A Coupled 3-D PNP/ECP Model for Ion Transport in Biological Ion Channels

Abstract

The Poisson-Nernst-Planck (PNP) or Drift-Diffusion theory can be used to compute macroscopic current in ion channels in an efficient manner. The major drawback of the standard PNP theory is that it is based on a continuum model for the charge flow, therefore it models ions as a gas of point particles. Water is also not simulated explicitly, but introduced as a background medium with a given permittivity. The PNP model can be modified to include effects of finite ion size and water occupation by including a correction term, the Excess Chemical Potential (ECP), in the standard model. Gillespie et al. [1] developed a model for ECP correction, based on Density Functional theory, which is introduced in an existing 3-D PNP solver for ion transport in biological ion channels realized using the numerical computational platform PROPHET. Since incorporation of the ECP correction directly into the PNP matrix formulation is not an easy task, for demonstration purposes we developed a relatively simple decoupled relaxed iteration algorithm. Preliminary tests were conducted on idealized channel geometries, showing how the adopted ECP correction model alters significantly the ion densities inside the channel from those predicted by the conventional PNP theory alone.