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

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