SIAM Journal on Applied Dynamical Systems, Volume 19, Issue 3, Page 1993-2029, January 2020.
Permanent charge is the major structural quantity of an ion channel. It defines the ion channel and its interaction with boundary conditions plays the predominate role for ionic flow properties or functions of the ion channel. In this work, we investigate effects of large magnitude permanent charges of a simple form on the ionic flow of a 1:1 solution (an ionic mixture with one positive charged ion species and one negatively charged ion species). The analysis is based on a quasi-one-dimensional classical steady-state Poisson--Nernst--Planck model. Our findings include (i) large permanent charges produce flux and current saturations at large transmembrane electric potentials; (ii) large permanent charges inhibit the flux of co-ions (ions with the same charge sign) but could either enhance or reduce the flux of counter-ions (ions with opposite charge signs), depending on boundary conditions and the channel geometry; (iii) the magnitude of the co-ion flux is decreasing with an increase in magnitude of the large permanent charge but the counter-ion flux could either decease or increase with an increase in magnitude of the large permanent charge, depending on boundary conditions and the channel geometry, and quite significantly; (iv) large permanent charges are responsible for the counterintuitive declining phenomenon---an increase in the electrochemical potential of counter-ion species in a particular manner leads to a reduction of the counter-ion flux. We would like to stress that the model in this paper includes only the ideal components of the electrochemical potentials so the model cannot be used to study some critical properties of ion channels such as selectivity and gating. Our work should be viewed as the first step of future analyses/numerics with more structural detail and more correlations between ions included. The basic findings in this work should provide guidance for further investigation.

中文翻译：

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通过Poisson-Nernst-Planck模型的大量永久电荷对离子流的影响

SIAM应用动力系统杂志，第19卷，第3期，第1993-2029页，2020年1月。
永久电荷是离子通道的主要结构量。它定义了离子通道，它与边界条件的相互作用在离子流特性或离子通道功能中起着主要作用。在这项工作中，我们研究了简单形式的大量永久电荷对1：1溶液（具有一种带正电的离子物种和一种带负电的离子物种的离子混合物）的离子流的影响。该分析基于准一维经典稳态Poisson-Nernst-Planck模型。我们的发现包括：（i）大的永久电荷在大的跨膜电位下产生通量和电流饱和；（ii）较大的永久电荷会抑制共离子（具有相同电荷符号的离子）的通量，但可能会增加或减少反离子（具有相反电荷符号的离子）的通量，具体取决于边界条件和通道的几何形状；（iii）共离子通量的大小随永久性大电荷量的增加而减小，但反离子通量可能随永久性大电荷量的增加而减小或增加，这取决于边界条件和通道的几何形状，并且非常重要；（iv）大的永久电荷是造成反直觉下降的原因-反离子物质的电化学势能以特定方式增加会导致反离子通量的减少。我们想强调的是，本文中的模型仅包含电化学势的理想成分，因此该模型不能用于研究离子通道的某些关键特性，例如选择性和门控。我们的工作应被视为未来分析/数字的第一步，它具有更多的结构细节和所含离子之间的更多相关性。这项工作的基本发现应为进一步调查提供指导。