A fast and robust Poisson-Boltzmann solver based on adaptive Cartesian grids

Journal of Chemical Theory and Computation

Volumn 7, Issue 5, 2011, Pages 1524-1540

  Boschitsch, Alexander H ^a   Fenley, Marcia O ^b  

^a Continuum Dynamics Inc ^*  (United States)

^b Florida State University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79955915303     PISSN: 15499618     EISSN: 15499626     Source Type: Journal    
DOI: 10.1021/ct1006983     Document Type: Article

References (78)

1. Lu, B.; Zhou, Y. C.; Holst, M. J.; McCammon, J. A. Recent progress in numerical methods for the Poisson-Boltzmann equation in biophysical applications Commun. Comput. Phys. 2008, 3, 973-1009
2. Lu, J.; Deutsch, C. Electrostatics in the Ribosomal Tunnel Modulate Chain Elongation Rates J. Mol. Biol. 2008, 384, 73-86
3. Zhang, D.; Konecny, R.; Baker, N. A.; McCammon, J. A. Electrostatic interaction between RNA and protein capsid in cowpea chlorotic mottle virus simulated by a coarse-grain RNA model and a Monte Carlo approach Biopolymers 2004, 75, 325-337 (Pubitemid 39452436)
4. Boschitsch, A. H.; Fenley, M. O.; Zhou, H.-X. Fast Boundary Element Method for the Linear Poisson-Boltzmann Equation J. Phys. Chem. B 2002, 106, 2741-2754 (Pubitemid 35275953)
5. Bharadwaj, R.; Windemuth, A.; Sridharan, S.; Honig, B.; Nicholls, A. The Fast Multipole Boundary Element Method for Molecular Electrostatics: An Optimal Approach for Large Systems J. Comput. Chem. 1995, 16, 898-913
6. Purisima, E. O. Fast Summation Boundary Element Method for Calculating Solvation Free Energies of Macromolecules J. Comput. Chem. 1998, 19, 1494-1504 (Pubitemid 128592640)
7. Zauhar, R. J.; Varnek, A. A Fast and Space Efficient Boundary Element Method for Computing Electrostatic and Hydration Effects in Large Molecules J. Comput. Chem. 1996, 17, 864-877 (Pubitemid 126579188)
8. Boschitsch, A. H.; Fenley, M. O.; Olson, W. K. A Fast Adaptive Multipole Algorithm for Calculating Screened Coulomb (Yukawa) Interactions J. Comput. Phys. 1999, 151, 212-241
9. Lu, B.; Cheng, X.; Huang, J.; McCammon, J. A. Order N algorithm for computation of electrostatic interactions in biomolecular systems Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 19314-19319 (Pubitemid 46026029)
10. Lu, B.; Cheng, X.; McCammon, J. A. "New-version-fast-multipole- method" accelerated electrostatic calculations in biomolecular systems J. Comput. Phys. 2007, 226, 1348-1366
11. Boschitsch, A. H.; Fenley, M. O. Hybrid Boundary Element and Finite Difference Method for Solving the Nonlinear Poisson-Boltzmann Equation J. Comput. Chem. 2004, 25, 935-955
12. Baker, N. A.; Holst, M. J.; Wang, F. Adaptive Multilevel Finite Element Solution of the Poisson-Boltzmann Equation II. Refinement at Solvent-Accessible surfaces in Biomolecular Systems J. Comput. Chem. 2000, 21, 1343-1352
13. Holst, M.; Baker, N.; Wang, F. Adaptive Multilevel Finite Element Solution of the Poisson-Boltzmann Equation I: Algorithms and Examples J. Comput. Chem. 2000, 21, 1319-1342
14. Baker, N. A.; Sept, D.; Joseph, S.; Holst, M. J.; McCammon, J. A. Electrostatics of Nanosystems: Application to Microtubules and the Ribosome Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 10037-10041 (Pubitemid 32802969)
15. Madura, J. D.; Briggs, J. M.; Wade, R. C.; Davis, M. E.; Luty, B. A.; Ilin, A.; Antosiewicz, J.; Gilson, M. K.; Bagheri, B.; Scott, L. R.; McCammon, J. A. Electrostatics and Diffusion of Molecules in Solution: Simulations with the University of Houston Brownian Dynamics Program Comput. Phys. Commun. 1995, 91, 57-95
16. Jo, S.; Vargyas, M.; Vasko-Szedlar, M.; Roux, B.; Im, B. PBEQ-Solver for online visualization of electrostatic potential of biomolecules Nucleic Acids Res. 2008, 36, W270-W275
17. Bashford, D.; Gerwert, K. Electrostatic Calculations of the pKa Values of Ionizable Groups in Bacteriorhodopsin J. Mol. Biol. 1992, 224, 473-486
18. Grant, J. A.; Pickup, B. T.; Nicholls, A. A smooth permittivity function for Poisson-Boltzmann solvation methods J. Comput. Chem. 2001, 22, 608-640 (Pubitemid 32382607)
19. Gilson, M. K.; Sharp, K.; Honig, B. Calculating the electrostatic potential of molecules in solution: Method and error assessment J. Comput. Chem. 1987, 9, 327-335
20. Cai, Q.; Hsieh, M.-J.; Wang, J.; Luo, R. Performance of Nonlinear Finite-Difference Poisson-Boltzmann Solvers J. Chem. Theory Comput. 2010, 6, 203-211
21. Luo, R.; David, L.; Gilson, M. K. Accelerated Poisson-Boltzmann calculations for static and dynamic systems J. Comput. Chem. 2002, 23, 1244-1253 (Pubitemid 35009216)
22. Wang, J.; Luo, R. Assessment of Linear Finite-Difference Poisson-Boltzmann Solvers J. Comput. Chem. 2010, 31, 1689-1698
23. Boschtisch, A. H.; Fenley, M. O. A New Outer Boundary Formulation and Energy Corrections for the Nonlinear Poisson-Boltzmann Equation J. Comput. Chem. 2007, 28, 909-921 (Pubitemid 46491699)
24. Gilson, M. K.; Sharp, K. A.; Honig, B. Calculating electrostatic interactions in biomolecules: method and error assessment J. Comput. Chem. 1988, 9, 327-335
25. Cortis, C. M.; Friesner, R. A. An Automatic Three-Dimensional Finite Element Mesh Generation System for the Poisson-Boltzmann Equation J. Comput. Chem. 1997, 18, 1570-1590 (Pubitemid 127677975)
26. 2-Smooth Molecular Surfaces Comput. Methods Appl. Mech. Eng. 2009, 198, 1684-1690
27. Samet, H. The Design and Analysis of Spatial Structures; Addison-Wesley Publishing Company, Inc.: Reading, MA, 1990; p 510.
28. Mirzadeh, M.; Theillard, M.; Gibou, F. A second-order discretization of the nonlinear Poisson-Boltzmann equation over irregular geometries using non-graded adaptive Cartesian grids J. Comput. Phys. 2011, 230, 2125-2140
29. Aftosmis, M. J.; Berger, M. J.; Melton, J. E. Robust and Efficient Cartesian Mesh Generation for Component-Based Geometry AIAA J. 1998, 36, 952-960 (Pubitemid 128584709)
30. Murman, S. M.; Aftosmis, M. J.; Berger, M. J., Simulations of Store Separation from an F/A-18 with a Cartesian Method. J. Aircraft 2004, 41, (4).
31. Aftosmis, M. J. Solution Adaptive Cartesian Grid Methods for Aerodynamic Flows with Complex Geometries; Lecture Notes 1997-02; Von Karman Institute for Fluid Dynamics: Rhode-St-Genèse, Belgium, 1997.
32. Aftosmis, M. J.; Berger, M. J.; Melton, J. E. Robust and Efficient Cartesian Mesh Generation for Component-Based Geometry. In 35th AIAA Aerospace Sciences Meeting & Exhibit, AIAA-97-0196, Reno, NV, 1997; AIAA: Reston, VA, 1997.
33. Berger, M. J.; LeVeque, R. J. An Adaptive Cartesian Mesh Algorithm for the Euler Equations in Arbitrary Geometries. In 89-1930-CP; AIAA: Reston, VA, 1989.
34. Wang, J.; Cai, Q.; Li, Z.-L.; Zhao, H.-K.; Luo, R. Achieving energy conservation in Poisson-Boltzmann molecular dynamics: Accuracy and precision with finite-difference algorithms Chem. Phys. Lett. 2009, 468, 112-118
35. Zhou, Z.; Payne, P.; Vasquez, M.; Kuhn, N.; Levitt, M. Finite-Difference Solution of the Poisson-Boltzmann Equation: Complete Elimination of Self-Energy J. Comput. Chem. 1996, 11, 1344-1351 (Pubitemid 126576751)
36. Bondi, A. Van der Waals Volumes and Radii J. Phys. Chem. 1964, 68, 441-451
37. Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollman, P. A. A 2nd generation force-field for simulation of proteins, nucleic-acids, and organic-molecules J. Am. Chem. Soc. 1995, 117, 11946-11975
38. Foloppe, N.; MacKerell, A. D. J. All-atom empirical force field for nucleic acids: I. Parameter optimization based on small molecule and condensed phase macromolecular target data J. Comput. Chem. 2000, 21, 86-104
39. Friedrichs, M.; Zhou, R.; Edinger, S. R.; Friesner, R. A. Poisson-Boltzmann Analytical Gradients for Molecular Modeling Calculations J. Phys. Chem. B 1999, 103, 3057-3061 (Pubitemid 129702437)
40. Chan, S. L.; Purisima, E. O. Molecular surface generation using marching tetrahedra J. Comput. Chem. 1998, 19, 1268-1277 (Pubitemid 128616669)
41. Protter, M.; Weinberger, H. F. Maximum Principles in Differential Equations; Prentice Hall: Englewood Cliffs, NJ, 1967; reprint by Springer-Verlag: New York, 1984.
42. Barth, T. J. Numerical Aspects of Computing Viscous High Reynolds Number Flows on Unstructured Meshes. In 29th Aerospace Sciences Meeting, AIAA-91-0721, Reno, NV, 1991; AIAA: Reston, VA, 1991.
43. Chen, S.-W. W.; Honig, B. Monovalent and Divalent Salt Effects on Electrostatic Free Energies Defined by the Nonlinear Poisson-Boltzmann Equation: Application to DNA Binding Reactions J. Phys. Chem. B 1997, 101, 9113-9118 (Pubitemid 127587695)
44. Greengard, L.; Huang, J. A New Version of the Fast Multipole Method for Screened Coulomb Interactions in Three Dimensions, 01-002; Courant Mathematics and Computing Laboratory, Courant Institute: New York, 2001; p 18.
45. Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes, 2nd ed.; Cambridge University Press: Cambridge, U. K., 1992; p 960.
46. Holst, M.; Saied, F. Multigrid Solution of the Poisson-Boltzmann Equation J. Comput. Chem. 1993, 14, 105-113
47. Oberoi, H.; Allewell, N. M. Multigrid Solution of the Nonlinear Poisson-Boltzmann Equation and Calculation of Titration Curves Biophys. J. 1993, 65, 48-55 (Pubitemid 23206037)
48. Sharp, K.; Honig, B. Calculating total electrostatic energies with the nonlinear Poisson-Boltzmann equation J. Phys. Chem. 1990, 94, 7684-7692
49. Sharp, K. A. Polyelectrolyte Electrostatics: Salt Dependence, Entropic, and Enthalpic Contributions to Free Energy in the Nonlinear Poisson-Boltzmann Model Biopolymers 1995, 36, 227-243
50. Sharp, K. A.; Friedman, R. A.; Misra, V.; Hecht, J.; Honig, B. Salt Effects on Polyelectrolyte-Ligand Binding: Comparison of Poisson-Boltzmann, and Limiting Law/Counterion Binding Models Biopolymers 1995, 36, 245-262
51. Kirkwood, J. G. Theory of Solutions of Molecules Containing Widely Separated Charges with Special Applications to Zwitterions J. Chem. Phys. 1934, 2, 351-361
52. Sader, J. E.; Lenhoff, A. M. Electrical Double-Layer Interaction between Heterogeneously Charged Colloidal Particles: A Superposition Formulation J. Colloid Interface Sci. 1998, 201, 233-243 (Pubitemid 28401792)
53. Zhou, H.-X. Macromolecular Electrostatic Energy Within the Nonlinear Poisson-Boltzmann Equation J. Chem. Phys. 1994, 100, 3152-3162
54. Schreiber, G.; Haran, G.; Zhou, H.-X. Fundamental aspects of protein-protein association kinetics Chem. Rev. 2009, 109, 839-860
55. Getzoff, E. D.; Cabelli, D. E.; Fisher, C. L.; Parge, H. E.; Viezzoli, M. S.; Banci, L.; Hallewell, R. A. Faster superoxide dismutase mutants designed by enhancing electrostatic guidance Nature 1992, 358, 347-351
56. Lago, H.; Parrott, A. M.; Moss, T.; Stonehouse, N. J.; Stockley, P. G. Probing the kinetics of formation of the bacteriophage MS2 translational operator complex: identification of a protein conformer unable to bind RNA J. Mol. Biol. 2001, 305, 1131-1144 (Pubitemid 33027748)
57. Zhou, H.-X. Boundary Element Solution to Macromolecular Electrostatics: Interaction energy between two proteins Biophys. J. 1993, 65, 955-963 (Pubitemid 23263906)
58. Bredenberg, J.; Boschitsch, A. H.; Fenley, M. O. The role of anionic protein residues on the salt dependence of the binding of aminoacyl-tRNA synthetases to tRNA: A Poisson-Boltzmann analysis Commun. Comput. Phys. 2008, 3, 1051-1070
59. Bredenberg, J. H.; Russo, C.; Fenley, M. O. Salt-mediated electrostatics in the association of TATA binding proteins to DNA: A combined molecular mechanics/Poisson-Boltzmann study Biophys. J. 2008, 94, 4634-4645
60. Bredenberg, J. H.; Fenley, M. O. Salt dependent association of novel mutants of TATA-binding proteins to DNA: Predictions from theory and experiments Commun. Comput. Phys. 2008, 3, 1132-1153
61. Fenley, M. O.; Harris, R. C.; Jayaram, B.; Boschitsch, A. H. Revisiting the association of cationic groove-binding drugs to DNA using a Poisson-Boltzmann approach Biophys. J. 2010, 99, 879-886
62. Harris, R. C.; Bredenberg, J. H.; Silalahi, A. R. J.; Boschitsch, A. H.; Fenley, M. O. Understanding the physical basis of the salt dependencd of the electrostatic binding free energy of mutated charged ligand-nucleic acid complexes. Biophys. Chem. 2011, not supplied.
63. Xu, D.; Greenbaum, N. L.; Fenley, M. O. Recognition of the spliceosomal branch site RNA helix on the basis of surface and electrostatic features Nucleic Acids Res. 2005, 33, 1154-1161 (Pubitemid 41439908)
64. Xu, D.; Landon, T.; Greenbaum, N. L.; Fenley, M. O. The electrostatic characteristics of G•U wobble base pairs Nucleic Acids Res. 2007, 35, 3836-3847 (Pubitemid 47244675)
65. Auweter, S. D.; Fasan, R.; Reymond, L.; Underwood, J. G.; Black, D. L.; Pitsch, S.; Allain, F., H.-T. Molecular Basis of RNA Recognition by the Human Alternative Splicing Factor Fox-1 EMBO J. 2006, 25, 163-173 (Pubitemid 43077305)
66. Auweter, S. D.; Oberstrass, F. C.; Allain, F., H.-T. Sequence-specific Binding of Single-stranded RNA: Is there a Code for Recognition? Nucleic Acids Res. 2006, 34, 4943-4959 (Pubitemid 44605637)
67. Xu, D. Electrostatics of Nucleic Acids and Hydration Properties of the Pseudouridine Dependent Spliceosomal Branch Site Helix; Florida State University: Tallahassee, FL, 2007.
68. Sayyed-Ahmad, A.; Miao, Y.; Ortoleva, P. Poisson-Boltzmann theory of bionanosystems Commun. Comput. Phys. 2008, 3, 1100-1116
69. Trylska, J.; Konecny, R.; Tama, F.; Brooks, C. L. I.; McCammon, J. A. Ribosome motions modulate electrostatic properties Biopolymers 2004, 74, 423-431 (Pubitemid 39128058)
70. Trylska, J.; McCammon, J. A.; Brooks, C. L. I. Exploring Assembly Energetics of the 30S Ribosomal Subunit Using an Implicit Solvent Approach J. Am. Chem. Soc. 2005, 127, 11125-11133 (Pubitemid 41129889)
71. Devkota, B.; Petrov, A.; Lemieux, S.; Bpz, M. B.; Tang, L.; Schneemann, A.; Jonhson, J. E.; Harvey, S. C. Structural and Electrostatic Characterization of Pariacoto Virus: Implications for Viral Assembly Biopolymers 2009, 91, 530-538
72. Dlugosz, M.; Trylska, J. Aminoglycoside association pathways with the 30S ribosomal subunit J. Phys. Chem. B 2009, 113, 7322-7330
73. Qin, S.; Zhou, H.-X. Dissection of the High Rate Constant for the Binding of a Ribotoxin to the Ribosome Proc. Natl. Acad. Sci. U.S.A. 2009, 106, 6974-6979
74. Lu, B.; Cheng, X.; Huang, J.; McCammon, J. A. An Adaptive Fast Multipole Boundary Element Method for Poisson-Boltzmann Electrostatics J. Chem. Theory Comput. 2009, 5, 1692-1699
75. Gordon, J. C.; Fenley, A. T.; Onufriev, A. An Analytical Approach to Computing Biomolecular Electrostatic Potential. II. Validation and Applications J. Chem. Phys. 2008, 129, 075102-1-075102-11
76. Pacios, L. F.; Garcia-Arenal, F. Comparison of Properties of particles of Cucumber mosaic virus and Tomato aspermy virus based on the analysis of molecular surfaces of capsids J. Gen. Virol. 2006, 87, 2073-2083 (Pubitemid 43985892)
77. Dolinsky, T. J.; Nielsen, J. E.; McCammon, J. A.; Baker, N. A. PDB2PQR: an automated pipeline for the setup, execution, and analysis of Poisson-Boltzmann electrostatics calculations Nucleic Acids Res. 2004, 32, W665-W667
78. Bahadur, R. P.; Zacharias, M.; Janin, J. Dissecting Protein-RNA Recognition Sites Nucleic Acids Res. 2008, 36, 2705-2716 (Pubitemid 351659584)