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

## TL;DR

This paper develops a new theoretical framework to accurately determine dissociation rates in single-molecule pulling experiments, especially under conditions of large thermal fluctuations or applied forces, improving upon traditional Kramers' theory.

## Contribution

The authors introduce a modified theoretical model supported by numerical simulations that extends Kramers' theory to regimes of large thermal fluctuations and applied forces.

## Key findings

- The new model provides physically meaningful dissociation rates across all force ranges.
- It aligns well with numerical simulations in both low and high thermal fluctuation regimes.
- The approach improves interpretation of single-molecule experiment data.

## Abstract

Theories that are used to extract energy-landscape information from single-molecule pulling experiments in biophysics are all invariably based on Kramers' theory of 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 $k_{B}T$ (limit of comparatively low thermal fluctuations). As was already shown in Dudko, Hummer, Szabo Phys. Rev. Lett. (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 $k_{B}T$ (limit of large thermal fluctuations). We propose a new 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.