Reaching to a small target: entropic barriers and rates of specific binding of polymer to substrate

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.