Estimating the dielectric constant of the channel protein and pore

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 protsein dielectric constant and 64 for the pore dielectric constant.