Coupled composition-deformation phase-field method for multicomponent lipid membranes

We present a method for modeling phase transitions and morphological evolution of binary lipid membranes with approximately planar geometries. The local composition and the shape of the membrane are coupled through composition-dependent spontaneous curvature in a Helfrich free energy. The evolution of the composition field is described by a Cahn-Hilliard-type equation, while shape changes are described by relaxation dynamics. Our method explicitly treats the full nonlinear form of the geometrical scalars, tensors, and differential operators associated with the curved shape of the membrane. The model is applied to examine morphological evolution and stability of lipid membranes initialized in a variety of compositional and geometric configurations. Specifically, we investigate the dynamics of systems which have a lamellar structure as their lowest energy state. We find that evolution is very sensitive to initial conditions; only membranes with sufficiently large lamellar-type compositional perturbations or ripple-type shape perturbations in their initial configuration can deterministically evolve into a lamellar equilibrium morphology. We also observe that rigid topographical surface patterns have a strong effect on the phase separation and compositional evolution in these systems.