The thermal Casimir effect in lipid bilayer tubules

TL;DR

This paper calculates the thermal Casimir effect in lipid membrane tubes, revealing an attractive force that slightly contracts the tube but is generally insufficient to stabilize it against bending stress.

Contribution

It introduces a field-theoretic approach to quantify the thermal Casimir effect in lipid bilayer tubules, providing specific estimates of the force magnitude.

Findings

The Casimir free energy behaves as -k_B T L kappa_C / R.

The Casimir force is attractive and tends to contract the tube.

The force magnitude is about 0.3 for typical lipid membranes.

Abstract

We calculate the thermal Casimir effect for a dielectric tube of radius $R$ and thickness delta formed from a membrane in water. The method uses a field-theoretic approach in the grand canonical ensemble. The leading contribution to the Casimir free energy behaves as -k_BTL kappa_C/R giving rise to an attractive force which tends to contract the tube. We find that kappa_C ~ 0.3 for the case of typical lipid membrane t-tubules. We conclude that except in the case of a very soft membrane this force is insufficient to stabilize such tubes against the bending stress which tends to increase the radius.