Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes I: Finite element solutions

doi:10.1016/j.jcp.2010.05.035

	Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes I: Finite element solutions
	Lu, Benzhuo2 ; Holst, Michael J.3,4; McCammon, J. Andrew 4,5,6; Zhou, Y. C.1
	2010-09-20
发表期刊	JOURNAL OF COMPUTATIONAL PHYSICS
ISSN	0021-9991
卷号	229 期号:19 页码:6979-6994
摘要	In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for simulating electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised for time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems. (C) 2010 Elsevier Inc. All rights reserved.
关键词	Electrodiffusion Poisson-Nernst-Planck equations Finite element Singular charges Molecular surface Boundary condition Conditioning
DOI	10.1016/j.jcp.2010.05.035
语种	英语
资助项目	Academy of Mathematics and Systems Science of Chinese Academy of Sciences ; State Key Laboratory of Scientific and Engineering Computing ; NSFC[NSFC10971218] ; NIH[P41RR008605] ; NSF[0715146] ; NSF[0821816] ; NSF[0822283] ; HHMI ; CTBP ; NBCR ; DOD/DTRA[09-1-0036] ; Colorado State University ; Center for Revolutionary Solar Photoconversion (CRSP)
WOS研究方向	Computer Science ; Physics
WOS类目	Computer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS记录号	WOS:000281570700019
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10995
专题	计算数学与科学工程计算研究所
通讯作者	Zhou, Y. C.
作者单位	1.Colorado State Univ, Dept Math, Ft Collins, CO 80523 USA 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China 3.Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA 4.Univ Calif San Diego, Ctr Theoret Biol Phys, La Jolla, CA 92093 USA 5.Univ Calif San Diego, Dept Chem & Biochem, La Jolla, CA 92093 USA 6.Univ Calif San Diego, Dept Pharmacol, La Jolla, CA 92093 USA
推荐引用方式 GB/T 7714	Lu, Benzhuo,Holst, Michael J.,McCammon, J. Andrew,et al. Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes I: Finite element solutions[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2010,229(19):6979-6994.
APA	Lu, Benzhuo,Holst, Michael J.,McCammon, J. Andrew,&Zhou, Y. C..(2010).Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes I: Finite element solutions.JOURNAL OF COMPUTATIONAL PHYSICS,229(19),6979-6994.
MLA	Lu, Benzhuo,et al."Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes I: Finite element solutions".JOURNAL OF COMPUTATIONAL PHYSICS 229.19(2010):6979-6994.