Lipid membranes with an edge

TLDR

An open lipid membrane with a free exposed edge has energy quadratic in extrinsic curvature and edge energy proportional to its length. The study aims to determine the boundary conditions satisfied by membrane equilibria at the free edge. The authors derive boundary conditions without assuming membrane symmetry and examine the effect of adding a Gaussian rigidity term. They find an additional boundary condition that vanishes in the axially symmetric limit and provide a physical interpretation based on force balance at the edge.

Abstract

Consider an open lipid membrane with a free exposed edge. The energy describing this membrane is quadratic in the extrinsic curvature; that describing the edge is proportional to its length. We determine the boundary conditions satisfied by the equilibria of the membrane on this edge. The derivation is free of any assumptions on the symmetry of the membrane geometry. With respect to the axially symmetric case, there is an additional boundary condition that is identically satisfied in that limit. By considering the balance of the forces operating at the edge, a physical interpretation for the boundary conditions is provided. The effect of the addition of a Gaussian rigidity term for the membrane is also considered.