Geodesic curvature driven surface microdomain formation

TL;DR

This paper introduces a geodesic curvature energy model to describe lipid raft microdomain formation in membranes, emphasizing geometry's role over classical phase separation models.

Contribution

The study develops a novel geodesic curvature-based model that predicts microdomain structures in lipid membranes, contrasting with traditional phase separation theories.

Findings

Model accepts intrinsic geodesic curvature as input

Numerical simulations demonstrate microdomain formation

Contrasts with classical phase separation predictions

Abstract

Lipid bilayer membranes are not uniform and clusters of lipids in a more ordered state exist within the generally disorder lipid milieu of the membrane. These clusters of ordered lipids microdomains are now referred to as lipid rafts. Recent reports attribute the formation of these microdomains to the geometrical and molecular mechanical mismatch of lipids of different species on the boundary. Here we introduce the geodesic curvature to characterize the geometry of the domain boundary, and develop a geodesic curvature energy model to describe the formation of these microdomains as a result of energy minimization. Our model accepts the intrinsic geodesic curvature of any binary lipid mixture as an input, and will produce microdomains of the given geodesic curvature as demonstrated by three sets of numerical simulations. Our results are in contrast to the surface phase separation predicted by the classical surface Cahn-Hilliard equation, which tends to generate large domains as a result of the minimizing line tension. Our model provides a direct and quantified description of the structure inhomogeneity of lipid bilayer membrane, and can be coupled to the investigations of biological processes on membranes for which such inhomogeneity plays essential roles.