基于Poisson-Nernst-Planck模型细胞膜离子通道的离子流动力学分析  

Dynamical Analysis of Ionic Flows through Cell Membrane via Poisson-Nernst-Planck Models

作　　者：张丽俊 王怡玮 ZHANG Lijun;WANG Yiwei(College of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao,Shandong 266590,China)

机构地区：[1]山东科技大学数学与系统科学学院,山东青岛266590

出　　处：《数学建模及其应用》2022年第2期1-10,共10页Mathematical Modeling and Its Applications

基　　金：国家自然科学基金(12172199)。

摘　　要：嵌在生物细胞膜上的离子通道是维持细胞内外环境物质交换的重要通道,离子流通过时产生电信号,进而控制生物众多与生命相关的功能,掌握通过离子通道的离子流的动力学性质至关重要.Poisson-Nernst-Planck(PNP)方程是基于把离子穿过离子通道的过程看作稀疏溶液中带电粒子自由扩散的一个基本的连续模型.本文将回顾PNP方程的建模,并介绍PNP系统的基于几何奇异摄动理论和渐近分析方法的动力系统研究方法、近些年取得的系列研究成果、面临的挑战以及进一步亟待解决的问题.Ion channels embedded in cell membrane are important channels for maintaining the material exchange in the internal and external environment of cells.The ionic flow produces electrical signals that control many life-related biological functions.It is critical to grasp the dynamic properties of ion flow through ion channels.Poisson-Nernst-Planck(PNP)system is a basic continuous model based on treating the process of ions passing through ion channels as the free diffusion of charged particles in dilute solutions.This paper reviews how PNP system is established,and introduces the dynamic system research method of PNP system based on geometric singular perturbation theory and asymptotic analysis method.It mainly expounds a series of research results of PNP system in recent years,the challenges it faces and the research problems that need to be solved further.

关 键 词：Poisson-Nernst-Planck系统 几何奇异摄动理论 离子流 离子通道 

分 类 号：O29[理学—应用数学]