@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 = {<p style="text-align: justify;">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.</p>},
issn = {2707-8523},
doi = {https://doi.org/ 10.4208/cmr.2022-0045},
url = {http://global-sci.org/intro/article_detail/cmr/21607.html}
}