Dynamics and self-organization of active surfaces

Biological cells are active systems and exhibit complex dynamic behaviours such as cell division, cell polarity establishment and cell locomotion. Such dynamic processes emerge from the collective interplay of many molecular components far from thermodynamic equilibrium. Active molecular processes such as the force generation of molecular motors along filaments of the cytoskeleton transduce chemical free energy to generate movements and mechanical work. The cell cortex, a thin film of active material assembled below the cell membrane, plays a key role in cellular symmetry breaking processes such as cell polarity establishment and cell division. I will present a minimal model of the mechano-chemical self-organization of the cell cortex that is based on a hydrodynamic theory of curved active surfaces and that can capture the emergence of shapes. Active stresses on this surface are regulated by a diffusing molecular species. We show that coupling of the active surface to a passive bulk fluid enables spontaneous polarization and the formation of a contractile ring on the surface via mechano-chemical instabilities. We discuss the role of external fields in guiding such pattern formation. Our work reveals that key features of cellular symmetry breaking and cell division can emerge in a minimal model via general dynamic instabilities. Self-organised active surfaces provide minimal models for the generation of shape and the emergence of dynamic patterns in basic cellular processes.