Poisson-Nernst-Planck-Fermi Theory for Ion Channels

TL;DR

This paper introduces a comprehensive Poisson-Nernst-Planck-Fermi (PNPF) model that accounts for finite particle sizes, water molecules, and voids to better understand ionic transport in biological channels, aligning well with experimental data.

Contribution

The paper develops a novel PNPF theory incorporating finite particle volumes, voids, and a new Gibbs-Fermi entropy, advancing the modeling of ion channels without force calculations.

Findings

Model accurately reproduces experimental calcium currents over a wide concentration range.

Reveals detailed physical mechanisms like water density and steric effects in ion channels.

Captures phenomena such as the anomalous mole fraction effect in calcium channels.

Abstract

A Poisson-Nernst-Planck-Fermi (PNPF) theory is developed for studying ionic transport through biological ion channels. Our goal is to deal with the finite size of particle using a Fermi like distribution without calculating the forces between the particles, because they are both expensive and tricky to compute. We include the steric effect of ions and water molecules with nonuniform sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of water molecules in an inhomogeneous aqueous electrolyte. Including the finite volume of water and the voids between particles is an important new part of the theory presented here. Fermi like distributions of all particle species are derived from the volume exclusion of classical particles. The classical Gibbs entropy is extended to a new entropy form --- called Gibbs-Fermi entropy --- that describes mixing configurations of all finite size particles and voids in a thermodynamic system where microstates do not have equal probabilities. The PNPF model describes the dynamic flow of ions, water molecules, as well as voids with electric fields and protein charges. The PNPF results are in good accord with experimental currents recorded in a 10^8-fold range of Ca++ concentrations. The results illustrate the anomalous mole fraction effect, a signature of L-type calcium channels. Moreover, numerical results concerning water density, dielectric permittivity, void volume, and steric energy provide useful details to study a variety of physical mechanisms ranging from binding, to permeation, blocking, flexibility, and charge/space competition of the channel.