Characterizing the resistance generated by a molecular bond as it is forcibly separated

The goal of measurements of the resisting force generated by a molecular bond as it is being forcibly separated under controlled conditions is to determine functional characteristics of the bond. Here, we establish the dependence of force history during unbinding on both those parameters chosen to characterize the bond itself and the controllable loading parameters. This is pursued for the practical range of behavior in which unbinding occurs diffusively rather than ballistically, building on the classic work of Kramers. For a bond represented by a one-dimensional energy landscape, modified by a second time-dependent energy profile representing applied loading, we present a mathematical analysis showing the dependence of the resistance of the bond-on-bond well shape, general time dependence of the imposed loading, and stiffness of the loading apparatus. The quality of the result is established through comparison with full numerical solutions of the underlying Smoluchowski equation.