Shape transformations of vesicles with intramembrane domains

Phase separation within the lipid bilayer of vesicles can lead to the formation of domains that affect the equilibrium shape of these vesicles. As a result of the competition between the bending energy of the bilayer and the line energy of the domain boundaries, the domains induce the formation of buds if their size is sufficiently large. This phenomenon of domain-induced budding is studied both for freely adapting and for fixed volume. The phase diagrams show that the constraint on the volume acts against the budding process, but will not, in general, suppress it. In many situations, domain-induced budding leads to limit shapes for which the bud consists of a closed sphere that is connected to the ''mother'' vesicle by an infinitesimal neck. This neck is characterized by a general and simple neck condition for the mean curvature of the membrane segments adjacent to the neck. Budding also occurs if the Gaussian bending energy is taken into account. The effect of the Gaussian curvature energy is to change the structure and the stability of those shapes that exhibit small necks.