Solutions to a reduced Poisson-Nernst-Planck system and determination of reaction rates.
Solutions to a reduced Poisson-Nernst-Planck system and determination of reaction rates.
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DOI：
10.1016/j.physa.2009.12.024
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发表时间：
2010-04-01
影响因子：
3.3
通讯作者：
McCammon, J. Andrew
中科院分区：
文献类型：
--
作者：
Li, Bo;Lu, Benzhuo;Wang, Zhongming;McCammon, J. Andrew
关键词：
我们研究了一个简化的Poisson-Nernst-Planck（PNP）系统，该系统用于将带电球形溶质浸入具有多个离子或分子物种的溶剂中，这些离子或分子物种在远场被静电中和。其中一些物种被认为处于平衡状态。这些物质的浓度由进一步线性化的玻尔兹曼分布描述。其他被认为是反应性的，这意味着当与带电溶质接触时，它们的浓度消失。我们提出了半解析解和数值迭代解的基本减少PNP系统，并计算反应速率的活性物种。我们给出了一个严格的分析，我们的简单迭代算法的收敛性。我们的数值计算结果表明，其远场浓度的大小，以及对所有的化学物种的离子强度的反应速率的强烈依赖性。我们还发现在某些参数制度的静电势的非单调性。反应系统和非反应系统的结果进行了比较，显示了两种情况下的显着差异。我们的方法提供了一种解决PNP系统，在一般情况下，没有一个封闭的形式的解决方案，即使有一个特殊的几何对称性。我们的研究结果也可以用来测试其他数值方法在大规模计算模拟生物系统中的电扩散。
We study a reduced Poisson–Nernst–Planck (PNP) system for a charged spherical solute immersed in a solvent with multiple ionic or molecular species that are electrostatically neutralized in the far field. Some of these species are assumed to be in equilibrium. The concentrations of such species are described by the Boltzmann distributions that are further linearized. Others are assumed to be reactive, meaning that their concentrations vanish when in contact with the charged solute. We present both semi-analytical solutions and numerical iterative solutions to the underlying reduced PNP system, and calculate the reaction rate for the reactive species. We give a rigorous analysis on the convergence of our simple iteration algorithm. Our numerical results show the strong dependence of the reaction rates of the reactive species on the magnitude of its far field concentration as well as on the ionic strength of all the chemical species. We also find non-monotonicity of electrostatic potential in certain parameter regimes. The results for the reactive system and those for the non-reactive system are compared to show the significant differences between the two cases. Our approach provides a means of solving a PNP system which in general does not have a closed-form solution even with a special geometrical symmetry. Our findings can also be used to test other numerical methods in large-scale computational modeling of electro-diffusion in biological systems.
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