Visualization and Analysis of Protein Structures Using Euclidean Voronoi Diagram of Atoms

Protein consists of amino acids, and an amino acid consists of atoms. Given a protein, understanding its functions is critical for various reasons for designing new drugs, treating diseases, and so on. Due to recent researches, it is now known that the structure of protein directly influences its functions. Hence, there have been strong research trends towards understanding the geometric structure of proteins. In this paper, we present a Euclidean Voronoi diagram of atoms constituting a protein and show how this computational tool can effectively and efficiently contribute to various important problems in biology. Some examples, among others, are the computations for molecular surface, solvent accessible surface, extraction of pockets, interaction interface, convex hull, etc.

[1]  Michael T. Goodrich,et al.  Drawing planar graphs with circular arcs , 2001, Discret. Comput. Geom..

[2]  Deok-Soo Kim,et al.  Edge-tracing algorithm for euclidean voronoi diagram of 3d spheres , 2004, CCCG.

[3]  Deok-Soo Kim,et al.  Voronoi diagram of a circle set from Voronoi diagram of a point set: II. Geometry , 2001, Comput. Aided Geom. Des..

[4]  V. P. Voloshin,et al.  Void space analysis of the structure of liquids , 2002 .

[5]  M. L. Connolly Solvent-accessible surfaces of proteins and nucleic acids. , 1983, Science.

[6]  I. Kuntz Structure-Based Strategies for Drug Design and Discovery , 1992, Science.

[7]  A. Goede,et al.  Voronoi cell: New method for allocation of space among atoms: Elimination of avoidable errors in calculation of atomic volume and density , 1997 .

[8]  H. Edelsbrunner,et al.  Anatomy of protein pockets and cavities: Measurement of binding site geometry and implications for ligand design , 1998, Protein science : a publication of the Protein Society.

[9]  Marina L. Gavrilova,et al.  Updating the topology of the dynamic Voronoi diagram for spheres in Euclidean d-dimensional space , 2003, Comput. Aided Geom. Des..

[10]  Jacques Chomilier,et al.  Nonatomic solvent‐driven voronoi tessellation of proteins: An open tool to analyze protein folds , 2002, Proteins.

[11]  F. Crick,et al.  Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid , 1953, Nature.

[12]  Deok-Soo Kim,et al.  Pocket Recognition on a Protein Using Euclidean Voronoi Diagram of Atoms , 2005, ICCSA.

[13]  David Taniar,et al.  Computational Science and Its Applications - ICCSA 2005, International Conference, Singapore, May 9-12, 2005, Proceedings, Part I , 2005, ICCSA.

[14]  Herbert Edelsbrunner,et al.  On the Definition and the Construction of Pockets in Macromolecules , 1998, Discret. Appl. Math..

[15]  Jon G. Rokne APPOLONIUS'S 10TH PROBLEM , 1991 .

[16]  Ho-Lun Cheng,et al.  Dynamic Skin Triangulation , 2001, SODA '01.

[17]  Deok-Soo Kim,et al.  Voronoi diagram of a circle set from Voronoi diagram of a point set: I. Topology , 2001, Computer Aided Geometric Design.

[18]  M. Levitt,et al.  The volume of atoms on the protein surface: calculated from simulation, using Voronoi polyhedra. , 1995, Journal of molecular biology.

[19]  Jean-Daniel Boissonnat,et al.  Sur la complexité combinatoire des cellules des diagrammes de Voronoï Euclidiens et des enveloppes convexes de sphères de , 2022 .

[20]  F. Richards The interpretation of protein structures: total volume, group volume distributions and packing density. , 1974, Journal of molecular biology.

[21]  Hans-Martin Will Fast and Efficient Computation of Additively Weighted Voronoi Cells for Applications in Molecular Biology , 1998, SWAT.

[22]  C. Frömmel,et al.  The automatic search for ligand binding sites in proteins of known three-dimensional structure using only geometric criteria. , 1996, Journal of molecular biology.

[23]  Sangsoo Kim,et al.  Euclidean Voronoi diagrams of 3D spheres and applications to protein structure analysis , 2005 .

[24]  Frederick P. Brooks,et al.  Computing smooth molecular surfaces , 1994, IEEE Computer Graphics and Applications.

[25]  Tomás Lozano-Pérez,et al.  Spatial Planning: A Configuration Space Approach , 1983, IEEE Transactions on Computers.

[26]  Marina L. Gavrilova,et al.  Proximity and applications in general metrics , 1999 .

[27]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[28]  B. Lee,et al.  The interpretation of protein structures: estimation of static accessibility. , 1971, Journal of molecular biology.

[29]  Franz Aurenhammer,et al.  Power Diagrams: Properties, Algorithms and Applications , 1987, SIAM J. Comput..

[30]  José L. F. Abascal,et al.  The Voronoi polyhedra as tools for structure determination in simple disordered systems , 1993 .

[31]  Valerio Pascucci,et al.  NURBS based B-rep models for macromolecules and their properties , 1997, SMA '97.

[32]  James Arvo,et al.  Graphics Gems II , 1994 .

[33]  F M Richards,et al.  Areas, volumes, packing and protein structure. , 1977, Annual review of biophysics and bioengineering.