Poisson-Boltzmann-Nernst-Planck model
Poisson-Boltzmann-Nernst-Planck model
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DOI：
10.1063/1.3581031
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发表时间：
2011-05-21
影响因子：
4.4
通讯作者：
Wei, Guo-Wei
中科院分区：
文献类型：
--
作者：
Zheng, Qiong;Wei, Guo-Wei
Poisson-Nernst-Planck（PNP）模型基于离子相互作用的平均场近似和浓度和静电势的连续描述。它提供了定性的解释和越来越多的定量预测的实验测量的离子输运问题在许多领域，如半导体器件，纳米流体系统，和生物系统，尽管有许多限制。虽然PNP模型对化学、物理和生物系统的离子传输现象给出了良好的预测，但是要求解的方程的数量和要确定的用于计算的扩散系数分布的数量直接取决于系统中的离子种类的数量，因为每个离子种类对应于一个能斯特-普朗克方程和一个位置相关的扩散系数分布。在具有多个离子种类的复杂系统中，PNP在计算上可能是昂贵的并且要求参数，因为扩散系数分布的实验测量对于大多数受限区域（诸如离子通道、纳米结构和纳米孔）通常是相当有限的。我们提出了一种替代模型，以减少在复杂的化学和生物系统中的多个离子物种的能斯特-普朗克方程的数量来解决取代能斯特-普朗克方程与玻尔兹曼分布的离子浓度。因此，我们求解耦合Poisson-Boltzmann和Nernst-Planck（PBNP）方程，而不是PNP方程。提出的PBNP方程是从总能量泛函出发，利用变分原理导出的。我们设计了一些计算技术，包括Dirichlet到Neumann映射，匹配的接口和边界，以及基于松弛的迭代过程，以确保有效的解决方案的建议PBNP方程。两个蛋白质分子，细胞色素c551和短杆菌肽A，被用来验证所提出的模型下的大范围的体离子浓度和外部电压。大量的数值实验表明，有一个很好的一致性从本PBNP模型和PNP模型的静电势，离子浓度分布，和电流-电压（I-V）曲线的预测结果。本PBNP模型进一步验证了在不同的离子体浓度下的I-V曲线的实验测量的比较。数值实验表明，提出的PBNP模型是更有效的比原来的PNP模型的模拟时间。c 2011年美国物理学会。[doi：10.1063/1.3581031]
The Poisson-Nernst-Planck (PNP) model is based on a mean-field approximation of ion interactions and continuum descriptions of concentration and electrostatic potential. It provides qualitative explanation and increasingly quantitative predictions of experimental measurements for the ion transport problems in many areas such as semiconductor devices, nanofluidic systems, and biological systems, despite many limitations. While the PNP model gives a good prediction of the ion transport phenomenon for chemical, physical, and biological systems, the number of equations to be solved and the number of diffusion coefficient profiles to be determined for the calculation directly depend on the number of ion species in the system, since each ion species corresponds to one Nernst-Planck equation and one position-dependent diffusion coefficient profile. In a complex system with multiple ion species, the PNP can be computationally expensive and parameter demanding, as experimental measurements of diffusion coefficient profiles are generally quite limited for most confined regions such as ion channels, nanostructures and nanopores. We propose an alternative model to reduce number of Nernst-Planck equations to be solved in complex chemical and biological systems with multiple ion species by substituting Nernst-Planck equations with Boltzmann distributions of ion concentrations. As such, we solve the coupled Poisson-Boltzmann and Nernst-Planck (PBNP) equations, instead of the PNP equations. The proposed PBNP equations are derived from a total energy functional by using the variational principle. We design a number of computational techniques, including the Dirichlet to Neumann mapping, the matched interface and boundary, and relaxation based iterative procedure, to ensure efficient solution of the proposed PBNP equations. Two protein molecules, cytochrome c551 and Gramicidin A, are employed to validate the proposed model under a wide range of bulk ion concentrations and external voltages. Extensive numerical experiments show that there is an excellent consistency between the results predicted from the present PBNP model and those obtained from the PNP model in terms of the electrostatic potentials, ion concentration profiles, and current-voltage (I-V) curves. The present PBNP model is further validated by a comparison with experimental measurements of I-V curves under various ion bulk concentrations. Numerical experiments indicate that the proposed PBNP model is more efficient than the original PNP model in terms of simulation time. c 2011 American Institute of Physics. [doi: 10.1063/1.3581031]