Energy minimization in low-frequency normal modes to efficiently allow for global flexibility during systematic protein-protein docking

Protein-protein association can frequently involve significant backbone conformational changes of the protein partners. A computationally rapid method has been developed that allows to approximately account for global conformational changes during systematic protein-protein docking starting from many thousands of start configurations. The approach employs precalculated collective degrees of freedom as additional variables during protein-protein docking minimization. The global collective degrees of freedom are obtained from normal mode analysis using a Gaussian network model for the protein. Systematic docking searches were performed on 10 test systems that differed in the degree of conformational change associated with complex formation and in the degree of overlap between observed conformational changes and precalculated flexible degrees of freedom. The results indicate that in case of docking searches that minimize the influence of local side chain conformational changes inclusion of global flexibility can significantly improve the agreement of the near-native docking solutions with the corresponding experimental structures. For docking of unbound protein partners in several cases an improved ranking of near native docking solutions was observed. This was achieved at a very modest ( approximately 2-fold) increase of computational demands compared to rigid docking. For several test cases the number of docking solutions close to experiment was also significantly enhanced upon inclusion of soft collective degrees of freedom. This result indicates that inclusion of global flexibility can facilitate in silico protein-protein association such that a greater number of different start configurations results in favorable complex formation.     

Protein docking using spherical polar Fourier correlations

We present a new computational method of docking pairs of proteins by using spherical polar Fourier correlations to accelerate the search for candidate low-energy conformations. Interaction energies are estimated using a hydrophobic excluded volume model derived from the notion of "overlapping surface skins," augmented by a rigorous but "soft" model of electrostatic complementarity. This approach has several advantages over former three-dimensional grid-based fast Fourier transform (FFT) docking correlation methods even though there is no analogue to the FFT in a spherical polar representation. For example, a complete search over all six rigid-body degrees of freedom can be performed by rotating and translating only the initial expansion coefficients, many unfeasible orientations may be eliminated rapidly using only low-resolution terms, and the correlations are easily localized around known binding epitopes when this knowledge is available. Typical execution times on a single processor workstation range from 2 hours for a global search (5 x 10(8) trial orientations) to a few minutes for a local search (over 6 x 10(7) orientations). The method is illustrated with several domain dimer and enzyme-inhibitor complexes and 20 large antibody-antigen complexes, using both the bound and (when available) unbound subunits. The correct conformation of the complex is frequently identified when docking bound subunits, and a good docking orientation is ranked within the top 20 in 11 out of 18 cases when starting from unbound subunits. Proteins 2000;39:178-194.     

On the computation of molecular surface correlations for protein docking using fourier techniques

The computation of surface correlations using a variety of molecular models has been applied to the unbound protein docking problem. Because of the computational complexity involved in examining all possible molecular orientations, the fast Fourier transform (FFT) (a fast numerical implementation of the discrete Fourier transform (DFT)) is generally applied to minimize the number of calculations. This approach is rooted in the convolution theorem which allows one to inverse transform the product of two DFTs in order to perform the correlation calculation. However, such a DFT calculation results in a cyclic or "circular" correlation which, in general, does not lead to the same result as the linear correlation desired for the docking problem. In this work, we provide computational bounds for constructing molecular models used in the molecular surface correlation problem. The derived bounds are then shown to be consistent with various intuitive guidelines previously reported in the protein docking literature. Finally, these bounds are applied to different molecular models in order to investigate their effect on the correlation calculation.     

RosettaDock in CAPRI rounds 6-12

A challenge in protein-protein docking is to account for the conformational changes in the monomers that occur upon binding. The RosettaDock method, which incorporates sidechain flexibility but keeps the backbone fixed, was found in previous CAPRI rounds (4 and 5) to generate docking models with atomic accuracy, provided that conformational changes were mainly restricted to protein sidechains. In the recent rounds of CAPRI (6-12), large backbone conformational changes occur upon binding for several target complexes. To address these challenges, we explicitly introduced backbone flexibility in our modeling procedures by combining rigid-body docking with protein structure prediction techniques such as modeling variable loops and building homology models. Encouragingly, using this approach we were able to correctly predict a significant backbone conformational change of an interface loop for Target 20 (12 A rmsd between those in the unbound monomer and complex structures), but accounting for backbone flexibility in protein-protein docking is still very challenging because of the significantly larger conformational space, which must be surveyed. Motivated by these CAPRI challenges, we have made progress in reformulating RosettaDock using a "fold-tree" representation, which provides a general framework for treating a wide variety of flexible-backbone docking problems.     

Protein-protein docking with a reduced protein model accounting for side-chain flexibility

A protein-protein docking approach has been developed based on a reduced protein representation with up to three pseudo atoms per amino acid residue. Docking is performed by energy minimization in rotational and translational degrees of freedom. The reduced protein representation allows an efficient search for docking minima on the protein surfaces within. During docking, an effective energy function between pseudo atoms has been used based on amino acid size and physico-chemical character. Energy minimization of protein test complexes in the reduced representation results in geometries close to experiment with backbone root mean square deviations (RMSDs) of approximately 1 to 3 A for the mobile protein partner from the experimental geometry. For most test cases, the energy-minimized experimental structure scores among the top five energy minima in systematic docking studies when using both partners in their bound conformations. To account for side-chain conformational changes in case of using unbound protein conformations, a multicopy approach has been used to select the most favorable side-chain conformation during the docking process. The multicopy approach significantly improves the docking performance, using unbound (apo) binding partners without a significant increase in computer time. For most docking test systems using unbound partners, and without accounting for any information about the known binding geometry, a solution within approximately 2 to 3.5 A RMSD of the full mobile partner from the experimental geometry was found among the 40 top-scoring complexes. The approach could be extended to include protein loop flexibility, and might also be useful for docking of modeled protein structures.     

On the use of distance constraints in protein-protein docking computations

Protein-protein docking (PPD) is a computational process that predicts the structure of a complex of two interacting proteins from their unbound structures. The accuracy of PPD predictions is low, but can be greatly enhanced if experimentally determined distance data are available for incorporation into the prediction. However, the specific effects of distance constraints on PPD predictions are largely uncharacterized. In this study, we systematically simulated the effects of using distance constraints both on a new distance constraint-driven PPD approach, called DPPD, and also, by re-ranking, on a well-established grid-based global search approach. Our results for a PPD benchmark dataset of 84 protein complexes of known structures showed that near 100% docking success rates could be obtained when the number of distance constraints exceeded six, the degrees of freedom of the system, but the success rate was significantly reduced by long distance constraints, large binding-induced conformational changes, and large errors in the distance data. Our results also showed that, under most conditions simulated, even two or three distance constraints were sufficient to achieve a much better success rate than those using a sophisticated physicochemical function to re-rank the results of the global search. Our study provides guidelines for the practical incorporation of experimental distance data to aid PPD predictions.     

Shape complementarity of protein-protein complexes at multiple resolutions

Biological complexes typically exhibit intermolecular interfaces of high shape complementarity. Many computational docking approaches use this surface complementarity as a guide in the search for predicting the structures of protein-protein complexes. Proteins often undergo conformational changes to create a highly complementary interface when associating. These conformational changes are a major cause of failure for automated docking procedures when predicting binding modes between proteins using their unbound conformations. Low resolution surfaces in which high frequency geometric details are omitted have been used to address this problem. These smoothed, or blurred, surfaces are expected to minimize the differences between free and bound structures, especially those that are due to side chain conformations or small backbone deviations. Despite the fact that this approach has been used in many docking protocols, there has yet to be a systematic study of the effects of such surface smoothing on the shape complementarity of the resulting interfaces. Here we investigate this question by computing shape complementarity of a set of 66 protein-protein complexes represented by multiresolution blurred surfaces. Complexed and unbound structures are available for these protein-protein complexes. They are a subset of complexes from a nonredundant docking benchmark selected for rigidity (i.e. the proteins undergo limited conformational changes between their bound and unbound states). In this work, we construct the surfaces by isocontouring a density map obtained by accumulating the densities of Gaussian functions placed at all atom centers of the molecule. The smoothness or resolution is specified by a Gaussian fall-off coefficient, termed "blobbyness." Shape complementarity is quantified using a histogram of the shortest distances between two proteins' surface mesh vertices for both the crystallographic complexes and the complexes built using the protein structures in their unbound conformation. The histograms calculated for the bound complex structures demonstrate that medium resolution smoothing (blobbyness = -0.9) can reproduce about 88% of the shape complementarity of atomic resolution surfaces. Complexes formed from the free component structures show a partial loss of shape complementarity (more overlaps and gaps) with the atomic resolution surfaces. For surfaces smoothed to low resolution (blobbyness = -0.3), we find more consistency of shape complementarity between the complexed and free cases. To further reduce bad contacts without significantly impacting the good contacts we introduce another blurred surface, in which the Gaussian densities of flexible atoms are reduced. From these results we discuss the use of shape complementarity in protein-protein docking.     

Monte Carlo replica‐exchange based ensemble docking of protein conformations

A replica‐exchange Monte Carlo (REMC) ensemble docking approach has been developed that allows efficient exploration of protein–protein docking geometries. In addition to Monte Carlo steps in translation and orientation of binding partners, possible conformational changes upon binding are included based on Monte Carlo selection of protein conformations stored as ordered pregenerated conformational ensembles. The conformational ensembles of each binding partner protein were generated by three different approaches starting from the unbound partner protein structure with a range spanning a root mean square deviation of 1–2.5 Å with respect to the unbound structure. Because MC sampling is performed to select appropriate partner conformations on the fly the approach is not limited by the number of conformations in the ensemble compared to ensemble docking of each conformer pair in ensemble cross docking. Although only a fraction of generated conformers was in closer agreement with the bound structure the REMC ensemble docking approach achieved improved docking results compared to REMC docking with only the unbound partner structures or using docking energy minimization methods. The approach has significant potential for further improvement in combination with more realistic structural ensembles and better docking scoring functions. Proteins 2017; 85:924–937. © 2016 Wiley Periodicals, Inc.     

Enhanced sampling of protein conformational states for dynamic cross-docking within the protein-protein docking server SwarmDock

The formation of specific protein-protein interactions is often a key to a protein's function. During complex formation, each protein component will undergo a change in the conformational state, for some these changes are relatively small and reside primarily at the sidechain level; however, others may display notable backbone adjustments. One of the classic problems in the protein-docking field is to be able to a priori predict the extent of such conformational changes. In this work, we investigated three protocols to find the most suitable input structure conformations for cross-docking, including a robust sampling approach in normal mode space. Counterintuitively, knowledge of the theoretically best combination of normal modes for unbound-bound transitions does not always lead to the best results. We used a novel spatial partitioning library, Aether Engine (see Supplementary Materials ), to efficiently search the conformational states of 56 receptor/ligand pairs, including a recent CAPRI target, in a systematic manner and selected diverse conformations as input to our automated docking server, SwarmDock, a server that allows moderate conformational adjustments during the docking process. In essence, here we present a dynamic cross-docking protocol, which when benchmarked against the simpler approach of just docking the unbound components shows a 10% uplift in the quality of the top docking pose.     

A Unified Conformational Selection and Induced Fit Approach to Protein-Peptide Docking

Protein-peptide interactions are vital for the cell. They mediate, inhibit or serve as structural components in nearly 40% of all macromolecular interactions, and are often associated with diseases, making them interesting leads for protein drug design. In recent years, large-scale technologies have enabled exhaustive studies on the peptide recognition preferences for a number of peptide-binding domain families. Yet, the paucity of data regarding their molecular binding mechanisms together with their inherent flexibility makes the structural prediction of protein-peptide interactions very challenging. This leaves flexible docking as one of the few amenable computational techniques to model these complexes. We present here an ensemble, flexible protein-peptide docking protocol that combines conformational selection and induced fit mechanisms. Starting from an ensemble of three peptide conformations (extended, a-helix, polyproline-II), flexible docking with HADDOCK generates 79.4% of high quality models for bound/unbound and 69.4% for unbound/unbound docking when tested against the largest protein-peptide complexes benchmark dataset available to date. Conformational selection at the rigid-body docking stage successfully recovers the most relevant conformation for a given protein-peptide complex and the subsequent flexible refinement further improves the interface by up to 4.5 Å interface RMSD. Cluster-based scoring of the models results in a selection of near-native solutions in the top three for ∼75% of the successfully predicted cases. This unified conformational selection and induced fit approach to protein-peptide docking should open the route to the modeling of challenging systems such as disorder-order transitions taking place upon binding, significantly expanding the applicability limit of biomolecular interaction modeling by docking.     

Accounting for global protein deformability during protein-protein and protein-ligand docking

Computational docking methods are valuable tools aimed to simplify the costly process of drug development and improvement. Most current approaches assume a rigid receptor structure to allow virtual screening of large numbers of possible ligands and putative binding sites on a receptor molecule. However, inclusion of receptor flexibility can be of critical importance since binding of a ligand can lead to changes in the receptor protein conformation that are sterically necessary to accommodate a ligand. Recent approaches to efficiently account for receptor flexibility during docking simulations are reviewed. In particular, accounting efficiently for global conformational changes of the protein backbone during docking is a still challenging unsolved problem. An approximate method has recently been suggested that is based on relaxing the receptor conformation during docking in pre-calculated soft collective degrees of freedom (M. Zacharias, Rapid protein-ligand docking using soft modes from molecular dynamics simulations to account for protein deformability: binding of FK506 to FKBP, Proteins: Struct., Funct., Genet. 54 (2004) 759-767). Test applications on protein-protein docking and on docking the inhibitor staurosporine to the apo-form of cAMP-dependent protein kinase A catalytic domain indicate significant improvement of docking results compared to rigid docking at a very modest computational demand. Accounting for receptor conformational changes in pre-calculated global degrees of freedom might offer a promising route to improve systematic docking screening simulations.     

Multi-LZerD: multiple protein docking for asymmetric complexes

The tertiary structures of protein complexes provide a crucial insight about the molecular mechanisms that regulate their functions and assembly. However, solving protein complex structures by experimental methods is often more difficult than single protein structures. Here, we have developed a novel computational multiple protein docking algorithm, Multi‐LZerD, that builds models of multimeric complexes by effectively reusing pairwise docking predictions of component proteins. A genetic algorithm is applied to explore the conformational space followed by a structure refinement procedure. Benchmark on eleven hetero‐multimeric complexes resulted in near‐native conformations for all but one of them (a root mean square deviation smaller than 2.5Å). We also show that our method copes with unbound docking cases well, outperforming the methodology that can be directly compared with our approach. Multi‐LZerD was able to predict near‐native structures for multimeric complexes of various topologies.Proteins 2012; © 2012 Wiley Periodicals, Inc.     

Modelling repressor proteins docking to DNA

The docking of repressor proteins to DNA starting from the unbound protein and model-built DNA coordinates is modeled computationally. The approach was evaluated on eight repressor/DNA complexes that employed different modes for protein/ DNA recognition. The global search is based on a protein-protein docking algorithm that evaluates shape and electrostatic complementarity, which was modified to consider the importance of electrostatic features in DNA-protein recognition. Complexes were then ranked by an empirical score for the observed amino acid /nucleotide pairings (i.e., protein-DNA pair potentials) derived from a database of 20 protein/DNA complexes. A good prediction had at least 65% of the correct contacts modeled. This approach was able to identify a good solution at rank four or better for three out of the eight complexes. Predicted complexes were filtered by a distance constraint based on experimental data defining the DNA footprint. This improved coverage to four out of eight complexes having a good model at rank four or better. The additional use of amino acid mutagenesis and phylogenetic data defining residues on the repressor resulted in between 2 and 27 models that would have to be examined to find a good solution for seven of the eight test systems. This study shows that starting with unbound coordinates one can predict three-dimensional models for protein/DNA complexes that do not involve gross conformational changes on association. Proteins 33:535–549, 1998. © 1998 Wiley-Liss, Inc.     

Comparing bound and unbound protein structures using energy calculation and rotamer statistics

Protein data in the PDB covers only a snapshot of a protein structure. For flexible docking conformational changes need to be considered. Rotamer statistics provide the likelihood for side chain conformations, and further comparison of bound and unbound state yields differences in preferred positions. Furthermore, we do a full sampling of selected chi angles and apply the AMBER force field. Conformation of energy minima complies with the rotamer statistics. Both types of information target the reduction of search space for enumerative docking algorithms and provide parameters for elastic docking.     

Mapping of antibody epitopes based on docking and homology modeling

Antibodies are key proteins produced by the immune system to target pathogen proteins termed antigens via specific binding to surface regions called epitopes. Given an antigen and the sequence of an antibody the knowledge of the epitope is critical for the discovery and development of antibody based therapeutics. In this work, we present a computational protocol that uses template-based modeling and docking to predict epitope residues. This protocol is implemented in three major steps. First, a template-based modeling approach is used to build the antibody structures. We tested several options, including generation of models using AlphaFold2. Second, each antibody model is docked to the antigen using the fast Fourier transform (FFT) based docking program PIPER. Attention is given to optimally selecting the docking energy parameters depending on the input data. In particular, the van der Waals energy terms are reduced for modeled antibodies relative to x-ray structures. Finally, ranking of antigen surface residues is produced. The ranking relies on the docking results, that is, how often the residue appears in the docking poses' interface, and also on the energy favorability of the docking pose in question. The method, called PIPER-Map, has been tested on a widely used antibody–antigen docking benchmark. The results show that PIPER-Map improves upon the existing epitope prediction methods. An interesting observation is that epitope prediction accuracy starting from antibody sequence alone does not significantly differ from that of starting from unbound (i.e., separately crystallized) antibody structure.     

ReFlexIn: A Flexible Receptor Protein-Ligand Docking Scheme Evaluated on HIV-1 Protease

For many targets of pharmaceutical importance conformational changes of the receptor protein are relevant during the ligand binding process. A new docking approach, ReFlexIn (Receptor Flexibility by Interpolation), that combines receptor flexibility with the computationally efficient potential grid representation of receptor molecules has been evaluated on the retroviral HIV-1 (Human Immunodeficiency Virus 1) protease system. An approximate inclusion of receptor flexibility is achieved by using interpolation between grid representations of individual receptor conformations. For the retroviral protease the method was tested on an ensemble of protease structures crystallized in the presence of different ligands and on a set of structures obtained from morphing between the unbound and a ligand-bound protease structure. Docking was performed on ligands known to bind to the protease and several non-binders. For the binders the ReFlexIn method yielded in almost all cases ligand placements in similar or closer agreement with experiment than docking to any of the ensemble members without degrading the discrimination with respect to non-binders. The improved docking performance compared to docking to rigid receptors allows for systematic virtual screening applications at very small additional computational cost.     

Side-chain conformational changes upon Protein-Protein Association

Conformational changes upon protein-protein association are the key element of the binding mechanism. The study presents a systematic large-scale analysis of such conformational changes in the side chains. The results indicate that short and long side chains have different propensities for the conformational changes. Long side chains with three or more dihedral angles are often subject to large conformational transition. Shorter residues with one or two dihedral angles typically undergo local conformational changes not leading to a conformational transition. A relationship between the local readjustments and the equilibrium fluctuations of a side chain around its unbound conformation is suggested. Most of the side chains undergo larger changes in the dihedral angle most distant from the backbone. The frequencies of the core-to-surface interface transitions of six nonpolar residues and Tyr are larger than the frequencies of the opposite surface-to-core transitions. The binding increases both polar and nonpolar interface areas. However, the increase of the nonpolar area is larger for all considered classes of protein complexes, suggesting that the protein association perturbs the unbound interfaces to increase the hydrophobic contribution to the binding free energy. To test modeling approaches to side-chain flexibility in protein docking, conformational changes in the X-ray set were compared with those in the docking decoy sets. The results lead to a better understanding of the conformational changes in proteins and suggest directions for efficient conformational sampling in docking protocols.     

Solvated protein–DNA docking using HADDOCK

Interfacial water molecules play an important role in many aspects of protein–DNA specificity and recognition. Yet they have been mostly neglected in the computational modeling of these complexes. We present here a solvated docking protocol that allows explicit inclusion of water molecules in the docking of protein–DNA complexes and demonstrate its feasibility on a benchmark of 30 high-resolution protein–DNA complexes containing crystallographically-determined water molecules at their interfaces. Our protocol is capable of reproducing the solvation pattern at the interface and recovers hydrogen-bonded water-mediated contacts in many of the benchmark cases. Solvated docking leads to an overall improvement in the quality of the generated protein–DNA models for cases with limited conformational change of the partners upon complex formation. The applicability of this approach is demonstrated on real cases by docking a representative set of 6 complexes using unbound protein coordinates, model-built DNA and knowledge-based restraints. As HADDOCK supports the inclusion of a variety of NMR restraints, solvated docking is also applicable for NMR-based structure calculations of protein–DNA complexes.     

Constructing ensembles of flexible fragments in native proteins by iterative stochastic elimination is relevant to protein-protein interfaces

We investigate the extent to which ensembles of flexible fragments (FF), generated by our loop conformational search method, include conformations that are near experimental and reflect conformational changes that these FFs undergo when binary protein-protein complexes are formed. Twenty-eight FFs, which are located in protein-protein interfaces and have different conformations in the bound structure (BS) and unbound structure (UbS) were extracted. The conformational space of these fragments in the BS and UbS was explored with our method which is based on the iterative stochastic elimination (ISE) algorithm. Conformational search of BSs generated bound ensembles and conformational search of UbSs produced unbound ensembles. ISE samples conformations near experimental (less than 1.05 A root mean square deviation, RMSD) for 51 out of the 56 examined fragments in the bound and unbound ensembles. In 14 out of the 28 unbound fragments, it also samples conformations within 1.05 A from the BS in the unbound ensemble. Sampling the bound conformation in the unbound ensemble demonstrates the potential biological relevance of the predicted ensemble. The 10 lowest energy conformations are the best choice for docking experiments, compared with any other 10 conformations of the ensembles. We conclude that generating conformational ensembles for FFs with ISE is relevant to FF conformations in the UbS and BS. Forming ensembles of the isolated proteins with our method prior to docking represents more comprehensively their inherent flexibility and is expected to improve docking experiments compared with results obtained by docking only UbSs.     

Conformer selection and induced fit in flexible backbone protein-protein docking using computational and NMR ensembles

Accommodating backbone flexibility continues to be the most difficult challenge in computational docking of protein-protein complexes. Towards that end, we simulate four distinct biophysical models of protein binding in RosettaDock, a multiscale Monte-Carlo-based algorithm that uses a quasi-kinetic search process to emulate the diffusional encounter of two proteins and to identify low-energy complexes. The four binding models are as follows: (1) key-lock (KL) model, using rigid-backbone docking; (2) conformer selection (CS) model, using a novel ensemble docking algorithm; (3) induced fit (IF) model, using energy-gradient-based backbone minimization; and (4) combined conformer selection/induced fit (CS/IF) model. Backbone flexibility was limited to the smaller partner of the complex, structural ensembles were generated using Rosetta refinement methods, and docking consisted of local perturbations around the complexed conformation using unbound component crystal structures for a set of 21 target complexes. The lowest-energy structure contained > 30% of the native residue-residue contacts for 9, 13, 13, and 14 targets for KL, CS, IF, and CS/IF docking, respectively. When applied to 15 targets using nuclear magnetic resonance ensembles of the smaller protein, the lowest-energy structure recovered at least 30% native residue contacts in 3, 8, 4, and 8 targets for KL, CS, IF, and CS/IF docking, respectively. CS/IF docking of the nuclear magnetic resonance ensemble performed equally well or better than KL docking with the unbound crystal structure in 10 of 15 cases. The marked success of CS and CS/IF docking shows that ensemble docking can be a versatile and effective method for accommodating conformational plasticity in docking and serves as a demonstration for the CS theory—that binding-competent conformers exist in the unbound ensemble and can be selected based on their favorable binding energies.