Two- and Three-Dimensional Poisson–Nernst–Planck Simulations of Current Flow Through Gramicidin A

We simulate sodium chloride currents through the gramicidin A channel using the spectral element method to solve the three-dimensional Poisson–Nernst–Planck (PNP) equations. Using the spectral element method, we are able to simulate the entire channel, plus large enough portions of the lipid bilayer and baths to ensure that all boundary conditions are realistic. In these simulations, we rely on the 3D charge distribution of the gramicidin molecule plus diffusion coefficients and dielectric coefficients. Our main results, which match the experimental data, are current-voltage (IV) curves for gramicidin at various concentrations of Na+Cl− in the surrounding baths. We give a detailed description of the numerical algorithms used to solve the PNP equations, and we present various sensitivity analyses which we have performed to determine which parameters of the model most affect the IV curves.