Stable spatially periodic patterns of ion channels in biomembranes

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Abstract
Ion flow through channels in a membrane may cause lateral gradients of the electrical potential which give rise to electrophoresis of charged channels. Coupled dynamics of the channel density and of the voltage across the membrane together with a binding-release reaction for the proteins leads via a pattern forming instability into a spatially periodic channel density. We derive near the onset of the spatial periodic pattern a Ginzburg-Landau equation and determine the parameter ranges with continuous transitions to periodic patterns. Above such a continuous transition the periodic patterns are stable within a wave-number band and within a finite range of the control parameter.