Mofidi Hamid, Eisenberg Bob, Liu Weishi
Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA.
Department of Physiology and Biophysics, Rush University, Chicago, IL 60612, USA.
Entropy (Basel). 2020 Mar 12;22(3):325. doi: 10.3390/e22030325.
In this work, the dependence of reversal potentials and zero-current fluxes on diffusion coefficients are examined for ionic flows through membrane channels. The study is conducted for the setup of a simple structure defined by the profile of permanent charges with two mobile ion species, one positively charged (cation) and one negatively charged (anion). Numerical observations are obtained from analytical results established using geometric singular perturbation analysis of classical Poisson-Nernst-Planck models. For 1:1 ionic mixtures with arbitrary diffusion constants, Mofidi and Liu (arXiv:1909.01192) conducted a rigorous mathematical analysis and derived an equation for reversal potentials. We summarize and extend these results with numerical observations for biological relevant situations. The numerical investigations on profiles of the electrochemical potentials, ion concentrations, and electrical potential across ion channels are also presented for the zero-current case. Moreover, the dependence of current and fluxes on voltages and permanent charges is investigated. In the opinion of the authors, many results in the paper are not intuitive, and it is difficult, if not impossible, to reveal all cases without investigations of this type.
在这项工作中，研究了通过膜通道的离子流的反转电位和零电流通量对扩散系数的依赖性。该研究针对由具有两种可移动离子物种（一种带正电（阳离子）和一种带负电（阴离子））的永久电荷分布所定义的简单结构设置进行。数值观测结果来自使用经典泊松 - 能斯特 - 普朗克模型的几何奇异摄动分析建立的解析结果。对于具有任意扩散常数的1:1离子混合物，莫菲迪和刘（arXiv:1909.01192）进行了严格的数学分析并推导了反转电位的方程。我们用生物相关情况的数值观测结果总结并扩展了这些结果。还给出了零电流情况下跨离子通道的电化学势、离子浓度和电势分布的数值研究。此外，研究了电流和通量对电压和永久电荷的依赖性。作者认为，本文中的许多结果并不直观，如果不进行此类研究，很难（即使不是不可能）揭示所有情况。
