Stable patterns of membrane domains at corrugated substrates

Multi-component membranes such as ternary mixtures of lipids and cholesterol can exhibit coexistence regions between two liquid phases. When such membranes adhere to a corrugated substrate, the phase separation process strongly depends on the interplay between substrate topography, bending rigidities, and line tension of the membrane domains as we show theoretically via energy minimization and Monte Carlo simulations. For sufficiently large bending rigidity contrast between the two membrane phases, the corrugated substrate truncates the phase separation process and leads to a stable pattern of membrane domains. Our theory is consistent with recent experimental observations and provides a possible control mechanism for domain patterns in biological membranes.