Determination of Gaussian curvature modulus and spontaneous curvature via membrane buckling

Abstract

The elastic properties of membranes are typically characterized by a few phenomenological parameters, including bending and Gaussian curvature moduli measuring the membrane rigidity against its deformation and topological change, as well as spontaneous curvature arising from the asymmetry between the two leaflets in the lipid bilayers. Though tether-based and fluctuation-based experiments are commonly utilized to measure the bending modulus, measuring the Gaussian curvature modulus and the spontaneous curvature of the membrane is considered to be much more difficult. In this paper, we study the buckling process of a circular membrane with nonzero spontaneous curvature under compressive stresses. It is found that when the stress exceeds a critical value, the circular membrane will transform from a spherical cap to a buckled shape, with its buckling degree enhanced with the increase of stress until its base is constricted to almost zero. As the stress-strain relationship of the buckled membrane strongly depends on the Gaussian curvature modulus and the spontaneous curvature,we therefore propose a method to determine the Gaussian curvature modulus and the spontaneous curvature simultaneously by measuring its stress-strain relationship during a buckling process.