Computational Geometry Applied to Modeling and Visualization of Proteins

Written by Martin Maňák

Martin Maňák

University of West Bohemia

Seminar in Czech
June 7, 2010 at 13:30
University of West Bohemia, UL411


The modeling of protein structures is a challenging task that closely relates to the field of computational geometry. A protein molecule is often modeled as a set of balls which represents its atoms. Since it is strongly agreed that the function of a protein is mostly determined by its shape, describing spatial relations among these balls is of a great importance for solving related problems. Many kinds of Voronoi diagrams and their duals have been used here to describe the spatial properties. The Voronoi diagram of balls, its dual and related concepts proved to be the best available choice in this area. This work gives a historical background to this area from the computational geometry point of view, provides an overview of the best available concepts in this area, i.e., the Voronoi diagram of balls, its dual structure and derived shape concepts, and shows some of their applications, such as the computation of molecular surfaces or pocket extraction. A part of this work is dedicated to an interesting extension of this kind of diagrams by allowing a ball to be inverted. This extension can be used as a convenient boundary constraint of the whole diagram or its parts. A new approach of fast construction of these diagrams is also discussed. This approach uses a three-dimensional Delaunay triangulation of atom centers and spatial filters in order to discover relevant parts of the diagram rapidly. Finally, future research directions are outlined.

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