A Poisson-Nernst-Planck Single Ion Channel Model and its Effective Finite Element Solver

28 Pages Posted: 7 Nov 2022

See all articles by Dexuan Xie

Dexuan Xie

University of Wisconsin-Milwaukee

Zhen Chao

affiliation not provided to SSRN


A single ion channel is a membrane protein with an ion selectivity filter that allows only a single species of ions (such as potassium ions) to pass through  in the ``open" state. Its selectivity filter also naturally separates a solvent domain into an intracellular domain and an extracellular domain.  Such biological and geometrical characteristics of a  single ion channel are novelly adopted in the construction of a new kind of dielectric continuum ion channel model, called the Poisson-Nernst-Planck single ion channel (PNPSIC) model, in this paper. An effective PNPSIC finite element solver is then developed and implemented as a software package workable for a single ion channel with a three-dimensional X-ray crystallographic molecular structure and  a mixture of multiple ionic species. Numerical results for a potassium channel confirm the convergence and efficiency of the PNPSIC finite element solver and demonstrate the high performance of the software package. Moreover, the PNPSIC model is applied to the calculation of electric current and validated by biophysical experimental data.

Keywords: Poisson-Nernst-Planck equations, finite element method, single ion channel, potassium channel, electric current calculation

Suggested Citation

Xie, Dexuan and Chao, Zhen, A Poisson-Nernst-Planck Single Ion Channel Model and its Effective Finite Element Solver. Available at SSRN: https://ssrn.com/abstract=4270098 or http://dx.doi.org/10.2139/ssrn.4270098

Dexuan Xie (Contact Author)

University of Wisconsin-Milwaukee ( email )

Dept of Biological Sciences
PO Box
Milwaukee, WI 53211
United States

Zhen Chao

affiliation not provided to SSRN ( email )

No Address Available

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