Tethered membranes do not remain flat for strong structural asymmetry

TL;DR

This paper develops a statistical mechanics model showing that structural asymmetry in tethered membranes can induce spontaneous curvature, leading to instability and crumpling, with potential experimental verification.

Contribution

It introduces a theoretical framework predicting how asymmetry causes spontaneous curvature and destabilizes flat membranes, a novel insight into membrane physics.

Findings

Asymmetry induces spontaneous curvature in membranes.

Above a threshold curvature, membranes become unstable.

Potential experimental setups to verify predictions.

Abstract

We set up the statistical mechanics for a nearly flat, thermally equilibrated fluid membrane, attached to an elastic network through one of its sides. We predict that the resulting structural (inversion) asymmetry of the membrane, notably due to the elastic network attached to one of its sides, can generate a local spontaneous curvature $C_0$, that may in turn destabilize the otherwise flat membrane. As $C_0$ rises above a threshold at a fixed temperature, a flat tethered membrane in the thermodynamic limit becomes structurally unstable, signaling {\em crumpling} of the flat membrane. In-vitro experiments on red blood cell membranes after depletion of adenosine-tri-phosphate molecules and artificial deposition of spectrin filaments on lipid bilayers may be used to verify our results.