Department of Applied Mathematics, Feng Chia University, 100 Wen-Hwa Road, Taichung, Taiwan 40724.
J Phys Chem B. 2012 Sep 20;116(37):11422-41. doi: 10.1021/jp305273n. Epub 2012 Sep 10.
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.
利用刘应用于离子溶液原始（隐溶剂）模型的能量变分方法研究电流通过离子通道的流动。该方法允许推导出描述球体通过通道流动的自洽（欧拉-拉格朗日）方程。导出的偏微分方程涉及球体的全局相互作用，这里用我们称之为空间 PNP（泊松-纳斯特-普朗克）（Lin，TC；Eisenberg，B. 即将提交出版，2012 年）的局部近似代替。Kong 结合规则被使用，并且研究了一系列空间相互作用参数的值。这些参数改变空间相互作用的能量，但对模型和模拟中的扩散系数没有影响。计算了钙（EEEE，EEEA）和钠通道（DEKA）的流动，这些通道在蒙特卡罗模拟中进行了与类似结果的先前研究。生物功能对空间相互作用参数非常敏感，我们推测通道和转运蛋白的功能范围很广，甚至酶，可能依赖于此类术语。我们指出，通道、转运蛋白和酶的经典理论依赖于离子溶液的理想表示，即使在蛋白质附近或电化学电池中的电极附近的巨大浓度下，也没有任何东西与任何东西相互作用。我们建议，设计用于处理相互作用的理论可能更合适。我们表明，有一种这样的理论是可行且可计算的：空间 PNP 允许与测量流动以及平衡性质的实验直接比较。空间 PNP 将原子和宏观尺度结合在一个可计算的公式中，允许计算原子尺度结构变化（大小~= 10（-10）米）的宏观效应，这些结构在通道学和分子生物学中得到了非常广泛的研究。
