Defining and characterizing protein surface using alpha shapes

Abstract

The alpha shape of a molecule is a geometrical representation that provides a unique surface decomposition and a means to filter atomic contacts. We used it to revisit and unify the definition and computation of surface residues, contiguous patches, and curvature. These descriptors are evaluated and compared with former approaches on 85 proteins for which both bound and unbound forms are available. Based on the local density of interactions, the detection of surface residues shows a sensibility of 98%, whereas preserving a well-formed protein core. A novel conception of surface patch is defined by traveling along the surface from a central residue or atom. By construction, all surface patches are contiguous and, therefore, allows to cope with common problems of wrong and nonselection of neighbors. In the case of protein-binding site prediction, this new definition has improved the signal-to-noise ratio by 2.6 times compared with a widely used approach. With most common approaches, the computation of surface curvature can be locally biased by the presence of subsurface cavities and local variations of atomic densities. A novel notion of surface curvature is specifically developed to avoid such bias and is parametrizable to emphasize either local or global features. It defines a molecular landscape composed on average of 38% knobs and 62% clefts where interacting residues (IR) are 30% more frequent in knobs. A statistical analysis shows that residues in knobs are more charged, less hydrophobic and less aromatic than residues in clefts. IR in knobs are, however, much more hydrophobic and aromatic and less charged than noninteracting residues (non-IR) in knobs. Furthermore, IR are shown to be more accessible than non-IR both in clefts and knobs. The use of the alpha shape as a unifying framework allows for formal definitions, and fast and robust computations desirable in large-scale projects. This swiftness is not achieved to the detriment of quality, as proven by valid improvements compared with former approaches. In addition, our approach is general enough to be applied on nucleic acids and any other biomolecules.