Composition-driven shape transformations of membranes of complex topology

The shape of a phase-separated two-component membrane, which forms a square lattice of passages, is investigated in the strong-segregation limit. We employ a model, in which the composition of the membrane is coupled to the spontaneous curvature. The shapes of both the membrane and the interface between the two components an calculated as a function of composition. We predict a phase transition between two different domain morphologies. In the limit of vanishing line tension, we conjecture the existence of smooth, piecewise constant mean-curvature surfaces.