Reversible bond kinetics from single-molecule force spectroscopy experiments close to equilibrium

Analysis of bond rupture data from single-molecule force spectroscopy experiments commonly relies on the strong assumption that the bond dissociation process is irreversible. However, with increased spatiotemporal resolution of instruments it is now possible to observe multiple unbinding-rebinding (or unfolding-refolding) events in a single pulling experiment. Here we augment the theory of force-induced unbinding by explicitly taking into account rebinding kinetics and provide approximate analytic solutions of the resulting rate equations. Furthermore, we use a short-time expansion of the exact kinetics to construct numerically efficient maximum likelihood estimators for the parameters of the force-dependent unbinding and rebinding rates, which pair well with and complement established methods, such as the analysis of rate maps. The estimators are independent of the applied force protocol and can therefore be used to globally analyze multiple force-extension traces for both force-ramp and force-clamp experiments. We provide an open-source implementation of the theory, evaluated for Bell-like rates, which we apply to synthetic data generated by a Gillespie stochastic simulation algorithm for time-dependent rates.