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

• Autorzy: Yi Jiang , Jinyong Ying , Dexuan Xie
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Poisson-Boltzmann equation; continuum electrostatics; finite element method; finite difference method; electrostatic potential

Kategorie tematyczne

• 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
• 92C40: Biochemistry, molecular biology
• 65N06: Finite difference methods
• 92-08: Computational methods

• Wydawca: De Gruyter Open
• Czasopismo: Molecular Based Mathematical Biology
• Rocznik: 2014
• Tom: 2
• Numer: 1

Daty

otrzymano

2014-04-13

zaakceptowano

2014-08-16

online

2014-09-27

Twórcy

autor

Yi Jiang

• Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201-0413, USA

autor

Jinyong Ying

• Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201-0413, USA

autor

Dexuan Xie

• Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201-0413, USA

Bibliografia

• [1] N. A. Baker, D. Sept, S. Joseph, M. Holst, and J. A. McCammon, Electrostatics of nanosystems: Application to microtubules and 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-Boltzmann equation 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: Simulations with 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-Boltzmann equation, 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 of biomolecules, 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 Equations by 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 equation in 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 electrostatic equations 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 dielectric constants 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 Differential Equations 15 (1999), no. 4, 503–520.
• [20] D. Xie, New solution decomposition and minimization schemes for Poisson-Boltzmann equation in calculation of biomolecular electrostatics, 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 Physics 126 (2007), 244108. [WoS]
• [24] Y. Zhou, M. Feig, and G. Wei, Highly accurate biomolecular electrostatics in continuum dielectric environments, Journal of Computational Chemistry 29 (2008), no. 1, 87–97.[WoS]

Identyfikatory

DOI

10.2478/mlbmb-2014-0006