Pattern formation of phase-separated lipid domains in membranes

Giant unilamellar vesicles (GUVs) composed of as few as three lipid species are able to phase separate into small-scale lipid domains on their membranes. Experimentally, the domains are found in both stripes and dots patterns, and the pattern's characteristic size and morphology vary with temperature, membrane tension, and lipid composition [Cornell et al., Biophys. J. 2018]. Here, we present a theoretical model that explains existing observations and makes predictions for future experiments. Our model takes into account the free energy of interactions and mixing of lipids, the elastic deformation energy of membranes, as well as the coupling between the local lipid composition and preferred membrane curvature. This coupling contributes to the selection of a preferred length scale for the emerging phase-separated lipid domains. We also determined the stable morphology of patterns (dots/stripes) by an analysis similar to the Swift-Hohenberg problem. The theory is verified by simulations, which confirm the existence of dots and stripes patterns and elucidate how the resulting patterns depend on parameters that can be controlled in the laboratory. We predict the hysteresis of patterns as a function of these parameters, which can be tested experimentally. Overall, this work helps improve our understanding of pattern formation due to liquid-liquid phase separation on curved surfaces.