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 non-redundant 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.