Abstract
In dynamic force spectroscopy, single (bio-)molecular bonds are actively broken to assess their range and strength. At low loading rates, the experimentally measured statistical distributions of rupture forces can be analysed using Kramers’ theory of spontaneous unbinding. The essentially deterministic unbinding events induced by the extreme forces employed to speed up full-scale molecular simulations have been interpreted in mechanical terms, instead. Here we start from a rigorous probabilistic model of bond dynamics to develop a unified systematic theory that provides exact closed-form expressions for the rupture force distributions and mean unbinding forces, for slow and fast loading protocols. Comparing them with Brownian dynamics simulations, we find them to work well also at intermediate pulling forces. This renders them an ideal companion to Bayesian methods of data analysis, yielding an accurate tool for analysing and comparing force spectroscopy data from a wide range of experiments and simulations.
Highlights
In dynamic force spectroscopy, singlemolecular bonds are actively broken to assess their range and strength
Thanks to the development of a variety of nanomanipulation methods, intermolecular interactions can nowadays be investigated on a single-molecule level using a number of techniques commonly referred to as ‘dynamic force spectroscopy’[7,8,9,10,11,12], allowing the experimentalist to isolate single binding sites and probe their strength by quickly and reliably inducing hundreds or thousands of unbinding events
To extract quantitatively useful predictions from this simple model, any theory of unbinding kinetics needs to provide a reasonable approximation to the underlying molecular dynamics
Summary
In dynamic force spectroscopy, single (bio-)molecular bonds are actively broken to assess their range and strength. At the relatively low loading rates that were conventionally realized in experiments, any transient effects arising from the finite relaxation time of the bond itself can be neglected This has allowed for the development of a range of analytical theories of forced bond breaking that greatly facilitate the analysis and interpretation of dynamic force spectroscopy data[13,14,15,16,17,18]. We provide explicit, closed-form analytical results for the most common experimental loading protocols They agree with exact numerical simulations of the microscopic bond model for all loading rates, save for a narrow region at the crossover from diffusiondominated to deterministic dynamics. We show that these results constitute the lowestorder approximation to a rigorous mathematical formulation of escape kinetics, which opens the way of their systematic extension to higher precision
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