Development of new indices to evaluate protein–protein interfaces: Assembling space volume, assembling space distance, and global shape descriptor

Protein–protein interaction is fundamental to initiate the cellular functions of proteins, and thus structural analyses of protein interfaces are the first step to understand their functions at the molecular level. Although shape complementarities have been used to evaluate the fitness of interfaces, the conventional method did not distinguish between two main components of complementarity, the well-fitting of the surface shapes and the size of the gap regions between the pair of molecules, and could not evaluate the global shape of the interfaces. Therefore, we now propose three new indices to describe protein interfaces: assembling space volume (ASV), assembling space distance (AS-distance), and global shape descriptor (GS). The ASV is calculated using Delaunay tessellation, and the AS-distance is calculated as the ratio of ASV to delta-ASA (accessible surface area). The GS is calculated as the ratio of the volume of Delaunay tetrahedra with a long edge to that of all tetrahedra in the assembling space. To evaluate the feasibility of the three indices, we applied our method to homo-dimer proteins, and performed systematic comparisons with SURFNET by Laskowski and shape complementarity by Lawrence and Colman. As a result, our indices behave differently from the existing ones, and shed light on new features of protein–protein interfaces, as general trends of AS-distances for all protein interfaces.