Feature-preserving adaptive mesh generation for molecular shape modeling and simulation

Journal of Molecular Graphics and Modelling

Volumn 26, Issue 8, 2008, Pages 1370-1380

  Yu, Zeyun ^a   Holst, Michael J ^a   Cheng, Yuhui ^a   McCammon, J Andrew ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Finite element method; Mesh generation; Molecular shape modeling; Molecular simulation; Numerical analysis

Indexed keywords

ALGORITHMS; FINITE ELEMENT METHOD; MOLECULAR MODELING; MOLECULAR STRUCTURE; VOLUMETRIC ANALYSIS;

FEATURE PRESERVATION; MOLECULAR SHAPE MODELING; MOLECULAR SIMULATION;

MESH GENERATION;

ALGORITHM; ARTICLE; ATOM; FINITE ELEMENT ANALYSIS; METHODOLOGY; MOLECULAR MODEL; NORMAL DISTRIBUTION; PRIORITY JOURNAL; SIMULATION;

ACETYLCHOLINESTERASE; ALGORITHMS; ANIMALS; COMPUTER SIMULATION; FINITE ELEMENT ANALYSIS; MICE; MODELS, MOLECULAR;

EID: 42749086211     PISSN: 10933263     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmgm.2008.01.007     Document Type: Article

References (55)

1. Ainsworth M., and Oden J.T. A Posterori Error Estimation in Finite Element Analysis (2000), Wiley-Interscience
2. Aksoylu B., Bond S., and Holst M. An odyssey into local refinement and multilevel preconditioning III: implementation and numerical experiments. SIAM J. Sci. Comput. 25 (2003) 478-498
3. Aksoylu B., and Holst M. Optimality of multilevel preconditioners for local mesh refinement in three dimensions. SIAM J. Numer. Anal. 44 (2006) 1005-1025
4. Bajaj C., Lee H., Merkert R., and Pascucci V. NURBS based B-rep models from macromolecules and their properties. Proceedings of Fourth Symposium on Solid Modeling and Applications (1997) 217-228
5. Bajaj C.L., Pascucci V., Shamir A., Holt R.J., and Netravali A.N. Dynamic maintenance and visualization of molecular surfaces. Discrete Appl. Math. 127 1 (2003) 23-51
6. Baker N.A., Sept D., Joseph S., Holst M., and McCammon J.A. Electrostatics of nanosystems: application to microtubules and the ribosome. Proc. Natl. Acad. Sci. 98 (2001) 10037-10041
7. Bank R., and Holst M. A new paradigm for parallel adaptive meshing algorithms. SIAM Rev. 45 (2003) 291-323
8. Bashford D., and Case D.A. Generalized Born models of macromolecular solvation effects. Annu. Rev. Phys. Chem. 51 (2000) 129-152
9. Bates P.W., Wei G.W., and Zhao S. Minimal molecular surfaces and their applications. J. Comput. Chem. 29 3 (2008) 380-391
10. Berman H.M., Westbrook J., Feng Z., Gilliland G., Bhat T.N., Weissig H., Shindyalov I.N., and Bourne P.E. The protein data bank. Nucl. Acids Res. 28 (2000) 235-242
11. Berzins M. A solution-based triangular and tetrahedral mesh quality indicator. SIAM J. Sci. Comput. 19 (1998) 2051-2060
12. Blinn J.F. A generalization of algegraic surface drawing. ACM Trans. Graph. 1 3 (1982) 235-256
13. Brandt A. Multi-level adaptive solutions to boundary-value problems. Math. Comp. 31 (1977) 333-390
14. Briggs W.L., Henson V.E., and McCormick S.F. A multigrid tutorial. 2nd ed. (2000), Society for Industrial and Applied Mathematics, Philadelphia, PA
15. Chena C.-Y., and Cheng K.-Y. A sharpness dependent filter for mesh smoothing. Comput. Aided Geom. Des. 22 5 (2005) 376-391
16. Cheng H.L., and Shi X. Quality mesh generation for molecular skin surfaces using restricted union of balls. Proc. IEEE Vis. (2005) 51-57
17. Cheng Y.H., Suen J.K., Zhang D.Q., Bond S.D., Zhang Y.J., Song Y.H., Baker N.A., Bajaj C.L., Holst M.J., and McCammon J.A. Finite element analysis of the time-dependent Smoluchowski equation for acetylcholinesterase reaction rate calculations. Biophys. J. 92 (2007) 3397-3406
18. Connolly M.L. Analytical molecular surface calculation. J. Appl. Cryst. 16 5 (1983) 548-558
19. Dolinsky T.J., Nielsen J.E., McCammon J.A., and Baker N.A. PDB2PQR: an automated pipeline for the setup, execution, and analysis of poisson-boltzmann electrostatics calculations. Nucl. Acids Res. 32 (2004) 665-667
20. Duncan B.S., and Olson A.J. Shape analysis of molecular surfaces. Biopolymers 33 (1993) 231-238
21. Fernandez J.-J., and Li S. An improved algorithm for anisotropic nonlinear diffusion for denoising cryo-tomograms. J. Struct. Biol. 144 (2003) 152-161
22. Freitag L.A., and Ollivier-Gooch C.F. Tetrahedral mesh improvement using swapping and smoothing. Int. J. Numer. Methods Eng. 40 21 (1997) 3979-4002
23. Grant J.A., and Pickup B.T. A Gaussian description of molecular shape. J. Phys. Chem. 99 (1995) 3503-3510
24. W. Hackbusch, A fast iterative method solving Poisson's equation in a general region, in: Proceedings of the Conference on the Numerical Treatment of Differential Equations (Lecture Notes in Mathematics), Springer-Verlag, 1978, vol. 631, pp. 51-62.
25. Hackbusch W. Multi-grid Methods and Applications (1985), Springer-Verlag, Berlin, Germany
26. Holst M. Adaptive numerical treatment of elliptic systems on manifolds. Adv. Comput. Math. 15 (2001) 139-191
27. Huebner K.H., Dewhirst D., Smith D.E., and Byrom T.G. The Finite Element Method for Engineers (2001), Wiley-IEEE
28. Im W., Beglov D., and Roux B. Continuum solvation model: electrostatic forces from numerical solutions to the poisson-boltzmann equation. Comp. Phys. Commun. 111 (1998) 59-75
29. Jollife I. Principal Component Analysis (1986), Springer-Verlag, NY
30. Ju T., Losasso F., Schaefer S., and Warren J. Dual contouring of hermite data. Proceedings of SIGGRAPH'02 (2002) 339-346
31. Lee B., and Richards F.M. The interpretation of protein structures: estimation of static accessibility. J. Mol. Biol. 55 3 (1971) 379-400
32. Liu A., and Joe B. Relationship between tetrahedron shape measures. BIT 34 (1994) 268-287
33. Lorensen W.E., and Cline H.E. Marching cubes: a high resolution 3D surface construction algorithm. Comput. Graph. 21 4 (1987) 163-169
34. Nina M., Im W., and Roux B. Optimized atomic radii for protein continuum electrostatics solvation forces. Biophys. Chem. 78 1-2 (1999) 89-96
35. Perona P., and Malik J. Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12 7 (1990) 629-639
36. Richards F.M. Areas, volumes, packing, and protein structure. Ann. Rev. Biophys. Bioeng. 6 (1977) 151-156
37. Sanner M.F., Olson A.J., and Spehner J.C. Reduced surface: an efficient way to compute molecular surfaces. Biopolymers 38 (1996) 305-320
38. Schnieders M.J., Baker N.A., Ren P., and Ponder J.W. Polarizable atomic multipole solutes in a poisson-boltzmann continuum. J. Chem. Phys. 126 (2007) 124114-124135
39. H. Si, Tetgen: a quality tetrahedral mesh generator and three-dimensional delaunay triangulator. Technical Report 9, Weierstrass Institute for Applied Analysis and Stochastics, 2004 (software download: http://tetgen.berlios.de).
40. Si H., and Gartner K. Meshing piecewise linear complexes by constrained delaunay tetrahedralizations. Proceedings of the 14th International Meshing Roundtable (2005)
41. Song Y., Zhang Y., Bajaj C.L., and Baker N.A. Continuum diffusion reaction rate calculations of wild type and mutant mouse acetylcholinesterase: adaptive finite element analysis. Biophys. J. 87 (2004) 1558-1566
42. Song Y., Zhang Y., Shen T., Bajaj C.L., McCammon J.A., and Baker N.A. Finite element solution of the steady-state Smoluchowski equation for rate constant calculations. Biophys. J. 86 (2004) 2017-2029
43. Totrov M., and Abagyan R. The contour-buildup algorithm to calculate the analytical molecular surface. J. Struct. Biol. 116 (1996) 138-143
44. Wagoner J.A., and Baker N.A. Assessing implicit models for nonpolar mean solvation forces: The importance of dispersion and volume terms. Proc. Natl. Acad. Sci. 103 22 (2006) 8331-8336
45. J. Weickert, Anisotropic Diffusion In Image Processing. ECMI Series, Teubner-Verlag, Stuttgart, 1998.
46. Xu H., and Newman T.S. 2D FE quad mesh smoothing via angle-based optimization. Proceedings of the 5th International Conference on Computational Science (2005) 9-16
47. H. Yagou, Y. Ohtake, A. Belyaev, Mesh Smoothing via Mean and Median Filtering Applied to Face Normals, 2002, pp. 124-131.
48. Young I.T., and Vliet L.J. Recursive implementation of the Gaussian filter. Signal Process. 44 (1995) 139-151
49. Yu Z., and Bajaj C. A segmentation-free approach for skeletonization of gray-scale images via anisotropic vector diffusion. Proceedings of International Conference Computer Vision and Pattern Recognition (2004) 415-420
50. Yu Z., and Bajaj C. A structure tensor approach for 3D image skeletonization: applications in protein secondary structural analysis. Proceedings of IEEE International Conference on Image Processing (2006) 2513-2516
51. Z. Yu, C. Bajaj, Computational approaches for automatic structural analysis of large bio-molecular complexes. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2007, http://doi.ieeecomputersociety.org/10.1109/TCBB.2007.70226.
52. Y. Zhang, C. Bajaj, B.-S. Sohn, 3D finite element meshing from imaging data, Comput. Methods Appl. Mech. Eng. 194 (48-49) (2005) 5083-5106.
53. Y. Zhang, G. Xu, C. Bajaj, Quality meshing of implicit solvation models of biomolecular structures, Comput. Aided Geom. Des. 23 (6) (2006) 510-530.
54. Zhao W., Xu G., and Bajaj C. An algebraic spline model of molecular surfaces. Proc. ACM Symp. Solid Phys. Model. 1 (2007) 297-302
55. Zhou T., and Shimada K. An angle-based approach to two-dimensional mesh smoothing. Proceedings of the Ninth International Meshing Roundtable (2000) 373-384