STATIONARY PATTERNS IN MEMBRANES BY NONLINEAR DIFFUSION OF ION CHANNELS

Ion flow through channels in a membrane may cause lateral gradients of the electrical potential which give rise to electrophoresis of charged channels. The coupled spatio-temporal dynamics of the channel density and of the voltage across the membrane is described by Smoluchowski's diffusion-drift equation and by Kelvin's cable equation. It is shown that this system of equations has multiple stationary solutions of spatial patterns far from equilibrium. Each stationary state may be assigned to an unstable eigenmode. The stationary pattern with lowest spatial frequency is stable. The stationary patterns of higher spatial frequencies are unstable. They play a role as metastable transients in the dynamics of pattern formation after perturbation of the homogeneous state.