Biology, Geometry and Voronoi Diagram

The functions of biological systems such as a proteins are critically related to the geometry of the system. In the analysis of the geometric structure of biological molecules, various kinds of computational geometry techniques have been applied since Richards (1971) first employed the Voronoi diagram of points. In this talk, the generalization of such a Voronoi diagram into the Voronoi diagram of atoms is discussed. Then, a new computational concept of the "beta shape" is introduced to facilitate a more efficient and correct computation for reasoning about the morphological structure of molecules. The solution techniques of some important biological problems, such as the extraction of pockets, the computation of molecular surfaces and interaction interfaces, etc., are also presented.