Local stress and elastic properties of lipid membranes obtained from elastic energy variation

TL;DR

This paper introduces a new theoretical and computational approach to determine elastic parameters of lipid membranes, including local stress, Poisson's ratio, and curvature moduli, applicable to both single- and multi-component membranes.

Contribution

It presents a novel method based on stress-profile derivatives and global incompressibility assumptions to accurately measure membrane elastic properties.

Findings

Major elastic parameters derived from stress-profile moments.

Global incompressibility enables local Poisson's ratio measurement.

Relation established between bending and Gaussian curvature moduli.

Abstract

A theory and computational method are provided for the calculation of lipid membranes elastic parameters, which overcomes the difficulties of the existing approaches and can be applied not only to single-component but also to multi-component membranes. It is shown that the major elastic parameters can be determined as the derivatives of the stress-profile moments with respect to stretching. The more general assumption of the global incompressibility, instead of the local one, is employed, which allows the measurement of the local Poisson's ratio from the response of the stress profile to the isotropic ambient pressure. In the case of the local incompressibility and quadratic energy law, a direct relation between the bending modulus and Gaussian curvature modulus is established.