Pattern formation, pulsation and traveling wave on active spherical membranes

Active force generation by actin-myosin cortex coupled to the cell-membrane allows the cell to deform, respond to environment, and plays an important role in cell motility and cell division. Several membrane bound activator proteins move along the membrane and couple to its local curvature. In addition, they can act as nucleating sites for the growth of filamentous actin. While actin polymerization can generate outward push on the membrane, inward pull from the contractile acto-myosin cortex can propagate to the membrane via actin filaments. Using linear stability analysis and numerical calculations we demonstrate the existence of three different dynamical phases depending on the activity. The spherical membrane gets destabilized towards pattern formation, generation of localized pulsation and traveling waves. We present our results in terms of various phase diagrams, and evolution of the coupled fields. Our results have implications for living cells and can be verified in experiments on artificial cell-like constructs.