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 micro-domains. 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 apply. In these cases, a critical point does exist, marking the onset toward macroscopic demixing.