Statistical Thermodynamics Approach for Intracellular Phase Separation.

Phase separation is one of the fundamental processes to compartmentalize biomolecules in living cells. RNA-protein complexes (RNPs) often scaffold biomolecular condensates formed through phase separation. We here present a statistical thermodynamics approach to investigate intracellular phase separation. We first present the statistical thermodynamic theory of the liquid-liquid phase separation (LLPS) of two molecules (such as proteins and solvent molecules) and of a polymer solution (such as RNPs and solvent molecules). Condensates produced by LLPS show coarsening and/or coalescence to minimize their total surface area. In addition to the LLPS, there are other types of self-assembly, such as microphase separation, micellization, emulsification, and vesiculation, with which the growth of the assembly stops with optimal size and shape. We also describe a scaling theory of micelles of block copolymers, where their structures are analogous to the core-shell structure of paraspeckle nuclear bodies scaffolded by RNPs of NEAT1_2 long noncoding RNAs (lncRNAs) and RNA-binding proteins (RBPs). These theories treat the self-assembly of polymers in the thermodynamic equilibrium, where their concentrations and compositions do not change with time. In contrast, RNPs are produced according to the transcription of RNAs and are degraded with time. We therefore take into account the dynamical aspect of the production of RNPs in an extension of the theory of the self-assembly of soft matter. Finally, we discuss the structure of paraspeckles as an example to demonstrate that an approach combining experiment and theory is powerful to investigate the mechanism of intracellular phase separation.