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Volume 39, Issue 3
Dynamics of Poisson-Nernst-Planck Systems and Ionic Flows Through Ion Channels: A Review

Weishi Liu

Commun. Math. Res., 39 (2023), pp. 342-385.

Published online: 2023-04

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  • Abstract

Poisson-Nernst-Planck systems are basic models for electrodiffusion process, particularly, for ionic flows through ion channels embedded in cell membranes. In this article, we present a brief review on a geometric singular perturbation framework for analyzing the steady-state of a quasi-one-dimensional Poisson-Nernst-Planck model. The framework is based on the general geometric singular perturbed theory from nonlinear dynamical system theory and, most crucially, on the reveal of two specific structures of Poisson-Nernst-Planck systems. As a result of the geometric framework, one obtains a governing system–an algebraic system of equations that involves all physical quantities such as protein structures of membrane channels as well as boundary conditions, and hence, provides a complete platform for studying the interplay between protein structure and boundary conditions and effects on ionic flow properties. As an illustration, we will present concrete applications of the theory to several topics of biologically significant based on collaboration works with many excellent researchers.

  • AMS Subject Headings

34A26, 34B16, 78A35, 92C35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-39-342, author = {Liu , Weishi}, title = {Dynamics of Poisson-Nernst-Planck Systems and Ionic Flows Through Ion Channels: A Review}, journal = {Communications in Mathematical Research }, year = {2023}, volume = {39}, number = {3}, pages = {342--385}, abstract = {

Poisson-Nernst-Planck systems are basic models for electrodiffusion process, particularly, for ionic flows through ion channels embedded in cell membranes. In this article, we present a brief review on a geometric singular perturbation framework for analyzing the steady-state of a quasi-one-dimensional Poisson-Nernst-Planck model. The framework is based on the general geometric singular perturbed theory from nonlinear dynamical system theory and, most crucially, on the reveal of two specific structures of Poisson-Nernst-Planck systems. As a result of the geometric framework, one obtains a governing system–an algebraic system of equations that involves all physical quantities such as protein structures of membrane channels as well as boundary conditions, and hence, provides a complete platform for studying the interplay between protein structure and boundary conditions and effects on ionic flow properties. As an illustration, we will present concrete applications of the theory to several topics of biologically significant based on collaboration works with many excellent researchers.

}, issn = {2707-8523}, doi = {https://doi.org/ 10.4208/cmr.2022-0045}, url = {http://global-sci.org/intro/article_detail/cmr/21607.html} }
TY - JOUR T1 - Dynamics of Poisson-Nernst-Planck Systems and Ionic Flows Through Ion Channels: A Review AU - Liu , Weishi JO - Communications in Mathematical Research VL - 3 SP - 342 EP - 385 PY - 2023 DA - 2023/04 SN - 39 DO - http://doi.org/ 10.4208/cmr.2022-0045 UR - https://global-sci.org/intro/article_detail/cmr/21607.html KW - Ion channel, ionic flow, Poisson-Nernst-Planck models. AB -

Poisson-Nernst-Planck systems are basic models for electrodiffusion process, particularly, for ionic flows through ion channels embedded in cell membranes. In this article, we present a brief review on a geometric singular perturbation framework for analyzing the steady-state of a quasi-one-dimensional Poisson-Nernst-Planck model. The framework is based on the general geometric singular perturbed theory from nonlinear dynamical system theory and, most crucially, on the reveal of two specific structures of Poisson-Nernst-Planck systems. As a result of the geometric framework, one obtains a governing system–an algebraic system of equations that involves all physical quantities such as protein structures of membrane channels as well as boundary conditions, and hence, provides a complete platform for studying the interplay between protein structure and boundary conditions and effects on ionic flow properties. As an illustration, we will present concrete applications of the theory to several topics of biologically significant based on collaboration works with many excellent researchers.

Weishi Liu. (2023). Dynamics of Poisson-Nernst-Planck Systems and Ionic Flows Through Ion Channels: A Review. Communications in Mathematical Research . 39 (3). 342-385. doi: 10.4208/cmr.2022-0045
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