Ion Channel Fluctuations in transmembrane proteins within cell membranes

The transmembrane proteins known as ion channels play a role in controlling and preserving the ionic concentrations across the cell membrane. Modeling the flux of ions in and out of these channels on an atomic level is essential for understanding several neurological diseases and related pharmaceutical discoveries. Recent experimental research has provided information on the channel's physical structure which can be used to create realistic ion transport models. Different trajectories exist for the ions entering the channel, each having its own probability of occurrence. Variables that measure these trajectories are the translocation and return probabilities, average lifetime, and spectral density of the ion number fluctuations. Theoretical analysis of ion transport has been restricted to low-resolution continuum diffusion-based or kinetic-based models which do not consider important factors that have an effect on ionic conduction. This paper extends previous models by an electro-diffusion model which takes into account the effects of electric fields, energy barriers, and rate-limited association/dissociation of ions with surface charges present inside the channel. Derived from the analytical model are the survival probability and spectral density.