Active suppression of Ostwald ripening: beyond mean-field theory
File(s)
Published version
Author(s)
Bressloff, Paul C
Type
Journal Article
Abstract
Active processes play a major role in the formation of membraneless cellular structures (biological condensates). Classical coarsening theory predicts that only a single droplet remains following Ostwald ripening.
However, in both the cell nucleus and cytoplasm there coexist several membraneless organelles of the same
basic composition, suggesting that there is some mechanism for suppressing Ostwald ripening. One potential
candidate is the active regulation of liquid-liquid phase separation by enzymatic reactions that switch proteins
between different conformational states (e.g., different levels of phosphorylation). Recent theoretical studies
have used mean-field methods to analyze the suppression of Ostwald ripening in three-dimensional (3D) systems
consisting of a solute that switches between two different conformational states, an S state that does not phase
separate and a P state that does. However, mean-field theory breaks down in the case of 2D systems, since the
concentration around a droplet varies as ln R rather than R−1, where R is the distance from the center of the
droplet. It also fails to capture finite-size effects. In this paper we show how to go beyond mean-field theory
by using the theory of diffusion in domains with small holes or exclusions (strongly localized perturbations).
In particular, we use asymptotic methods to study the suppression of Ostwald ripening in a 2D or 3D solution
undergoing active liquid-liquid phase separation. We proceed by partitioning the region outside the droplets into
a set of inner regions around each droplet together with an outer region where mean-field interactions occur.
Asymptotically matching the inner and outer solutions, we derive leading-order conditions for the existence and
stability of a multidroplet steady state. We also show how finite-size effects can be incorporated into the theory
by including higher-order terms in the asymptotic expansion, which depend on the positions of the droplets and
the boundary of the 2D or 3D domain. The theoretical framework developed in this paper provides a general
method for analyzing active phase separation for dilute droplets in bounded domains such as those found in
living cells.
However, in both the cell nucleus and cytoplasm there coexist several membraneless organelles of the same
basic composition, suggesting that there is some mechanism for suppressing Ostwald ripening. One potential
candidate is the active regulation of liquid-liquid phase separation by enzymatic reactions that switch proteins
between different conformational states (e.g., different levels of phosphorylation). Recent theoretical studies
have used mean-field methods to analyze the suppression of Ostwald ripening in three-dimensional (3D) systems
consisting of a solute that switches between two different conformational states, an S state that does not phase
separate and a P state that does. However, mean-field theory breaks down in the case of 2D systems, since the
concentration around a droplet varies as ln R rather than R−1, where R is the distance from the center of the
droplet. It also fails to capture finite-size effects. In this paper we show how to go beyond mean-field theory
by using the theory of diffusion in domains with small holes or exclusions (strongly localized perturbations).
In particular, we use asymptotic methods to study the suppression of Ostwald ripening in a 2D or 3D solution
undergoing active liquid-liquid phase separation. We proceed by partitioning the region outside the droplets into
a set of inner regions around each droplet together with an outer region where mean-field interactions occur.
Asymptotically matching the inner and outer solutions, we derive leading-order conditions for the existence and
stability of a multidroplet steady state. We also show how finite-size effects can be incorporated into the theory
by including higher-order terms in the asymptotic expansion, which depend on the positions of the droplets and
the boundary of the 2D or 3D domain. The theoretical framework developed in this paper provides a general
method for analyzing active phase separation for dilute droplets in bounded domains such as those found in
living cells.
Date Issued
2020-04
Date Acceptance
2020-04-01
Citation
Physical Review E, 2020, 101 (4)
ISSN
2470-0045
Publisher
American Physical Society (APS)
Journal / Book Title
Physical Review E
Volume
101
Issue
4
Copyright Statement
©2020 American Physical Society
Identifier
http://dx.doi.org/10.1103/physreve.101.042804
Publication Status
Published
Article Number
042804
Date Publish Online
2020-04-29