Gravitationally induced oscillations of active droplets

Oscillations in the formation and dissolution of compartments inside living cells are pivotal in orchestrating various cellular functions and processes. Recent experiments on synthetic cells showed the spontaneous emergence of spatio-temporal oscillations in the number of droplets, their size, and position. Oscillations occur because droplets grow via gravitationally induced fusion above their stationary size. As a result droplets shrink, feeding the nucleation of new sedimenting droplets, restarting the cycle. The stationary droplet size is a consequence of deactivating droplet material inside and activating outside. Here we present a theoretical model for phase separation with non equilibrium chemical fuelling including a sharp interface model for many active droplets. The model quantitatively describes the stationary droplet size and the oscillation frequency observed experimentally. Such engineered oscillations in synthetic cells could serve as autonomous time-keeping systems that regulate the internal organisations of the synthetic cell.