Abstract
In a typical single-molecule force spectroscopy experiment, the ends of the molecule of interest are connected by long polymer linkers to a pair of mesoscopic beads trapped in the focus of two laser beams. At constant force load, the total extension, i.e., the end-to-end distance of the molecule plus linkers, is measured as a function of time. In the simplest systems, the measured extension fluctuates about two values characteristic of folded and unfolded states, with occasional transitions between them. We have recently shown that molecular (un)folding rates can be recovered from such trajectories, with a small linker correction, as long as the characteristic time of the bead fluctuations is shorter than the residence time in the unfolded (folded) state. Here, we show that accurate measurements of the molecular transition path times require an even faster apparatus response. Transition paths, the trajectory segments in which the molecule (un)folds, are properly resolved only if the beads fluctuate more rapidly than the end-to-end distance of the molecule. Therefore, over a wide regime, the measured rates may be meaningful but not the transition path times. Analytic expressions for the measured mean transition path times are obtained for systems diffusing anisotropically on a two-dimensional free energy surface. The transition path times depend on the properties both of the molecule and of the pulling device.
Highlights
We developed a quantitative theory of force spectroscopy experiments that accounts for the effects of the mesoscopic pulling device on the apparent rates of conformational transitions.1 Here, we adapt this theoretical framework to examine the effects of the measurement apparatus on the apparent transition path times
To the molecular mean transition path time along x, we find that the mean transition path times for the 2D and hopping models are about an order of magnitude larger than that of the molecule
Single-molecule force spectroscopy experiments are able to probe the transitions of individual biomolecules over high activation barriers, making it possible to characterize transition paths and transition states in protein and nucleic acid folding
Summary
We developed a quantitative theory of force spectroscopy experiments that accounts for the effects of the mesoscopic pulling device on the apparent rates of conformational transitions. Here, we adapt this theoretical framework to examine the effects of the measurement apparatus on the apparent transition path times. We developed a quantitative theory of force spectroscopy experiments that accounts for the effects of the mesoscopic pulling device on the apparent rates of conformational transitions.. We developed a quantitative theory of force spectroscopy experiments that accounts for the effects of the mesoscopic pulling device on the apparent rates of conformational transitions.1 We adapt this theoretical framework to examine the effects of the measurement apparatus on the apparent transition path times. The mean transition path time for protein folding was first determined experimentally by Chung and Eaton using single-molecule Forster resonance energy transfer (FRET) measurements. Using single-molecule force spectroscopy, Woodside and co-workers determined the mean and the distribution of the transition path times. Motivated by the success of these experiments, we concentrate on the effect of the measurement device on the transition paths
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