Effects of diffusion coefficients on reversal potentials in ionic channels

TL;DR

This paper investigates how diffusion coefficients influence reversal potentials and fluxes in ionic channels, combining analytical and numerical methods to extend previous models and explore complex behaviors in biologically relevant scenarios.

Contribution

It extends existing mathematical analysis of ionic flow models by providing numerical insights into the effects of diffusion coefficients on reversal potentials and fluxes in ion channels.

Findings

Reversal potentials depend on diffusion coefficients in complex ways.

Numerical results reveal non-intuitive behaviors of ion fluxes.

The study extends classical models with new numerical observations.

Abstract

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 coefficients, Mofidi and Liu [arXiv:1909.01192] conducted a rigorous mathematical analysis and derived an equation for reversal potentials that, in its particular case, can be compared to Goldman-Hodgkin-Katz equation. 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 behavior of current and fluxes with respect to voltages and permanent charges are investigated. In the opinion of the authors, many results in the paper are not intuitive, and it is difficult, if not impossible, to see all cases without investigations of this type.