Dissociation rates from single-molecule pulling experiments under large thermal fluctuations or large applied force

Theories that are used to extract energy-landscape information from single-molecule pulling experiments in biophysics are all invariably based on Kramers' theory of the thermally activated escape rate from a potential well. As is well known, this theory recovers the Arrhenius dependence of the rate on the barrier energy and crucially relies on the assumption that the barrier energy is much larger than $k_\text{B}T$ (limit of comparatively low thermal fluctuations). As was shown already in Dudko $\textit{et al.}$ [Phys. Rev. Lett. 96, 108101 (2006)], this approach leads to the unphysical prediction of dissociation time increasing with decreasing binding energy when the latter is lowered to values comparable to $k_\text{B}T$ (limit of large thermal fluctuations). We propose a theoretical framework (fully supported by numerical simulations) which amends Kramers' theory in this limit and use it to extract the dissociation rate from single-molecule experiments where now predictions are physically meaningful and in agreement with simulations over the whole range of applied forces (binding energies). These results are expected to be relevant for a large number of experimental settings in single-molecule biophysics.EPSRC (Ph.D. studentship