ParaDock: a flexible non-specific DNA--rigid protein docking algorithm

Accurate prediction of protein-DNA complexes could provide an important stepping stone towards a thorough comprehension of vital intracellular processes. Few attempts were made to tackle this issue, focusing on binding patch prediction, protein function classification and distance constraints-based docking. We introduce ParaDock: a novel ab initio protein-DNA docking algorithm. ParaDock combines short DNA fragments, which have been rigidly docked to the protein based on geometric complementarity, to create bent planar DNA molecules of arbitrary sequence. Our algorithm was tested on the bound and unbound targets of a protein-DNA benchmark comprised of 47 complexes. With neither addressing protein flexibility, nor applying any refinement procedure, CAPRI acceptable solutions were obtained among the 10 top ranked hypotheses in 83% of the bound complexes, and 70% of the unbound. Without requiring prior knowledge of DNA length and sequence, and within <2?h per target on a standard 2.0?GHz single processor CPU, ParaDock offers a fast ab initio docking solution.     

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.     

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.     

Docking unbound proteins using shape complementarity, desolvation, and electrostatics

A comprehensive docking study was performed on 27 distinct protein-protein complexes. For 13 test systems, docking was performed with the unbound X-ray structures of both the receptor and the ligand. For the remaining systems, the unbound X-ray structure of only molecule was available; therefore the bound structure for the other molecule was used. Our method optimizes desolvation, shape complementarity, and electrostatics using a Fast Fourier Transform algorithm. A global search in the rotational and translational space without any knowledge of the binding sites was performed for all proteins except nine antibodies recognizing antigens. For these antibodies, we docked their well-characterized binding site-the complementarity-determining region defined without information of the antigen-to the entire surface of the antigen. For 24 systems, we were able to find near-native ligand orientations (interface C(alpha) root mean square deviation less than 2.5 A from the crystal complex) among the top 2,000 choices. For three systems, our algorithm could identify the correct complex structure unambiguously. For 13 other complexes, we either ranked a near-native structure in the top 20 or obtained 20 or more near-native structures in the top 2,000 or both. The key feature of our algorithm is the use of target functions that are highly tolerant to conformational changes upon binding. If combined with a post-processing method, our algorithm may provide a general solution to the unbound docking problem. Our program, called ZDOCK, is freely available to academic users (http://zlab.bu.edu/~rong/dock/).     

Effect of local shape modifications of molecular surfaces on rigid-body protein-protein docking

Geometric complementarity is the most dominant term in protein-protein docking and therefore, a good geometric representation of the molecules, which takes into account the flexibility of surface residues, is desirable. We present a modified geometric representation of the molecular surface that down-weighs the contribution of specified parts of the surface to the complementarity score. We apply it to the mobile ends of the most flexible side chains: lysines, glutamines and arginines (trimming). The new representation systematically reduces the complementarity scores of the false-positive solutions, often more than the scores of the correct solutions, thereby improving significantly our ability to identify nearly correct solutions in rigid-body docking of unbound structures. The effect of trimming lysine residues is larger than trimming of glutamine or arginine residues. It appears to be independent of the conformations of the trimmed residues but depends on the relative abundance of such residues at the interface and on the non-interacting surface. Combining the modified geometric representation with electrostatic complementarity further improves the docking results.     

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.     

Looking at enzymes from the inside out: the proximity of catalytic residues to the molecular centroid can be used for detection of active sites and enzyme-ligand interfaces

Analysis of the distances of the exposed residues in 175 enzymes from the centroids of the molecules indicates that catalytic residues are very often found among the 5% of residues closest to the enzyme centroid. This property of catalytic residues is implemented in a new prediction algorithm (named EnSite) for locating the active sites of enzymes and in a new scheme for re-ranking enzyme-ligand docking solutions. EnSite examines only 5% of the molecular surface (represented by surface dots) that is closest to the centroid, identifying continuous surface segments and ranking them by their area size. EnSite ranks the correct prediction 1-4 in 97% of the cases in a dataset of 65 monomeric enzymes (rank 1 for 89% of the cases) and in 86% of the cases in a dataset of 176 monomeric and multimeric enzymes from all six top-level enzyme classifications (rank 1 in 74% of the cases). Importantly, identification of buried or flat active sites is straightforward because EnSite "looks" at the molecular surface from the inside out. Detailed examination of the results indicates that the proximity of the catalytic residues to the centroid is a property of the functional unit, defined as the assembly of domains or chains that form the active site (in most cases the functional unit corresponds to a single whole polypeptide chain). Using the functional unit in the prediction further improves the results. The new property of active sites is also used for re-evaluating enzyme-inhibitor unbound docking results. Sorting the docking solutions by the distance of the interface to the centroid of the enzyme improves remarkably the ranks of nearly correct solutions compared to ranks based on geometric-electrostatic-hydrophobic complementarity scores.     

Protein-DNA docking with a coarse-grained force field

ABSTRACT: BACKGROUND: Protein-DNA interactions are important for many cellular processes, however structural knowledge for a large fraction of known and putative complexes is still lacking. Computational docking methods aim at the prediction of complex architecture given detailed structures of its constituents. They are becoming an increasingly important tool in the field of macromolecular assemblies, complementing particularly demanding protein-nucleic acids X ray crystallography and providing means for the refinement and integration of low resolution data coming from rapidly advancing methods such as cryoelectron microscopy. RESULTS: We present a new coarse-grained force field suitable for protein-DNA docking. The force field is an extension of previously developed parameter sets for protein-RNA and protein-protein interactions. The docking is based on potential energy minimization in translational and orientational degrees of freedom of the binding partners. It allows for fast and efficient systematic search for native-like complex geometry without any prior knowledge regarding binding site location. CONCLUSIONS: We find that the force field gives very good results for bound docking. The quality of predictions in the case of unbound docking varies, depending on the level of structural deviation from bound geometries. We analyze the role of specific protein-DNA interactions on force field performance, both with respect to complex structure prediction, and the reproduction of experimental binding affinities. We find that such direct, specific interactions only partially contribute to protein-DNA recognition, indicating an important role of shape complementarity and sequence-dependent DNA internal energy, in line with the concept of indirect protein-DNA readout mechanism.     

Electrostatic contributions to protein-protein interactions: fast energetic filters for docking and their physical basis

The methods of continuum electrostatics are used to calculate the binding free energies of a set of protein-protein complexes including experimentally determined structures as well as other orientations generated by a fast docking algorithm. In the native structures, charged groups that are deeply buried were often found to favor complex formation (relative to isosteric nonpolar groups), whereas in nonnative complexes generated by a geometric docking algorithm, they were equally likely to be stabilizing as destabilizing. These observations were used to design a new filter for screening docked conformations that was applied, in conjunction with a number of geometric filters that assess shape complementarity, to 15 antibody-antigen complexes and 14 enzyme-inhibitor complexes. For the bound docking problem, which is the major focus of this paper, native and near-native solutions were ranked first or second in all but two enzyme-inhibitor complexes. Less success was encountered for antibody-antigen complexes, but in all cases studied, the more complete free energy evaluation was able to identify native and near-native structures. A filter based on the enrichment of tyrosines and tryptophans in antibody binding sites was applied to the antibody-antigen complexes and resulted in a native and near-native solution being ranked first and second in all cases. A clear improvement over previously reported results was obtained for the unbound antibody-antigen examples as well. The algorithm and various filters used in this work are quite efficient and are able to reduce the number of plausible docking orientations to a size small enough so that a final more complete free energy evaluation on the reduced set becomes computationally feasible.     

Protein docking using a genetic algorithm

A genetic algorithm (GA) for protein-protein docking is described, in which the proteins are represented by dot surfaces calculated using the Connolly program. The GA is used to move the surface of one protein relative to the other to locate the area of greatest surface complementarity between the two. Surface dots are deemed complementary if their normals are opposed, their Connolly shape type is complementary, and their hydrogen bonding or hydrophobic potential is fulfilled. Overlap of the protein interiors is penalized. The GA is tested on 34 large protein-protein complexes where one or both proteins has been crystallized separately. Parameters are established for which 30 of the complexes have at least one near-native solution ranked in the top 100. We have also successfully reassembled a 1,400-residue heptamer based on the top-ranking GA solution obtained when docking two bound subunits.     

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.     

Molecular recognition via face center representation of a molecular surface

While docking methodologies are now frequently being developed, a careful examination of the molecular surface representation, which necessarily is employed by them, is largely overlooked. There are two important aspects here that need to be addressed: how the surface representation quantifies surface complementarity, and whether a minimal representation is employed. Although complementarity is an accepted concept regarding molecular recognition, its quantification for computation is not trivial, and requires verification. A minimal representation is important because docking searches a conformational space whose extent and/ or dimensionality grows quickly with the size of surface representation, making it especially costly with big molecules, imperfect interfaces, and changes of conformation that occur in binding. It is essential for a docking methodology to establish that it employs an accurate, concise molecular surface representation.Here we employ the face center representation of molecular surface, developed by Lin et al.,¹ to investigate the complementarity of molecular interface. We study a wide variety of complexes: protein/small ligand, oligomeric chain-chain interfaces, proteinase/protein inhibitors, antibody/antigen, NMR structures, and complexes built from unbound, separately solved structures. The complementarity is examined at different levels of reduction, and hence roughness, of the surface representation, from one that describes subatomic details to a very sparse one that captures only the prominent features on the surface. Our simulation of molecular recognition indicates that in all cases, quality interface complementarity is obtained. We show that the representation is powerful in monitoring the complementarity either in its entirety, or in selected subsets that maintain a fraction of the face centers, and is capable of supporting molecular docking at high fidelity and efficiency. Furthermore, we also demonstrate that the presence of explicit hydrogens in molecular structures may not benefit docking, and that the different classes of protein complexes and may hold slightly different degrees of interface complementarity.     

BiGGER: a new (soft) docking algorithm for predicting protein interactions

A new computationally efficient and automated "soft docking" algorithm is described to assist the prediction of the mode of binding between two proteins, using the three-dimensional structures of the unbound molecules. The method is implemented in a software package called BiGGER (Bimolecular Complex Generation with Global Evaluation and Ranking) and works in two sequential steps: first, the complete 6-dimensional binding spaces of both molecules is systematically searched. A population of candidate protein-protein docked geometries is thus generated and selected on the basis of the geometric complementarity and amino acid pairwise affinities between the two molecular surfaces. Most of the conformational changes observed during protein association are treated in an implicit way and test results are equally satisfactory, regardless of starting from the bound or the unbound forms of known structures of the interacting proteins. In contrast to other methods, the entire molecular surfaces are searched during the simulation, using absolutely no additional information regarding the binding sites. In a second step, an interaction scoring function is used to rank the putative docked structures. The function incorporates interaction terms that are thought to be relevant to the stabilization of protein complexes. These include: geometric complementarity of the surfaces, explicit electrostatic interactions, desolvation energy, and pairwise propensities of the amino acid side chains to contact across the molecular interface. The relative functional contribution of each of these interaction terms to the global scoring function has been empirically adjusted through a neural network optimizer using a learning set of 25 protein-protein complexes of known crystallographic structures. In 22 out of 25 protein-protein complexes tested, near-native docked geometries were found with C(alpha) RMS deviations < or =4.0 A from the experimental structures, of which 14 were found within the 20 top ranking solutions. The program works on widely available personal computers and takes 2 to 8 hours of CPU time to run any of the docking tests herein presented. Finally, the value and limitations of the method for the study of macromolecular interactions, not yet revealed by experimental techniques, are discussed.     

Examination of shape complementarity in docking of unbound proteins.

Here we carry out an examination of shape complementarity as a criterion in protein-protein docking and binding. Specifically, we examine the quality of shape complementarity as a critical determinant not only in the docking of 26 protein-protein "bound" complexed cases, but in particular, of 19 "unbound" protein-protein cases, where the structures have been determined separately. In all cases, entire molecular surfaces are utilized in the docking, with no consideration of the location of the active site, or of particular residues/atoms in either the receptor or the ligand that participate in the binding. To evaluate the goodness of the strictly geometry-based shape complementarity in the docking process as compared to the main favorable and unfavorable energy components, we study systematically a potential correlation between each of these components and the root mean square deviation (RMSD) of the "unbound" protein-protein cases. Specifically, we examine the non-polar buried surface area, polar buried surface area, buried surface area relating to groups bearing unsatisfied buried charges, and the number of hydrogen bonds in all docked protein-protein interfaces. For these cases, where the two proteins have been crystallized separately, and where entire molecular surfaces are considered without a predefinition of the binding site, no correlation is observed. None of these parameters appears to consistently improve on shape complementarity in the docking of unbound molecules. These findings argue that simplicity in the docking process, utilizing geometrical shape criteria may capture many of the essential features in protein-protein docking. In particular, they further reinforce the long held notion of the importance of molecular surface shape complementarity in the binding, and hence in docking. This is particularly interesting in light of the fact that the structures of the docked pairs have been determined separately, allowing side chains on the surface of the proteins to move relatively freely. This study has been enabled by our efficient, computer vision-based docking algorithms. The fast CPU matching times, on the order of minutes on a PC, allow such large-scale docking experiments of large molecules, which may not be feasible by other techniques. Proteins 1999;36:307-317.     

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.     

Hydrophobic complementarity in protein-protein docking

Formation of hydrophobic contacts across a newly formed interface is energetically favorable. Based on this observation we developed a geometric-hydrophobic docking algorithm that estimates quantitatively the hydrophobic complementarity at protein-protein interfaces. Each molecule to be docked is represented as a grid of complex numbers, storing information regarding the shape of the molecule in the real part and information regarding the hydropathy of the surface in the imaginary part. The grid representations are correlated using fast Fourier transformations. The algorithm is used to compare the extent of hydrophobic complementarity in oligomers (represented by D2 tetramers) and in hetero-dimers of soluble proteins (complexes). We also test the implication of hydrophobic complementarity in distinguishing correct from false docking solutions. We find that hydrophobic complementarity at the interface exists in oligomers and in complexes, and in both groups the extent of such complementarity depends on the size of the interface. Thus, the non-polar portions of large interfaces are more often juxtaposed than non-polar portions of small interfaces. Next we find that hydrophobic complementarity helps to point out correct docking solutions. In oligomers it significantly improves the ranks of nearly correct reassembled and modeled tetramers. Combining geometric, electrostatic and hydrophobic complementarity for complexes gives excellent results, ranking a nearly correct solution < 10 for 5 of 23 tested systems, < 100 for 8 systems and < 1000 for 19 systems.     

Use of pair potentials across protein interfaces in screening predicted docked complexes.

Empirical residue-residue pair potentials are used to screen possible complexes for protein-protein dockings. A correct docking is defined as a complex with not more than 2.5 A root-mean-square distance from the known experimental structure. The complexes were generated by "ftdock" (Gabb et al. J Mol Biol 1997;272:106-120) that ranks using shape complementarity. The complexes studied were 5 enzyme-inhibitors and 2 antibody-antigens, starting from the unbound crystallographic coordinates, with a further 2 antibody-antigens where the antibody was from the bound crystallographic complex. The pair potential functions tested were derived both from observed intramolecular pairings in a database of nonhomologous protein domains, and from observed intermolecular pairings across the interfaces in sets of nonhomologous heterodimers and homodimers. Out of various alternate strategies, we found the optimal method used a mole-fraction calculated random model from the intramolecular pairings. For all the systems, a correct docking was placed within the top 12% of the pair potential score ranked complexes. A combined strategy was developed that incorporated "multidock," a side-chain refinement algorithm (Jackson et al. J Mol Biol 1998;276:265-285). This placed a correct docking within the top 5 complexes for enzyme-inhibitor systems, and within the top 40 complexes for antibody-antigen systems.     

Protein docking using surface matching and supervised machine learning

Computational prediction of protein complex structures through docking offers a means to gain a mechanistic understanding of protein interactions that mediate biological processes. This is particularly important as the number of experimentally determined structures of isolated proteins exceeds the number of structures of complexes. A comprehensive docking procedure is described in which efficient sampling of conformations is achieved by matching surface normal vectors, fast filtering for shape complementarity, clustering by RMSD, and scoring the docked conformations using a supervised machine learning approach. Contacting residue pair frequencies, residue propensities, evolutionary conservation, and shape complementarity score for each docking conformation are used as input data to a Random Forest classifier. The performance of the Random Forest approach for selecting correctly docked conformations was assessed by cross-validation using a nonredundant benchmark set of X-ray structures for 93 heterodimer and 733 homodimer complexes. The single highest rank docking solution was the correct (near-native) structure for slightly more than one third of the complexes. Furthermore, the fraction of highly ranked correct structures was significantly higher than the overall fraction of correct structures, for almost all complexes. A detailed analysis of the difficult to predict complexes revealed that the majority of the homodimer cases were explained by incorrect oligomeric state annotation. Evolutionary conservation and shape complementarity score as well as both underrepresented and overrepresented residue types and residue pairs were found to make the largest contributions to the overall prediction accuracy. Finally, the method was also applied to docking unbound subunit structures from a previously published benchmark set.