Mesoscale properties of non-equilibrium liquid-liquid phase separation with molecular production and degradation

The role of liquid-liquid phase separation (LLPS) in the formation of cellular, membraneless organelles and chromatin organization is only starting to be elucidated by a large number of experimental studies. However, the theoretical understanding of the phenomenon is largely based on soft matter research of systems that are in thermodynamic equilibrium, which is not the case in many biological systems. Motivated by cellular LLPS, we present a theoretical framework for the analysis of out-of-equilibrium LLPS, where the phase-separating molecules are constantly synthesized and degraded. We show that while the concentrations of solutes in the coexisting domains remain the same as in equilibrium systems, the non-equilibrium nature of biological systems may modify the large-scale properties of the phase separated domains. These include the shapes and number of phase separated domains, which do not undergo Ostwald ripening, the fluctuations of the interface, and effective interactions of the ribosomes (responsible for production). For each of these properties, our theoretical model predicts the deviations from the equilibrium case and their magnitude, which may be significant in some biological scenarios.