Active interface growth and pattern formation in membrane-protein systems

Inspired by recent experimental observation of patterning at the membrane of a living cell, we propose a generic model for the dynamics of a fluctuating interface driven by particle-like inclusions which stimulate its growth. We find that the coupling between interfacial and inclusions dynam- ics yields microphase separation and the self-organisation of travelling waves. These patterns are strikingly similar to those detected in the aforementioned experiments on actin-protein systems. Our results further show that the active growth kinetics does not fall into the Kardar-Parisi-Zhang universality class for growing interfaces, displaying instead a novel superposition of equilibrium-like scaling and sustained oscillations.