Pseudo-time-coupled nonlinear models for biomolecular surface representation and solvation analysis

International Journal for Numerical Methods in Biomedical Engineering

Volumn 27, Issue 12, 2011, Pages 1964-1981

  Zhao, Shan ^a  

^a UNIVERSITY OF ALABAMA   (United States)

Author keywords

Biological surface formation and evolution; Generalized nonlinear Poisson Boltzmann equation; Multiscale models; Potential driving geometric flows; Solvation free energy

Indexed keywords

BIOLOGICAL SURFACES; GEOMETRIC FLOWS; MULTISCALE MODELS; NONLINEAR POISSON-BOLTZMANN EQUATION; SOLVATION FREE ENERGY;

BINDING ENERGY; BIOCHEMISTRY; BOLTZMANN EQUATION; DIFFERENTIAL EQUATIONS; ELECTROSTATICS; FREE ENERGY; MATHEMATICAL MODELS; NONLINEAR ANALYSIS; POISSON EQUATION; PROTEINS; SOLVATION;

NONLINEAR EQUATIONS;

EID: 82255162971     PISSN: 20407939     EISSN: 20407947     Source Type: Journal    
DOI: 10.1002/cnm.1450     Document Type: Article

References (36)

1. Sharp KA, Honig B. Electrostatic interactions in macromolecules: theory and applications. Annual Review Biophysics and Biophysical Chemistry 1990; 19:301-332.
2. Ponder JW, Case DA. Force fields for protein simulations. Advances in Protein Chemistry 2003; 66:27-85.
3. Roux B, Simonson T. Implicit solvent models. Biophysical Chemistry 1999; 78:1-20.
4. Baker NA. Improving implicit solvent simulations: a Poisson-centric view. Current Opinion in Structural Biology 2005; 15:137-143.
5. Dong F, Olsen B, Baker NA. Computational methods for biomolecular electrostatics. Methods in Cell Biology 2008; 84:843-870.
6. Feig M, Brooks III CL. Recent advances in the development and application of implicit solvent models in biomolecule simulations. Current Opinion in Structural Biology 2004; 14:217-224.
7. Feig M, Onufriev A, Lee MS, Im W, Case DA, Brooks III CL. Performance comparison of generalized born and Poisson methods in the calculation of electrostatic solvation energies for protein structures. Journal of Computational Chemistry 2004; 25:265-284.
8. Davis ME, McCammon JA. Electrostatics and diffusion of molecules in solution: simulations with the University of Houston Brownian dynamics program. Computer Physics Communications 1991; 62:187-197.
9. Lee B, Richards FM. The interpretation of protein structures: estimation of static accessibility. Journal of Molecular Biology 1973; 55:379-400.
10. Connolly ML. Analytical molecular surface calculation. Journal of Applied Crystallography 1983; 16:548-558.
11. Richards FM. Areas, volumes, packing and protein structure. Annual Review of Biophysics and Bioengineering 1977; 6:151-176.
12. Dong F, Vijaykumar M, Zhou HZ. Electrostatic contribution to the binding stability of protein-protein complexes. Proteins 2006; 65:87-102.
13. Dong F, Zhou HZ. Comparison of calculation and experiment implicates significant electrostatic contributions to the binding stability of barnase and barstar. Biophysical Journal 2003; 85: 49-60.
14. Grant JA, Pickup BT, Nicholls A. A smooth permittivity function for Poisson-Boltzmann solvation methods. Journal of Computational Chemistry 2001; 22:608-640.
15. Im W, Beglov D, Roux B. Continuum solvation model: computation of electrostatic forces from numerical solutions to the Poisson-Boltzmann equation. Computer Physics Communications 1998; 111:59-75.
16. Connolly ML. Molecular surface triangulation. Journal of Applied Crystallography 1985; 18:499-505.
17. Sanner MF, Olson AJ, Spehner JC. Reduced surface: an efficient way to compute molecular surfaces. Biopolymers 1996; 38:305-320.
18. Swanson JMJ, Henchman RH, McCammon JA. Revisiting free energy calculations: a theoretical connection to MM/PBSA and direct calculation of the association free energy. Biophysical Journal 2004; 86:67-74.
19. Wei GW, Sun YH, Zhou YC, Feig M. Molecular multiresolution surfaces, arXiv:math-ph, 0511001, Nov. 1 (2005).
20. Xu G, Pan Q, Bajaj C. Discrete surface modelling using partial differential equations. Computer Aided Geometric Design 2006; 23:125-145.
21. Zhang Y, Xu G, Bajaj C. Quality meshing of implicit solvation models of biomolecular structures. Computer Aided Geometric Design 2006; 23:510-530.
22. Bates PW, Wei GW, Zhao S. The minimal molecular surface, arXiv:q-bio/0610038v1, [q-bio.BM], 2006.
23. Bates PW, Wei GW, Zhao S. Minimal molecular surfaces and their applications. Journal of Computational Chemistry 2008; 29: 380-391.
24. Bates PW, Chen Z, Sun YH, Wei GW, Zhao S. Geometric and potential driving formation and evolution of biomolecular surfaces. Journal of Mathematical Biology 2009; 59:193-231.
25. Wei GW. Differential geometry based multiscale models. Bulletin of Mathematical Biology 2010; 72:1562-1622.
26. Chen Z, Baker N, Wei GW. Differential geometry based solvation model I: Eulerian formation. Journal of Computational Physics 2010; 229:8231-8258.
27. Chen Z, Baker N, Wei GW. Differential geometry based solvation model II: Lagrangian formation, accepted. Journal of Mathematical Biology 2011. DOI: 10.1007/s00285-011-0402-z.
28. Sharp KA, Honig B. Calculating total electrostatic energies with the nonlinear Poisson-Boltzmann equation. Journal of Physical Chemistry 1990; 94:7684-7692.
29. Gilson MK, Davis ME, Luty BA, McCammon JA. Computation of electrostatic forces on solvated molecules using the Poisson-Boltzmann equation. Journal of Physical Chemistry 1993; 97:3591-3600.
30. Wagoner J, Baker NA. Assessing implicit models for nonpolar mean solvation forces: the importance of dispersion and volume terms. Proceedings of the National Academy of Sciences of the USA 2006; 103:8331-8336.
31. Zhao S. High order matched interface and boundary methods for the Helmholtz equation in media with arbitrarily curved interfaces. Journal of Computional Physics 2010; 229:3155-3170.
32. Zhou YC, Zhao S, Feig M, Wei GW. High order matched interface and boundary (MIB) schemes for elliptic equations with discontinuous coefficients and singular sources. Journal of Computional Physics 2006; 213:1-30.
33. Weeks JD, Chandler D, Anderson HC. Role of repulsive forces in determining the equilibrium structure of simple liquids. Journal of Chemical Physics 1971; 54:5237-5247.
34. Holst MJ. The Poisson-Boltzmann equation: analysis and multilevel numerical solution. PhD thesis, University of Illinois at Urbana-Champaign, 1993.
35. Nicholls A, Mobley DL, Guthrie PJ, Chodera JD, Pande VS. Predicting small-molecule solvation free energies: An informal blind test for computational chemistry. Journal of Medicinal Chemistry 2008; 51:769-779.
36. Geng W, Yu S, Wei GW. Treatment of charge singularities in implicit solvent models. Journal of Chemical Physics 2007; 127:114-106.