Higher-order level-set method and its application in Biomolecular surfaces construction

Journal of Computer Science and Technology

Volumn 23, Issue 6, 2008, Pages 1026-1036

  Bajaj, Chandrajit L ^a   Xu, Guo Liang ^b   Zhang, Qin ^b,c  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b CHINESE ACADEMY OF SCIENCES   (China)

^c BEIJING INFORMATION SCIENCE AND TECHNOLOGY UNIVERSITY   (China)

Author keywords

Biomolecular surface; Geometric partial differential equation; Higher order spline level set

Indexed keywords

ATOMIC COORDINATES; BIOMOLECULAR; BIOMOLECULAR SURFACE; CUBIC SPLINE INTERPOLATION ALGORITHMS; CUBIC SPLINES; DATA VALUES; ENERGY FUNCTIONAL; FIRST ORDERS; GENERAL FRAMEWORKS; GEOMETRIC PARTIAL DIFFERENTIAL EQUATION; HIGHER-ORDER SPLINE LEVEL-SET; LEVEL SET FORMULATIONS; PRE-REQUISITES; SPLINE BASIS; Z-TRANSFORM;

BIOMOLECULES; COMPUTATIONAL FLUID DYNAMICS; IMAGE SEGMENTATION; PARTIAL DIFFERENTIAL EQUATIONS; SPLINES;

MATHEMATICAL TRANSFORMATIONS;

EID: 57049166084     PISSN: 10009000     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11390-008-9184-1     Document Type: Article

References (28)

1. Osher S, Fedkiw R. Level Set Method and Dynamic Implicit Surfaces. New York: Springer, 2003.
2. Sethian J A. Level Set Methods and Fast Marching Methods: Evolving Interfaces in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science. Cambridge Monographs on Applied and Computational Mathematical, Second edition, Cambridge University Press, 1999.
3. S Osher J Sethian 1988 Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations Journal of Computational Physics 79 1 12 49
4. M Sanner A Olson J Spehner 1996 Reduced surface: An efficient way to compute molecular surfaces Biopolymers 38 3 305 320
5. M Connolly 1983 Analytical molecular surface calculation J. Appl. Cryst. 16 5 548 558
6. F M Richards 1997 Areas, volumes, packing, and protein structure Ann. Rev. Biophys. Bioeng. 6 151 176
7. J Liang H Edelsbrunner P Fu P V Sudhakar S Subramaniam 1998 Analytical shape computation of macromolecules: I. molecular area and volume through Alpha shape Proteins: Structure, Function, and Genetics 33 1 1 17
8. Cazals F, Proust F. Revisiting the description of Protein-Protein interfaces, part I: Algorithms. Research Report 5346, INRIA, 2004.
9. Cazals F, Proust F. Revisting the description of Protein-Protein interface, part II: Experimental study. Research Report 5501, INRIA, 2005.
10. F Cazals F Proust R P Bahadur J Janin 2006 Revisiting the Voronoi description of Protein-Protein interfaces Protein Sci. 15 9 2082 2092
11. N Akkiraju H Edelsbrunner 1996 Triangulating the surface of a molecule Discr. Appl. Math. 71 1-3 5 22
12. J Liang H Edelsbrunner P Fu P V Sudhakar S Subramaniam 1998 Analytical shape computation of macromolecules: II. inaccessible cavities in protein Proteins: Structure, Function, and Genetics 33 1 18 29
13. H Edelsbrunner 1999 Deformable smooth surface design Discrete & Computational Geometry 21 1 87 115
14. H-L Cheng T K Dey H Edelsbrunner J Sullivan 2001 Dynamic skin triangulation Discrete & Computational Geometry 25 4 525 568
15. Bajaj C, Lee H, Merkert R, Pascucci V. NURBS based B-rep Models from Macro-molecules and their properties. In Proc. Fourth Symposium on Solid Modeling and Applications, 1997, pp.217-228.
16. C Bajaj V Pascucci A Shamir R Holt A Netravali 2003 Dynamic maintenance and visualization of molecular surfaces Discrete Applied Mathematics 127 1 23 51
17. J Blinn 1982 A generalization of algebraic surface drawing ACM Transactions on Graphics 1 3 235 256
18. B S Duncan A J Olson 1993 Shape analysis of molecular surfaces Biopolymers 33 2 231 238
19. J Grant B Pickup 1995 A Gaussian description of molecular shape Journal of Phys. Chem. 99 11 3503 3510
20. Y Zhang G Xu C Bajaj 2006 Quality meshing of implicit solvation models of biomolecular structures Computer Aided Geometric Design 23 6 510 530
21. Baker N, Sept D, Joseph S, Holst M, Mc-Cammon J. Electrostatics of nanosystems: Application to microtubules and the ribosome. In Proc. Natl. Acad. Sci., USA, 2001, pp.10037-10041.
22. M Holst F Saied 1993 Multigrid solution of the Poisson-Boltzmann equation J. Comput. Chem. 14 1 105 113
23. Bajaj C L, Xu G, Zhang Q. Smooth surface constructions via a higher-order level-set method. ICES Report 06-18, Institute for Computational and Engineering Sciences, The University of Texas at Austin, 2006.
24. O D Faugeras R Keriven 1998 Variational principles, surface evolution, PDE's, level-set methods, and the stereo problem IEEE Trans. Image Process. 7 3 336 344
25. G Xu Q Zhang 2006 Construction of geometric partial differential equations in computational geometry Mathematica Numerica Sinica 28 4 337 356
26. S Osher C W Shu 1991 High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations SIAM Journal of Numerical Analysis 28 4 907 922
27. D Peng B Merriman S Osher H Zhao M Kang 1999 A PDE-based fast local level set method Journal of Computational Physics 155 2 410 438
28. Bajaj C L, Djeu P, Siddavanahalli V, Thane A. Texmol: Interactive visual exploration of large flexible multi-component molecular complexes. In Proc. the Annual IEEE Visualization Conference'04, Austin, Texas, USA, 2004, pp.243-250.