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Liquid Liquid Phase Separation

Coexisting Condensates
Liquid-liquid phase separation is an emerging mechanism for intracellular organization. Found in both the nucleus and the cytoplasm, liquid-like droplets condense to create compartments that are thought to promote and inhibit specific biochemistry. This work used 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 explored 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 showed 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. 
Work performed in collaboration with Dr. Greg Forest, Dr. Amy Gladfelter, and 
Dr. Jay Newby.
Intra-droplet Patterning
In this work, a multiphase, Cahn-Hilliard diffuse interface model with a double-well chemical potential is used to examine RNA-protein interactions driving LLPS. We created a bivalent system that allows for two different species of protein-RNA complexes and model the competition that arises for a shared binding partner, free protein. With this system we demonstrated that the binding and unbinding of distinct RNA-protein complexes leads to diverse spatial pattern formation and dynamics within droplets. Both the initial formation and transient behavior of spatial patterning are subject to the exchange of free proteins between RNA-protein complexes. This study illustrated that spatiotemporal heterogeneity can emerge within phase-separated biological condensates with simple binding reactions and competition. Intra-droplet patterning may influence droplet composition and, subsequently, cellular organization on a larger scale.
Work performed in collaboration with Dr. Jia Zhao, Grace McLaughlin, Dr. Greg Forest, Dr. Amy Gladfelter, and Dr. Jay Newby.
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