On artifacts in single-molecule force spectroscopy

Abstract

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 ratedependent 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.anisotropic diffusion | free energy surface | pulling device | unfolding rate T he mechanical manipulation of single molecules by laser tweezers or atomic force microscopes has led to remarkable insights into how biomolecules respond to external forces. In conceptually the simplest experiment, a single molecule is connected by a flexible polymer linker to a bead, say a micrometer in diameter, that is trapped in the focus of a laser beam. The position of this beam is adjusted so that the force on the construct is kept constant (see Fig. 1A). Suppose the molecule of interest can exist in folded and unfolded states, and that the applied force is chosen so that the populations of these states are about equal. Then the total extension hops between short (i.e., folded) and long (i.e., unfolded) values (see Fig. 1B). From such trajectories, one can extract the folding and unfolding rates. These observables are commonly analyzed using the phenomenological BellEvans model (1, 2), which ignores the possible influence of the "apparatus" that we define here as both the linker and the bead. The same is true of the simplest microscopic descriptions of force-induced transitions, where the dynamics is described as diffusion along the molecular (not total) extension, in the presence of a force-dependent free energy profile (3-7). However, such a description would be rigorously valid only when the response of the apparatus is much faster than the fluctuations of the molecular extension. In reality, this is far from being true, and, in principle, the observed transition rate...

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“…13,15,24 In practice, all these paths are similar, as illustrated by the above comparison between the values of the transition path velocity at the top of the barrier estimated using Eq. (22) and using the theory of dominant transition paths in Ref. 15.…”

“…Our analysis would then still apply to the dynamics of the observed quantity y(t), but recovering the intrinsic properties of x(t) may require explicit consideration of the coupling between the instrument and the molecule of interest, possibly along the lines of Refs. 22 …”

“…5 These studies have attracted considerable theoretical attention. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] One hopes that such data could provide a direct experimental answer to the question: what kind of motion is the dynamics along a reaction coordinate x? Based on decades of simulation studies of solution-phase dynamics, we expect that a transition from a reactant A to a product B does not occur in a straight shot.…”

Direct Measurement of Sequence-Dependent Transition Path Times and Conformational Diffusion in DNA Duplex Formation

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“…Having attracted recent attention, [48][49][50] such artifacts can be accounted for by introducing an additional degree of freedom describing the instrument itself.…”