Abstract
Thermally activated energy-barrier crossing is ubiquitous in physical, chemical, and biological processes. Most barrier-crossing attempts have insufficient energy to overcome the barrier; hence, productive transition paths that successfully cross the barrier are very rare compared to nonproductive fluctuations that enter the barrier region but return without crossing it. Recent experimental advances have yielded important insights into transition paths, but nonproductive attempts remain little studied experimentally or theoretically, even though they can reveal information about parts of the reaction energy landscape not visited during transition paths. Observing the diffusive dynamics of a bead hopping between bistable optical traps as a model system, we measured the duration, maximum position along the reaction coordinate, and occupancy statistics of unsuccessful crossing attempts. Experimental results agreed quantitatively with expectations of an analytical framework we derived from committor theory. Applying these analyses to a more complex example, DNA hairpin folding under tension, we found that some properties differed from those of transition paths, such as the asymmetric occupancies for folding and unfolding attempts, whereas others were similar, such as the diffusion coefficient reflecting landscape roughness. These results show how nonproductive crossing attempts can be detected and analyzed rigorously, enabling characterization of the full dynamics within the transition region.
- Received 26 June 2023
- Revised 27 October 2023
- Accepted 17 November 2023
DOI:https://doi.org/10.1103/PhysRevX.14.011017
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Viewpoint
ViewpointFailed Barrier Crossings Tell a Story
Published 14 February 2024
Researchers have measured short-timescale fluctuations in metastable systems, uncovering information about failed attempts to cross the barriers that define the metastable state.
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Popular Summary
A wide range of phenomena in the physical and life sciences—from electron transport to protein folding—involves crossing energy barriers that separate initial and final states, driven by thermal fluctuations from the environment. Events having enough energy to cross the barrier are typically rare: Most crossing attempts are unsuccessful. The properties of unsuccessful crossing attempts remain largely unknown, even though they can contain information about regions of the barrier not explored during successful crossing events. Here, we explore these properties in two systems: a hopping bead and folding DNA.
We first watch a small bead hopping in a bistable potential defined by optical traps, extracting the unsuccessful hopping attempts from the bead trajectory. We find that properties of these unsuccessful attempts—such as their occupancy, duration, and maximum extent—match theoretical expectations when we extend transition-path theory to include unsuccessful attempts. We then repeat the analysis on the folding and unfolding of a DNA hairpin. Although fluctuations of the force probe made identifying barrier crossing attempts more difficult, unfolding attempts reaching far into the barrier region are described well by theory.
The ability to characterize and predict the properties of unsuccessful reaction attempts provides a more complete understanding of thermally activated barrier crossing dynamics and opens a new window on off-pathway reaction dynamics. Future applications include better characterization of unsuccessful protein folding attempts that lead to misfolding, which is implicated in numerous human diseases.
