Lattice model for the kinetics of rupture of fluid bilayer membranes.

We have constructed a model for the kinetics of rupture of membranes under tension, applying physical principles relevant to lipid bilayers held together by hydrophobic interactions. The membrane is characterized by the bulk compressibility (for expansion) K, the thickness 2h(t) of the hydrophobic part of the bilayer, the hydrophobicity sigma, and a parameter gamma characterizing the tail rigidity of the lipids. The model is a lattice model which incorporates strain relaxation, and considers the nucleation of pores at constant area, constant temperature, and constant particle number. The particle number is conserved by allowing multiple occupancy of the sites. An equilibrium "phase diagram" is constructed as a function of temperature and strain with the total pore surface and distribution as the order parameters. A first-order rupture line is found with increasing tension, and a continuous increase in protopore concentration with rising temperature till instability. The model explains current results on saturated and unsaturated phosphatidylcholine lipid bilayers and thicker artificial bilayers made of diblock copolymers. Pore size distributions are presented for various values of area expansion and temperature, and the fractal dimension of the pore edge is evaluated.