Coupling between line tension and domain contact angle in heterogeneous membranes

The compositional differences between domains in phase-separated membranes are associated with differences in bilayer thickness and moduli. The resulting packing deformation at the phase boundary gives rise to a line tension, the one dimensional equivalent of surface tension. In this paper we calculate the line tension between a large membrane domain and a continuous phase as a function of the thickness mismatch and the contact angle between the phases. We find that the packing-induced line tension is sensitive to the contact angle, reaching a minimum at a specific value. The difference in the line tension between a flat domain (that is within the plane of the continuous phase) and a domain at the optimal contact angle may be of order 40%. This could explain why previous calculations of the thickness mismatch based line tension tend to yield values that are higher than those measured experimentally.