Equilibrium phase separation with many conserved order parameters - Analytical theory and applications in biomolecular condensation

Abstract

In this PhD thesis I study the analytical theory of phase separation with many conserved order parameters, with a particular focus on applying new insights to understand membraneless organelles formed by proteins. There, the relevant order parameters are concentrations of various solute components, and the large number of interacting molecular species in physiological systems translates into a set of many intractable transcendental equations when solving for thermodynamic equilibrium, presenting a major hurdle towards understanding practical systems of interest. In the first half of my thesis, I present analytical approaches in the case where only one or two solute components are present, and highlight the difficulty in generalising them towards higher-dimensional scenarios. In the second half, I tackle the problem from a new perspective: instead of solving for the equilibrium, I study the perturbation around an assumed solution, and show that this perturbation relates to both the energetics as well as experimentally measurable quantities. This framework allows one to determine the `dominant' component in any phase-separating system, and when combined with more detailed models and analysis, can inform the interactions and modulations of the solute molecules. Taken together, this thesis highlights the difficulty in studying phase equilibria in high dimensions, but also illuminates a path forward that allows an analytical understanding of complex condensate systems to be gained. The theoretical and experimental methods developed in this thesis are highly generalisable, and have found applications in many emerging lines of research.