Strength of a weak bond connecting flexible polymer chains

Bond dissociation under steadily rising force occurs most frequently at a t ime governed by the rate of loading (Evans and Ritchie, 1997 Biophys. J. 72 :1541-1555). Multiplied by the loading rate, the breakage time specifies th e force for most frequent failure (called bond strength) that obeys the sam e dependence on loading rate. The spectrum of bond strength versus log(load ing rate) provides an image of the energy landscape traversed in the course of unbonding. However, when a weak bond is connected to very compliant ele ments like long polymers, the load applied to the bond does not rise steadi ly under constant pulling speed, Because of nonsteady loading, the most fre quent breakage force can differ significantly from that of a bond loaded at constant rate through stiff linkages. Using generic models for wormlike an d freely jointed chains, we have analyzed the kinetic process of failure fo r a bond loaded by pulling the polymer linkages at constant speed. We find that when linked by either type of polymer chain, a bond is likely to fail at lower force under steady separation than through stiff linkages. Quite u nexpectedly, a discontinuous jump can occur in bond strength at slow separa tion speed in the case of long polymer linkages. We demonstrate that the pr edictions of strength versus log(loading rate) can rationalize conflicting results obtained recently for unfolding Ig domains along muscle titin with different force techniques.