Scoring a diverse set of high-quality docked conformations: a metascore based on electrostatic and desolvation interactions

Predicting protein-protein interactions involves sampling and scoring docked conformations. Barring some large structural rearrangement, rapidly sampling the space of docked conformations is now a real possibility, and the limiting step for the successful prediction of protein interactions is the scoring function used to reduce the space of conformations from billions to a few, and eventually one high affinity complex. An atomic level free-energy scoring function that estimates in units of kcal/mol both electrostatic and desolvation interactions (plus van der Waals if appropriate) of protein-protein docked conformations is used to rerank the blind predictions (860 in total) submitted for six targets to the community-wide Critical Assessment of PRediction of Interactions (CAPRI; http://capri.ebi.ac.uk). We found that native-like models often have varying intermolecular contacts and atom clashes, making unlikely that one can construct a universal function that would rank all these models as native-like. Nevertheless, our scoring function is able to consistently identify the native-like complexes as those with the lowest free energy for the individual models of 16 (out of 17) human predictors for five of the targets, while at the same time the modelers failed to do so in more than half of the cases. The scoring of high-quality models developed by a wide variety of methods and force fields confirms that electrostatic and desolvation forces are the dominant interactions determining the bound structure. The CAPRI experiment has shown that modelers can predict valuable models of protein-protein complexes, and improvements in scoring functions should soon solve the docking problem for complexes whose backbones do not change much upon binding. A scoring server and programs are available at http://structure.pitt.edu.     

Improved protein structure selection using decoy-dependent discriminatory functions

Background  

A key component in protein structure prediction is a scoring or discriminatory function that can distinguish near-native conformations from misfolded ones. Various types of scoring functions have been developed to accomplish this goal, but their performance is not adequate to solve the structure selection problem. In addition, there is poor correlation between the scores and the accuracy of the generated conformations.     

An effective docking strategy for virtual screening based on multi-objective optimization algorithm

Background  

Development of a fast and accurate scoring function in virtual screening remains a hot issue in current computer-aided drug research. Different scoring functions focus on diverse aspects of ligand binding, and no single scoring can satisfy the peculiarities of each target system. Therefore, the idea of a consensus score strategy was put forward. Integrating several scoring functions, consensus score re-assesses the docked conformations using a primary scoring function. However, it is not really robust and efficient from the perspective of optimization. Furthermore, to date, the majority of available methods are still based on single objective optimization design.     

A collaborative filtering approach for protein-protein docking scoring functions

A protein-protein docking procedure traditionally consists in two successive tasks: a search algorithm generates a large number of candidate conformations mimicking the complex existing in vivo between two proteins, and a scoring function is used to rank them in order to extract a native-like one. We have already shown that using Voronoi constructions and a well chosen set of parameters, an accurate scoring function could be designed and optimized. However to be able to perform large-scale in silico exploration of the interactome, a near-native solution has to be found in the ten best-ranked solutions. This cannot yet be guaranteed by any of the existing scoring functions. In this work, we introduce a new procedure for conformation ranking. We previously developed a set of scoring functions where learning was performed using a genetic algorithm. These functions were used to assign a rank to each possible conformation. We now have a refined rank using different classifiers (decision trees, rules and support vector machines) in a collaborative filtering scheme. The scoring function newly obtained is evaluated using 10 fold cross-validation, and compared to the functions obtained using either genetic algorithms or collaborative filtering taken separately. This new approach was successfully applied to the CAPRI scoring ensembles. We show that for 10 targets out of 12, we are able to find a near-native conformation in the 10 best ranked solutions. Moreover, for 6 of them, the near-native conformation selected is of high accuracy. Finally, we show that this function dramatically enriches the 100 best-ranking conformations in near-native structures.     

Docking and scoring with alternative side-chain conformations

We describe a scoring and modeling procedure for docking ligands into protein models that have either modeled or flexible side-chain conformations. Our methodical contribution comprises a procedure for generating new potentials of mean force for the ROTA scoring function which we have introduced previously for optimizing side-chain conformations with the tool IRECS. The ROTA potentials are specially trained to tolerate small-scale positional errors of atoms that are characteristic of (i) side-chain conformations that are modeled using a sparse rotamer library and (ii) ligand conformations that are generated using a docking program. We generated both rigid and flexible protein models with our side-chain prediction tool IRECS and docked ligands to proteins using the scoring function ROTA and the docking programs FlexX (for rigid side chains) and FlexE (for flexible side chains). We validated our approach on the forty screening targets of the DUD database. The validation shows that the ROTA potentials are especially well suited for estimating the binding affinity of ligands to proteins. The results also show that our procedure can compensate for the performance decrease in screening that occurs when using protein models with side chains modeled with a rotamer library instead of using X-ray structures. The average runtime per ligand of our method is 168 seconds on an Opteron V20z, which is fast enough to allow virtual screening of compound libraries for drug candidates.     

Amino acid network and its scoring application in protein-protein docking

Protein-protein complex, composed of hydrophobic and hydrophilic residues, can be divided into hydrophobic and hydrophilic amino acid network structures respectively. In this paper, we are interested in analyzing these two different types of networks and find that these networks are of small-world properties. Due to the characteristic complementarity of the complex interfaces, protein-protein docking can be viewed as a particular network rewiring. These networks of correct docked complex conformations have much more increase of the degree values and decay of the clustering coefficients than those of the incorrect ones. Therefore, two scoring terms based on the network parameters are proposed, in which the geometric complementarity, hydrophobic-hydrophobic and polar-polar interactions are taken into account. Compared with a two-term energy function, a simple scoring function HPNet which includes the two network-based scoring terms shows advantages in two aspects, not relying on energy considerations and better discrimination. Furthermore, combing the network-based scoring terms with some other energy terms, a new multi-term scoring function HPNet-combine can also make some improvements to the scoring function of RosettaDock.     

A statistical rescoring scheme for protein-ligand docking: Consideration of entropic effect

Computational prediction of protein-ligand binding modes provides useful information on the relationship between structure and activity needed for drug design. A statistical rescoring method that incorporates entropic effect is proposed to improve the accuracy of binding mode prediction. A probability function for two sampled conformations to belong to the same broad basin in the potential energy surface is introduced to estimate the contribution of the state represented by a sampled conformation to the configurational integral. The rescoring function is reduced to the colony energy introduced by Xiang et al. (Proc Natl Acad Sci USA 2002;99:7432-7437) when a particular functional form for the probability function is used. The scheme is applied to rescore protein-ligand complex conformations generated by AutoDock. It is demonstrated that this simple rescoring improves prediction accuracy substantially when tested on 163 protein-ligand complexes with known experimental structures. For example, the percentage of complexes for which predicted ligand conformations are within 1 A root-mean-square deviation from the native conformations is doubled from about 20% to more than 40%. Rescoring with 11 different scoring functions including AutoDock scoring functions were also tested using the ensemble of conformations generated by Wang et al. (J Med Chem 2003;46:2287-2303). Comparison with other methods that use clustering and estimation of conformational entropy is provided. Examination of the docked poses reveals that the rescoring corrects the predictions in which ligands are tightly fit into the binding pockets and have low energies, but have too little room for conformational freedom and thus have low entropy.     

Protein-protein docking with multiple residue conformations and residue substitutions

The protein docking problem has two major aspects: sampling conformations and orientations, and scoring them for fit. To investigate the extent to which the protein docking problem may be attributed to the sampling of ligand side‐chain conformations, multiple conformations of multiple residues were calculated for the uncomplexed (unbound) structures of protein ligands. These ligand conformations were docked into both the complexed (bound) and unbound conformations of the cognate receptors, and their energies were evaluated using an atomistic potential function. The following questions were considered: (1) does the ensemble of precalculated ligand conformations contain a structure similar to the bound form of the ligand? (2) Can the large number of conformations that are calculated be efficiently docked into the receptors? (3) Can near‐native complexes be distinguished from non‐native complexes? Results from seven test systems suggest that the precalculated ensembles do include side‐chain conformations similar to those adopted in the experimental complexes. By assuming additivity among the side chains, the ensemble can be docked in less than 12 h on a desktop computer. These multiconformer dockings produce near‐native complexes and also non‐native complexes. When docked against the bound conformations of the receptors, the near‐native complexes of the unbound ligand were always distinguishable from the non‐native complexes. When docked against the unbound conformations of the receptors, the near‐native dockings could usually, but not always, be distinguished from the non‐native complexes. In every case, docking the unbound ligands with flexible side chains led to better energies and a better distinction between near‐native and non‐native fits. An extension of this algorithm allowed for docking multiple residue substitutions (mutants) in addition to multiple conformations. The rankings of the docked mutant proteins correlated with experimental binding affinities. These results suggest that sampling multiple residue conformations and residue substitutions of the unbound ligand contributes to, but does not fully provide, a solution to the protein docking problem. Conformational sampling allows a classical atomistic scoring function to be used; such a function may contribute to better selectivity between near‐native and non‐native complexes. Allowing for receptor flexibility may further extend these results.     

Design of an optimal Chebyshev-expanded discrimination function for globular proteins

We describe the construction of a scoring function designed to model the free energy of protein folding. An optimization technique is used to determine the best functional forms of the hydrophobic, residue-residue and hydrogen-bonding components of the potential. The scoring function is expanded by use of Chebyshev polynomials, the coefficients of which are determined by minimizing the score, in units of standard deviation, of native structures in the ensembles of alternate decoy conformations. The derived effective potential is then tested on decoy sets used conventionally in such studies. Using our scoring function, we achieve a high level of discrimination between correct and incorrect folds. In addition, our method is able to represent functions of arbitrary shape with fewer parameters than the usual histogram potentials of similar resolution. Finally, our representation can be combined easily with many optimization methods, because the total energy is a linear function of the parameters. Our results show that the techniques of Z-score optimization and Chebyshev expansion work well.     

Distance geometry generates native-like folds for small helical proteins using the consensus distances of predicted protein structures.

For successful ab initio protein structure prediction, a method is needed to identify native-like structures from a set containing both native and non-native protein-like conformations. In this regard, the use of distance geometry has shown promise when accurate inter-residue distances are available. We describe a method by which distance geometry restraints are culled from sets of 500 protein-like conformations for four small helical proteins generated by the method of Simons et al. (1997). A consensus-based approach was applied in which every inter-Calpha distance was measured, and the most frequently occurring distances were used as input restraints for distance geometry. For each protein, a structure with lower coordinate root-mean-square (RMS) error than the mean of the original set was constructed; in three cases the topology of the fold resembled that of the native protein. When the fold sets were filtered for the best scoring conformations with respect to an all-atom knowledge-based scoring function, the remaining subset of 50 structures yielded restraints of higher accuracy. A second round of distance geometry using these restraints resulted in an average coordinate RMS error of 4.38 A.     

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.     

Combination of scoring functions improves discrimination in protein-protein docking

Two structure-based potentials are used for both filtering (i.e., selecting a subset of conformations generated by rigid-body docking), and rescoring and ranking the selected conformations. ACP (atomic contact potential) is an atom-level extension of the Miyazawa-Jernigan potential parameterized on protein structures, whereas RPScore (residue pair potential score) is a residue-level potential, based on interactions in protein-protein complexes. These potentials are combined with other energy terms and applied to 13 sets of protein decoys, as well as to the results of docking 10 pairs of unbound proteins. For both potentials, the ability to discriminate between near-native and non-native docked structures is substantially improved by refining the structures and by adding a van der Waals energy term. It is observed that ACP and RPScore complement each other in a number of ways (e.g., although RPScore yields more hits than ACP, mainly as a result of its better performance for charged complexes, ACP usually ranks the near-native complexes better). As a general solution to the protein-docking problem, we have found that the best discrimination strategies combine either an RPScore filter with an ACP-based scoring function, or an ACP-based filter with an RPScore-based scoring function. Thus, ACP and RPScore capture complementary structural information, and combining them in a multistage postprocessing protocol provides substantially better discrimination than the use of the same potential for both filtering and ranking the docked conformations.     

Protein docking by Rotation-Based Uniform Sampling (RotBUS) with fast computing of intermolecular contact distance and residue desolvation

Background  

Protein-protein interactions are fundamental for the majority of cellular processes and their study is of enormous biotechnological and therapeutic interest. In recent years, a variety of computational approaches to the protein-protein docking problem have been reported, with encouraging results. Most of the currently available protein-protein docking algorithms are composed of two clearly defined parts: the sampling of the rotational and translational space of the interacting molecules, and the scoring and clustering of the resulting orientations. Although this kind of strategy has shown some of the most successful results in the CAPRI blind test , more efforts need to be applied. Thus, the sampling protocol should generate a pool of conformations that include a sufficient number of near-native ones, while the scoring function should discriminate between near-native and non-near-native proposed conformations. On the other hand, protocols to efficiently include full flexibility on the protein structures are increasingly needed.     

DockRank: Ranking docked conformations using partner‐specific sequence homology‐based protein interface prediction

Selecting near‐native conformations from the immense number of conformations generated by docking programs remains a major challenge in molecular docking. We introduce DockRank, a novel approach to scoring docked conformations based on the degree to which the interface residues of the docked conformation match a set of predicted interface residues. DockRank uses interface residues predicted by partner‐specific sequence homology‐based protein–protein interface predictor (PS‐HomPPI), which predicts the interface residues of a query protein with a specific interaction partner. We compared the performance of DockRank with several state‐of‐the‐art docking scoring functions using Success Rate (the percentage of cases that have at least one near‐native conformation among the top m conformations) and Hit Rate (the percentage of near‐native conformations that are included among the top m conformations). In cases where it is possible to obtain partner‐specific (PS) interface predictions from PS‐HomPPI, DockRank consistently outperforms both (i) ZRank and IRAD, two state‐of‐the‐art energy‐based scoring functions (improving Success Rate by up to 4‐fold); and (ii) Variants of DockRank that use predicted interface residues obtained from several protein interface predictors that do not take into account the binding partner in making interface predictions (improving success rate by up to 39‐fold). The latter result underscores the importance of using partner‐specific interface residues in scoring docked conformations. We show that DockRank, when used to re‐rank the conformations returned by ClusPro, improves upon the original ClusPro rankings in terms of both Success Rate and Hit Rate. DockRank is available as a server at http://einstein.cs.iastate.edu/DockRank/ . Proteins 2014; 82:250–267. © 2013 Wiley Periodicals, Inc.     

Discrimination of native loop conformations in membrane proteins: decoy library design and evaluation of effective energy scoring functions

The recent determination of crystal structures for several important membrane proteins opens the way for comparative modeling of their membrane-spanning regions. However, the ability to predict correctly the structures of loop regions, which may be critical, for example, in ligand binding, remains a considerable challenge. To meet this challenge, accurate scoring methods have to discriminate between candidate conformations of an unknown loop structure. Some success in loop prediction has been reported for globular proteins; however, the proximity of membrane protein loops to the lipid bilayer casts doubt on the applicability of the same scoring methods to this problem. In this work, we develop "decoy libraries" of non-native folds generated, using the structures of two membrane proteins, with molecular dynamics and Monte Carlo techniques over a range of temperatures. We introduce a new approach for decoy library generation by constructing a flat distribution of conformations covering a wide range of Calpha-root-mean-square deviation (RMSD) from the native structure; this removes possible bias in subsequent scoring stages. We then score these decoy conformations with effective energy functions, using increasingly more cpu-intensive implicit solvent models, including (1) simple Coulombic electrostatics with constant or distance-dependent dielectrics; (2) atomic solvation parameters; (3) the effective energy function (EEF1) of Lazaridis and Karplus; (4) generalized Born/Analytical Continuum Solvent; and (5) finite-difference Poisson-Boltzmann energy functions. We show that distinction of native-like membrane protein loops may be achieved using effective energies with the assumption of a homogenous environment; thus, the absence of the adjacent lipid bilayer does not affect the scoring ability. In particular, the Analytical Continuum Solvent and finite-difference Poisson-Boltzmann energy functions are seen to be the most powerful scoring functions. Interestingly, the use of the uncharged states of ionizable sidechains is shown to aid prediction, particularly for the simplest energy functions.     

Side-chain modeling with an optimized scoring function

Modeling side-chain conformations on a fixed protein backbone has a wide application in structure prediction and molecular design. Each effort in this field requires decisions about a rotamer set, scoring function, and search strategy. We have developed a new and simple scoring function, which operates on side-chain rotamers and consists of the following energy terms: contact surface, volume overlap, backbone dependency, electrostatic interactions, and desolvation energy. The weights of these energy terms were optimized to achieve the minimal average root mean square (rms) deviation between the lowest energy rotamer and real side-chain conformation on a training set of high-resolution protein structures. In the course of optimization, for every residue, its side chain was replaced by varying rotamers, whereas conformations for all other residues were kept as they appeared in the crystal structure. We obtained prediction accuracy of 90.4% for chi(1), 78.3% for chi(1 + 2), and 1.18 A overall rms deviation. Furthermore, the derived scoring function combined with a Monte Carlo search algorithm was used to place all side chains onto a protein backbone simultaneously. The average prediction accuracy was 87.9% for chi(1), 73.2% for chi(1 + 2), and 1.34 A rms deviation for 30 protein structures. Our approach was compared with available side-chain construction methods and showed improvement over the best among them: 4.4% for chi(1), 4.7% for chi(1 + 2), and 0.21 A for rms deviation. We hypothesize that the scoring function instead of the search strategy is the main obstacle in side-chain modeling. Additionally, we show that a more detailed rotamer library is expected to increase chi(1 + 2) prediction accuracy but may have little effect on chi(1) prediction accuracy.     

Protein side‐chain modeling with a protein‐dependent optimized rotamer library

Despite years of effort, the problem of predicting the conformations of protein side chains remains a subject of inquiry. This problem has three major issues, namely defining the conformations that a side chain may adopt within a protein, developing a sampling procedure for generating possible side‐chain packings, and defining a scoring function that can rank these possible packings. To solve the former of these issues, most procedures rely on a rotamer library derived from databases of known protein structures. We introduce an alternative method that is free of statistics. We begin with a rotamer library that is based only on stereochemical considerations; this rotamer library is then optimized independently for each protein under study. We show that this optimization step restores the diversity of conformations observed in native proteins. We combine this protein‐dependent rotamer library (PDRL) method with the self‐consistent mean field (SCMF) sampling approach and a physics‐based scoring function into a new side‐chain prediction method, SCMF–PDRL. Using two large test sets of 831 and 378 proteins, respectively, we show that this new method compares favorably with competing methods such as SCAP, OPUS‐Rota, and SCWRL4 for energy‐minimized structures. Proteins 2014; 82:2000–2017. © 2014 Wiley Periodicals, Inc.     

Modeling mutations in protein structures

We describe an automated method for the modeling of point mutations in protein structures. The protein is represented by all non-hydrogen atoms. The scoring function consists of several types of physical potential energy terms and homology-derived restraints. The optimization method implements a combination of conjugate gradient minimization and molecular dynamics with simulated annealing. The testing set consists of 717 pairs of known protein structures differing by a single mutation. Twelve variations of the scoring function were tested in three different environments of the mutated residue. The best-performing protocol optimizes all the atoms of the mutated residue, with respect to a scoring function that includes molecular mechanics energy terms for bond distances, angles, dihedral angles, peptide bond planarity, and non-bonded atomic contacts represented by Lennard-Jones potential, dihedral angle restraints derived from the aligned homologous structure, and a statistical potential for non-bonded atomic interactions extracted from a large set of known protein structures. The current method compares favorably with other tested approaches, especially when predicting long and flexible side-chains. In addition to the thoroughness of the conformational search, sampled degrees of freedom, and the scoring function type, the accuracy of the method was also evaluated as a function of the flexibility of the mutated side-chain, the relative volume change of the mutated residue, and its residue type. The results suggest that further improvement is likely to be achieved by concentrating on the improvement of the scoring function, in addition to or instead of increasing the variety of sampled conformations.     

Computer-based screening of functional conformers of proteins

A long-standing goal in biology is to establish the link between function, structure, and dynamics of proteins. Considering that protein function at the molecular level is understood by the ability of proteins to bind to other molecules, the limited structural data of proteins in association with other bio-molecules represents a major hurdle to understanding protein function at the structural level. Recent reports show that protein function can be linked to protein structure and dynamics through network centrality analysis, suggesting that the structures of proteins bound to natural ligands may be inferred computationally. In the present work, a new method is described to discriminate protein conformations relevant to the specific recognition of a ligand. The method relies on a scoring system that matches critical residues with central residues in different structures of a given protein. Central residues are the most traversed residues with the same frequency in networks derived from protein structures. We tested our method in a set of 24 different proteins and more than 260,000 structures of these in the absence of a ligand or bound to it. To illustrate the usefulness of our method in the study of the structure/dynamics/function relationship of proteins, we analyzed mutants of the yeast TATA-binding protein with impaired DNA binding. Our results indicate that critical residues for an interaction are preferentially found as central residues of protein structures in complex with a ligand. Thus, our scoring system effectively distinguishes protein conformations relevant to the function of interest.     

Designing coarse grained-and atom based-potentials for protein-protein docking

Background  

Protein-protein docking is a challenging computational problem in functional genomics, particularly when one or both proteins undergo conformational change(s) upon binding. The major challenge is to define a scoring function soft enough to tolerate these changes and specific enough to distinguish between near-native and "misdocked" conformations.