Asymptotic analysis of conversion-limited phase separation

TL;DR

This paper develops an asymptotic analysis framework for understanding how slow interfacial conversion limits the coarsening process in biological phase separation, accounting for cellular geometry and multiple condensates.

Contribution

It introduces a matched asymptotic analysis approach to model conversion-limited phase separation in cells, extending mean-field theory with geometric corrections.

Findings

Derived kinetic equations for condensate growth and shrinkage.

Provided systematic corrections to mean-field theory.

Analyzed the impact of cellular geometry on phase separation dynamics.

Abstract

Liquid-liquid phase separation plays a major role in the formation and maintenance of various membrane-less subcellular structures in the cytoplasm and nucleus of cells. Biological condensates contain enhanced concentrations of proteins and RNA, many of which can be continually exchanged with the surrounding medium. Coarsening is an important step in the kinetics of phase separation, whereby an emulsion of polydisperse condensates transitions to a single condensate in thermodynamic equilibrium with a surrounding dilute phase. A key feature of biological phase separation is the co-existence of multiple condensates over significant time scales, which is consistent with experimental observations showing a slowing of coarsening rates. It has recently been proposed that one rate limiting step could be the slow interfacial conversion of a molecular constituent between the dilute and dense phases. In this paper we analyze conversion-limited phase separation within the framework of diffusion in singularly perturbed domains, which exploits the fact that biological condensates tend to be much smaller than the size of a cell. Using matched asymptotic analysis, we solve the quasi-static diffusion equation for the concentration in the dilute phase, and then derive kinetic equations for the slow growth/shrinkage of the condensates. This provides a systematic way of obtaining corrections to mean-field theory that take into account the geometry of the cell and the locations of all the condensates.