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A model of mobile, charged ion channels embedded in a biomembrane isinvestigated. The ion channels fluctuate between an opened and a closed stateaccording to a simple two-state reaction scheme whereas the total number of ionchannels is a conserved quantity. Local transport mechanisms suggest that theion channel densities are governed by electrodiffusion-like equations that haveto be supplemented by a cable-type equation describing the dynamics of thetransmembrane voltage. It is shown that the homogeneous distribution of ionchannels may become unstable to either a stationary or an oscillatoryinstability. The nonlinear behavior immediately above threshold of anoscillatory bifurcation occuring at finite wave number is analyzed in terms ofamplitude equations. Due to the conservation law imposed on ion channelslarge-scale modes couple to the finite wave number instability and have thus tobe included in the asymptotic analysis near onset of pattern formation. Amodified Ginzburg-Landau equation extended by long-wavelength stationaryexcitations is established and it is highlighted how the global conservationlaw affects the stability of traveling ion channel density waves.Comment: Currently submitted to Physical Review

Traveling ion channel density waves affected by a conservation law