Second-order Poisson Nernst-Planck solver for ion channel transport.
Second-order Poisson Nernst-Planck solver for ion channel transport.
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DOI：
10.1016/j.jcp.2011.03.020
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发表时间：
2011-06
影响因子：
4.1
通讯作者：
Wei, Guo-Wei
中科院分区：
文献类型：
--
作者：
Zheng, Qiong;Chen, Duan;Wei, Guo-Wei
关键词：
Poisson Nernst-Planck（PNP）理论是一种简化的连续介质模型，适用于各种化学，物理和生物学应用。它提供定量解释和越来越多的定性预测的实验测量的能力，赢得了自己在研究界的认可。许多计算算法已经被构造用于PNP方程的解。然而，在现实的离子通道的情况下，没有二阶收敛的PNP算法在文献中报道过，由于许多数值障碍，包括不连续系数，奇异电荷，几何奇异性，和非线性耦合。本工作介绍了一些数值算法，以克服上述数值挑战，并构建了第一个二阶收敛PNP求解器的离子通道的上下文中。首先，设计了一种Dirichlet到Neumann映射（DNM）算法，以减轻由于蛋白质结构引起的电荷奇异性。此外，匹配界面和边界（MIB）方法求解PNP方程。MIB方法系统地强制界面跳跃条件，并在存在复杂几何形状和几何奇异性的分子表面上达到二阶精度。此外，两个迭代格式被用来处理耦合的非线性方程组。此外，广泛和严格的数值验证进行了一些几何形状，包括一个球体，两个蛋白质和离子通道，检查目前的数值算法的数值精度和收敛阶。最后，应用被认为是一个真实的跨膜蛋白，短杆菌肽A通道蛋白。对一些因素，包括网格尺寸，扩散系数分布，迭代方案，离子浓度，和施加的电压，所提出的数值技术的性能进行测试。数值预测与实验测量进行了比较。
The Poisson Nernst-Planck (PNP) theory is a simplified continuum model for a wide variety of chemical, physical and biological applications. Its ability of providing quantitative explanation and increasingly qualitative predictions of experimental measurements has earned itself much recognition in the research community. Numerous computational algorithms have been constructed for the solution of the PNP equations. However, in the realistic ion-channel context, no second order convergent PNP algorithm has ever been reported in the literature, due to many numerical obstacles, including discontinuous coefficients, singular charges, geometric singularities, and nonlinear couplings. The present work introduces a number of numerical algorithms to overcome the abovementioned numerical challenges and constructs the first second-order convergent PNP solver in the ion-channel context. First, a Dirichlet to Neumann mapping (DNM) algorithm is designed to alleviate the charge singularity due to the protein structure. Additionally, the matched interface and boundary (MIB) method is reformulated for solving the PNP equations. The MIB method systematically enforces the interface jump conditions and achieves the second order accuracy in the presence of complex geometry and geometric singularities of molecular surfaces. Moreover, two iterative schemes are utilized to deal with the coupled nonlinear equations. Furthermore, extensive and rigorous numerical validations are carried out over a number of geometries, including a sphere, two proteins and an ion channel, to examine the numerical accuracy and convergence order of the present numerical algorithms. Finally, application is considered to a real transmembrane protein, the Gramicidin A channel protein. The performance of the proposed numerical techniques is tested against a number of factors, including mesh sizes, diffusion coefficient profiles, iterative schemes, ion concentrations, and applied voltages. Numerical predictions are compared with experimental measurements.
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