Buckling Gel-Phase Membranes is a Way to Measure their Mean Bending Regidity

Abstract

The elasticity of lipid membranes can be characterized by two curvature moduli: the mean bending modulus and the Gaussian curvature modulus. Due to the relevance of the mean bending modulus for countless biological processes, considerable effort has been devoted to determine it_both in experiment and in computational studies. The most common computational approach is to measure the power spectrum of shape undulation modes [1]. Unfortunately, this technique is challenging for gel-phase membranes, because their larger modulus renders their fluctuations correspondingly smaller. In contrast, methods that infer a membrane's rigidity from actively bending it yield a signal that becomes stronger as the membrane becomes stiffer. One recently proposed method derives the modulus from the stress-strain relation of a buckled membrane, and it has been shown to provide accurate results for fluid membranes [2,3]. Using a coarse-grained lipid model, we show that this buckling method can also calculate the mean bending modulus of a gel phase membrane. We discuss the efficient implementation of the technique, paying special attention to difficulties that can arise while simulating a membrane in the gel phase. The method also provides insights into the contribution of entropy to the bending modulus, and hence its the temperature dependence.[1] Goetz R., Gompper G., and Lipowsky R., “Mobility and elasticity of self-assembled membranes”, Phys. Rev. Lett. 82, 221-224 (1999).[2] Noguchi H., “Anisotropic surface tension of buckled fluid membranes”, Phys. Rev. E 83, 061919 (2011).[3] Hu M., Diggins P., and Deserno M., “Determining the bending modulus of a lipid membrane by simulating buckling”, J. Chem. Phys. 138, 214110 (2013).