Determining Material Elastic Properties of Arbitrarily-Shaped Membranes using Molecular Dynamics Simulations with Application to the Inverted Hexagonal Phase

Abstract

Accumulating evidence indicates that diverse physiological processes are influenced by the lipid composition of the membrane and by its material properties. This has notably been shown for the function of diverse proteins and their oligomerization, and processes on larger scales such as membrane reshaping and fusion. Determination of the elastic properties of lipidic membranes is therefore of great importance to our understanding of these processes. Experimental approaches to determine the material properties of lipids remain challenging and usually rely on their study in a relaxed environment or in flat bilayers, although it is widely accepted that cell membranes can be under considerable stress and frustration as well as high local curvature. Whether this impacts the measured properties is a matter of debate so that studying membranes under more realistic conditions is key for our understanding how these material properties impact different physiological processes. In this context, we propose a computational method to determine the elastic properties of lipid assemblies of arbitrarily shaped interfaces and use it to study the impact of the curvature of a membrane on its elastic properties. Specifically, we apply the methodology to mixtures of DOPE (dioleoylphosphatidylethanolamine) lipids and cholesterol in the inverted-hexagonal and lamellar phases and find that the bending rigidity for a particular lipid composition critically depends on the geometry of the lipidic system. This dependence correlates on the molecular level to the changes in lipid chain order imposed by the membrane curvature, implying that these results should pertain to other situations where the membrane is deformed, stressed or frustrated that notably emerge around integral membrane proteins or during membrane remodeling processes such as budding.