Euclidean Voronoi diagrams of 3D spheres and applications to protein structure analysis

Japan Journal of Industrial and Applied Mathematics

Volumn 22, Issue 2, 2005, Pages 251-265

  Kim, Deok Soo ^a   Cho, Youngsong ^a   Kim, Donguk ^a   Kim, Sangsoo ^b   Bhak, Jonghwa ^c   Lee, Sung Hoon ^b  

^a Hanyang University   (South Korea)

^b Korea Research Institute of Bioscience and Biotechnology (KRIBB)   (South Korea)

^c Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

Edge tracing; Euclidean Voronoi diagrams; Protein structure

Indexed keywords

EID: 22544461060     PISSN: 09167005     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03167441     Document Type: Conference Paper

References (24)

1. B. Angelov, J.-F. Sadoc, R. Jullien, A. Soyer, J.-P. Mornon and J. Chomilier, Nonatomic solvent-driven Voronoi tessellation of proteins: an open tool to analyze protein folds. Proteins: Structure, Function, and Genetics, 49, No. 4, (2002), 446-456.
2. F. Aurenhammer, Power diagrams: properties, algorithms and applications. SIAM Journal of Computing, 16 (1987), 78-96.
3. Computational Geometry Algorithms Library, http://www.cgal.org/, (2004).
4. P. Dafas, D. Bolser, J. Gomoluch, J. Park and M. Schroeder, Using convex hulls to compute protein interactions from known structures. Bioinformatics, 20, No. 10 (2004), 1486-1490.
5. G. Farin, Curves and Surfaces for Computer-Aided Geometric Design: A Practical Guide (4th edition). Academic Press, San Diego, 1996.
6. M. Gavrilova, Proximity and Applications in General Metrics. Ph.D. Thesis, The University of Calgary, Dept. of Computer Science, Calgary, AB, Canada, 1998.
7. M. Gavrilova and J. Rokne, Updating the topology of the dynamic Voronoi diagram for spheres in Euclidean d-dimensional space. Computer Aided Geometric Design, 20, No. 4 (2003), 231-242.
8. M. Gerstein, J. Tsai and M. Levitt, The volume of atoms on the protein surface: calculated from simulation, using Voronoi polyhedra. Journal of Molecular Biology, 249, No. 5 (1995), 955-966.
9. A. Goede, R. Preissner and C. Frömmel, Voronoi cell: new method for allocation of space among atoms: elimination of avoidable errors in calculation of atomic volume and density. Journal of Computational Chemistry, 18, No. 9 (1997), 1113-1123.
10. D.-S. Kim, D. Kim and K. Sugihara, Voronoi diagram of a circle set from Voronoi diagram of a point set: I. Topology. Computer Aided Geometric Design, 18, No. 6 (2001), 541-562.
11. D.-S Kim, D. Kim and K. Sugihara, Voronoi diagram of a circle set from Voronoi diagram of a point set: II. Geometry. Computer Aided Geometric Design, 18, No. 6 (2001), 563-585.
12. D.-S. Kim, Y. Cho and D. Kim, Edge-tracing algorithm for Euclidean Voronoi diagram of 3D spheres. Proc. 16th Canadian Conference on Computational Geometry, 2004, 176-179.
13. S.H. Lee and K. Lee, Partial entity structrue: a compact non-manifold boundary representation based on partial topological entities. Proc. 6th ACM Symposium on Solid Modeling and Application, Sheraton Inn Ann Arbor, Michigan, June 6-8, 2001, 159-170.
14. V.A. Luchnikov, N.N. Medvedev, L. Oger and J.-P. Troadec, Voronoi-Delaunay analysis of voids in systems of nonspherical particles. Physical Review E, 59, No. 6 (1999), 7205-7212.
15. J.C.G. Montoro and J.L.F. Abascal, The Voronoi polyhedra as tools for structure determination in simple disordered systems. The Journal of Physical Chemistry, 97, No. 16 (1993), 4211-4215.
16. A. Okabe, B. Boots and K. Sugihara, Spatial Tessellations: Concepts and Applications of Voronoi Diagram. John Wiley & Sons, 1992.
17. M. Paluszny and W. Boehm, General cyclides. Computer Aided Geometric Design, 15, No. 7 (1998), 699-710.
18. H. Pottman, Personal communication. (May 2004).
19. F.P. Preparata and M.I. Shamos, Computational Geometry: An Introduction. Springer-Verlag, 1985.
20. RCSB Protein Data Bank, http://www.rcsb.org/pdb/, (2004).
21. F.M. Richards, The interpretation of protein structures: total volume, group volume distributions and packing density. Journal of Molecular Biology, 82 (1974), 1-14.
22. J. Rokne, Appolonius's 10th problem. Graphics Gems II (ed. J. Arvo), Academic Press, 1991, 19-24.
23. V.P. Voloshin, S. Beaufils and N.N. Medvedev, Void space analysis of the structure of liquids. Journal of Molecular Liquids, 96-97 (2002), 101-112.
24. H.-M. Will, Computation of Additively Weighted Voronoi Cells for Applications in Molecular Biology. Ph.D. Thesis, Swiss Federal Institute of Technology, Zurich, 1999.