  The wrapping equilibria of one and two adsorbing cylinders are studied along
a semi-flexible filament (polymer) due to the interplay between elastic
rigidity and short-range adhesive energy between the cylinder and the filament.
We show that statistical mechanics of the system can be solved exactly using a
path integral formalism which gives access to the full effect of thermal
fluctuations, going thus beyond the usual Gaussian approximations which take
into account only the contributions from the minimal energy configuration and
small fluctuations about this minimal energy solution. We obtain the free
energy of the wrapping-unwrapping transition of the filament around the
cylinders as well as the effective interaction between two wrapped cylinders
due to thermal fluctuations of the elastic filament. A change of entropy due to
wrapping of the filament around the adsorbing cylinders as they move closer
together is identified as an additional source of interactions between them.
Such entropic wrapping effects should be distinguished from the usual entropic
configuration effects in semi-flexible polymers. Our results may be applicable
to the problem of adsorption of proteins as well as synthetic nano-particles on
semi-flexible polymers such as DNA.
