Theory of Electrodynamic Instabilities in Biological Cells

Electric behavior of biological cells is driven by ion transport through the membrane induced by specific proteins. The cable model classically describes the membrane potential dynamics by analogy with an electrical circuit. We show the failure of this description when the various ion species get different diffusion times. The pertinent parameter which describes the membrane electrical stability is not its global differential conductance but an effective conductance taking the diffusion into account. For a membrane with a positive global differential conductance we predict a striking linear instability with formation of a periodic pattern reminiscent of biological observations.