| Abstract: | Poisson-Nernst-Planck systems are basic models for electrodiffusionprocess, particularly, for ionic flows through ion channels embedded in cellmembranes. In this article, we present a brief review on a geometric singularperturbation framework for analyzing the steady-state of a quasi-one-dimensional Poisson-Nernst-Planck model. The framework is based on the generalgeometric singular perturbed theory from nonlinear dynamical system theoryand, 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 boundaryconditions, and hence, provides a complete platform for studying the interplaybetween protein structure and boundary conditions and effects on ionic flowproperties. As an illustration, we will present concrete applications of the theory to several topics of biologically significant based on collaboration workswith many excellent researchers. |
