On artifacts in single-molecule force spectroscopy

In typical force spectroscopy experiments, a small biomolecule is attached to a soft polymer linker that is pulled with a relatively large bead or cantilever. At constant force, the total extension stochastically changes between two (or more) values, indicating that the biomolecule undergoes transitions between two (or several) conformational states. In this paper, we consider the influence of the dynamics of the linker and mesoscopic pulling device on the force-dependent rate of the conformational transition extracted from the time dependence of the total extension, and the distribution of rupture forces in force-clamp and force-ramp experiments, respectively. For these different experiments, we derive analytic expressions for the observables that account for the mechanical response and dynamics of the pulling device and linker. Possible artifacts arise when the characteristic times of the pulling device and linker become comparable to, or slower than, the lifetimes of the metastable conformational states, and when the highly anharmonic regime of stretched linkers is probed at high forces. We also revisit the problem of relating force-clamp and force-ramp experiments, and identify a linker and loading rate-dependent correction to the rates extracted from the latter. The theory provides a framework for both the design and the quantitative analysis of force spectroscopy experiments by highlighting, and correcting for, factors that complicate their interpretation.