Applications of Computational Geometry, Statistical Analysis, and Graphics to the Study of Molecular Systems
Daniel B. Carr, (George Mason University), email@example.com, and
Iosif Vaisman, (George Mason University), firstname.lastname@example.org
Methods of computational geometry provide a robust and effective approach to studying topology and architecture of molecular systems. A molecule or molecular system can be represented by the set of points in three-dimensional space, where each point designate an atom or a site (group of atoms). The Delaunay tessellation of such a set of points generates an aggregate of space-filling irregular tetrahedra, or Delaunay simplices. The vertices of each simplex define objectively four nearest neighbor atoms. The collection of all simplices describes the topology of a molecular system. We use statistical analysis of geometrical and compositional properties of the Delaunay simplices to characterize structure and connectivity of the molecular system and to correlate chemical composition with the three-dimensional molecular architecture. In protein structure analysis the Delaunay tessellation facilitates objective identification of neighboring residues for a quantitative description of nonlocal contacts in three-dimensional protein structures. Analysis of the patterns of spatial proximity of residues in known protein structures based on the Delaunay tessellation reveals highly nonrandom clustering of amino acids. The talk presents a variety of graphics for showing statistics associated with the molecular systems. We also present graphics showing statistics computed from databases of peptides that bind with immune system molecules.