A Beta-Complex Solves All Geometry Problems In A Molecule

Abstract

Abstract.Geometry-related problems in bio-molecules are new challenges as well as opportunities for geometers since it is now strongly agreed that the shape of molecules mostly determines their functions. To analyze the shape of molecule, a systematic approach of handling the constituting atoms is inevitable. The Voronoi diagram of atoms and the other structures derived from the Voronoi diagram have proven their powerful capabilities on analyzing the structural molecular biology problems related with geometry or shape of molecules. In this paper, we show that a single -complex for a molecule can be used to efficiently solve many bio-molecular problems which are based on some geometry among atoms in the molecule. We explain the -complex in the context of molecular geometry and shape analysis based on the Voronoi diagram of atoms and the quasi-triangulation.We also compare the capabilities of -complex with the -complex and -shape which are based on the power diagram.