Stable spatially periodic patterns of ion channels in biomembranes
Peter Fromherz and Walter Zimmermann
Physical Review E 51 (3) (1995) 1659-1662
Abstract
Ion flow through channels in a membrane may cause lateral gradients of the
elctrical 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 apattern forming instability into a spatially periodic channel density.
We derive near the onset of the spatial periodic pattern a Ginzburg-Landau
and determine the parameter ranges with continous transitions to periodic patterns.
Above such a continous transition the periodic patterns are stable within a
wave-number band and within a finite range of the control parameter.
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