An algorithm for the calculation of volume and surface of unions of spheres. Application for solvation shells

Proceedings - 2011 8th International Symposium on Voronoi Diagrams in Science and Engineering, ISVD 2011

Volumn , Issue , 2011, Pages 170-176

  Voloshin, V P ^a   Anikeenko, A V ^a   Medvedev, N N ^a,b   Geiger, A ^c  

^a INSTITUTE OF CHEMICAL KINETICS AND COMBUSTION   (Russian Federation)

^b NOVOSIBIRSK STATE UNIVERSITY   (Russian Federation)

^c TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Power Voronoi diagram; solvation shell; solvent accessible surface; union of balls

Indexed keywords

ANALYTICAL FORMULAS; COMPLEX SOLUTES; DELAUNAY; MOLECULAR-DYNAMICS MODEL; SIMPLE ALGORITHM; SIMPLE LIQUIDS; SOLVATION SHELL; SOLVENT ACCESSIBLE SURFACE; SURFACE AREA; UNION OF BALLS; VORONOI; VORONOI DIAGRAMS;

COMPUTATIONAL GEOMETRY; GRAPHIC METHODS; MOLECULAR DYNAMICS; SOLVATION; SPHERES;

ALGORITHMS;

EID: 80052614487     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISVD.2011.30     Document Type: Conference Paper

References (27)

1. S. Sastry, D. S. Corti, P. G. Debenedetti, F. H. Stillinger, "Statistical geometry of particle packings. I. Algorithm for exact determination of connectivity, volume, and surface areas of void space in monodisperse and polydisperse sphere parkings," Phys. Rev. E, vol. 56, N5, 1997, pp. 5524-5532, doi:10.1103/PhysRevE.56.5524. (Pubitemid 127654668)
2. F. Cazals, H. Kanhere, and S. Loriot, "Computing the volume of a union of balls: A certified algorithm," ACM Transactions on Mathematical Software; 38 (1), 2011, in press.
3. B. Lee and F. M. Richards, "The interpretation of protein structures: Estimation of static accesibility," J. Mol. Biol., vol. 55, 1971, pp. 379-400.
4. F. M. Richards, "Calculation of molecular volumes and areas for structures of known geometry," Methods in Enzymology, vol. 115, 1985, pp. 440-464.
5. M. G. Alinchenko, A. V. Anikeenko, N. N. Medvedev and V. P. Voloshin, M. Mezei, P. Jedlovszky, "Morphology of voids in molecular systems. A Voronoi-Delaunay analysis of a simulated DMPC membrane," J. Phys. Chem. B, vol. 108 (49), 2004, 19056-19067. (Pubitemid 40003270)
6. I. Brovchenko, R. R. Burri, A. Krukau, A. Oleinikova, R. Winter, "Intrinsic thermal expansivity and hydrational properties of amyloid peptide Abeta42 in liquid water," J. Chem. Phys., vol. 129, 2008, 195101.
7. D. Czapiewski, J. Zielkiewicz, "Structural properties of hydration shell around various conformations of simple polypeptides," J. Phys. Chem. B, vol. 114, 2010, pp. 4536-4550.
8. V. P. Voloshin et al., "Volumetric properties of hydrated peptides: Voronoi-Delaunay analysis of molecular simulation runs," J. Phys. Chem. B., 2011, in press.
9. R. Pavani, G. Ranghino, "A method to compute the volume of a molecule," Computers and Chemistry, vol. 6 (3), 1982, pp. 133-135.
10. P. G. Spirakis, "The volume of the union of many spheres and point inclusion problems," Lecture Notes in Computer Science, vol. 182, 1985, pp. 328-338, doi:10.1007/BFb0024021.
11. M. Till, G. Ullmann, "McVol-A program for calculating protein volumes and identifying cavities by a Monte Carlo algorithm," J. Mol. Model., vol. 16, 2010, pp. 419-429, doi:10.1007/s00894-009- 0541-y.
12. K. D. Gibson; H. A. Scheraga, "Exact calculation of the volume and surface area of fused hard-sphere molecules with unequal atomic radii," Molecular Physics, vol. 62 (5), 1987, pp. 1247-1265.
13. L. R. Dodd, D. N. Theodorou, "Analytical treatment of the volume and surface area of molecules formed by an arbitrary collection of unequal spheres intersected by planes," Molecular Physics, vol. 72 (6), 1991, pp. 1313-1345.
14. M. Petitjean, "On the analytical calculation of van der Waals surfaces and volumes: some numerical aspects," J. Comp. Chem., vol. 15, Issue 5, 1994, pp. 507-523, doi:10.1002/jcc.540150504.
15. J. Dzurina, J. Plavka, "O(N2) Algorithm for computing volume of overlapping spheres," Acta Electrotechnica et Informatica, vol. 8, No. 4, 2008, pp. 39-42.
16. J. Busa, E. Hayryan, Chin-Kun Hu, J. Skrivanek, Ming-Chya Wu., "CAVE: A package for detection and quantitative analysis of internal cavities in a system of overlapping balls: Application to proteins, "Computer Physics Communications, vol. 181, 2010, pp. 2116-2125.
17. M.Irisa, "An elegant algorithm of the analytical calculation for the volume of fused spheres with different radii" Computer Physics Communications, vol. 98, 1996, pp.317-338.
18. J. Liang, H. Edelsbrunner, P. Fu, P. V. Sudhakar, S. Subramaniam, "Analytical shape computation of macromolecules, I: Molecular area and volume through alpha shape," Proteins: Struct. Func. Genet., vol. 33, 1998, pp. 1-17. (Pubitemid 28413009)
19. H. Edelsbrunner, P. Koehl, "The geometry of biomolecular solvation," in Combinatorial and computational geometry, MSRI Publications, vol. 52, J. E. Goodman, J. Pach, E. Welzl, Eds. Cambridge University Press, 2005, pp. 243-275.
20. J. Ryua, R. Parka, D.-S. Kim, "Molecular surfaces on proteins via beta shapes," Computer-Aided Design, vol. 39, 2007, pp. 1042-1057. (Pubitemid 350166325)
21. S. V Anishchik, N. N. Medvedev, "Three-dimensional Apollonian packing as a model for dense granular systems," Phys. Rev. Lett., 75(23), pp. 4314-4317, 1995.
22. A. Okabe, B. Boots, K. Sugihara, S. Chiu, Spatial tessellations - concepts and applications of Voronoi diagrams, New York: John Wiley & Sons, 2000.
23. F. Aurenhammer, "Power diagrams: Properties, algorithms and applications," SIAM J Comput, vol. 16, 1987, pp. 78-96. (Pubitemid 17526776)
24. M. Mezei, "Modified proximity criteria for the analysis of the solvation of a polyfunctional solute," Molecular Simulation, vol. 1, Issue 5, August 1988, pp. 327-332.
25. B. J. Gellatly, J. L. Finney, "Calculation of protein volumes: An alternative to the Voronoi procedure," J. Mol. Biol., vol. 161, 1982, pp. 305-322.
26. http://koehllab.genomecenter.ucdavis.edu/people/koehl/research/proshape.
27. J. Tsai, R. Taylor, C. Chothia, M. Gerstein, "The packing density in proteins: Standard radii and volumes," J. Mol. Biol., 290 (1), 1999, pp. 253-266. (Pubitemid 29308589)