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Title: Poisson-Nernst-Planck-Fermi theory for modeling biological ion 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. Volume exclusion and the resulting saturation phenomena are especially important to describe the binding and permeation mechanisms of ions in a narrow channel pore. The Gibbs free energy of the Fermi distribution reduces to that of a Boltzmann distribution when these effects are not considered. 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 notmore » 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 model also provides a quantitative mean-field description of the charge/space competition mechanism of particles within the highly charged and crowded channel pore. The PNPF results are in good accord with experimental currents recorded in a 10{sup 8}-fold range of Ca{sup 2+} 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.« less

Authors:
 [1];  [2]
  1. Department of Applied Mathematics, National Hsinchu University of Education, Hsinchu 300, Taiwan (China)
  2. Department of Molecular Biophysics and Physiology, Rush University, Chicago, Illinois 60612 (United States)
Publication Date:
OSTI Identifier:
22423771
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 141; Journal Issue: 22; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CALCIUM; CALCIUM IONS; COMPETITION; DIELECTRIC MATERIALS; DISTRIBUTION; ELECTRIC FIELDS; ELECTROLYTES; ENTROPY; FLEXIBILITY; FREE ENTHALPY; MOLECULES; PARTICLES; PERMITTIVITY; PROBABILITY; SATURATION; SIMULATION; WATER

Citation Formats

Liu, Jinn-Liang, and Eisenberg, Bob. Poisson-Nernst-Planck-Fermi theory for modeling biological ion channels. United States: N. p., 2014. Web. doi:10.1063/1.4902973.
Liu, Jinn-Liang, & Eisenberg, Bob. Poisson-Nernst-Planck-Fermi theory for modeling biological ion channels. United States. https://doi.org/10.1063/1.4902973
Liu, Jinn-Liang, and Eisenberg, Bob. 2014. "Poisson-Nernst-Planck-Fermi theory for modeling biological ion channels". United States. https://doi.org/10.1063/1.4902973.
@article{osti_22423771,
title = {Poisson-Nernst-Planck-Fermi theory for modeling biological ion channels},
author = {Liu, Jinn-Liang and Eisenberg, Bob},
abstractNote = {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. Volume exclusion and the resulting saturation phenomena are especially important to describe the binding and permeation mechanisms of ions in a narrow channel pore. The Gibbs free energy of the Fermi distribution reduces to that of a Boltzmann distribution when these effects are not considered. 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 model also provides a quantitative mean-field description of the charge/space competition mechanism of particles within the highly charged and crowded channel pore. The PNPF results are in good accord with experimental currents recorded in a 10{sup 8}-fold range of Ca{sup 2+} 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.},
doi = {10.1063/1.4902973},
url = {https://www.osti.gov/biblio/22423771}, journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 22,
volume = 141,
place = {United States},
year = {Sun Dec 14 00:00:00 EST 2014},
month = {Sun Dec 14 00:00:00 EST 2014}
}