Pattern formation in ionic currents of cells

Stationary and nonstationary spatiotemporal pattern formation emerging from the cellular electric activity is a common feature of biological cells and tissues. Using an electrodiffusive model describing the transport of two ionic species, we study the stability of the membrane voltage. Provided that the diffusive coefficients of the two ions differ, stationary patterns of transcellular ionic currents arise at finite wavelength in the two following cases: (i) negative differential conductance of one of the two ions, when the transport occurs through voltage-gated ion channels; (ii) opposite charge for the two ions when co-transported by a symport (carrier protein). The characteristic time is diffusive, not capacitive. The mechanism involved is reminiscent of the Turing instability