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We investigate theoretically the effect of polymer tension on the collectivebehavior of reversibly binding cross-links. For this purpose, we employ a modelof two weakly bending wormlike chains aligned in parallel by a tensile force,with a sequence of inter-chain binding sites regularly spaced along thecontours. Reversible cross-links attach and detach at the sites with anaffinity controlled by a chemical potential. In a mean-field approach, wecalculate the free energy of the system and find the emergence of a free-energybarrier which controls the reversible (un)binding. The tension affects theconformational entropy of the chains which competes with the binding energy ofthe cross-links. This competition gives rise to a sudden increase in thefraction of bound sites as the tension increases. We show that this transitionis related to the cross-over between weak and strong localization of a directedpolymer in a pinning potential. The cross-over to the strongly bound state canbe interpreted as a mechanism for force-stiffening of cross-linked polymers --beyond the elasticity of a single wormlike chain.

Tension-induced binding of semiflexible biopolymers