  We investigate theoretically the effect of polymer tension on the collective
behavior of reversibly binding cross-links. For this purpose, we employ a model
of two weakly bending wormlike chains aligned in parallel by a tensile force,
with a sequence of inter-chain binding sites regularly spaced along the
contours. Reversible cross-links attach and detach at the sites with an
affinity controlled by a chemical potential. In a mean-field approach, we
calculate the free energy of the system and find the emergence of a free-energy
barrier which controls the reversible (un)binding. The tension affects the
conformational entropy of the chains which competes with the binding energy of
the cross-links. This competition gives rise to a sudden increase in the
fraction of bound sites as the tension increases. We show that this transition
is related to the cross-over between weak and strong localization of a directed
polymer in a pinning potential. The cross-over to the strongly bound state can
be interpreted as a mechanism for force-stiffening of cross-linked polymers --
beyond the elasticity of a single wormlike chain.
