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.     

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.     

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.     

Donor–Acceptor Shape Matching Drives Performance in Photovoltaics

While the demonstrated power conversion efficiency of organic photovoltaics (OPVs) now exceeds 10%, new design rules are required to tailor interfaces at the molecular level for optimal exciton dissociation and charge transport in higher efficiency devices. We show that molecular shape‐complementarity between donors and acceptors can drive performance in OPV devices. Using core hole clock (CHC) X‐ray spectroscopy and density functional theory (DFT), we compare the electronic coupling, assembly, and charge transfer rates at the interface between C₆₀ acceptors and flat‐ or contorted‐hexabenzocorone (HBC) donors. The HBC donors have similar optoelectronic properties but differ in molecular contortion and shape matching to the fullerene acceptors. We show that shape‐complementarity drives self‐assembly of an intermixed morphology with a donor/acceptor (D/A) ball‐and‐socket interface, which enables faster electron transfer from HBC to C₆₀. The supramolecular assembly and faster electron transfer rates in the shape complementary heterojunction lead to a larger active volume and enhanced exciton dissociation rate. This work provides fundamental mechanistic insights on the improved efficiency of organic photovoltaic devices that incorporate these concave/convex D/A materials.     

Profiling charge complementarity and selectivity for binding at the protein surface

A novel analysis and representation of the protein surface in terms of electrostatic binding complementarity and selectivity is presented. The charge optimization methodology is applied in a probe-based approach that simulates the binding process to the target protein. The molecular surface is color coded according to calculated optimal charge or according to charge selectivity, i.e., the binding cost of deviating from the optimal charge. The optimal charge profile depends on both the protein shape and charge distribution whereas the charge selectivity profile depends only on protein shape. High selectivity is concentrated in well-shaped concave pockets, whereas solvent-exposed convex regions are not charge selective. This suggests the synergy of charge and shape selectivity hot spots toward molecular selection and recognition, as well as the asymmetry of charge selectivity at the binding interface of biomolecular systems. The charge complementarity and selectivity profiles map relevant electrostatic properties in a readily interpretable way and encode information that is quite different from that visualized in the standard electrostatic potential map of unbound proteins.     

Docking of protein molecular surfaces with evolutionary trace analysis

We have developed a new method to predict protein- protein complexes based on the shape complementarity of the molecular surfaces, along with sequence conservation obtained by evolutionary trace (ET) analysis. The docking is achieved by optimization of an object function that evaluates the degree of shape complementarity weighted by the conservation of the interacting residues. The optimization is carried out using a genetic algorithm in combination with Monte Carlo sampling. We applied this method to CAPRI targets and evaluated the performance systematically. Consequently, our method could achieve native-like predictions in several cases. In addition, we have analyzed the feasibility of the ET method for docking simulations, and found that the conservation information was useful only in a limited category of proteins (signal related proteins and enzymes).     

Recognition and interactions controlling the assemblies of beta barrel domains.

We present a qualitative computer graphics approach to the characterization of forces important to the assembly of beta domains that should have general utility for examining protein interactions and assembly. In our approach, the nature of the molecular surface buried by the domain contacts, the specificity of the residue-to-residue interactions, and the identity of electrostatic, hydrophobic, and hydrophilic interactions are elucidated. These techniques are applied to the beta barrel domains of Cu, Zn superoxide dismutase (SOD), immunoglobulin Fab, and tomato bushy stunt virus coat protein (TBSV), a plant viral capsid protein. By looking at a set of proteins having different numbers of interacting beta domains, we have been able to see some of the variety and also some of the patterns common to these assembled domains. Strong beta domain interactions (identified by their biochemical integrity) are apparently due to chemical, electrostatic, and shape complementarity of the molecular surfaces buried from interaction with solvent molecules. Although the amount of hydrophobic buried surface area appears to correlate with the strength of the interaction, electrostatic forces appear to be important in both stabilizing and destabilizing specific contacts. In TBSV, analysis of electrostatic interactions may help explain mechanisms of subunit accommodation to different environments, particle expansion, and pathways of assembly. The possible molecular basis for observed differences in the stability and flexibility of the domain complexes is discussed.     

Statistical method for surface pattern-matching between dissimilar molecules: electrostatic potentials and accessible surfaces

This paper outlines a statistical method for patternmatching between surfaces and is applicable to structural and energetic patterns found on molecular surfaces. Correlation coefficients generated for the pattern match are scale invariant. Regression analysis applied to the patterns reveals the scaling and displacement relationships. The method for measuring the similarities between molecular surfaces of two dissimilar molecules held infixed orientations is given explicitly. Implicit in this procedure is a method for studying the inverse phenomenon, namely complementarity between surface parameters at a binding site and its ligand. The method has been used to assess surface differences in structural similarities generated by computer fitting and by visual comparison. Various pitfalls likely to be encountered in evaluating molecular structural similarities are noted.     

Effect of the solvent on recognition properties of molecularly imprinted polymer specific for ochratoxin A

A molecularly imprinted polymer specific for the mycotoxin ochratoxin A has been synthesised using a non-covalent approach. The polymer has shown an excellent affinity and specificity for the target template in aqueous solutions. The binding experiments, NMR study and molecular modelling have proven that the template recognition by polymer originates from the shape complementarity of binding sites. The binding mechanism is critically depended on factors that affect the polymer conformation. Thus the variation in buffer concentration, pH and presence of organic solvent, which affect the polymer swelling or shrinking, had a profound effect on the polymer recognition properties.     

The symmetry of self-complementary surfaces.

The concept of molecular complementarity is defined, and a theorem given which describes the symmetry required of self-complementary surfaces. We show in detail that the surfaces of chymotrypsin and concanavalin A have this symmetry, while that of the α chain of human deoxyhemoglobin does not.     

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.     

Distribution and complementarity of hydropathy in multisubunit proteins

A survey of 40 multisubunit proteins and 2 protein-protein complexes was performed to assay quantitatively the distribution of hydropathy among the exterior surface, interior, contact surface, and noncontact exterior surface of the isolated subunits. We suggest a useful way to present this distribution by using a "hydropathy level diagram." Additionally, we have devised a function called "hydropathy complementarity" to quantitate the degree to which interacting surfaces have matching hydropathy distributions. Our survey revealed the following patterns: (1) The difference in hydropathy between the interior and exterior of subunits is a fairly invariant quantity. (2) On average, the hydropathy of the contact surface is higher than that of the exterior surface, but is not greater than that of the protein as a whole. There was variation, however, among the proteins. In some instances, the contact surface was more hydrophilic than the noncontact exterior, and in a few cases the contact surface was as hydrophobic as the protein interior. (3) The average interface manifests significant hydropathy complementarity, signifying that proteins interact by placing hydrophobic centers of one surface against hydrophobic centers of the other surface, and by similarly matching hydrophilic centers. As a measure of recognition and specificity, hydropathy complementarity could be a useful tool for predicting correct docking of interacting proteins. We suggest that high hydropathy complementarity is associated with static inflexible interactions. (4) We have found that some subunits that bind predominantly through hydrophilic forces, such as hydrogen bonds, ionic pairs, and water and metal bridges, are involved in dynamic quaternary organization and allostery.     

Shape variation in protein binding pockets and their ligands

A common assumption about the shape of protein binding pockets is that they are related to the shape of the small ligand molecules that can bind there. But to what extent is that assumption true? Here we use a recently developed shape matching method to compare the shapes of protein binding pockets to the shapes of their ligands. We find that pockets binding the same ligand show greater variation in their shapes than can be accounted for by the conformational variability of the ligand. This suggests that geometrical complementarity in general is not sufficient to drive molecular recognition. Nevertheless, we show when considering only shape and size that a significant proportion of the recognition power of a binding pocket for its ligand resides in its shape. Additionally, we observe a "buffer zone" or a region of free space between the ligand and protein, which results in binding pockets being on average three times larger than the ligand that they bind.     

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.     

Gradient fit functions for two-body potential energy surfaces based upon a harmonic series

While force-field development has been discussed extensively in the literature, the question of what analytical expressions make the best function choices, particularly in the context of matching quantum mechanic potential energy surfaces (PES), is less explored. Traditional forms based upon harmonic oscillators and Lennard-Jones types have dominated the field owing to the focus on fitting properties. However, with the advent of gradient-fitting approaches, it is now possible with the correct force-field expressions to achieve consistent high-accuracy results with molecular dynamics calculations. Using the general principle that power series can fit surfaces of any shape well, we have utilised harmonic series functions to fit a two-body PES represented by a Morse function. The harmonic functions are fast because they have only integer exponents, and they fit accurately with a limited number of terms.