Beta-decomposition for the volume and area of the union of three-dimensional balls and their offsets

Journal of Computational Chemistry

Volumn 33, Issue 13, 2012, Pages 1252-1273

  Kim, Deok Soo ^a   Ryu, Joonghyun ^a   Shin, Hayong ^b   Cho, Youngsong ^a  

^a Hanyang University   (South Korea)

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

Author keywords

accessible area; accessible volume; beta complex; beta shape; Lee Richards (accessible) surface; molecular area; molecular surface; molecular volume; offset surface; offset area; offset volume; quasi triangulation; solvent accessible surface; van der Waals area; van der Waals volume; Voronoi diagram of spheres

Indexed keywords

ACCESSIBLE AREA; ACCESSIBLE VOLUME; BETA-COMPLEX; BETA-SHAPE; MOLECULAR AREAS; MOLECULAR SURFACES; MOLECULAR VOLUME; OFFSET SURFACE; OFFSET-AREA; OFFSET-VOLUME; QUASI-TRIANGULATION; SOLVENT-ACCESSIBLE SURFACES; VAN DER WAALS; VAN DER WAALS VOLUME; VORONOI DIAGRAMS;

ALGORITHMS; COMPUTATIONAL GEOMETRY; GRAPHIC METHODS; SOFTWARE TESTING; SPHERES; THREE DIMENSIONAL; VAN DER WAALS FORCES;

ATOMS;

EID: 84862776651     PISSN: 01928651     EISSN: 1096987X     Source Type: Journal    
DOI: 10.1002/jcc.22956     Document Type: Article

References (66)

1. F. M. Richards, J. Mol. Biol. 1974, 82, 1.
2. D.-S. Kim, C.-I. Won, J. Bhak, J. Biomol. Struct. Dyn. 2010, 28, 277.
3. L. R. Dodd, D. N. Theodorou, Mol. Phys. 1991, 72, 1313.
4. RCSB Protein Data Bank, 2009, Available at. Accessed on September 2010.
5. Voronoi Diagram Research Center, 2011, Available at.
6. A. Shrake, J. A. Rupley, J. Mol. Biol. 1973, 79, 351.
7. R. Abagyan, M. Totrov, D. Kuznetsov, J. Comput. Chem. 1994, 15, 488.
8. A. Gavezzotti, J. Am. Chem. Soc. 1983, 105, 5220.
9. J. Higo, N. Go, J. Comput. Chem. 1989, 10, 376.
10. H. R. Karfunkel, V. Eyraud, J. Comput. Chem. 1989, 10, 628.
11. E. Silla, F. Villar, O. Nilsson, J. L. Pascual-Ahuir, O. Tapia, J. Mol. Graph. 1990, 8, 168.
12. E. Silla, I. Tunon, J. L. Pascual-Ahuir, J. Comput. Chem. 1991, 12, 1077.
13. M. L. Connolly, J. Am. Chem. Soc. 1985, 107, 1118.
14. F. Eisenhaber, P. Lijnzaad, P. Argos, C. Sander, M. Scharf, J. Comput. Chem. 1995, 16, 273.
15. K. Rother, P. W. Hildebrand, A. Goede, B. Gruening, R. Preissner, Nucleic Acids Res. 2009, 37, 393.
16. M. S. Till, G. M. Ullmann, J. Mol. Model. 2010, 16, 419.
17. J. D. Bernal, J. L. Finney, Discuss. Faraday Soc. 1967, 43, 62.
18. B. J. Gellatly, J. L. Finney, J. Mol. Biol., 1982, 161, 305.
19. M. Gerstein, J. Tsai, M. Levitt, J. Mol. Biol. 1995, 249, 955.
20. A. Goede, R. Preissner, C. Frömmel, J. Comput. Chem. 1997, 18, 1113.
21. H.-M. Will, Fast and Efficient Computation of Additively Weighted Voronoi Cells for Applications in Molecular Biology. In Proceedings of the 6th Skandinavian Workshop on Algorithm Theory, S. Arnborg, L. Ivansson, Eds., Vol. 1432 of Lecture Notes in Computer Science, 1998; pp. 310-321.
22. D.-S. Kim, Y. Cho, D. Kim, Comput.-Aid. Des. 2005, 37, 1412.
23. D. Kim, D.-S. Kim, Comput.-Aid. Des. 2006, 38, 417.
24. H. Edelsbrunner, E. P. Mücke, ACM Trans. Graph. 1994, 13, 43.
25. H. Edelsbrunner, Weighted alpha shapes, Technical Report UIUCDCS-R-92-1760, Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL, 1992.
26. D.-S. Kim, J. Seo, D. Kim, J. Ryu, C.-H. Cho, Comput.-Aid. Des. 2006, 38, 1179.
27. D.-S. Kim, Y. Cho, K. Sugihara, J. Ryu, D. Kim, Comput.-Aid. Des. 2010, 42, 911.
28. M. L. Connolly, J. Appl. Crystallogr. 1983, 16, 548.
29. G. Perrot, B. Cheng, K. Gibson, J. Vila, K. Palmer, A. Nayeem, B. Maigret, H. Scheraga, J. Comput. Chem. 1992, 13, 1.
30. D. Avis, B. K. Bhattacharya, H. Imai, Vis. Comput. 1988, 3, 323.
31. R. Fraczkiewicz, W. Braun, J. Comput. Chem. 1998, 19, 319.
32. M. Irisa, Comput. Phys. Commun. 1996, 98, 317.
33. B. J. McConkey, V. Sobolev, M. Edelman, Bioinformatics 2002, 18, 1365.
34. A. Fabri, G.-J. Giezeman, L. Kettner, S. Schirra, S. Schönherr, Soft.: Pract. Exp. 2000, 30, 1167.
35. CGAL Library Homepage,. Accessed on August 2009.
36. F. Cazals, H. Kanhere, S. Loriot, Computing the Volume of a Union of Balls: A Certified Algorithm Technical Report, INRIA Sophia Antipolis, August, 2009.
37. F. Cazals, H. Kanhere, S. Loriot, ACM Trans. Math. Soft. 2011, 38, 1.
38. K. W. Kratky, J. Phys. A: Math. Gen. 1978, 11, 1017.
39. K. D. Gibson, H. A. Scheraga, Mol. Phys. 1987, 62, 1247.
40. R. Pavani, G. Ranghino, Comput. Chem. 1982, 6, 133.
41. L. S. Chkhartishvili, Math. Notes 2001, 69, 421.
42. D. Q. Naiman, H. P. Wynn, Ann. Stat. 1992, 20, 43.
43. M. Petitjean, J. Comput. Chem. 1994, 15, 507.
44. H. Edelsbrunner, Discrete Comput. Geom. 1995, 13, 415.
45. D. Attali, H. Edelsbrunner, In Proceedings of the 21st Annual Symposium on Computational Geometry (SoCG06), Pisa, Italy, 2006; pp. 247-254.
46. H. Edelsbrunner, M. Facello, P. Fu, J. Liang, In Proceedings of the 28th Annual Hawaii International Conference on System Sciences (HICSS95), 1995; pp. 256-264.
47. T. Nishida, K. Sugihara, In Proceedings of the 5th International Symposium on Voronoi diagrams in Science and Engineering, 2008; pp. 22-28.
48. F. Aurenhammer, SIAM J. Comput. 1987, 16, 78.
49. N. N. Medvedev, Doklady Phys. Chem. 1994, 337, 157.
50. S. V. Anishchik, N. N. Medvedev, Phys. Rev. Lett. 1995, 75, 4314.
51. H.-M. Will, Computation of Additively Weighted Voronoi Cells for Applications in Molecular Biology, PhD thesis, Swiss Federal Institute of Technology, Zurich, 1999.
52. J.-D. Boissonnat, M. I. Karavelas, In Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms, 2003; pp. 305-312.
53. M. Gavrilova, Proximity and Applications in General Metrics, PhD thesis, Department of Computer Science, The University of Calgary, Calgary, Canada, 1998.
54. M. Gavrilova, J. Rokne, Comput. Aid. Geom. Des. 2003, 20, 231.
55. V. A. Luchnikov, N. N. Medvedev, L. Oger, J.-P. Troadec, Phys. Rev. E 1999, 59, 7205.
56. D.-S. Kim, Y. Cho, D. Kim, In Proceedings of the 16th Canadian Conference on Computational Geometry, 2004; pp. 176-179.
57. N. N. Medvedev, V. P. Voloshin, V. A. Luchnikov, M. L. Gavrilova, J. Comput. Chem. 2006, 27, 1676.
58. D.-S. Kim, D. Kim, Y. Cho, K. Sugihara, Comput.-Aid. Des. 2006, 38, 808.
59. D.-S. Kim, Y. Cho, K. Sugihara, Comput.-Aid. Des. 2010, 42, 874.
60. D.-S. Kim, J.-K. Kim, Y. Cho, C.-M. Kim, Comput.-Aid. Des. 2012, 44, 85.
61. D.-S. Kim, Y. Cho, J. Ryu, C.-M. Kim, Comput.-Aid. Des. 2010, 42, 795.
62. J. Harris, H. Stocker, J. W. Harris, Handbook of Mathematics and Computational Science; Springer-Verlag New York Inc, New York, 1998.
63. R. PDB, RCSB PDB 2008 annual Technical report, RCSB PDB, 2008.
64. S. Dutta, K. Burkhardt, J. Young, G. J. Swaminathan, T. Matsuura, K. Henrick, H. Nakamura, H. M. Berman, Mol. Biotechnol. 2009, 42, 1.
65. M.-Z. Shao, N. Badler, Spherical sampling by archimedes' theorem, Technical Report, University of Pennsylvania, 1996.
66. P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer-Verlag New York Inc, New York, 2000.