Robust Stability of Multicomponent Membranes: the Role of Glycolipids

TL;DR

This paper develops a mathematical framework to analyze how glycolipids like cholesterol stabilize multicomponent membranes by examining low-energy configurations through dynamical systems and geometric singular perturbation techniques.

Contribution

It introduces a novel approach linking membrane stability to connecting orbits in a reduced dynamical system, specifically modeling glycolipids' stabilizing effects.

Findings

Established criteria for membrane stability based on connecting orbit structures.

Identified the stabilizing role of glycolipids in membrane configurations.

Presented examples using geometric singular perturbation techniques.

Abstract

We present the multicomponent functionalized free energies that characterize the low-energy packings of amphiphilic molecules within a membrane through a correspondence to connecting orbits within a reduced dynamical system. To each connecting orbits we associate a manifold of low energy membrane-type configurations parameterized by a large class of admissible interfaces. The normal coercivity of the manifolds is established through criteria depending solely on the structure of the associated connecting orbit. We present a class of examples that arise naturally from geometric singular perturbation techniques, focusing on a model that characterizes the stabilizing role of cholesterol-like glycolipids within phospholipid membranes.