Attractive asymmetric inclusions in elastic membranes under tension: cluster phases and membrane invaginations

TL;DR

This paper investigates how asymmetric inclusions in tense elastic membranes form clusters and cause invaginations, revealing a new curvature-driven demixing mechanism with implications for biological membranes.

Contribution

It extends the statistical mechanics of membrane inclusions to include tension and attractive interactions, uncovering cluster formation and demixing phenomena.

Findings

Inclusions form small clusters under tension leading to membrane invaginations.

Oppositely curved inclusions tend to demix into separate clusters.

The work provides a theoretical framework for protein behavior in lipid bilayers.

Abstract

Up-down asymmetric inclusions impose a local, spontaneous curvature to an elastic membrane. When several of them are inserted in a same membrane, they feel effective forces mediated by the membrane, both of elastic and entropic nature. Following an approach initiated by Dommersnes and Fournier in the vanishing tension case [Eur. Phys. J. B 12, 9 (1999)], and also using a pseudo-analytical micellization theory, we derive the statistical mechanics of asymmetric inclusion assemblies when they are also subject to an additional short-range, attractive interaction. Our main conclusion is that generically, when the membrane is under tension, these inclusions live in small clusters at equilibrium, leading to local membrane invaginations. We also propose a novel curvature-induced demixing mechanism: when inclusions imposing local curvatures of opposite sign coexist, they tend to demix in distinct clusters under realistic conditions. This work has potential implications in the context of the thermodynamics of proteins embedded in biological lipid bilayers.