Ng Jin Aun, Vora Taira, Krishnamurthy Vikram, Chung Shin-Ho
Research School of Biological Sciences, Australian National University, Canberra, Australia.
Eur Biophys J. 2008 Feb;37(2):213-22. doi: 10.1007/s00249-007-0218-3. Epub 2007 Sep 18.
When modelling biological ion channels using Brownian dynamics (BD) or Poisson-Nernst-Planck theory, the force encountered by permeant ions is calculated by solving Poisson's equation. Two free parameters needed to solve this equation are the dielectric constant of water in the pore and the dielectric constant of the protein forming the channel. Although these values can in theory be deduced by various methods, they do not give a reliable answer when applied to channel-like geometries that contain charged particles. To determine the appropriate values of the dielectric constants, here we solve the inverse problem. Given the structure of the MthK channel, we attempt to determine the values of the protein and pore dielectric constants that minimize the discrepancies between the experimentally-determined current-voltage curve and the curve obtained from BD simulations. Two different methods have been applied to determine these values. First, we use all possible pairs of the pore dielectric constant of water, ranging from 20 to 80 in steps of 10, and the protein dielectric constant of 2-10 in steps of 2, and compare the simulated results with the experimental values. We find that the best agreement is obtained with experiment when a protein dielectric constant of 2 and a pore water dielectric constant of 60 is used. Second, we employ a learning-based stochastic optimization algorithm to pick out the optimum combination of the two dielectric constants. From the algorithm we obtain an optimum value of 2 for the protein dielectric constant and 64 for the pore dielectric constant.
当使用布朗动力学（BD）或泊松 - 能斯特 - 普朗克理论对生物离子通道进行建模时，通过求解泊松方程来计算渗透离子所受的力。求解此方程所需的两个自由参数是孔中水分子的介电常数和构成通道的蛋白质的介电常数。尽管这些值理论上可以通过各种方法推导得出，但当应用于包含带电粒子的类似通道的几何结构时，它们并不能给出可靠的答案。为了确定介电常数的合适值，我们在此解决反问题。给定MthK通道的结构，我们尝试确定蛋白质和孔介电常数的值，以使实验测定的电流 - 电压曲线与从BD模拟获得的曲线之间的差异最小化。已应用两种不同的方法来确定这些值。首先，我们使用孔中水分子介电常数的所有可能对，范围从20到80，步长为10，以及蛋白质介电常数从2到10，步长为2，并将模拟结果与实验值进行比较。我们发现，当使用蛋白质介电常数为2和孔中水分子介电常数为60时，与实验的一致性最佳。其次，我们采用基于学习的随机优化算法来挑选出两个介电常数的最佳组合。从该算法中，我们得到蛋白质介电常数的最佳值为2，孔介电常数的最佳值为64。
