Elastic Properties of Lipid Bilayers: Theory and Possible Experiments

TLDR

Curvature elasticity governs nonspherical shapes of vesicles. The paper proposes a theory of lipid bilayer elasticity. The authors distinguish stretching, tilt, and curvature strains, derive Euler–Lagrange equations for vesicle shapes in magnetic fields and excess pressure, and discuss experiments to measure elastic properties. Magnetic fields deform spherical vesicles into ellipsoids, excess pressure destabilizes the spherical shape at a threshold, and spontaneous curvature modulates both effects.

Abstract

Abstract A theory of the elasticity of lipid bilayers is proposed. Three types of strain, i. e. stretching, tilt and curvature, are distinguished and the associated stresses are identified. It is argued that in the case of vesicles (= closed bilayer films) the only elasticity controlling nonspherical shapes is that of curvature. Euler-Lagrange equations are derived for the shape in magnetic fields and under excess outside pressure. It is shown that magnetic fields can deform spherical vesicles into ellipsoids of revolution. Under excess outside pressure the spherical shape becomes unstable at a certain threshold pressure. Both effects can be influenced by a spontaneous curvature of the bilayer. Some possible experiments to determine the elastic properties are also discussed