Determining the Mean Curvature Modulus of a Lipid Membrane by Simulating Buckling

Abstract

Membrane remodeling is central to a large number of cell biological processes, and the cost for elastically deforming the lipid bilayer features prominently in the energetic budget of such events. It is quantified by the mean curvature modulus, the determination of which is hence a prominent task for experimental and computational membrane scientists alike. The standard approach in simulations is to monitor the undulation spectrum [1], but in order to reach the continuum regime one needs large membranes that take disproportionately long to equilibrate. It has been suggested to instead simulate curved membrane tethers and measure their axial force [2], but this method has technical difficulties for models that are not strongly coarse grained. Here we consider an alternative strategy recently proposed by Noguchi [3], namely, measuring the response of a membrane to buckling. We provide highly accurate analytical expressions to analyze parallel and perpendicular stresses, valid far into the highly nonlinear regime, and we derive fluctuation corrections. Using a variety of membrane models, ranging from strongly coarse grained to atomistic, we show that highly accurate values of the mean curvature modulus can be obtained with remarkable computational ease. The technique also permits to check whether deviations from quadratic curvature elasticity are important, and it offers insights into the thermodynamics of the bending energetics itself.[1] Goetz R., Gompper G., and Lipowsky R., “Mobility and elasticity of self-assembled membranes”, Phys. Rev. Lett. 82, 221-224 (1999).[2] Harmandaris V.A. and Deserno M., “A novel method for measuring the bending rigidity of model lipid membranes by simulating tethers”, J. Chem. Phys. 125, 204905 (2006).[3] Noguchi H., “Anisotropic surface tension of buckled fluid membranes”, Phys. Rev. E 83, 061919 (2011).