  This paper considers a broadly biologically relevant question of a chain
(such as a protein) binding to a sequence of receptors with matching multiple
ligands distributed along the chain. This binding is critical in cell adhesion
events, and in protein self-assembly. Using a mean field approximation of
polymer dynamics, we first calculate the characteristic binding time for a
tethered ligand reaching for a specific binding site on the surface. This time
is determined by two separate entropic effects: an entropic barrier for the
chain to be stretched sufficiently to reach the distant target, and a
restriction on chain conformations near the surface. We then derive the
characteristic time for a sequence of single binding events, and find that it
is determined by the `zipper effect', optimizing the sequence of single and
multiple binding steps.
