Molecular surfaces on proteins via beta shapes

A protein consists of linearly combined amino acids via peptide bonds, and an amino acid consists of atoms. It is known that the geometric structure of a protein is the primary factor which determines the functions of the protein.Given the atomic complex of a protein, one of the most important geometric structures of a protein is its molecular surface since this distinguishes between the interior and exterior of the protein and plays an important role in protein folding, docking, interactions between proteins, and other functions.This paper presents an algorithm for the precise and efficient computation of the molecular surface of a protein, using a recently proposed geometric construct called the ββ-shape based on the Voronoi diagram of atoms in a protein. Given a Voronoi diagram of atoms, based on the Euclidean distance from the atom surfaces, the proposed algorithm first computes the ββ-shape with an appropriate sized probe. Then, the molecular surface is computed by employing a blending operation on the atomic complex of the protein. In this paper, it is also shown that for a given Voronoi diagram of atoms, the multiple molecular surfaces can be computed by using various sized probes.