Tension-induced binding of semiflexible biopolymers

We investigate theoretically the effect of polymer tension on the collective behaviour of reversible cross-links. We use a model of two parallel-aligned, weakly-bending wormlike chains with a regularly spaced sequence of binding sites subjected to a tensile force. Reversible cross-links attach and detach at the binding sites with an affinity controlled by a chemical potential. In a mean-field approach, we calculate the free energy of the system and we show 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 polymer tension increases. The force-induced first-order transition in the number of cross-links implies a sudden force-induced stiffening of the effective stretching modulus of the polymers. This mechanism may be relevant to the formation and stress-induced strengthening of stress fibers in the cytoskeleton.