Mathematics Colloquium
Kelsey Gasior
University of Notre Dame
Title: The Molecular Dynamics Underlying Intracellular Phase Separation
Date: Friday, November 14th
Place and Time: Love 101, 3:05-3:55 pm
Abstract. 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. This work focuses on a multiphase, Cahn-Hilliard diffuse interface model to examining the RNA-protein interactions driving LLPS. Using a "start simple, build up" approach to model construction, these models explore how the molecular interactions underlying protein-RNA dynamics and RNA species competition control observable, droplet-scale phenomena. Numerical simulations reveal that RNA competition for free protein molecules contributes to intra-droplet patterning and the emergence of a heterogeneous droplet field. More in-depth analysis using combined sensitivity analysis techniques, such as Morris Method screening and Sobol method, highlights the complicated relationships underlying protein-RNA interactions and the results we can measure. Finally, droplet-level patterns are complicated when the initial conditions are considered. Under in vitro conditions, this model shows how experimental set up and initial conditions can produce complex droplet Turing patterns at phase separation. In-depth analysis using numerical simulations, shape analysis, and sensitivity analyses show that these systems are also susceptible to changes in the protein-RNA binding dynamics. The addition of a second RNA species competing for free protein introduces an element of asymmetry to the system and alters the emerging patterns at the onset of phase separation. But both systems show that certain initial conditions can produce sustained multi-droplet patterns as t goes to infinity. Ultimately, this targeted approach to intracellular LLPS begins to peel back the layers of complex molecular dynamics controlling observable LLPS phenomena that contribute to droplet regulation and, ultimately, cellular function.