A Stabilized Finite Element Method for Modified Poisson-Nernst-Planck Equations to Determine Ion Flow Through a Nanopore

作     者：Jehanzeb Hameed Chaudhry Jeffrey Comer Aleksei Aksimentiev Luke N.Olson 

作者机构：Department for MathematicsColorado State UniversityFort CollinsCO 80523USA. Department for PhysicsUniversity of Illinois at Urbana-ChampaignUrbanaIL 61801USA. Department for Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaIL 61801USA 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2014年第15卷第1期

页      面：93-125页

核心收录：

学科分类：07[理学] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

基　　金：National Science Foundation, NSF, (0955959) National Science Foundation, NSF 

主　　题：Steric effects nucleic acids ionic current continuum transport theory ion channels PNP SUPG finite element method. 

摘      要：The conventional Poisson-Nernst-Planck equations do not account for the finite size of ions *** leads to solutions featuring unrealistically high ionic concentrations in the regions subject to external potentials,in particular,near highly charged surfaces.A modified form of the Poisson-Nernst-Planck equations accounts for steric effects and results in solutions with finite ion ***,we evaluate numerical methods for solving the modified Poisson-Nernst-Planck equations by modeling electric field-driven transport of ions through a *** describe a novel,robust finite element solver that combines the applications of the Newton’s method to the nonlinear Galerkin form of the equations,augmented with stabilization terms to appropriately handle the drift-diffusion *** make direct comparison with particle-based simulations possible,our method is specifically designed to produce solutions under periodic boundary conditions and to conserve the number of ions in the solution *** test our finite element solver on a set of challenging numerical experiments that include calculations of the ion distribution in a volume confined between two charged plates,calculations of the ionic current though a nanopore subject to an external electric field,and modeling the effect of a DNA molecule on the ion concentration and nanopore current.