Microscopic elasticity from MD. II. Liquid interfaces and lipid membranes

Lipid membranes not only play critical roles in many cellular functions but are also unique in that they have properties of both fluid and elastic materials. While 2D elasticity theories, such as Canham-Helfrich-Evans, adequately capture the dominant energetics of membrane deformation, a full characterization of the 3D elastic response is necessary to account for the many modes of deformation and the role that lipid structure plays in determining the elastic energy. We use the stress-stress fluctuation (SSF) method to obtain local elasticity profiles of a simple water-dodecane interface and a lipid membrane from coarse-grained MARTINI molecular dynamics simulations. We validate the results from the SSF method through the explicit deformation method, which measures the change in the local stress tensor relative to a specific strain. Furthermore, we show that some expected symmetries of the elasticity tensor are locally broken due to the lateral fluidity of the interfacial systems and the physical constraint of mechanical equilibrium. Profiles of the lateral and transverse shear moduli show that the membrane is locally fluid, while the transverse shear modulus is locally nonzero, but its integral vanishes. We define the area, Young's, and bulk moduli, as well as the Poisson ratio for a lipid membrane through the compliance tensor, and use the area modulus to estimate the position of the neutral surface and the macroscopic bending modulus. Our elasticity calculations provide critical insights into the local mechanical properties of lipid bilayers and unravel the role of lateral fluidity in the membrane's elastic response.