Analytical Modeling of the Ion Number Fluctuations in Biological Ion Channels

Ion channels are transmembrane proteins that regulate and maintain the ionic concentrations across the cell membrane. Modeling the atomistic-level ionic flux through these channels is crucial for the understandingof several neurological diseases and related pharmaceutical discoveries. Experimental techniques now provide information about the channel's physical structure which helps in developing realisticion transport models. Ions entering a channel follow different trajectories as they traverse the channel; each associated with a certain probability. Quantities that explain these trajectories are the translocation and return probabilities, average lifetime, and spectral density (an experimentally accessible parameter) of ion number fluctuations. Theoretical analysis of ion transport has been limited to low-resolution continuum diffusion-based or kinetic-based models. Such analytical models fail to include key factors affecting the ionic conduction. In this paper, we extend previous models by an electro-diffusion model incorporating the effects of electric field, energy barrier, and rate-limited association/dissociation of ions with surface charges inside the channel. Survival probability and spectral density are derived from the analytical model.