Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2014 | 2 | 1 |
Tytuł artykułu

A Poisson-Boltzmann Equation Test Model for Protein in Spherical Solute Region and its Applications

Treść / Zawartość
Warianty tytułu
Języki publikacji
The Poisson-Boltzmann equation (PBE) is one important implicit solvent continuum model for calculating electrostatics of protein in ionic solvent. Several numerical algorithms and program packages have been developed but verification and comparison between them remains an interesting topic. In this paper, a PBE test model is presented for a protein in a spherical solute region, along with its analytical solution. It is then used to verify a PBE finite element solver and applied to a numerical comparison study between a finite element solver and a finite difference solver. Such a study demonstrates the importance of retaining the interface conditions in the development of PBE solvers.
  • Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201-0413, USA
  • Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201-0413, USA
  • Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201-0413, USA,
  • [1] N. A. Baker, D. Sept, S. Joseph, M. Holst, and J. A. McCammon, Electrostatics of nanosystems: Application to microtubulesand the ribosome, Proc. Natl. Acad. Sci. USA 98 (2001), no. 18, 10037–10041.[Crossref]
  • [2] N.A. Baker, Improving implicit solvent simulations: a Poisson-centric view, Curr. Opin. Struc. Biol. 15 (2005), 137–143.[Crossref]
  • [3] N.A. Baker, D. Sept, M. Holst, and J. A. McCammon, The adaptive multilevel finite element solution of the Poisson-Boltzmannequation on massively parallel computers, IBM Journal of Research and Development 45 (2001), 427–438.
  • [4] M.Z. Born, Volumen und hydratationswärme der ionen, Zeitschrift für Physik A Hadrons and Nuclei 1 (1920), no. 1, 45–48.
  • [5] S.C. Brenner and L.R. Scott, The mathematical theory of finite element methods, third ed., Springer-Verlag, New York, 2008.
  • [6] M.E. Davis, J.D. Madura, B.A. Luty, and J.A. McCammon, Electrostatics and diffusion of molecules in solution: Simulationswith the University of Houston Browian dynamics program, Comp. Phys. Comm. 62 (1991), 187–197.[Crossref]
  • [7] W. Geng, S. Yu, and G. Wei, Treatment of charge singularities in implicit solvent models, The Journal of chemical physics 127(2007), 114106.[WoS]
  • [8] M. Holst, J.A. McCammon, Z. Yu, Y. Zhou, and Y. Zhu, Adaptive finite element modeling techniques for the Poisson-Boltzmannequation, Communications in computational physics 11 (2012), no. 1, 179.[WoS]
  • [9] B. Honig and A. Nicholls, Classical electrostatics in biology and chemistry, Science 268 (1995), 1144–1149.
  • [10] W. Im, D. Beglov, and B. Roux, Continuum solvation model: electrostatic forces from numerical solutions to the Poisson-Bolztmann equation, Comput. Phys. Comm. 111 (1998), 59–75.[Crossref]
  • [11] S. Jo, M. Vargyas, J. Vasko-Szedlar, B. Roux, and W. Im, PBEQ-Solver for online visualization of electrostatic potential ofbiomolecules, Nucleic Acids Research 36 (2008), W271–W275.[WoS]
  • [12] J.G. Kirkwood, Theory of solutions of molecules containing widely separated charges with special application to zwitterions,The Journal of Chemical Physics 2 (1934), 351.
  • [13] P. Koehl, Electrostatics calculations: Latest methodological advances, Current Opinion in Structural Biology 16 (2006), no. 2,142–151.
  • [14] A. Logg, G. N. Wells, and J. Hake, DOLFIN: A C++/Python finite element library, Automated Solution of Differential Equationsby the Finite Element Method, Lect. Notes Comput. Sci. Eng., vol. 84, Springer, Heidelberg, 2012, pp. 173–225.
  • [15] B. Lu, Y. Zhou, M.J. Holst, and J.A. McCammon, Recent progress in numerical methods for the Poisson-Boltzmann equationin biophysical applications, Commun. Comput. Phys. 3 (2008), no. 5, 973–1009.
  • [16] M.T. Neves-Petersen and S.B. Petersen, Protein electrostatics: A review of the equations and methods used to model electrostaticequations in biomolecules – Applications in biotechnology, Biotech. Annu. Rev. 9 (2003), 315–395.
  • [17] A. Nicholls and B. Honig, A rapid finite difference algorithm, utilizing successive over-relaxation to solve the Poisson-Boltzmann equation, J. Comp. Chem. 12 (1991), 435–445.[Crossref]
  • [18] W. Rocchia, E. Alexov, and B. Honig, Extending the applicability of the nonlinear Poisson-Boltzmann equation: Multiple dielectricconstants and multivalent ions, J. Phys. Chem. B 105 (2001), 6507–6514.
  • [19] J.Waldén, On the approximation of singular source terms in differential equations, Numerical Methods for Partial DifferentialEquations 15 (1999), no. 4, 503–520.
  • [20] D. Xie, New solution decomposition and minimization schemes for Poisson-Boltzmann equation in calculation of biomolecularelectrostatics, Journal of Computational Physics, 275 (2014), 294–309.
  • [21] D. Xie and S. Zhou, A new minimization protocol for solving nonlinear Poisson-Boltzmann mortar finite element equation,BIT Num. Math. 47 (2007), 853–871.
  • [22] D. M. Young, Iterative solution of large linear system, Academic press, New York, 1971.
  • [23] S. Yu, W. Geng, and G. Wei, Treatment of geometric singularities in implicit solvent models, The Journal of Chemical Physics126 (2007), 244108.[WoS]
  • [24] Y. Zhou, M. Feig, and G. Wei, Highly accurate biomolecular electrostatics in continuum dielectric environments, Journal ofComputational Chemistry 29 (2008), no. 1, 87–97.[WoS]
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.