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Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model
Entropy ( IF 2.7 ) Pub Date : 2020-05-14 , DOI: 10.3390/e22050550
Jinn-Liang Liu , Bob Eisenberg

We have developed a molecular mean-field theory—fourth-order Poisson–Nernst–Planck–Bikerman theory—for modeling ionic and water flows in biological ion channels by treating ions and water molecules of any volume and shape with interstitial voids, polarization of water, and ion-ion and ion-water correlations. The theory can also be used to study thermodynamic and electrokinetic properties of electrolyte solutions in batteries, fuel cells, nanopores, porous media including cement, geothermal brines, the oceanic system, etc. The theory can compute electric and steric energies from all atoms in a protein and all ions and water molecules in a channel pore while keeping electrolyte solutions in the extra- and intracellular baths as a continuum dielectric medium with complex properties that mimic experimental data. The theory has been verified with experiments and molecular dynamics data from the gramicidin A channel, L-type calcium channel, potassium channel, and sodium/calcium exchanger with real structures from the Protein Data Bank. It was also verified with the experimental or Monte Carlo data of electric double-layer differential capacitance and ion activities in aqueous electrolyte solutions. We give an in-depth review of the literature about the most novel properties of the theory, namely Fermi distributions of water and ions as classical particles with excluded volumes and dynamic correlations that depend on salt concentration, composition, temperature, pressure, far-field boundary conditions etc. in a complex and complicated way as reported in a wide range of experiments. The dynamic correlations are self-consistent output functions from a fourth-order differential operator that describes ion-ion and ion-water correlations, the dielectric response (permittivity) of ionic solutions, and the polarization of water molecules with a single correlation length parameter.

中文翻译:

离子溶液的分子平均场理论:泊松-能斯特-普朗克-比克曼模型

我们开发了一种分子平均场理论——四阶 Poisson-Nernst-Planck-Bikerman 理论——通过处理具有间隙空隙、水极化的任何体积和形状的离子和水分子来模拟生物离子通道中的离子和水流,以及离子-离子和离子-水相关性。该理论还可用于研究电池、燃料电池、纳米孔、多孔介质(包括水泥、地热盐水、海洋系统等)中电解质溶液的热力学和电动特性。 该理论可以计算所有原子的电能和空间能。蛋白质以及通道孔中的所有离子和水分子,同时将电解质溶液保持在细胞外和细胞内浴中,作为具有模拟实验数据的复杂特性的连续介电介质。该理论已通过来自短杆菌肽 A 通道、L 型钙通道、钾通道和具有来自蛋白质数据库的真实结构的钠/钙交换器的实验和分子动力学数据得到验证。它还通过双电层微分电容和电解质水溶液中离子活动的实验或蒙特卡罗数据进行了验证。我们深入回顾了有关该理论最新颖特性的文献,即水和离子作为经典粒子的费米分布,具有排除的体积和动态相关性,取决于盐浓度、成分、温度、压力、远场边界条件等以复杂和复杂的方式在广泛的实验中报告。
更新日期:2020-05-14
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