We present a new size‐modified Poisson–Boltzmann ion channel (SMPBIC) model and use it to calculate the electrostatic potential, ionic concentrations, and electrostatic solvation free energy for a voltage‐dependent anion channel (VDAC) on a biological membrane in a solution mixture of multiple ionic species. In particular, the new SMPBIC model adopts a membrane surface charge density and a natural Neumann boundary condition to reflect the charge effect of the membrane on the electrostatics of VDAC. To avoid the singularity difficulties caused by the atomic charges of VDAC, the new SMPBIC model is split into three submodels such that the solution of one of the submodels is obtained analytically and contains all the singularity points of the SMPBIC model. The other two submodels are then solved numerically much more efficiently than the original SMPBIC model. As an application of this SMPBIC submodel partitioning scheme, we derive a new formula for computing the electrostatic solvation free energy. Numerical results for a human VDAC isoform 1 (hVDAC1) in three different salt solutions, each with up to five different ionic species, confirm the significant effects of membrane surface charges on both the electrostatics and ionic concentrations. The results also show that the new SMPBIC model can describe well the anion selectivity property of hVDAC1, and that the new electrostatic solvation free energy formula can significantly improve the accuracy of the currently used formula. © 2019 Wiley Periodicals, Inc.

中文翻译：

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多种离子物质溶剂中尺寸修正的泊松-玻尔兹曼离子通道模型：在电压依赖性阴离子通道中的应用

我们提出了一种新的尺寸修正泊松-玻尔兹曼离子通道 (SMPBIC) 模型，并用它来计算溶液中生物膜上电压依赖性阴离子通道 (VDAC) 的静电势、离子浓度和静电溶剂化自由能多种离子物质的混合物。特别是，新的 SMPBIC 模型采用膜表面电荷密度和自然诺依曼边界条件来反映膜的电荷对 VDAC 静电的影响。为了避免VDAC原子电荷引起的奇点困难，新的SMPBIC模型被分成三个子模型，使得其中一个子模型的解通过解析获得并包含SMPBIC模型的所有奇点。其他两个子模型的数值求解效率比原始 SMPBIC 模型高得多。作为该 SMPBIC 子模型划分方案的应用，我们推导了计算静电溶剂化自由能的新公式。人类 VDAC 亚型 1 (hVDAC1) 在三种不同盐溶液中的数值结果（每种盐溶液最多含有五种不同的离子种类）证实了膜表面电荷对静电和离子浓度的显着影响。结果还表明，新的SMPBIC模型可以很好地描述hVDAC1的阴离子选择性特性，并且新的静电溶剂化自由能公式可以显着提高目前使用的公式的准确性。© 2019 Wiley 期刊公司。