Polarity patterns of stress fibers.

Stress fibers are contractile actomyosin bundles commonly observed in the cytoskeleton of metazoan cells. The spatial profile of the polarity of actin filaments inside contractile actomyosin bundles is either monotonic (graded) or periodic (alternating). In the framework of linear irreversible thermodynamics, we write the constitutive equations for a polar, active, elastic one-dimensional medium. An analysis of the resulting equations for the dynamics of polarity shows that the transition from graded to alternating polarity patterns is a nonequilibrium Lifshitz point. Active contractility is a necessary condition for the emergence of sarcomeric, alternating polarity patterns.

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.