Electrostatics of ions inside the nanopores and trans-membrane channels

TL;DR

This paper presents an analytical model for the electrostatics of ions in nanopores and channels, providing exact solutions for potential energy profiles that aid in understanding ionic transport.

Contribution

The study introduces a semi-exact analytical solution to the Poisson equation for ion distributions in cylindrical nanopores, applicable at physiological ionic strengths.

Findings

Analytical solutions closely match numerical results at physiological concentrations.

Electrostatic barrier sizes are accurately predicted by the model.

Potential energy profiles for charged residues are effectively calculated.

Abstract

A model of a finite cylindrical ion channel through a phospholipid membrane of width $L$ separating two electrolyte reservoirs is studied. Analytical solution of the Poisson equation is obtained for an arbitrary distribution of ions inside the trans-membrane pore. The solution is asymptotically exact in the limit of large ionic strength of electrolyte on the two sides of membrane. However, even for physiological concentrations of electrolyte, the electrostatic barrier sizes found using the theory are in excellent agreement with the numerical solution of the Poisson equation. The analytical solution is used to calculate the electrostatic potential energy profiles for pores containing charged protein residues. Availability of a semi-exact interionic potential should greatly facilitate the study of ionic transport through nanopores and ion channels.