Kinetic models of ion transport through a nanopore

TL;DR

This paper develops and solves kinetic models for ion transport through nanopores, providing analytic expressions for ion current and predicting current saturation at high fields, aiding understanding of ion channel behavior.

Contribution

It introduces new kinetic models incorporating surface interactions and energy barriers, with analytic solutions for ion current in nanopores.

Findings

Analytic expressions for stationary ion current derived.

Current saturation predicted at high external fields.

Models incorporate pore surface interactions and energy barriers.

Abstract

Kinetic equations for the stationary state distribution function of ions moving through narrow pores are solved for a number of one-dimensional models of single ion transport. Ions move through pores of length $L$, under the action of a constant external field and of a concentration gradient. The interaction of single ions with the confining pore surface and with water molecules inside the pore are modelled by a Fokker-Planck term in the kinetic equation, or by uncorrelated collisions with thermalizing centres distributed along the pore. The temporary binding of ions to polar residues lining the pore is modelled by stopping traps or energy barriers. Analytic expressions for the stationary ion current through the pore are derived for several versions of the model, as functions of key physical parameters. In all cases, saturation of the current at high fields is predicted. Such simple models, for which results are analytic, may prove useful in the study of the current/voltage relations of ion channels through membranes.