Domain formation in membranes with quenched protein obstacles: Lateral heterogeneity and the connection to universality classes

We show that lateral fluidity in membranes containing quenched protein obstacles belongs to the universality class of the two-dimensional random-field Ising model. The main feature of this class is the absence of a phase transition: there is no critical point and macroscopic domain formation does not occur. Instead there is only one phase. This phase is highly heterogeneous with a structure consisting of microdomains. The presence of quenched protein obstacles thus provides a mechanism to stabilize lipid rafts in equilibrium. Crucial for two-dimensional random-field Ising universality is that the obstacles are randomly distributed and have a preferred affinity to one of the lipid species. When these conditions are not met standard Ising or diluted Ising universality applies. In these cases a critical point does exist which then marks the onset toward macroscopic demixing.