Pattern formation of liquid condensates at surfaces

In living cells, the cytoplasm or the nucleoplasm is confined by membranes separating their chemically distinct inside from their environment. Specific proteins can not only bind to such membranes but can also undergo phase separation in the cytoplasm or nucleoplasm, respectively. These properties suggest an assembly pathway for phase-separated, protein-rich condensates at membranes that are controlled by membrane binding. Interestingly, in living systems, these binding processes are typically regulated by active chemical reactions which involve irreversible steps such as phosphorylation. Here, we theoretically investigate how active binding processes control the liquid condensates using irreversible thermodynamics and active binding kinetics that breaks the detailed balance of the rates. We found that these active binding processes lead to non-spherical droplets wetting on the surface. Moreover, the ripening of condensates is suppressed causing various stationary patterns composed of multiple equally-sized droplets. Strikingly, for small systems or molecules that can be sufficiently densified on the membrane, we report the emergence of condensates continuously oscillating between two opposite membranes. Our findings indicate that active binding in the bulk-surface coupled system can facilitate temporal and spatial control of liquid condensates, which might provide insights into the tempo-spatial organization of membrane-less organelles in the living cells.