Cotransport-induced instability of membrane voltage in tip-growing cells.

A salient feature of stationary patterns in tip-growing cells is the key role played by the symports and antiports, membrane proteins that translocate two ionic species at the same time. It is shown that these cotransporters destabilize generically the membrane voltage if the two translocated ions diffuse differently and carry a charge of opposite (same) sign for symports (antiports). The orders of magnitude obtained for the time and length scale are in agreement with experiments. A weakly nonlinear analysis characterizes the bifurcation.