Modeling the Mechanisms by Which Coexisting Biomolecular RNA–Protein Condensates Form

Abstract

Liquid–liquid phase separation is an emerging mechanism for intracellular organization. This work presents a mathematical model to examine molecular mechanisms that yield phase-separated droplets composed of different RNA–protein complexes. Using a Cahn–Hilliard diffuse interface model with a Flory–Huggins free energy scheme, we explore how multiple (here two, for simplicity) protein–RNA complexes (species) can establish a heterogeneous droplet field where droplets with single or multiple species phase separate and evolve during coarsening. We show that the complex–complex de-mixing energy tunes whether the complexes co-exist or form distinct droplets, while the transient binding kinetics dictate both the timescale of droplet formation and whether distinct species phase separate into droplets simultaneously or sequentially. For specific energetics and kinetics, a field of droplets driven by the formation of only one protein–RNA complex will emerge. Slowly, the other droplet species will accumulate inside the preformed droplets of the other species, allowing them to occupy the same droplet space. Alternatively, unfavorable species mixing creates a parasitic relationship: the slow-to-form protein–RNA complex will accumulate at the surface of a competing droplet species, siphoning off the free protein as it is released. Once this competing protein–RNA complex has sufficiently accumulated on the droplet surface, it can form a new droplet that is capable of sharing an interface with the first complex droplet but is not capable of mixing. These results give insights into a wide range of phase-separation scenarios and heterogeneous droplets that coexist but do not mix within the nucleus and the cytoplasm of cells.