In this paper, an improved Poisson-Nernst-Planck ion channel (PNPic) model is presented, along with its effective finite element solver and software package for an ion channel protein in a solution of multiple ionic species. Numerical studies are then done on the effects of boundary value conditions, membrane charges, and bulk concentrations on electrostatics and ionic concentrations for an ion channel protein, a gramicidin A (gA), and five different ionic solvents with up to four species. Numerical results indicate that the cation selectivity property of gA occurs within a central portion of ion channel pore, insensitively to any change of boundary value condition, membrane charge, or bulk concentration. Moreover, a numerical scheme for computing the electric currents induced by ion transports across membrane via an ion channel pore is presented and implemented as a part of the PNPic finite element package. It is then applied to the calculation of current–voltage curves, well validating the PNPic model and finite element package by electric current experimental data.

中文翻译：

---

改进的 Poisson-Nernst-Planck 离子通道模型和对边界条件、膜电荷和体积浓度影响的数值研究

在本文中，提出了一种改进的 Poisson-Nernst-Planck 离子通道 (PNPic) 模型，以及其有效的有限元求解器和用于多种离子种类溶液中离子通道蛋白的软件包。然后对边界值条件、膜电荷和体积浓度对离子通道蛋白、短杆菌肽 A (gA) 和五种不同离子溶剂（最多四种）的静电和离子浓度的影响进行了数值研究。数值结果表明，gA 的阳离子选择性特性发生在离子通道孔的中心部分，对边界值条件、膜电荷或体积浓度的任何变化不敏感。而且，作为 PNPic 有限元包的一部分，提出并实现了用于计算由离子通过离子通道孔跨膜传输引起的电流的数值方案。然后将其应用于电流-电压曲线的计算，通过电流实验数据很好地验证了PNPic模型和有限元包。