Modeling multicomponent phase behavior inspired by membraneless compartmentalization in cells

Recent evidence shows that intracellular phase separation can drive the formation of membraneless liquid-like droplets composed of protein RNA and other biomolecules. Gibbs rule suggests that the number of possible coexisting phases scales linearly with the number of components, which is on the order of hundreds in cells. However, in typical biological systems only a small number of phases are observed and they are often assembled in highly organized structures. To resolve this puzzle, we first employ Flory-Huggins theory to examine the global phase structure of many components, whose interaction energies are randomly drawn from a Gaussian distribution. We find that the typical number of coexisting phases is primarily determined by the composition and the mean strength of interaction. However, the enhanced variance of interaction increases the range of parameters, where small number of coexisting phases are observed. In order to see, how different phases evolve in time and arrange in space, we used the Cahn-Hilliard formalism. We investigate the nucleation and growth of domains as well as their relative packing for 3, 4, 5 and more components.