Modeling the electrostatic contribution to the line tension between lipid membrane domains using Poisson–Boltzmann theory

Abstract

The line tension, which characterizes the excess free energy per unit length of the boundary between different lipid membrane domains, is one of the factors that determines domain size and dynamics. Consequently, experimental methods and corresponding modeling studies related to the line tension continue to attract significant interest. Considering a planar binary lipid layer with two domains consisting of neutral and anionic lipids, one with a higher and one with a lower average surface charge density, we calculate the electrostatic contribution to the line tension at the domain boundary using mean-field electrostatics. The influence of lipid mobility in each phase is studied through solutions of the Poisson–Boltzmann equation for different sets of boundary conditions that include the limiting cases of fixing the local surface charge density or surface potential, and the intermediate case of allowing the lipids to migrate subject to a demixing entropy penalty. In addition to our numerical results, we derive simple analytic expressions for the electrostatic contribution to the line tension in the linearized Debye–Huckel limit. We find the electrostatic contribution to the line tension to be negative with magnitudes on the order of piconewton close to physiological conditions. Because this is comparable to experimentally reported values of the total line tension, we conclude that electrostatic interactions generally provide an important contribution to the total line tension between differently charged domains in lipid bilayers.