| In this thesis, we develop and employ coarse-grained continuum models to investigate the structure and dynamics of compositional lipid microdomains in lipid bilayer membranes, both synthetic and natural. In the case of synthetic membranes, a novel diffuse-interface model is employed to study phase transition kinetics in immiscible lipid systems. The model couples the Cahn-Hilliard equation to the Stokes equation in order to assess the roles of membrane and solvent hydrodynamics on coarsening kinetics. In contrast to the conventional wisdom, simulation results demonstrate that compositional domain morphologies evolve in time in a non-self similar manner at large Peclet numbers, implying the breakdown of dynamical scaling.;In the case of natural membranes, a non-equilibrium model is developed to account for the presence of vesicular and non-vesicular lipid transport to and from the membrane in living cells. Simulations and analytical arguments imply that the emerging lipid microdomain structure is controlled by these lipid "recycling" processes. Furthermore, the spatial distribution and life times of lipid microdomains are also affected by membrane proteins. In particular, such proteins can both stabilize small domains and induce the growth of larger, spatially extended ones.;Finally, a comprehensive classification scheme for theoretical lipid microdomain formation scenarios is proposed, enabling the experimental verification/falsification of the scenarios based on structural and temporal correlation data. The feasibility of the method is demonstrated by developing a hybrid particle-continuum model to extract these correlations from simulated multiple particle tracking experiments. |
