Monolayerwise application of linear elasticity theory well describes strongly deformed lipid membranes and the effect of solvent

Abstract

The theory of elasticity of lipid membranes is used widely to describe processes of cell membrane remodeling. Classically, the functional of a membrane's elastic energy is derived under assumption of small deformations; the membrane is considered as an infinitely thin film. This functional is quadratic on membrane surface curvature, with half of the splay modulus as its proportionality coefficient; it is generally applicable for small deformations only. Any validity of this functional for the regime of strong deformations should be verified experimentally. Recently, research using molecular dynamics simulations challenged the validity of this classic, linear model, i.e. the constancy of the splay modulus for strongly bent membranes. Here we demonstrate that the quadratic energy functional still can be applied for calculation of the elastic energy of strongly deformed membranes without introducing higher order terms with additional elastic moduli, but only if applied separately for each lipid monolayer. For cylindrical membranes, both classic and monolayerwise models yield equally accurate results. For cylindrical deformations we experimentally show that the elastic energy of lipid monolayers is additive: a low molecular weight solvent leads to an approximately twofold decrease in the membrane bending stiffness. Accumulation of solvent molecules in the inner monolayer of a membrane cylinder can explain these results, as the solvent partially prevents lipid molecules from splaying there. Thus, the linear theory of elasticity can be expanded through the range from weak to strong deformations—its simplicity and physical transparency describe various membrane phenomena.