  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 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. 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.
