Pattern Formation of Ion Channels with State Dependent Electrophoretic Charges and Diffusion Constants in Fluid Membranes

A model of mobile, charged ion channels in a fluid membrane is studied. The channels may switch between an open and a closed state according to a simple two-state kinetics with constant rates. The effective electrophoretic charge and the diffusion constant of the channels may be different in the closed and in the open state. The system is modeled by densities of channel species, obeying simple equations of electro-diffusion. The lateral transmembrane voltage profile is determined from a cable-type equation. Bifurcations from the homogeneous, stationary state appear as hard-mode, soft-mode or hard-mode oscillatory transitions within physiologically reasonable ranges of model parameters. We study the dynamics beyond linear stability analysis and derive non-linear evolution equations near the transitions to stationary patterns.