## Efficient and qualified mesh generation for Gaussian molecular surface using adaptive partition and piecewise polynomial approximation.(English)Zbl 1393.65027

### MSC:

 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs 68N01 General topics in the theory of software 65D17 Computer-aided design (modeling of curves and surfaces) 65-04 Software, source code, etc. for problems pertaining to numerical analysis

Zbl 1186.92005

### Software:

SIMS; TMSmesh; PAFMPB; MetaMol; GTEngine; TetGen; PDB2PQR
Full Text:

### References:

 [1] P. W. Bates, G. W. Wei, and S. Zhao, Minimal molecular surfaces and their applications, J. Comput. Chem., 29 (2008), pp. 380–391. [2] M. Bayrhuber, T. Meins, M. Habeck, S. Becker, K. Giller, S. Villinger, C. Vonrhein, and C. Griesinger, Structure of the human voltage-dependent anion channel, Proc. Natl. Acad. Sci. USA, 105 (2008), pp. 15370–15375. [3] T. Can, C. Chen, and Y. Wang, Efficient molecular surface generation using level-set methods, J. Molecular Graphics Model., 25 (2006), pp. 442–454. [4] M. Chavent, B. Levy, and B. Maigret, Metamol: High-quality visualization of molecular skin surface, J. Molecular Graphics Model., 27 (2008), pp. 209–216. [5] B. Chazelle, Triangulating a simple polygon in linear time, Discrete Comput. Geom., 6 (1991), pp. 485–524. · Zbl 0753.68090 [6] M. Chen and B. Lu, TMSmesh: A robust method for molecular surface mesh generation using a trace technique, J. Chem. Theory Comput., 7 (2011), pp. 203–212. [7] M. Chen, B. Tu, and B. Lu, Triangulated manifold meshing method preserving molecular surface topology, J. Molecular Graphics Model., 38 (2012), pp. 411–418. [8] H.-L. Cheng and X. Shi, Quality mesh generation for molecular skin surfaces using restricted union of balls, Comput. Geom., 42 (2009), pp. 196–206. · Zbl 1158.65014 [9] M. L. Connolly, Analytical molecular surface calculation, J. Appl. Crystallogr., 16 (1983), pp. 548–558. [10] M. L. Connolly, Solvent-accessible surfaces of proteins and nucleic acids, Science, 221 (1983), pp. 709–713. [11] M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf, Computational Geometry, Springer-Verlag, New York, 2000; Chapter 3: Polygon Triangulation, pp. 45–61. · Zbl 0939.68134 [12] S. Decherchi and W. Rocchia, A general and robust ray casting based algorithm for triangulating surfaces at the nanoscale, PLoS One, 8 (2013), e59744. [13] T. J. Dolinsky, J. E. Nielsen, J. A. McCammon, and N. A. Baker, PDB$$2$$PQR: An automated pipeline for the setup, execution, and analysis of Poisson-Boltzmann electrostatics calculations, Nucleic Acids Res., 32 (2004), pp. W665–W667. [14] B. S. Duncan and A. J. Olson, Shape analysis of molecular surfaces., Biopolymers, 33 (1993), pp. 231–238. [15] D. Eberly, Triangulation by Ear Clipping, Geometric Tools, LLC, , 1998. [16] H. Edelsbrunner, Deformable smooth surface design, Discrete Comput. Geom., 21 (1999), pp. 87–115. · Zbl 0924.68197 [17] H. Edelsbrunner and E. P. Mucke, Three-dimensional alpha shapes, ACM Trans. Graphics, 13 (1994), pp. 43–72. · Zbl 0806.68107 [18] J. A. Grant, M. A. Gallardo, and B. T. Pickup, A fast method of molecular shape comparison: A simple application of a Gaussian description of molecular shape, J. Comput. Chem., 17 (1996), pp. 1653–1666. [19] T. Ju, F. Losasso, S. Schaefer, and J. D. Warren, Dual contouring of hermite data, ACM Trans. Graphics, 21 (2002), pp. 339–346. [20] T. G. Kolda and B. W. Bader, Tensor decompositions and applications, SIAM Rev., 51 (2009), pp. 455–500, . · Zbl 1173.65029 [21] B. Lee and F. Richards, The interpretation of protein structures: Estimation of static accessibility, J. Mol. Biol., 55 (1971), pp. 379–400. [22] T. Liao, Y. Zhang, P. M. Kekenes-Huskey, Y, Cheng, A. Michailova, A. McCulloch, M. Holst, and A. McCammon, Multi-core CPU or GPU-accelerated multiscale modeling for biomolecular complexes, Mol. Based Math. Biol., 1 (2013), pp. 164–179. · Zbl 1276.92030 [23] T. Liu, M. Chen, and B. Lu, Parameterization for molecular Gaussian surface and a comparison study of surface mesh generation, J. Molecular Model., 21 (2015), 113. [24] W. Lorensen and H. E. Cline, Marching cubes: A high resolution 3d surface construction algorithm, Computer Graphics, 21 (1987), pp. 163–169. [25] B. Z. Lu, Y. C. Zhou, M. J. Holst, and J. A. MaCammon, Recent progress in numerical methods for the Poisson-Boltzmann equation in biophysical applications, Commun. Comput. Phys., 3 (2008), pp. 973–1009. · Zbl 1186.92005 [26] M. R. Mcgann, H. R. Almond, A. Nicholls, A. J. Grant, and F. K. Brown, Gaussian docking functions, Biopolymers, 68 (2003), pp. 76–90. [27] G. H. Meisters, Polygons have ears, Amer. Math. Monthly, 82 (1975), pp. 648–651. · Zbl 0304.54038 [28] J. Milnor, Morse Theory, Princeton University Press, Princeton, NJ, 1963. [29] A. Nicholls, R. Bharadwaj, and B. Honig, Grasp: Graphical representation and analysis of surface properties, Biophys. J., 64 (1995), pp. 166–167. [30] F. M. Richards, Areas, volumes, packing and protein structure, Ann. Rev. Biophys. Bioengineering, 6 (1977), pp. 151–176. [31] J. Ryu, R. Park, and D.-S. Kim, Molecular surfaces on proteins via beta shapes, Comput. Aided Des., 39 (2007), pp. 1042–1057. [32] M. Sanner, A. Olson, and J. Spehner, Reduced surface: An efficient way to compute molecular surface properties, Biopolymers, 38 (1996), pp. 305–320. [33] R. Seidel, A simple and fast incremental randomized algorithm for computing trapezoidal decompositions and for triangulating polygons, Comput. Geom. Theory Appl., 1 (1991), pp. 51–64. · Zbl 0733.68092 [34] H. Si, TetGen, a Delaunay-based quality tetrahedral mesh generator, ACM Trans. Math. Softw., 41 (2015), 11. · Zbl 1369.65157 [35] Y. Vorobjev and J. Hermans, SIMS: Computation of a smooth invariant molecular surface, Biophys. J., 73 (1997), pp. 722–732. [36] J. Weiser, P. Shenkin, and W. Still, Optimization of Gaussian surface calculations and extension to solvent-accessible surface areas, J. Comput. Chem., 20 (1999), pp. 688–703. [37] D. Xu and Y. Zhang, Generating triangulated macromolecular surfaces by Euclidean distance transform, PLoS ONE, 4 (2009), e8140. [38] Z. Yu, M. J. Holst, and J. McCammon, High-fidelity geometric modeling for biomedical applications, Finite Elem. Anal. Des., 44 (2008), pp. 715–723. [39] Z. Yun, P. Matthew, and A. Richard, What role do surfaces play in GB models? A new-generation of surface-generalized Born model based on a novel Gaussian surface for biomolecules, J. Comput. Chem., 27 (2005), pp. 72–89. [40] R. Zauhar, SMART: A solvent-accessible triangulated surface generator for molecular graphics and boundary element applications, J. Computer-Aided Mol. Des., 9 (1995), pp. 149–159. [41] B. Zhang, B. Peng, J. Huang, N. P. Pitsianis, X. Sun, and B. Lu, Parallel AFMPB solver with automatic surface meshing for calculations of molecular solvation free energy, Comput. Phys. Comm., 190 (2015), pp. 173–181. · Zbl 1344.78004 [42] Y. Zhang, G. Xu, and C. Bajaj, Quality meshing of implicit solvation models of biomolecular structures, Comput. Aided Geom. Des., 23 (2006), pp. 510–530. · Zbl 1098.92034
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.