Geometry of Biomolecules via Beta-Complex

Abstract

It is very well-known that the geometric structure is one of the most important factors determining the functions of a protein. Compared to its importance, efforts to understand the morphological structure of biomolecules has not been sufficient. In this talk, we will define “BioGeometry” and show how useful it is for reasoning the shape-related characteristics of molecules. In the course of presentation, we will introduce the beta-complex and beta-shape which can be efficiently computed from the Voronoi diagram of atoms in the molecule. Then, we will show how these constructs can be used for analyzing the shape of molecule. The applications include the computation of the molecular surface, the extraction of pockets on the boundary of molecule, the computation of areas of various types of surfaces defined on a molecule, the computation of various kinds of volumes defined on a molecule, the superposition of two structures, the docking simulation, and so on. We will show that the beta-complex and beta-shape will facilitate the exact, efficient and robust computation of all these (possibly others as well) applications. In this talk, we will not only discuss the theory but also show the developed software, BetaMol.