Theoretical and computational study of phase transformations of biomolecular condensates: growth, coarsening, and aging

Abstract

Many mesoscopic membraneless organelles, also called biomolecular condensates, have shown significant biological functions in cells. Some condensates rich in proteins and nucleic acids form via liquid-liquid phase separation (LLPS), and can undergo liquid-to-solid phase transition when aging, which is related to numerous neurodegenerative diseases. In this dissertation, we develop theoretical and computational models to study phase transformations of protein-rich biomolecular condensates, focusing on the growth, coarsening, and aging behaviors. In our studies of chemically reactive macromolecular mixtures, we formulate a thermodynamic model to describe complex formation, LLPS and aging via gelation concurrently. Phase behaviors of quaternary mixtures are characterized by constructing ternary phase diagrams. We also develop a thermodynamically consistent kinetic framework to study how reaction, gelation and Brownian motion of condensates affect the coarsening and morphology of such mixtures. We find that physical cross-links in biomolecular condensates slow down the coarsening rate, while Brownian motion promotes the coarsening of gel-like domains above certain volume fraction threshold, leading to percolated structures. Aging via formation of amyloid fibrils is investigated using an integrated atomistic and continuum theory approach. We identify a new mechanism for amyloid fibrils to elongate, i.e., surface-mediated growth, different from conventional understanding. We provide quantitative analysis by constructing a continuum model that incorporates surface diffusion and attachment kinetics. There exists a critical length below which the fibril undergoes accelerated growth, and above which it reaches steady-state growth. In addition, we extend our studies to fiber growth in heterogeneous protein solutions using a phase-field modeling framework. We find that the fiber reaches a steady state characterized by its growth velocity and tip radius at different degrees of anisotropyduring the unidirectional growth in a homogeneous solution. The growth of a fiber from a protein-rich condensate to protein-poor regions results in a significant decline in growth velocity and an increase in tip radius when the fiber crosses the condensate interface. Finally, the complex and anisotropic morphologies of multiple fibers growing in a solution with multiple condensates are also illustrated. Results from this dissertation provide a better understanding of how phase transformations occur and develop in biological systems.