Patterning of multicomponent elastic shells by gaussian curvature

Area of Science:

• Biophysics
• Materials Science
• Synthetic Biology

Background:

• Shell protein distribution and morphology of bacterial microcompartments are crucial for regulating chemical fluxes and biological functions.
• Understanding the interplay between morphology and component patterning in these structures is key to deciphering their roles.

Purpose of the Study:

• To investigate the coupling between morphology and component patterning in multicomponent elastic shells.
• To explore how mean and Gaussian bending energies influence the formation of three-component irregular polyhedra.
• To identify patterning mechanisms relevant to bacterial microcompartments and synthetic vesicles.

Main Methods:

• Computational modeling of multicomponent elastic shells with varying bending rigidities and interfacial line tensions.
• Analysis of component distribution on edges, vertices, and faces of polyhedral shells.
• Investigation of subdomain formation and fractionation mediated by Gaussian curvature.

Main Results:

• Softer components preferentially localize to edges and vertices, while harder components occupy faces in three-component shells.
• Nonzero interfacial line tension induces subdomain separation in softer components, influenced by Gaussian curvature.
• Maximal fractionation of softer components occurs with weaker line tension and a specific bending rigidity ratio (≈2).

Conclusions:

• A novel patterning mechanism for multicomponent shells is identified, explaining bacterial microcompartment morphologies.
• This mechanism, driven by competing bending energies and line tension, can be applied to design synthetic vesicles with controlled structures.
• The findings provide a framework for understanding and engineering complex biological and synthetic shell structures.