Replica Exchange Improves Sampling in Low-Resolution Docking Stage of RosettaDock

Many protein-protein docking protocols are based on a shotgun approach, in which thousands of independent random-start trajectories minimize the rigid-body degrees of freedom. Another strategy is enumerative sampling as used in ZDOCK. Here, we introduce an alternative strategy, ReplicaDock, using a small number of long trajectories of temperature replica exchange. We compare replica exchange sampling as low-resolution stage of RosettaDock with RosettaDock''s original shotgun sampling as well as with ZDOCK. A benchmark of 30 complexes starting from structures of the unbound binding partners shows improved performance for ReplicaDock and ZDOCK when compared to shotgun sampling at equal or less computational expense. ReplicaDock and ZDOCK consistently reach lower energies and generate significantly more near-native conformations than shotgun sampling. Accordingly, they both improve typical metrics of prediction quality of complex structures after refinement. Additionally, the refined ReplicaDock ensembles reach significantly lower interface energies and many previously hidden features of the docking energy landscape become visible when ReplicaDock is applied.     

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.     

A novel approach to decoy set generation: designing a physical energy function having local minima with native structure characteristics

We suggest a new approach to the generation of candidate structures (decoys) for ab initio prediction of protein structures. Our method is based on random sampling of conformation space and subsequent local energy minimization. At the core of this approach lies the design of a novel type of energy function. This energy function has local minima with native structure characteristics and wide basins of attraction. The current work presents our motivation for deriving such an energy function and also tests the derived energy function.Our approach is novel in that it takes advantage of the inherently rough energy landscape of proteins, which is generally considered a major obstacle for protein structure prediction. When local minima have wide basins of attraction, the protein's conformation space can be greatly reduced by the convergence of large regions of the space into single points, namely the local minima corresponding to these funnels. We have implemented this concept by an iterative process. The potential is first used to generate decoy sets and then we study these sets of decoys to guide further development of the potential. A key feature of our potential is the use of cooperative multi-body interactions that mimic the role of the entropic and solvent contributions to the free energy.The validity and value of our approach is demonstrated by applying it to 14 diverse, small proteins. We show that, for these proteins, the size of conformation space is considerably reduced by the new energy function. In fact, the reduction is so substantial as to allow efficient conformational sampling. As a result we are able to find a significant number of near-native conformations in random searches performed with limited computational resources.     

Multi‐scale characterization of the energy landscape of proteins with application to the C3D/Efb‐C complex

We present a novel multi‐level methodology to explore and characterize the low energy landscape and the thermodynamics of proteins. Traditional conformational search methods typically explore only a small portion of the conformational space of proteins and are hard to apply to large proteins due to the large amount of calculations required. In our multi‐scale approach, we first provide an initial characterization of the equilibrium state ensemble of a protein using an efficient computational conformational sampling method. We then enrich the obtained ensemble by performing short Molecular Dynamics (MD) simulations on selected conformations from the ensembles as starting points. To facilitate the analysis of the results, we project the resulting conformations on a low‐dimensional landscape to efficiently focus on important interactions and examine low energy regions. This methodology provides a more extensive sampling of the low energy landscape than an MD simulation starting from a single crystal structure as it explores multiple trajectories of the protein. This enables us to obtain a broader view of the dynamics of proteins and it can help in understanding complex binding, improving docking results and more. In this work, we apply the methodology to provide an extensive characterization of the bound complexes of the C3d fragment of human Complement component C3 and one of its powerful bacterial inhibitors, the inhibitory domain of Staphylococcus aureus extra‐cellular fibrinogen‐binding domain (Efb‐C) and two of its mutants. We characterize several important interactions along the binding interface and define low free energy regions in the three complexes. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Potential energy landscape and robustness of a gene regulatory network: toggle switch

Finding a multidimensional potential landscape is the key for addressing important global issues, such as the robustness of cellular networks. We have uncovered the underlying potential energy landscape of a simple gene regulatory network: a toggle switch. This was realized by explicitly constructing the steady state probability of the gene switch in the protein concentration space in the presence of the intrinsic statistical fluctuations due to the small number of proteins in the cell. We explored the global phase space for the system. We found that the protein synthesis rate and the unbinding rate of proteins to the gene were small relative to the protein degradation rate; the gene switch is monostable with only one stable basin of attraction. When both the protein synthesis rate and the unbinding rate of proteins to the gene are large compared with the protein degradation rate, two global basins of attraction emerge for a toggle switch. These basins correspond to the biologically stable functional states. The potential energy barrier between the two basins determines the time scale of conversion from one to the other. We found as the protein synthesis rate and protein unbinding rate to the gene relative to the protein degradation rate became larger, the potential energy barrier became larger. This also corresponded to systems with less noise or the fluctuations on the protein numbers. It leads to the robustness of the biological basins of the gene switches. The technique used here is general and can be applied to explore the potential energy landscape of the gene networks.     

Discovery of binding proteins for a protein target using protein–protein docking‐based virtual screening

Target structure‐based virtual screening, which employs protein‐small molecule docking to identify potential ligands, has been widely used in small‐molecule drug discovery. In the present study, we used a protein–protein docking program to identify proteins that bind to a specific target protein. In the testing phase, an all‐to‐all protein–protein docking run on a large dataset was performed. The three‐dimensional rigid docking program SDOCK was used to examine protein–protein docking on all protein pairs in the dataset. Both the binding affinity and features of the binding energy landscape were considered in the scoring function in order to distinguish positive binding pairs from negative binding pairs. Thus, the lowest docking score, the average Z‐score, and convergency of the low‐score solutions were incorporated in the analysis. The hybrid scoring function was optimized in the all‐to‐all docking test. The docking method and the hybrid scoring function were then used to screen for proteins that bind to tumor necrosis factor‐α (TNFα), which is a well‐known therapeutic target for rheumatoid arthritis and other autoimmune diseases. A protein library containing 677 proteins was used for the screen. Proteins with scores among the top 20% were further examined. Sixteen proteins from the top‐ranking 67 proteins were selected for experimental study. Two of these proteins showed significant binding to TNFα in an in vitro binding study. The results of the present study demonstrate the power and potential application of protein–protein docking for the discovery of novel binding proteins for specific protein targets. Proteins 2014; 82:2472–2482. © 2014 Wiley Periodicals, Inc.     

How common is the funnel‐like energy landscape in protein‐protein interactions?

The goal of this study is to verify the concept of the funnel-like intermolecular energy landscape in protein-protein interactions by use of a series of computational experiments. Our preliminary analysis revealed the existence of the funnel in many protein-protein interactions. However, because of the uncertainties in the modeling of these interactions and the ambiguity of the analysis procedures, the detection of the funnels requires detailed quantitative approaches to the energy landscape analysis. A number of such approaches are presented in this study. We show that the funnel detection problem is equivalent to a problem of distinguishing between distributions of low-energy intermolecular matches in the funnel and in the low-frequency landscape fluctuations. If the fluctuations are random, the decision about whether the minimum is the funnel is equivalent to determining whether this minimum is significantly different from a would-be random one. A database of 475 nonredundant cocrystallized protein-protein complexes was used to re-dock the proteins by use of smoothed potentials. To detect the funnel, we developed a set of sophisticated models of random matches. The funnel was considered detected if the binding area was more populated by the low-energy docking predictions than by the matches generated in the random models. The number of funnels detected by use of different random models varied significantly. However, the results confirmed that the funnel may be the general feature in protein-protein association.     

Interaction cutoff effect on ruggedness of protein-protein energy landscape

The concept of the energy landscape is important for better understanding of protein-protein interactions and for designing adequate docking procedures. The intermolecular landscape has a rugged terrain that impedes search procedures. Its inherent ruggedness is related to the conformational characteristics of the molecules and to the form of the potential function--more rugged for short-range potentials and less rugged for "soft," typically long-range potentials. Our study determined that the landscape ruggedness is further substantially exacerbated by truncation of the potentials. This additional ruggedness appears below certain critical interaction ranges that depend on the form of the potential. The theoretical model describing the cutoff effect on the landscape ruggedness is confirmed by the energy calculation on a dataset of protein-protein complexes. The negative effect of the potentials cutoff is well known. However, revealing its physical basis in terms of the energy landscape is important for better understanding of intermolecular interactions.     

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.     

Complexity and simplicity of ligand-macromolecule interactions: the energy landscape perspective

The energy landscape approach has contributed to recent progress in understanding the complexity and simplicity of ligand-macromolecule interactions. Significant advances in computational structure prediction of ligand-protein complexes have been made using approaches that include the effects of protein flexibility and incorporate a hierarchy of energy functions. The results suggest that the complexity of structure prediction in molecular recognition may be determined by low-resolution properties of the underlying binding energy landscapes and by the nature of the energy funnels near the native structures of the complexes.     

iATTRACT: Simultaneous global and local interface optimization for protein–protein docking refinement

Protein‐protein interactions are abundant in the cell but to date structural data for a large number of complexes is lacking. Computational docking methods can complement experiments by providing structural models of complexes based on structures of the individual partners. A major caveat for docking success is accounting for protein flexibility. Especially, interface residues undergo significant conformational changes upon binding. This limits the performance of docking methods that keep partner structures rigid or allow limited flexibility. A new docking refinement approach, iATTRACT, has been developed which combines simultaneous full interface flexibility and rigid body optimizations during docking energy minimization. It employs an atomistic molecular mechanics force field for intermolecular interface interactions and a structure‐based force field for intramolecular contributions. The approach was systematically evaluated on a large protein‐protein docking benchmark, starting from an enriched decoy set of rigidly docked protein–protein complexes deviating by up to 15 Å from the native structure at the interface. Large improvements in sampling and slight but significant improvements in scoring/discrimination of near native docking solutions were observed. Complexes with initial deviations at the interface of up to 5.5 Å were refined to significantly better agreement with the native structure. Improvements in the fraction of native contacts were especially favorable, yielding increases of up to 70%. Proteins 2015; 83:248–258. © 2014 Wiley Periodicals, Inc.     

Computational analyses of interactions between ALK-5 and bioactive ligands: insights for the design of potential anticancer agents

Activin Receptor-Like Kinase 5 (ALK-5) is related to some types of cancer, such as breast, lung, and pancreas. In this study, we have used molecular docking, molecular dynamics simulations, and free energy calculations in order to explore key interactions between ALK-5 and six bioactive ligands with different ranges of biological activity. The motivation of this work is the lack of crystal structure for inhibitor–protein complexes for this set of ligands. The understanding of the molecular structure and the protein–ligand interaction could give support for the development of new drugs against cancer. The results show that the calculated binding free energy using MM-GBSA, MM-PBSA, and SIE is correlated with experimental data with r² = 0.88, 0.80, and 0.94, respectively, which indicates that the calculated binding free energy is in excellent agreement with experimental data. In addition, the results demonstrate that H bonds with Lys232, Glu245, Tyr249, His283, Asp351, and one structural water molecule play an important role for the inhibition of ALK-5. Overall, we discussed the main interactions between ALK-5 and six inhibitors that may be used as starting points for designing new molecules to the treatment of cancer.     

Exploring protein-protein interactions using the site-identification by ligand competitive saturation methodology

Protein docking methods are powerful computational tools to study protein-protein interactions (PPI). While a significant number of docking algorithms have been developed, they are usually based on rigid protein models or with limited considerations of protein flexibility and the desolvation effect is rarely considered in docking energy functions, which may lower the accuracy of the predictions. To address these issues, we introduce a PPI energy function based on the site-identification by ligand competitive saturation (SILCS) framework and utilize the fast Fourier transform (FFT) correlation approach. The free energy content of the SILCS FragMaps represent an alternative to traditional energy grids and they can be efficiently utilized to guide FFT-based protein docking. Application of the approach to eight diverse test cases, including seven from Protein Docking Benchmark 5.0, showed the PPI prediction using SILCS approach (SILCS-PPI) to be competitive with several commonly used protein docking methods indicating that the method has the ability to both qualitatively and quantitatively inform the prediction of PPI. Results show the utility of the SILCS-PPI docking approach for determination of probability distributions of PPI interactions over the surface of both partner proteins, allowing for identification of alternate binding poses. Such binding poses are confirmed by experimental crystal contacts in our test cases. While more computationally demanding than available PPI docking technologies, we anticipate that the SILCS-PPI docking approach will offer an alternative methodology for improved evaluation of PPIs that could be used in a variety of fields from systems biology to excipient design for biologics-based drugs.     

DARS (Decoys As the Reference State) potentials for protein-protein docking

Decoys As the Reference State (DARS) is a simple and natural approach to the construction of structure-based intermolecular potentials. The idea is generating a large set of docked conformations with good shape complementarity but without accounting for atom types, and using the frequency of interactions extracted from these decoys as the reference state. In principle, the resulting potential is ideal for finding near-native conformations among structures obtained by docking, and can be combined with other energy terms to be used directly in docking calculations. We investigated the performance of various DARS versions for docking enzyme-inhibitor, antigen-antibody, and other type of complexes. For enzyme-inhibitor pairs, DARS provides both excellent discrimination and docking results, even with very small decoy sets. For antigen-antibody complexes, DARS is slightly better than a number of interaction potentials tested, but results are worse than for enzyme-inhibitor complexes. With a few exceptions, the DARS docking results are also good for the other complexes, despite poor discrimination, and we show that the latter is not a correct test for docking accuracy. The analysis of interactions in antigen-antibody pairs reveals that, in constructing pairwise potentials for such complexes, one should account for the asymmetry of hydrophobic patches on the two sides of the interface. Similar asymmetry does occur in the few other complexes with poor DARS docking results.     

Improved side-chain modeling for protein-protein docking

Success in high-resolution protein-protein docking requires accurate modeling of side-chain conformations at the interface. Most current methods either leave side chains fixed in the conformations observed in the unbound protein structures or allow the side chains to sample a set of discrete rotamer conformations. Here we describe a rapid and efficient method for sampling off-rotamer side-chain conformations by torsion space minimization during protein-protein docking starting from discrete rotamer libraries supplemented with side-chain conformations taken from the unbound structures, and show that the new method improves side-chain modeling and increases the energetic discrimination between good and bad models. Analysis of the distribution of side-chain interaction energies within and between the two protein partners shows that the new method leads to more native-like distributions of interaction energies and that the neglect of side-chain entropy produces a small but measurable increase in the number of residues whose interaction energy cannot compensate for the entropic cost of side-chain freezing at the interface. The power of the method is highlighted by a number of predictions of unprecedented accuracy in the recent CAPRI (Critical Assessment of PRedicted Interactions) blind test of protein-protein docking methods.     

A hierarchical method for molecular docking using cloud computing

Discovering small molecules that interact with protein targets will be a key part of future drug discovery efforts. Molecular docking of drug-like molecules is likely to be valuable in this field; however, the great number of such molecules makes the potential size of this task enormous. In this paper, a method to screen small molecular databases using cloud computing is proposed. This method is called the hierarchical method for molecular docking and can be completed in a relatively short period of time. In this method, the optimization of molecular docking is divided into two subproblems based on the different effects on the protein–ligand interaction energy. An adaptive genetic algorithm is developed to solve the optimization problem and a new docking program (FlexGAsDock) based on the hierarchical docking method has been developed. The implementation of docking on a cloud computing platform is then discussed. The docking results show that this method can be conveniently used for the efficient molecular design of drugs.     

Protein-Protein Docking: From Interaction to Interactome

The protein-protein docking problem is one of the focal points of activity in computational biophysics and structural biology. The three-dimensional structure of a protein-protein complex, generally, is more difficult to determine experimentally than the structure of an individual protein. Adequate computational techniques to model protein interactions are important because of the growing number of known protein structures, particularly in the context of structural genomics. Docking offers tools for fundamental studies of protein interactions and provides a structural basis for drug design. Protein-protein docking is the prediction of the structure of the complex, given the structures of the individual proteins. In the heart of the docking methodology is the notion of steric and physicochemical complementarity at the protein-protein interface. Originally, mostly high-resolution, experimentally determined (primarily by x-ray crystallography) protein structures were considered for docking. However, more recently, the focus has been shifting toward lower-resolution modeled structures. Docking approaches have to deal with the conformational changes between unbound and bound structures, as well as the inaccuracies of the interacting modeled structures, often in a high-throughput mode needed for modeling of large networks of protein interactions. The growing number of docking developers is engaged in the community-wide assessments of predictive methodologies. The development of more powerful and adequate docking approaches is facilitated by rapidly expanding information and data resources, growing computational capabilities, and a deeper understanding of the fundamental principles of protein interactions.     

Curcumin binds in silico to anti-cancer drug target enzyme MMP-3 (human stromelysin-1) with affinity comparable to two known inhibitors of the enzyme

In silico interaction of curcumin with the enzyme MMP-3 (human stromelysin-1) was studied by molecular docking using AutoDock 4.2 as the docking software application. AutoDock 4.2 software serves as a valid and acceptable docking application to study the interactions of small compounds with proteins. Interactions of curcumin with MMP-3 were compared to those of two known inhibitors of the enzyme, PBSA and MPPT. The calculated free energy of binding (ΔG binding) shows that curcumin binds with affinity comparable to or better than the two known inhibitors. Binding interactions of curcumin with active site residues of the enzyme are also predicted. Curcumin appears to bind in an extendended conformation making extensive VDW contacts in the active site of the enzyme. Hydrogen bonding and pi-pi interactions with key active site residues is also observed. Thus, curcumin can be considered as a good lead compound in the development of new inhibitors of MMP-3 which is a potential target of anticancer drugs. The results of these studies can serve as a starting point for further computational and experimental studies.