Phase Separation on Deformable Membranes: interplay of mechanical coupling and dynamic surface geometry

TL;DR

This paper investigates how mechanical coupling and dynamic surface geometry influence phase separation and pattern formation of membrane-bound proteins, revealing that membrane-mediated interactions can arrest coarsening and induce stable patterns.

Contribution

It introduces a systematic analysis of membrane-mediated interactions in phase-separating proteins, showing their role in pattern formation and length-scale selection on deformable membranes.

Findings

Membrane-mediated interactions qualitatively alter protein equilibrium states.

Long-range interactions lead to arrested coarsening and stable pattern formation.

The model maps out phase space and characterizes phase transitions.

Abstract

The self-organization of proteins into enriched compartments and the formation of complex patterns are crucial processes for life on the cellular level. Liquid-liquid phase separation is one mechanism for forming such enriched compartments. When phase-separating proteins are membrane-bound and locally disturb it, the mechanical response of the membrane mediates interactions between these proteins. How these membrane-mediated interactions influence the steady state of the protein density distribution is thus an important question to investigate in order to understand the rich diversity of protein and membrane-shape patterns present at the cellular level. This work starts with a widely used model for membrane-bound phase-separating proteins. We numerically solve our system to map out its phase space and perform a careful, systematic expansion of the model equations to characterize the phase transitions through linear stability analysis and free energy arguments. We observe that the membrane-mediated interactions, due to their long-range nature, are capable of qualitatively altering the equilibrium state of the proteins. This leads to arrested coarsening and length-scale selection instead of simple demixing and complete coarsening. In this study, we unambiguously show that long-range membrane-mediated interactions lead to pattern formation in a system that otherwise would not do so. This work provides a basis for further systematic study of membrane-bound pattern-forming systems.