Size selection of phase-separated liquid droplets in strain-stiffening elastic networks

Membraneless organelles are formed via phase separation inside cells, but it remains unclear how cytoskeleton affects this process. Recent experiments showed the size of separated droplets is controlled by the stiffness of the surrounding elastic network. This is in contrast to phase separation of liquid mixtures, which continue to coarsen indefinitely (Ostwald ripening). Motivated by these observations, we developed a model to investigate the coupling between the separating liquid mixture and the elastic network. We find that the elastic energy of distorted network effectively modifies the nucleation barrier and the critical nucleus size for the separating mixture. For a neo-Hookean elastic network we find that the coarsening proceeds indefinitely. On the other hand, for networks with sufficiently strong strain-stiffening considered in experiments we find that the elastic energy arrests the coarsening once droplets reach certain size. Furthermore, finite element simulations indicate that the interactions between droplets via the distorted elastic network are rather short-ranged, which explains why observed droplets in experiments achieve a uniform size.