Probing the elastic response of lipid bilayers and nanovesicles to leaflet tensions via volume per lipid

Biological and biomimetic membranes are based on lipid bilayers, consisting of two monolayers or leaflets. One important but challenging physical parameter of these membranes is their tension. For a long time, this tension was explicitly or implicitly taken to be the bilayer tension, acting on the whole bilayer membrane. More recently, it has been realized that it is useful to decompose the bilayer tension into two leaflet tensions and that these tensions are accessible to molecular dynamics simulations. To divide the bilayer up into two leaflets, it is necessary to introduce a midsurface that defines the spatial extent of the two leaflets. In previous studies, this midsurface was obtained from the density profiles across the bilayer and was then used to compute the molecular area per lipid. Here, we develop an alternative approach based on three-dimensional Voronoi tessellation and molecular volume per lipid. Using this volume-based approach, we determine the reference states with tensionless leaflets as well as the optimal volumes and areas per lipid. The optimal lipid volumes have practically the same value in both leaflets, irrespective of the size and curvature of the nanovesicles, whereas the optimal lipid areas are different for the two leaflets and depend on the vesicle size. In addition, we introduce lateral volume compressibilities to describe the elastic response of the lipid volume to the leaflet tensions. We show that the outer leaflet of a nanovesicle is more densely packed and less compressible than the inner leaflet and that this difference becomes more pronounced for smaller vesicles.