Wrapping of a spherical colloid by a fluid membrane

We theoretically study the elastic deformation of a fluid membrane induced by an adhering spherical colloidal particle within the framework of a Helfrich energy. Based on a full optimization of the membrane shape we find a continuous binding and a discontinuous envelopment transition, the latter displaying a potentially substantial energy barrier. A small-gradient approximation permits membrane shape and complex energy to be calculated analytically. While this only leads to a good representation of the complex geometry for very small degrees of wrapping, it still gives the correct phase boundaries in the regime of low tension.