Membrane stress tensor in the presence of lipid density and composition inhomogeneities

TL;DR

This paper derives a generalized membrane stress tensor accounting for density and composition inhomogeneities, extending existing models to better understand forces in complex lipid membranes.

Contribution

It introduces a new expression for the membrane stress tensor that incorporates inhomogeneities, unifying and extending the Helfrich and ADE models.

Findings

Derived a generalized stress tensor for inhomogeneous membranes

Provided a covariant formalism for force density calculations

Applied the model to analyze forces from local perturbations

Abstract

We derive the expression of the stress tensor for one and two-component lipid membranes with density and composition inhomogeneities. We first express the membrane stress tensor as a function of the free-energy density by means of the principle of virtual work. We then apply this general result to a monolayer model which is shown to be a local version of the area-difference elasticity (ADE) model. The resulting stress tensor expression generalizes the one associated with the Helfrich model, and can be specialized to obtain the one associated with the ADE model. Our stress tensor directly gives the force exchanged through a boundary in a monolayer with density and composition inhomogeneities. Besides, it yields the force density, which is also directly obtained in covariant formalism. We apply our results to study the forces induced in a membrane by a local perturbation.