On the edge energy of lipid membranes and the thermodynamic stability of pores
To perform its barrier function, the lipid bilayer membrane requires a robust resistance against pore formation. Using a self-consistent field (SCF) theory and a molecularly detailed model for membranes composed of charged or zwitterionic lipids, it is possible to predict structural, mechanical, and thermodynamical parameters for relevant lipid bilayer membranes. We argue that the edge energy in membranes is a function of the spontaneous lipid monolayer curvature, the mean bending modulus, and the membrane thickness. An analytical Helfrich-like model suggests that most bilayers should have a positive edge energy. This means that there is a natural resistance against pore formation. Edge energies evaluated explicitly in a two-gradient SCF model are consistent with this. Remarkably, the edge energy can become negative for phosphatidylglycerol (e.g., dioleoylphosphoglycerol) bilayers at a sufficiently low ionic strength. Such bilayers become unstable against the formation of pores or the formation of lipid disks. In the weakly curved limit, we study the curvature dependence of the edge energy and evaluate the preferred edge curvature and the edge bending modulus. The latter is always positive, and the former increases with increasing ionic strength. These results point to a small window of ionic strengths for which stable pores can form as too low ionic strengths give rise to lipid disks. Higher order curvature terms are necessary to accurately predict relevant pore sizes in bilayers. The electric double layer overlap across a small pore widens the window of ionic strengths for which pores are stable.