Pattern Formation in Membranes with Quenched Disorder

The lateral heterogeneity in the plasma membrane of eukaryotic cells is an important factor for regulating biological functions. As opposed to plasma membranes, model membranes (either artificially prepared membranes, or membranes extracted from living cells) typically phase separate. To address this paradox, we present computer simulations of a coarse-grained membrane model that undergoes macroscopic phase separation at low temperature. Considering a coupling between local composition and local curvature of the membrane, we show that the system exhibits composition fluctuations with a nontrivial length scale, resembling microemulsion. The latter is identified as a region where lipid rafts can form. Additionally, we probe the nature of phase transition between the phase-separating regime and the mixed state. This transition is shown to be continuous and belongs to the two-dimensional Ising universality class for weak coupling to curvature, but becomes first-order for strong curvature-composition coupling. We furthermore consider the effect of quenched disorder, for example due to cytoskeleton network, on phase-separating model membranes in order to investigate physical mechanisms that prevent macroscopic phase separation in cells.