Adhesion of cylindrical colloids to the surface of a membrane

We study the system of cylindrical colloids adhering to an originally flat fluid membrane, on the basis of a full treatment of the Helfrich model. Our approach allows for numerical calculation of the free energy in both shallow-and deep-wrapping conformations. We show that the free energy of two cylinders adhering to the same side of a membrane has two branches corresponding to shallow and deep wrapping and that the system of two cylinders adhering to opposite sides of a membrane can undergo a first-order phase transition between two membrane-mediated attractive states.