PNP equations with steric effects

A model of ion flow through channels

Tzyy Leng Horng, Tai Chia Lin, Chun Liu, Bob Eisenberg

Research output: Contribution to journalArticle

69 Citations (Scopus)

Abstract

The flow of current through an ionic channel is studied using the energetic variational approach of Liu applied to the primitive (implicit solvent) model of ionic solutions. This approach allows the derivation of self-consistent (Euler-Lagrange) equations to describe the flow of spheres through channels. The partial differential equations derived involve the global interactions of the spheres and are replaced here with a local approximation that we call steric PNP (Poisson-Nernst-Planck) (Lin, T. C.; Eisenberg, B. To be submitted for publication, 2012). Kong combining rules are used and a range of values of steric interaction parameters are studied. These parameters change the energetics of steric interaction but have no effect on diffusion coefficients in models and simulations. Calculations are made for the calcium (EEEE, EEEA) and sodium channels (DEKA) previously studied in Monte Carlo simulations with comparable results. The biological function is quite sensitive to the steric interaction parameters, and we speculate that a wide range of the function of channels and transporters, even enzymes, might depend on such terms. We point out that classical theories of channels, transporters, and enzymes depend on ideal representations of ionic solutions in which nothing interacts with nothing, even in the enormous concentrations found near and in these proteins or near electrodes in electrochemical cells for that matter. We suggest that a theory designed to handle interactions might be more appropriate. We show that one such theory is feasible and computable: steric PNP allows a direct comparison with experiments measuring flows as well as equilibrium properties. Steric PNP combines atomic and macroscales in a computable formulation that allows the calculation of the macroscopic effects of changes in atomic scale structures (size ≅ 10-10 meters) studied very extensively in channology and molecular biology.

Original languageEnglish (US)
Pages (from-to)11422-11441
Number of pages20
JournalJournal of Physical Chemistry B
Volume116
Issue number37
DOIs
StatePublished - Sep 20 2012

Fingerprint

channel flow
Enzymes
Ions
Molecular biology
Electrochemical cells
Sodium Channels
Calcium Channels
transporter
Ion Channels
Partial differential equations
Calcium
ions
Sodium
interactions
enzymes
Proteins
Electrodes
molecular biology
Euler-Lagrange equation
electrochemical cells

All Science Journal Classification (ASJC) codes

  • Physical and Theoretical Chemistry
  • Surfaces, Coatings and Films
  • Materials Chemistry

Cite this

Horng, Tzyy Leng ; Lin, Tai Chia ; Liu, Chun ; Eisenberg, Bob. / PNP equations with steric effects : A model of ion flow through channels. In: Journal of Physical Chemistry B. 2012 ; Vol. 116, No. 37. pp. 11422-11441.
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PNP equations with steric effects : A model of ion flow through channels. / Horng, Tzyy Leng; Lin, Tai Chia; Liu, Chun; Eisenberg, Bob.

In: Journal of Physical Chemistry B, Vol. 116, No. 37, 20.09.2012, p. 11422-11441.

Research output: Contribution to journalArticle

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AU - Lin, Tai Chia

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AB - The flow of current through an ionic channel is studied using the energetic variational approach of Liu applied to the primitive (implicit solvent) model of ionic solutions. This approach allows the derivation of self-consistent (Euler-Lagrange) equations to describe the flow of spheres through channels. The partial differential equations derived involve the global interactions of the spheres and are replaced here with a local approximation that we call steric PNP (Poisson-Nernst-Planck) (Lin, T. C.; Eisenberg, B. To be submitted for publication, 2012). Kong combining rules are used and a range of values of steric interaction parameters are studied. These parameters change the energetics of steric interaction but have no effect on diffusion coefficients in models and simulations. Calculations are made for the calcium (EEEE, EEEA) and sodium channels (DEKA) previously studied in Monte Carlo simulations with comparable results. The biological function is quite sensitive to the steric interaction parameters, and we speculate that a wide range of the function of channels and transporters, even enzymes, might depend on such terms. We point out that classical theories of channels, transporters, and enzymes depend on ideal representations of ionic solutions in which nothing interacts with nothing, even in the enormous concentrations found near and in these proteins or near electrodes in electrochemical cells for that matter. We suggest that a theory designed to handle interactions might be more appropriate. We show that one such theory is feasible and computable: steric PNP allows a direct comparison with experiments measuring flows as well as equilibrium properties. Steric PNP combines atomic and macroscales in a computable formulation that allows the calculation of the macroscopic effects of changes in atomic scale structures (size ≅ 10-10 meters) studied very extensively in channology and molecular biology.

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