Relative dielectric constants and selectivity ratios in open ionic channels

TL;DR

This paper analyzes how the relative dielectric coefficient influences ionic flows in open channels, revealing that certain properties are surprisingly insensitive to its variations, which explains unexpected simulation results.

Contribution

It provides a mathematical analysis showing that key ionic ratios in open channels are largely unaffected by changes in the dielectric coefficient, using singular perturbation theory.

Findings

Ion ratios are insensitive to dielectric coefficient variations.

Theoretical explanation for unexpected simulation results.

Mathematical analysis using singular perturbation theory.

Abstract

We investigate the effects of the relative dielectric coefficient on ionic flows in open ion channels, using mathematical analysis of reasonably general Poisson-Nernst-Planck type models that can include the finite sizes of ions. The value of the relative dielectric coefficient is of course a crucial parameter for ionic behavior in general. Using the powerful theory of singularly perturbed problems in applied mathematics, we show that some properties of open channels are quite insensitive to variation in the relative dielectric coefficient, thereby explaining such effects seen unexpectedly in simulations. The ratio between the total number of one ion species and that of another ion species, and the ratio between the flux of one ion species and that of another ion species do not depend significantly on the relative dielectric coefficient.