Correlated Ions in a Calcium Channel Model: A Poisson鈥揊ermi Theory

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• 作者：Jinn-Liang Liu ; Bob Eisenberg
• 刊名：Journal of Physical Chemistry B
• 出版年：2013
• 出版时间：October 10, 2013
• 年：2013
• 卷：117
• 期：40
• 页码：12051-12058
• 全文大小：344K
• 年卷期：v.117,no.40(October 10, 2013)
• ISSN：1520-5207

文摘

We derive a continuum model, called the Poisson鈥揊ermi equation, of biological calcium channels (of cardiac muscle, for example) designed to deal with crowded systems in which ionic species and side chains nearly fill space. The model is evaluated in three dimensions. It includes steric and correlation effects and is derived from classical hard-sphere lattice models of configurational entropy of finite size ions and solvent molecules. The maximum allowable close packing (saturation) condition is satisfied by all ionic species with different sizes and valences in a channel system, as shown theoretically and numerically. Unphysical overcrowding (鈥渄ivergence鈥? predicted by the Gouy鈥揅hapman diffuse model (produced by a Boltzmann distribution of point charges with large potentials) does not occur with the Fermi-like distribution. Using probability theory, we also provide an analytical description of the implicit dielectric model of ionic solutions that gives rise to a global and a local formula for the chemical potential. In this primitive model, ions are treated as hard spheres and solvent molecules are described as a dielectric medium. The Poisson鈥揊ermi equation is a local formula dealing with different correlations at different places. The correlation effects are apparent in our numerical results. Our results show variations of dielectric permittivity from bath to channel pore described by a new dielectric function derived as an output from the Poisson鈥揊ermi analysis. The results are consistent with existing theoretical and experimental results. The binding curve of Poisson鈥揊ermi is shown to match Monte Carlo data and illustrates the anomalous mole fraction effect of calcium channels, an effective blockage of permeation of sodium ions by a tiny concentration (or number) of calcium ions.