Docking with PIPER and refinement with SDU in rounds 6-11 of CAPRI

Our approach to protein-protein docking includes three main steps. First we run PIPER, a new rigid body docking program. PIPER is based on the Fast Fourier Transform (FFT) correlation approach that has been extended to use pairwise interactions potentials, thereby substantially increasing the number of near-native structures generated. The interaction potential is also new, based on the DARS (Decoys As the Reference State) principle. In the second step, the 1000 best energy conformations are clustered, and the 30 largest clusters are retained for refinement. Third, the conformations are refined by a new medium-range optimization method SDU (Semi-Definite programming based Underestimation). SDU has been developed to locate global minima within regions of the conformational space in which the energy function is funnel-like. The method constructs a convex quadratic underestimator function based on a set of local energy minima, and uses this function to guide future sampling. The combined method performed reliably without the direct use of biological information in most CAPRI problems that did not require homology modeling, providing acceptable predictions for targets 21, and medium quality predictions for targets 25 and 26.     

Progress in protein-protein docking: atomic resolution predictions in the CAPRI experiment using RosettaDock with an improved treatment of side-chain flexibility

RosettaDock uses real-space Monte Carlo minimization (MCM) on both rigid-body and side-chain degrees of freedom to identify the lowest free energy docked arrangement of 2 protein structures. An improved version of the method that uses gradient-based minimization for off-rotamer side-chain optimization and includes information from unbound structures was used to create predictions for Rounds 4 and 5 of CAPRI. First, large numbers of independent MCM trajectories were carried out and the lowest free energy docked configurations identified. Second, new trajectories were started from these lowest energy structures to thoroughly sample the surrounding conformation space, and the lowest energy configurations were submitted as predictions. For all cases in which there were no significant backbone conformational changes, a small number of very low-energy configurations were identified in the first, global search and subsequently found to be close to the center of the basin of attraction in the free energy landscape in the second, local search. Following the release of the experimental coordinates, it was found that the centers of these free energy minima were remarkably close to the native structures in not only the rigid-body orientation but also the detailed conformations of the side-chains. Out of 8 targets, the lowest energy models had interface root-mean-square deviations (RMSDs) less than 1.1 A from the correct structures for 6 targets, and interface RMSDs less than 0.4 A for 3 targets. The predictions were top submissions to CAPRI for Targets 11, 12, 14, 15, and 19. The close correspondence of the lowest free energy structures found in our searches to the experimental structures suggests that our free energy function is a reasonable representation of the physical chemistry, and that the real space search with full side-chain flexibility to some extent solves the protein-protein docking problem in the absence of significant backbone conformational changes. On the other hand, the approach fails when there are significant backbone conformational changes as the steric complementarity of the 2 proteins cannot be modeled without incorporating backbone flexibility, and this is the major goal of our current work.     

Chasing funnels on protein-protein energy landscapes at different resolutions

Studies of intermolecular energy landscapes are important for understanding protein association and adequate modeling of protein interactions. Landscape representation at different resolutions can be used for the refinement of docking predictions and detection of macro characteristics, like the binding funnel. A representative set of protein-protein complexes was used to systematically map the intermolecular landscape by grid-based docking. The change of the resolution was achieved by varying the range of the potential, according to the variable resolution GRAMM methodology. A formalism was developed to consistently parameterize the potential and describe essential characteristics of the landscape. The results of gradual landscape smoothing, from high to low resolution, indicate that i), the number of energy basins, the landscape ruggedness, and the slope decrease accordingly; ii), the number of near-native matches, defined as those inside the funnel, increases until the trend breaks down at critical resolution; the rate of the increase and the critical resolution are specific to the type of a complex (enzyme inhibitor, antigen-antibody, and other), reflect known underlying recognition factors, and correlate with earlier determined estimates of the funnel size; iii), the native/nonnative energy gap, a major characteristic of the energy minima hierarchy, remains constant; and iv), the putative funnel (defined as the deepest basin) has the largest average depth-related ruggedness and slope, at all resolutions. The results facilitate better understanding of the binding landscapes and suggest directions for implementation in practical docking protocols.     

Predicting protein complex geometries with a neural network

A major challenge of the protein docking problem is to define scoring functions that can distinguish near‐native protein complex geometries from a large number of non‐native geometries (decoys) generated with noncomplexed protein structures (unbound docking). In this study, we have constructed a neural network that employs the information from atom‐pair distance distributions of a large number of decoys to predict protein complex geometries. We found that docking prediction can be significantly improved using two different types of polar hydrogen atoms. To train the neural network, 2000 near‐native decoys of even distance distribution were used for each of the 185 considered protein complexes. The neural network normalizes the information from different protein complexes using an additional protein complex identity input neuron for each complex. The parameters of the neural network were determined such that they mimic a scoring funnel in the neighborhood of the native complex structure. The neural network approach avoids the reference state problem, which occurs in deriving knowledge‐based energy functions for scoring. We show that a distance‐dependent atom pair potential performs much better than a simple atom‐pair contact potential. We have compared the performance of our scoring function with other empirical and knowledge‐based scoring functions such as ZDOCK 3.0, ZRANK, ITScore‐PP, EMPIRE, and RosettaDock. In spite of the simplicity of the method and its functional form, our neural network‐based scoring function achieves a reasonable performance in rigid‐body unbound docking of proteins. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

New insights into the mechanism of protein-protein association

Association of a protein complex follows a two-step mechanism, with the first step being the formation of an encounter complex that evolves into the final complex. Here, we analyze recent experimental data of the association of TEM1-beta-lactamase with BLIP using theoretical calculations and simulation. We show that the calculated Debye-Hückel energy of interaction for a pair of proteins during association resembles an energy funnel, with the final complex at the minima. All attraction is lost at inter-protein distances of 20 A, or rotation angles of >60 degrees from the orientation of the final complex. For faster-associating protein complexes, the energy funnel deepens and its volume increases. Mutations with the largest impact on association (hotspots for association) have the largest effect on the size and depth of the energy funnel. Analyzing existing evidence, we suggest that the transition state along the association pathway is the formation of the final complex from the encounter complex. Consequently, pairs of proteins forming an encounter complex will tend to dissociate more readily than to evolve into the final complex. Increasing directional diffusion by increasing favorable electrostatic attraction results in a faster forming and slower dissociating encounter complex. The possible applicability of electrostatic calculations for protein-protein docking is discussed.     

Visualization of Protein Folding Funnels in Lattice Models

Protein folding occurs in a very high dimensional phase space with an exponentially large number of states, and according to the energy landscape theory it exhibits a topology resembling a funnel. In this statistical approach, the folding mechanism is unveiled by describing the local minima in an effective one-dimensional representation. Other approaches based on potential energy landscapes address the hierarchical structure of local energy minima through disconnectivity graphs. In this paper, we introduce a metric to describe the distance between any two conformations, which also allows us to go beyond the one-dimensional representation and visualize the folding funnel in 2D and 3D. In this way it is possible to assess the folding process in detail, e.g., by identifying the connectivity between conformations and establishing the paths to reach the native state, in addition to regions where trapping may occur. Unlike the disconnectivity maps method, which is based on the kinetic connections between states, our methodology is based on structural similarities inferred from the new metric. The method was developed in a 27-mer protein lattice model, folded into a 3×3×3 cube. Five sequences were studied and distinct funnels were generated in an analysis restricted to conformations from the transition-state to the native configuration. Consistent with the expected results from the energy landscape theory, folding routes can be visualized to probe different regions of the phase space, as well as determine the difficulty in folding of the distinct sequences. Changes in the landscape due to mutations were visualized, with the comparison between wild and mutated local minima in a single map, which serves to identify different trapping regions. The extension of this approach to more realistic models and its use in combination with other approaches are discussed.     

Exploring the primary electron acceptor (QA)-site of the bacterial reaction center from Rhodobacter sphaeroides. Binding mode of vitamin K derivatives.

The functional replacement of the primary ubiquinone (QA) in the photosynthetic reaction center (RC) from Rhodobacter sphaeroides with synthetic vitamin K derivatives has provided a powerful tool to investigate the electron transfer mechanism. To investigate the binding mode of these quinones to the QA binding site we have determined the binding free energy and charge recombination rate from QA(-) to D+ (kAD) of 29 different 1,4-naphthoquinone derivatives with systematically altered structures. The most striking result was that none of the eight tested compounds carrying methyl groups in both positions 5 and 8 of the aromatic ring exhibited functional binding. To understand the binding properties of these quinones on a molecular level, the structures of the reaction center-naphthoquinone complexes were predicted with ligand docking calculations. All protein--ligand structures show hydrogen bonds between the carbonyl oxygens of the quinone and AlaM260 and HisM219 as found for the native ubiquinone-10 in the X-ray structure. The center-to-center distance between the naphthoquinones at QA and the native ubiquinone-10 at QB (the secondary electron acceptor) is essentially the same, compared to the native structure. A detailed analysis of the docking calculations reveals that 5,8-disubstitution prohibits binding due to steric clashes of the 5-methyl group with the backbone atoms of AlaM260 and AlaM249. The experimentally determined binding free energies were reproduced with an rmsd of approximately 4 kJ x mol(-1) in most cases providing a valuable tool for the design of new artificial electron acceptors and inhibitors.     

Optimized distance‐dependent atom‐pair‐based potential DOOP for protein structure prediction

The DOcking decoy‐based Optimized Potential (DOOP) energy function for protein structure prediction is based on empirical distance‐dependent atom‐pair interactions. To optimize the atom‐pair interactions, native protein structures are decomposed into polypeptide chain segments that correspond to structural motives involving complete secondary structure elements. They constitute near native ligand–receptor systems (or just pairs). Thus, a total of 8609 ligand–receptor systems were prepared from 954 selected proteins. For each of these hypothetical ligand–receptor systems, 1000 evenly sampled docking decoys with 0–10 Å interface root‐mean‐square‐deviation (iRMSD) were generated with a method used before for protein–protein docking. A neural network‐based optimization method was applied to derive the optimized energy parameters using these decoys so that the energy function mimics the funnel‐like energy landscape for the interaction between these hypothetical ligand–receptor systems. Thus, our method hierarchically models the overall funnel‐like energy landscape of native protein structures. The resulting energy function was tested on several commonly used decoy sets for native protein structure recognition and compared with other statistical potentials. In combination with a torsion potential term which describes the local conformational preference, the atom‐pair‐based potential outperforms other reported statistical energy functions in correct ranking of native protein structures for a variety of decoy sets. This is especially the case for the most challenging ROSETTA decoy set, although it does not take into account side chain orientation‐dependence explicitly. The DOOP energy function for protein structure prediction, the underlying database of protein structures with hypothetical ligand–receptor systems and their decoys are freely available at http://agknapp.chemie.fu‐berlin.de/doop/ . Proteins 2015; 83:881–890. © 2015 Wiley Periodicals, Inc.     

The size of the intermolecular energy funnel in protein-protein interactions

Revealing the fundamental principles of protein interactions is essential for the basic knowledge of molecular processes and designing better predictive tools. Protein docking procedures allow systematic sampling of intermolecular energy landscapes, revealing the distribution of energy basins and their characteristics. A systematic search docking procedure GRAMM-X was applied to a comprehensive nonredundant database of nonobligate protein-protein complexes to determine the size of the intermolecular energy funnel. The unbound structures were simulated using rotamer library. The procedure generated grid-based matches, based on a smoothed Lennard-Jones potential, and minimized them off the grid with the same potential. The minimization generated a distribution of distances, based on a variety of metrics, between the grid-based and the minimized matches. The metric selected for the analysis, ligand interface RMSD, provided three independent estimates of the funnel size: based on the distribution amplitude for the near-native matches, deviation from random, and correlation with the energy values. The three methods converge to similar estimates of approximately 6-8 A ligand interface RMSD. The results indicated dependence of the funnel size on the type of the complex (smaller for antigen-antibody, medium for enzyme-inhibitor, and larger for the rest of the complexes) and the funnel size correlation with the size of the interface. Guidelines for the optimal sampling of docking coordinates, based on the funnel size estimates, were explored.     

Unfolding the fold of cyclic cysteine-rich peptides

We propose a method to extensively characterize the native state ensemble of cyclic cysteine-rich peptides. The method uses minimal information, namely, amino acid sequence and cyclization, as a topological feature that characterizes the native state. The method does not assume a specific disulfide bond pairing for cysteines and allows the possibility of unpaired cysteines. A detailed view of the conformational space relevant for the native state is obtained through a hierarchic multi-resolution exploration. A crucial feature of the exploration is a geometric approach that efficiently generates a large number of distinct cyclic conformations independently of one another. A spatial and energetic analysis of the generated conformations associates a free-energy landscape to the explored conformational space. Application to three long cyclic peptides of different folds shows that the conformational ensembles and cysteine arrangements associated with free energy minima are fully consistent with available experimental data. The results provide a detailed analysis of the native state features of cyclic peptides that can be further tested in experiment.     

A simple reference state makes a significant improvement in near-native selections from structurally refined docking decoys

Near-native selections from docking decoys have proved challenging especially when unbound proteins are used in the molecular docking. One reason is that significant atomic clashes in docking decoys lead to poor predictions of binding affinities of near native decoys. Atomic clashes can be removed by structural refinement through energy minimization. Such an energy minimization, however, will lead to an unrealistic bias toward docked structures with large interfaces. Here, we extend an empirical energy function developed for protein design to protein-protein docking selection by introducing a simple reference state that removes the unrealistic dependence of binding affinity of docking decoys on the buried solvent accessible surface area of interface. The energy function called EMPIRE (EMpirical Protein-InteRaction Energy), when coupled with a refinement strategy, is found to provide a significantly improved success rate in near native selections when applied to RosettaDock and refined ZDOCK docking decoys. Our work underlines the importance of removing nonspecific interactions from specific ones in near native selections from docking decoys.     

Discrimination of near-native structures in protein-protein docking by testing the stability of local minima

Fast Fourier transform (FFT) correlation methods of protein-protein docking, combined with the clustering of low energy conformations, can find a number of local minima on the energy surface. For most complexes, the locations of the near-native structures can be constrained to the 30 largest clusters, each surrounding a local minimum. However, no reliable further discrimination can be obtained by energy measures because the differences in the energy levels between the minima are comparable with the errors in the energy evaluation. In fact, no current scoring function accounts for the entropic contributions that relate to the width rather than the depth of the minima. Since structures at narrow minima loose more entropy, some of the nonnative states can be detected by determining whether or not a local minimum is surrounded by a broad region of attraction on the energy surface. The analysis is based on starting Monte Carlo Minimization (MCM) runs from random points around each minimum, and observing whether a certain fraction of trajectories converge to a small region within the cluster. The cluster is considered stable if such a strong attractor exists, has at least 10 convergent trajectories, is relatively close to the original cluster center, and contains a low energy structure. We studied the stability of clusters for enzyme-inhibitor and antibody-antigen complexes in the Protein Docking Benchmark. The analysis yields three main results. First, all clusters that are close to the native structure are stable. Second, restricting considerations to stable clusters eliminates around half of the false positives, that is, solutions that are low in energy but far from the native structure of the complex. Third, dividing the conformational space into clusters and determining the stability of each cluster, the combined approach is less dependent on a priori information than exploring the potential conformational space by Monte Carlo minimizations.     

ClusPro: an automated docking and discrimination method for the prediction of protein complexes

MOTIVATION: Predicting protein interactions is one of the most challenging problems in functional genomics. Given two proteins known to interact, current docking methods evaluate billions of docked conformations by simple scoring functions, and in addition to near-native structures yield many false positives, i.e. structures with good surface complementarity but far from the native. RESULTS: We have developed a fast algorithm for filtering docked conformations with good surface complementarity, and ranking them based on their clustering properties. The free energy filters select complexes with lowest desolvation and electrostatic energies. Clustering is then used to smooth the local minima and to select the ones with the broadest energy wells-a property associated with the free energy at the binding site. The robustness of the method was tested on sets of 2000 docked conformations generated for 48 pairs of interacting proteins. In 31 of these cases, the top 10 predictions include at least one near-native complex, with an average RMSD of 5 A from the native structure. The docking and discrimination method also provides good results for a number of complexes that were used as targets in the Critical Assessment of PRedictions of Interactions experiment. AVAILABILITY: The fully automated docking and discrimination server ClusPro can be found at http://structure.bu.edu     

Protein-inhibitor flexible docking by a multicanonical sampling: native complex structure with the lowest free energy and a free-energy barrier distinguishing the native complex from the others

Flexible docking between a protein (lysozyme) and an inhibitor (tri-N-acetyl-D-glucosamine, tri-NAG) was carried out by an enhanced conformational sampling method, multicanonical molecular dynamics simulation. We used a flexible all-atom model to express lysozyme, tri-NAG, and water molecules surrounding the two bio-molecules. The advantages of this sampling method are as follows: the conformation of system is widely sampled without trapping at energy minima, a thermally equilibrated conformational ensemble at an arbitrary temperature can be reconstructed from the simulation trajectory, and the thermodynamic weight can be assigned to each sampled conformation. During the simulation, exchanges between the binding and free (i.e., unbinding) states of the protein and the inhibitor were repeatedly observed. The conformational ensemble reconstructed at 300 K involved various conformational clusters. The main outcome of the current study is that the most populated conformational cluster (i.e., the cluster of the lowest free energy) was assigned to the native complex structure (i.e., the X-ray complex structure). The simulation also produced non-native complex structures, where the protein and the inhibitor bound with different modes from that of the native complex structure, as well as the unbinding structures. A free-energy barrier (i.e., activation free energy) was clearly detected between the native complex structures and the other structures. The thermal fluctuations of tri-NAG in the lowest free-energy complex correlated well with the X-ray B-factors of tri-NAG in the X-ray complex structure. The existence of the free-energy barrier ensures that the lowest free-energy structure can be discriminated naturally from the other structures. In other words, the multicanonical molecular dynamics simulation can predict the native complex structure without any empirical objective function. The current study also manifested that the flexible all-atom model and the physico-chemically defined atomic-level force field can reproduce the native complex structure. A drawback of the current method is that it requires a time consuming computation due to the exhaustive conformational sampling. We discussed a possibility for combining the current method with conventional docking methods.     

Development and validation of an empirical free energy function for calculating protein–protein binding free energy surfaces

In a previous paper, we described a novel empirical free energy function that was used to accurately predict experimental binding free energies for a diverse test set of 31 protein–protein complexes to within ≈ 1.0 kcal. Here, we extend that work and show that an updated version of the function can be used to (1) accurately predict native binding free energies and (2) rank crystallographic, native-like and non-native binding modes in a physically realistic manner. The modified function includes terms designed to capture some of the unfavorable interactions that characterize non-native interfaces. The function was used to calculate one-dimensional binding free energy surfaces for 21 protein complexes. In roughly 90% of the cases tested, the function was used to place native-like and crystallographic binding modes in global free energy minima. Our analysis further suggests that buried hydrogen bonds might provide the key to distinguishing native from non-native interactions. To the best of our knowledge our function is the only one of its kind, a single expression that can be used to accurately calculate native and non-native binding free energies for a large number of proteins. Given the encouraging results presented in this paper, future work will focus on improving the function and applying it to the protein–protein docking problem.     

Docking enzyme-inhibitor complexes using a preference-based free-energy surface

We present a docking scheme that utilizes both a surface complementarity screen as well as an energetic criterion based on surface area burial. Twenty rigid enzyme/inhibitor complexes with known coordinate sets are arbitrarily separated and reassembled to an average all-atom rms (root mean square) deviation of 1.0 Å from the native complexes. Docking is accomplished by a hierarchical search of geometrically compatible triplets of surface normals on each molecule. A pruned tree of possible bound configurations is built up using successive consideration of larger and larger triplets. The best scoring configurations are then passed through a free-energy screen where the lowest energy member is selected as the predicted native state. The free energy approximation is derived from observations of surface burial by atom pairs across the interface of known enzyme/inhibitor complexes. The occurrence of specific atom-atom surface burial, for a set of complexes with well-defined secondary structure both in the bound and unbound states, is parameterized to mimic the free energy of binding. The docking procedure guides the inhibitor into its native state using orientation and distance-dependent functions that reproduce the ideal model of free energies with an average rms deviation of 0.9 kcal/mol. For all systems studied, this docking procedure identifies a single, unique minimum energy configuration that is highly compatible with the native state. © 1996 Wiley-Liss, Inc.     

Molecular docking of superantigens with class II major histocompatibility complex proteins

The molecular recognition of two superantigens with class II major histocompatibility complex molecules was simulated by using protein– protein docking. Superantigens studied were staphylococcal enterotoxin B (SEB) and toxic shock syndrome toxin-1 (TSST-1) in their crystallographic assemblies with HLA-DR1. Rigid-body docking was performed sampling configurational space of the interfacial surfaces by employing a strategy of partitioning the contact regions on HLA-DR1 into separate molecular recognition units. Scoring of docked conformations was based on an electrostatic continuum model evaluated with the finite-difference Poisson– Boltzmann method. Estimates of nonpolar contributions were derived from the buried molecular surface areas. We found for both superantigens that docking the HLA-DR1 surface complementary with the SEB and TSST-1 contact regions containing a homologous hydrophobic surface loop provided sufficient recognition for the reconstitution of native-like conformers exhibiting the highest-scoring free energies. For the SEB complex, the calculations were successful in reproducing the total association free energy. A comparison of the free-energy determinants of the conserved hydrophobic contact residue indicates functional similarity between the two proteins for this interface. Though both superantigens share a common global association mode, differences in binding topology distinguish the conformational specificities underlying recognition. © 1998 John Wiley & Sons, Ltd.     

The nature of cation-pi binding: interactions between tetramethylammonium ion and benzene in aqueous solution.

A combined quantum mechanical and molecular mechanical Monte Carlo simulation method was used to determine the free energy of binding between tetramethylammonium ion (TMA+) and benzene in water. The computed free energy as a function of distance (the potential of mean force) has two minima that represent contact and solvent-separated complexes. These species are separated by a broad barrier of about 3 kJ/mol. The results are in good accord with experimental data and suggest that TMA+ binds to benzene more favorably than to chloride ion, with an association constant of about 0.8 M-1.     

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.