods while performing only a moderate amount of computation in each node, thereby reducing the total running time. To achieve that, BroMAP attempts reduction of the problem size within each node through DEE and elimination by lower bounds from approximate maximum-a-posteriori (MAP) estimation. The lower bounds are also exploited in branching and subproblem selection for fast discovery of strong upper bounds. Our computational results show that BroMAP tends to be faster than DEE/A* for large protein design cases. BroMAP also solved cases that were not solved by DEE/A* within the maximum allowed time, and did not incur significant disadvantage for cases where DEE/A* performed well. Therefore, BroMAP is particularly applicable to large protein design problems where DEE/A* struggles and can also substitute for DEE/A* in general GMEC search.

Molecular docking screens using comparative models of proteins

Two orders of magnitude more protein sequences can be modeled by comparative modeling than have been determined by X-ray crystallography and NMR spectroscopy. Investigators have nevertheless been cautious about using comparative models for ligand discovery because of concerns about model errors. We suggest how to exploit comparative models for molecular screens, based on docking against a wide range of crystallographic structures and comparative models with known ligands. To account for the variation in the ligand-binding pocket as it binds different ligands, we calculate "consensus" enrichment by ranking each library compound by its best docking score against all available comparative models and/or modeling templates. For the majority of the targets, the consensus enrichment for multiple models was better than or comparable to that of the holo and apo X-ray structures. Even for single models, the models are significantly more enriching than the template structure if the template is paralogous and shares more than 25% sequence identity with the target.

Principles of flexible protein-protein docking

Treating flexibility in molecular docking is a major challenge in cell biology research. Here we describe the background and the principles of existing flexible protein-protein docking methods, focusing on the algorithms and their rational. We describe how protein flexibility is treated in different stages of the docking process: in the preprocessing stage, rigid and flexible parts are identified and their possible conformations are modeled. This preprocessing provides information for the subsequent docking and refinement stages. In the docking stage, an ensemble of pre-generated conformations or the identified rigid domains may be docked separately. In the refinement stage, small-scale movements of the backbone and side-chains are modeled and the binding orientation is improved by rigid-body adjustments. For clarity of presentation, we divide the different methods into categories. This should allow the reader to focus on the most suitable method for a particular docking problem.

Volume-based solvation models out-perform area-based models in combined studies of wild-type and mutated protein-protein interfaces

BACKGROUND

Empirical binding models have previously been investigated for the energetics of protein complexation (DeltaG models) and for the influence of mutations on complexation (i.e. differences between wild-type and mutant complexes, DeltaDeltaG models). We construct binding models to directly compare these processes, which have generally been studied separately.

RESULTS

Although reasonable fit models were found for both DeltaG and DeltaDeltaG cases, they differ substantially. In a dataset curated for the absence of mainchain rearrangement upon binding, non-polar area burial is a major determinant of DeltaG models. However this DeltaG model does not fit well to the data for binding differences upon mutation. Burial of non-polar area is weighted down in fitting of DeltaDeltaG models. These calculations were made with no repacking of sidechains upon complexation, and only minimal packing upon mutation. We investigated the consequences of more extensive packing changes with a modified mean-field packing scheme. Rather than emphasising solvent exposure with relatively extended sidechains, rotamers are selected that exhibit maximal packing with protein. This provides solvent accessible areas for proteins that are much closer to those of experimental structures than the more extended sidechain regime. The new packing scheme increases changes in non-polar burial for mutants compared to wild-type proteins, but does not substantially improve agreement between DeltaG and DeltaDeltaG binding models.

CONCLUSION

We conclude that solvent accessible area, based on modelled mutant structures, is a poor correlate for DeltaDeltaG upon mutation. A simple volume-based, rather than solvent accessibility-based, model is constructed for DeltaG and DeltaDeltaG systems. This shows a more consistent behaviour. We discuss the efficacy of volume, as opposed to area, approaches to describe the energetic consequences of mutations at interfaces. This knowledge can be used to develop simple computational screens for binding in comparative modelled interfaces.

Optimal drug cocktail design: methods for targeting molecular ensembles and insights from theoretical model systems

Drug resistance is a significant obstacle in the effective treatment of diseases with rapidly mutating targets, such as AIDS, malaria, and certain forms of cancer. Such targets are remarkably efficient at exploring the space of functional mutants and at evolving to evade drug binding while still maintaining their biological role. To overcome this challenge, drug regimens must be active against potential target variants. Such a goal may be accomplished by one drug molecule that recognizes multiple variants or by a drug "cocktail"--a small collection of drug molecules that collectively binds all desired variants. Ideally, one wants the smallest cocktail possible due to the potential for increased toxicity with each additional drug. Therefore, the task of designing a regimen for multiple target variants can be framed as an optimization problem--find the smallest collection of molecules that together "covers" the relevant target variants. In this work, we formulate and apply this optimization framework to theoretical model target ensembles. These results are analyzed to develop an understanding of how the physical properties of a target ensemble relate to the properties of the optimal cocktail. We focus on electrostatic variation within target ensembles, as it is one important mechanism by which drug resistance is achieved. Using integer programming, we systematically designed optimal cocktails to cover model target ensembles. We found that certain drug molecules covered much larger regions of target space than others, a phenomenon explained by theory grounded in continuum electrostatics. Molecules within optimal cocktails were often dissimilar, such that each drug was responsible for binding variants with a certain electrostatic property in common. On average, the number of molecules in the optimal cocktails correlated with the number of variants, the differences in the variants' electrostatic properties at the binding interface, and the level of binding affinity required. We also treated cases in which a subset of target variants was to be avoided, modeling the common challenge of closely related host molecules that may be implicated in drug toxicity. Such decoys generally increased the size of the required cocktail and more often resulted in infeasible optimizations. Taken together, this work provides practical optimization methods for the design of drug cocktails and a theoretical, physics-based framework through which useful insights can be achieved.

FireDock: a web server for fast interaction refinement in molecular docking

Structural details of protein–protein interactions are invaluable for understanding and deciphering biological mechanisms. Computational docking methods aim to predict the structure of a protein–protein complex given the structures of its single components. Protein flexibility and the absence of robust scoring functions pose a great challenge in the docking field. Due to these difficulties most of the docking methods involve a two-tier approach: coarse global search for feasible orientations that treats proteins as rigid bodies, followed by an accurate refinement stage that aims to introduce flexibility into the process. The FireDock web server, presented here, is the first web server for flexible refinement and scoring of protein–protein docking solutions. It includes optimization of side-chain conformations and rigid-body orientation and allows a high-throughput refinement. The server provides a user-friendly interface and a 3D visualization of the results. A docking protocol consisting of a global search by PatchDock and a refinement by FireDock was extensively tested. The protocol was successful in refining and scoring docking solution candidates for cases taken from docking benchmarks. We provide an option for using this protocol by automatic redirection of PatchDock candidate solutions to the FireDock web server for refinement. The FireDock web server is available at http://bioinfo3d.cs.tau.ac.il/FireDock/.

FireDock: fast interaction refinement in molecular docking

Here, we present FireDock, an efficient method for the refinement and rescoring of rigid-body docking solutions. The refinement process consists of two main steps: (1) rearrangement of the interface side-chains and (2) adjustment of the relative orientation of the molecules. Our method accounts for the observation that most interface residues that are important in recognition and binding do not change their conformation significantly upon complexation. Allowing full side-chain flexibility, a common procedure in refinement methods, often causes excessive conformational changes. These changes may distort preformed structural signatures, which have been shown to be important for binding recognition. Here, we restrict side-chain movements, and thus manage to reduce the false-positive rate noticeably. In the later stages of our procedure (orientation adjustments and scoring), we smooth the atomic radii. This allows for the minor backbone and side-chain movements and increases the sensitivity of our algorithm. FireDock succeeds in ranking a near-native structure within the top 15 predictions for 83% of the 30 enzyme-inhibitor test cases, and for 78% of the 18 semiunbound antibody-antigen complexes. Our refinement procedure significantly improves the ranking of the rigid-body PatchDock algorithm for these cases. The FireDock program is fully automated. In particular, to our knowledge, FireDock's prediction results are comparable to current state-of-the-art refinement methods while its running time is significantly lower. The method is available at http://bioinfo3d.cs.tau.ac.il/FireDock/.

Complex-type-dependent scoring functions in protein–protein docking

A major challenge in the field of protein-protein docking is to discriminate between the many wrong and few near-native conformations, i.e. scoring. Here, we introduce combinatorial complex-type-dependent scoring functions for different types of protein-protein complexes, protease/inhibitor, antibody/antigen, enzyme/inhibitor and others. The scoring functions incorporate both physical and knowledge-based potentials, i.e. atomic contact energy (ACE), the residue pair potential (RP), electrostatic and van der Waals' interactions. For different type complexes, the weights of the scoring functions were optimized by the multiple linear regression method, in which only top 300 structures with ligand root mean square deviation (L_RMSD) less than 20 A from the bound (co-crystallized) docking of 57 complexes were used to construct a training set. We employed the bound docking studies to examine the quality of the scoring function, and also extend to the unbound (separately crystallized) docking studies and extra 8 protein-protein complexes. In bound docking of the 57 cases, the first hits of protease/inhibitor cases are all ranked in the top 5. For the cases of antibody/antigen, enzyme/inhibitor and others, there are 17/19, 5/6 and 13/15 cases with the first hits ranked in the top 10, respectively. In unbound docking studies, the first hits of 9/17 protease/inhibitor, 6/19 antibody/antigen, 1/6 enzyme/inhibitor and 6/15 others' complexes are ranked in the top 10. Additionally, for the extra 8 cases, the first hits of the two protease/inhibitor cases are ranked in the top for the bound and unbound test. For the two enzyme/inhibitor cases, the first hits are ranked 1st for bound test, and the 119th and 17th for the unbound test. For the others, the ranks of the first hits are the 1st for the bound test and the 12th for the 1WQ1 unbound test. To some extent, the results validated our divide-and-conquer strategy in the docking study, which might hopefully shed light on the prediction of protein-protein interactions.

Residue-rotamer-reduction algorithm for the protein side-chain conformation problem

MOTIVATION

The protein side-chain conformation problem is a central problem in proteomics with wide applications in protein structure prediction and design. Computational complexity results show that the problem is hard to solve. Yet, instances from realistic applications are large and demand fast and reliable algorithms.

RESULTS

We propose a new global optimization algorithm, which for the first time integrates residue reduction and rotamer reduction techniques previously developed for the protein side-chain conformation problem. We show that the proposed approach simplifies dramatically the topology of the underlining residue graph. Computations show that our algorithm solves problems using only 1-10% of the time required by the mixed-integer linear programming approach available in the literature. In addition, on a set of hard side-chain conformation problems, our algorithm runs 2-78 times faster than SCWRL 3.0, which is widely used for solving these problems.

AVAILABILITY

The implementation is available as an online server at http://eudoxus.scs.uiuc.edu/r3.html

PatchDock and SymmDock: servers for rigid and symmetric docking

Here, we describe two freely available web servers for molecular docking. The PatchDock method performs structure prediction of protein–protein and protein–small molecule complexes. The SymmDock method predicts the structure of a homomultimer with cyclic symmetry given the structure of the monomeric unit. The inputs to the servers are either protein PDB codes or uploaded protein structures. The services are available at . The methods behind the servers are very efficient, allowing large-scale docking experiments.

Modeling correlated main-chain motions in proteins for flexible molecular recognition

We describe a new method for modeling protein and ligand main-chain flexibility, and show its ability to model flexible molecular recognition. The goal is to sample the full conformational space, including large-scale motions that typically cannot be reached in molecular dynamics simulations due to the computational intensity, as well as conformations that have not been observed yet by crystallography or NMR. A secondary goal is to assess the degree of flexibility consistent with protein-ligand recognition. Flexibility analysis of the target protein is performed using the graph-theoretic algorithm FIRST, which also identifies coupled networks of covalent and noncovalent bonds within the protein. The available conformations of the flexible regions are then explored with ROCK by random-walk sampling of the rotatable bonds. ROCK explores correlated motions by only sampling dihedral angles that preserve the coupled bond networks in the protein and generates conformers with good stereochemistry, without using a computationally expensive potential function. A representative set of the conformational ensemble generated this way can be used as targets for docking with SLIDE, which handles the flexibility of protein and ligand side-chains. The realism of this protein main-chain conformational sampling is assessed by comparison with time-resolved NMR studies of cyclophilin A motions. ROCK is also effective for modeling the flexibility of large cyclic and polycyclic ligands, as demonstrated for cyclosporin and zearalenol. The use of this combined approach to perform docking with main-chain flexibility is illustrated for the cyclophilin A-cyclosporin complex and the estrogen receptor in complex with zearalenol, while addressing the question of how much flexibility is allowed without hindering molecular recognition.