An emerging mechanism for intracellular organization is liquid-liquid phase separation (LLPS). Found in both the nucleus and the cytoplasm, liquidlike droplets condense to create compartments that are thought to localize factors, such as RNAs and proteins, and promote biochemical interactions. Many RNA-binding proteins interact with different RNA species to create droplets necessary for cellular functions, such as polarity and nuclear division. Additionally, the proteins that promote phase separation are frequently coupled to multiple RNA binding domains and several RNAs can interact with a single protein, leading to a large number of potential multivalent interactions.

In this work, we present a multiphase, Cahn-Hilliard diffuse interface model to examine the RNA-protein interactions driving LLPS. Using a ‘start simple, build up’ approach, we incorporate a double-well chemical potential in our initial model of bivalent protein-RNA dynamics and then use a Flory Huggins free energy scheme to examine to droplet field patterning in a subsequent model. Numerical simulations reveal that RNA competition for a shared resource, protein, contributes to both intra-droplet patterning and the establishment of a heterogeneous droplet field. Further, our approach is also applicable to other phase separated systems; our model predicted that protein annuli associated with amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD) were actually part of an intra-droplet shell/core pattern, which was then confirmed experimentally by our biological collaborators.