Patterning of multicomponent elastic shells by Gaussian curvature

TL;DR

This study investigates how the interplay of bending energies and Gaussian curvature influences the patterning and morphology of multicomponent elastic shells, providing insights into bacterial microcompartments and synthetic vesicles.

Contribution

It introduces a model explaining the coupling of component distribution and shape in multicomponent shells via Gaussian curvature and line tension effects.

Findings

Softer components localize on edges and vertices

Harder components occupy face regions

Patterning is maximized at low line tension and specific rigidity ratios

Abstract

Recent findings suggest that shell protein distribution and morphology of bacterial microcompartments regulate the chemical fluxes facilitating reactions which dictate their biological function. We explore how the morphology and component patterning are coupled through the competition of mean and Gaussian bending energies in multicomponent elastic shells that form three component irregular polyhedra. We observe two softer components with lower bending rigidities allocate on the edges and vertices while the harder component occupies the faces. When subjected to a non-zero interfacial line tension, the two softer components further separate and pattern into subdomains that are mediated by the Gaussian curvature. We find that this degree of fractionation is maximized when there is a weaker line tension and when the ratio of bending rigidities between the two softer domains $\approx 2$. Our results reveal a patterning mechanism in multicomponent shells that can capture the observed morphologies of bacterial microcompartments and, moreover, can be realized in synthetic vesicles.