  Vesicle budding induced by protein binding that generates an isotropic
spontaneous curvature is studied using a mean-field theory. Many spherical buds
are formed via protein binding. As the binding chemical potential increases,
the proteins first bind to the buds and then to the remainder of the vesicle.
For a high spontaneous curvature and/or high bending rigidity of the bound
membrane, it is found that a first-order transition occurs between a small
number of large buds and a large number of small buds. These two states coexist
around the transition point. The proposed scheme is simple and easily
applicable to many interaction types, so we investigate the effects of
inter-protein interactions, the protein-insertion-induced changes in area, the
variation of the saddle-splay-modulus, and the area-difference-elasticity
energy. The differences in the preferred curvatures for curvature sensing and
generation are also clarified.
