Prediction of protein-protein interactions based on surface patch comparison

A method to predict if two proteins interact, based on their three-dimensional structures, is presented. It consists of five steps: (i) the surface of each protein, represented by the solvent accessible atoms, is divided into small patches; (ii) the shape of each patch is described by the atom distributions along its principal axes; (iii) the shape complementarity between two patches is estimated by comparing, through contingency table analysis, their atom distributions along their principal axes; (iv) given protein A, with nA surface patches, and protein B, with nB surface patches, nA x nB shape complementarity values are obtained; and (v) the distribution of the latter allows one to discriminate pairs of interacting and of noninteracting proteins. Only a few seconds are necessary to predict if two proteins interact, with accuracy close to 80%, sensitivity over 70% and specificity close to 50%.     

Searching for geometric molecular shape complementarity using bidimensional surface profiles

The study presented herein is a bidimensional approach to the complementarity of two molecular surfaces. From two chosen sections we have established a methodology of generating the optimal matching of two shapes. Our approach consists in describing two molecular surface sections by a shape vector (the angular profile), in finding their matching patterns by comparison of the two profiles, and in optimizing the relative locations of the two sections in two-dimensional space, using rotations and translations defined by geometric characteristics. The set of optimal configurations are successively displayed on a screen. Satisfying results have been obtained for the matching of the complex kallikreine Atrypsin pancreatic bovin 2. This efficient method could be used as a preprocessing for a tridimensional shape complementarity approach between two molecular surfaces.     

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.     

Context shapes: Efficient complementary shape matching for protein-protein docking

We describe an efficient method for partial complementary shape matching for use in rigid protein-protein docking. The local shape features of a protein are represented using boolean data structures called Context Shapes. The relative orientations of the receptor and ligand surfaces are searched using precalculated lookup tables. Energetic quantities are derived from shape complementarity and buried surface area computations, using efficient boolean operations. Preliminary results indicate that our context shapes approach outperforms state-of-the-art geometric shape-based rigid-docking algorithms.     

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.     

New Docking Algorithm Based on Fuzzy Set Theory

A new docking algorithm based on shape complementarity is presented. The algorithm is based on Fuzzy Logic strategies. A small number of possible docking configurations is selected using partial ordering of a fuzzy measure of topographical properties between complementary surface patches. The algorithm was tested with the structures of three protein-protein-complexes of serin proteases. In one case the components determined separately by x-ray investigations whereas in the other cases the components obtained from the known complex structure were used.Electronic Supplementary Material available.     

Taking geometry to its edge: fast unbound rigid (and hinge-bent) docking

We present a very efficient rigid "unbound" soft docking methodology, which is based on detection of geometric shape complementarity, allowing liberal steric clash at the interface. The method is based on local shape feature matching, avoiding the exhaustive search of the 6D transformation space. Our experiments at CAPRI rounds 1 and 2 show that although the method does not perform an exhaustive search of the 6D transformation space, the "correct" solution is never lost. However, such a solution might rank low for large proteins, because there are alternatives with significantly larger geometrically compatible interfaces. In many cases this problem can be resolved by successful a priori focusing on the vicinity of potential binding sites as well as the extension of the technique to flexible (hinge-bent) docking. This is demonstrated in the experiments performed as a lesson from our CAPRI experience.     

Understanding crown shyness from a 3-D perspective

Background and AimsCrown shyness describes the phenomenon whereby tree crowns avoid growing into each other, producing a puzzle-like pattern of complementary tree crowns in the canopy. Previous studies found that tree slenderness plays a role in the development of crown shyness. Attempts to quantify crown shyness have largely been confined to 2-D approaches. This study aimed to expand the current set of metrics for crown shyness by quantifying the characteristic of 3-D surface complementarity between trees displaying crown shyness, using LiDAR-derived tree point clouds. Subsequently, the relationship between crown surface complementarity and slenderness of trees was assessed.MethodsFourteen trees were scanned using a laser scanning device. Individual tree points clouds were extracted semi-automatically and manually corrected where needed. A metric that quantifies the surface complementarity (S_c) of a pair of protein molecules is applied to point clouds of pairs of adjacent trees. Then 3-D tree crown surfaces were generated from point clouds by computing their α shapes.Key ResultsTree pairs that were visually determined to have overlapping crowns scored significantly lower S_c values than pairs that did not overlap (n = 14, P < 0.01). Furthermore, average slenderness of pairs of trees correlated positively with their S_c score (R² = 0.484, P < 0.01), showing agreement with previous studies on crown shyness.ConclusionsThe characteristic of crown surface complementarity present in trees displaying crown shyness was succesfully quantified using a 3-D surface complementarity metric adopted from molecular biology. Crown surface complementarity showed a positive relationship to tree slenderness, similar to other metrics used for measuring crown shyness. The 3-D metric developed in this study revealed how trees adapt the shape of their crowns to those of adjacent trees and how this is linked to the slenderness of the trees.     

Investigating protein-protein interaction surfaces using a reduced stereochemical and electrostatic model

A method of calculating the electrostatic potential energy between two molecules, using finite difference potential, is presented. A reduced charge set is used so that the interaction energy can be calculated as the two static molecules explore their full six-dimensional configurational space. The energies are contoured over surfaces fixed to each molecule with an interactive computer graphics program. For two crystal structures (trypsin-trypsin inhibitor and anti-lysozyme Fab-lysozyme), it is found that the complex corresponds to highly favourable interacting regions in the contour plots. These matches arise from a small number of protruding basic residues interacting with enhanced negative potential in each case. The redox pair cytochrome c peroxidase-cytochrome c exhibits an extensive favourably interacting surface within which a possible electron transfer complex may be defined by an increased electrostatic complementarity, but a decreased electrostatic energy. A possible substrate transfer configuration for the glycolytic enzyme pair glyceraldehyde phosphate dehydrogenase-phosphoglycerate kinase is presented.     

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.     

FitEM2EM--tools for low resolution study of macromolecular assembly and dynamics

Studies of the structure and dynamics of macromolecular assemblies often involve comparison of low resolution models obtained using different techniques such as electron microscopy or atomic force microscopy. We present new computational tools for comparing (matching) and docking of low resolution structures, based on shape complementarity. The matched or docked objects are represented by three dimensional grids where the value of each grid point depends on its position with regard to the interior, surface or exterior of the object. The grids are correlated using fast Fourier transformations producing either matches of related objects or docking models depending on the details of the grid representations. The procedures incorporate thickening and smoothing of the surfaces of the objects which effectively compensates for differences in the resolution of the matched/docked objects, circumventing the need for resolution modification. The presented matching tool FitEM2EMin successfully fitted electron microscopy structures obtained at different resolutions, different conformers of the same structure and partial structures, ranking correct matches at the top in every case. The differences between the grid representations of the matched objects can be used to study conformation differences or to characterize the size and shape of substructures. The presented low-to-low docking tool FitEM2EMout ranked the expected models at the top.     

A novel shape complementarity scoring function for protein-protein docking

Shape complementarity is the most basic ingredient of the scoring functions for protein-protein docking. Most grid-based docking algorithms use the total number of grid points at the binding interface to quantify shape complementarity. We have developed a novel Pairwise Shape Complementarity (PSC) function that is conceptually simple and rapid to compute. The favorable component of PSC is the total number of atom pairs between the receptor and the ligand within a distance cutoff. When applied to a benchmark of 49 test cases, PSC consistently ranks near-native structures higher and produces more near-native structures than the traditional grid-based function, and the improvement was seen across all prediction levels and in all categories of the benchmark. Without any post-processing or biological information about the binding site except the complementarity-determining region of antibodies, PSC predicts the complex structure correctly for 6 test cases, and ranks at least one near-native structure in the top 20 predictions for 18 test cases. Our docking program ZDOCK has been parallelized and the average computing time is 4 minutes using sixteen IBM SP3 processors. Both ZDOCK and the benchmark are freely available to academic users (http://zlab.bu.edu/~ rong/dock).     

Small angle x-ray scattering of the hemoglobin from Biomphalaria glabrata

The hemoglobin from Biomphalaria glabrata is an extracellular respiratory protein of high molecular mass composed by subunits of 360 kDa, each one containing two 180 kDa chains linked by disulfide bridges. In this work, small angle x-ray scattering (SAXS) measurements were performed with the hemoglobin at pH 5.0 and 7.5. Radii of gyration of 98.6 +/- 0.5 and 101.8 +/- 0.2 A and maximum diameters of 300 +/- 10 and 305 +/- 10 A, respectively, were obtained from Guinier plot extrapolation and analytical curve fitting. The pair distance distribution functions p(r) corresponded to globular particles with a somewhat anisotropic shape for both preparations. Computer analysis of the low angle part of the scattering curve led to the determination of the low resolution envelope of the protein, revealing a P(222) symmetry. Shape reconstruction from ab initio calculations using the complete scattering curve furnished a compact prolate three-dimensional (3D) bead model for the protein. Hydrodynamic parameters were obtained from experiments and theoretical calculations using the 3D model. The results of the structural and biochemical studies reported herein indicate that the multisubunit structure of this hemoglobin is compatible with a tetrameric arrangement.     

Effect of branching in 4-alkylpyrazoles on liver alcohol dehydrogenase inhibition: A shape analysis study

Shape analysis methodology is applied to the study of 4-alkylpyrazoles which are known inhibitors of liver alcohol dehydrogenase. Elongation of the alkyl chain increases the inhibitory power, whereas branching of the chain diminishes the activity. These two counterpoised effects are studied simultaneously in a selected set of 4-alkylpyrazoles. A systematic conformational analysis followed by topological characterization of the van der Waals surfaces of all the local minima restricts the conformational space to potential bioactive structures. The analysis of the interrelation between the molecular electrostatic potential and van der Waals surfaces provides certain shape codes characteristic of each 4-alkylpyrazole. In both topological analyses van der Waals surfaces and molecular electrostatic potential van der Waals surface interrelations) graphical representations and analytical methods were used. A good correlation between the shape codes and the inhibitory activity is found for the linear derivatives. For branched pyrazoles, a tendency in their inhibitory power is predicted. Isopentylpyrazole is suggested to have the same inhibitory profile as 4-butylpyrazole, the linear derivative with one less carbon atom.     

DNurbs: DNA modeled with NURBS

DNurbs (dee-in-urbs) are a small number of bicubic patches wrapping each base pair in complementary DNA. NURBS, the nonuniform rational B-spline surfaces now popular in computer graphics, are employed for the patches. Control points for the surface patches are generated from the molecular surface based on canonical base pairs.     

A fast protein-ligand docking algorithm based on hydrogen bond matching and surface shape complementarity

With the rapid development of structural determination of target proteins for human diseases, high throughout virtual screening based drug discovery is gaining popularity gradually. In this paper, a fast docking algorithm (H-DOCK) based on hydrogen bond matching and surface shape complementarity was developed. In H-DOCK, firstly a divide-and-conquer strategy based enumeration approach is applied to rank the intermolecular modes between protein and ligand by maximizing their hydrogen bonds matching, then each docked conformation of the ligand is calculated according to the matched hydrogen bonding geometry, finally a simple but effective scoring function reflecting mainly the van der Waals interaction is used to evaluate the docked conformations of the ligand. H-DOCK is tested for rigid ligand docking and flexible one, the latter is implemented by repeating rigid docking for multiple conformations of a small molecule and ranking all together. For rigid ligands, H-DOCK was tested on a set of 271 complexes where there is at least one intermolecular hydrogen bond, and H-DOCK achieved success rate (RMSD<2.0?Å) of 91.1%. For flexible ligands, H-DOCK was tested on another set of 93 complexes, where each case was a conformation ensemble containing native ligand conformation as well as 100 decoy ones generated by AutoDock [1], and the success rate reached 81.7%. The high success rate of H-DOCK indicates that the hydrogen bonding and steric hindrance can grasp the key interaction between protein and ligand. H-DOCK is quite efficient compared with the conventional docking algorithms, and it takes only about 0.14 seconds for a rigid ligand docking and about 8.25 seconds for a flexible one on average. According to the preliminary docking results, it implies that H-DOCK can be potentially used for large scale virtual screening as a pre-filter for a more accurate but less efficient docking algorithm.