Membrane lipid segregation in endocytosis

We explore the equilibrium mechanics of a binary lipid membrane that wraps around a spherical or cylindrical particle. One of the lipid membrane components induces a positive spontaneous curvature, while the other induces a negative local curvature. Using a Hamiltonian approach, we derive the equations governing the membrane shape and lipid concentrations near the wrapped object. Asymptotic expressions and numerical solutions for membrane shapes are presented. We determine the regimes of bending rigidity, surface tension, intrinsic lipid curvature, and effective receptor binding energies that lead to efficient wrapping and endocytosis. Our model is directly applicable to the study of invagination of clathrin-coated pits and receptor-induced wrapping of colloids such as spherical virus particles.