Diffuse interface model for fluid lipid vesicles with area-difference elasticity

Lipid bilayer membranes are fundamental biological barriers both at the cellular and sub-cellular level. They are both very stable and extremely deformable, characteristics that make membrane vesicles an efficient system for drug delivery applications. In most cases, due to the scale separation between the membrane thickness and the vesicle size, fluid lipid vesicles can be described as elastic sheets that deform as prescribed by a curvature dependent energy. At the same time, vesicle scale and membrane thickness may become simultaneously important in several key biological processes, such as vesicle fusion/fission, which are also pivotal steps for drug delivery. Recently, we provided a diffuse interface description of lipid vesicles that contains both the large scale of the vesicle and the small thickness of the membrane, allowing to account for multiscale effects in membrane fusion/fission (Bottacchiari et al. in PNAS Nexus 3:300, 2024). Here, after reviewing the main features of the approach and the related results, we analyze an additional term for the diffuse interface that takes into account the so-called area-difference elasticity, namely an energy term that considers the cost for the flip-flop motion of a lipid between the two monolayers constituting the bilayer membrane. Results are validated against those obtained with the (sharp-interface) area-difference elasticity model.