When do fluid membranes engulf sticky colloids?

Binding of a spherical colloid to a fluid membrane, which is an interplay between the energies of adhesion and elastic deformation, is studied within the framework of a Helfrich Hamiltonian. The solution of the full nonlinear shape equations for the membrane profile reveals a continuous binding and a discontinuous envelopment transition, the latter with a tension dependent substantial energy barrier. In the bending dominated regime this scenario is analytically confirmed by a small gradient expansion.