Transition paths are the most interesting part of folding reactions but remain little studied. We measured the local velocity along transition paths in DNA hairpin folding using optical tweezers. The velocity distribution agreed well with diffusive theories, yielding the diffusion coefficient. We used the average velocity to calculate the transmission factor in transition-state theory (TST), finding observed rates that were ∼10^{5}-fold slower than predicted by TST. This work quantifies the importance of barrier recrossing events and highlights the effectiveness of the diffusive model of folding.

The RNA pseudoknot that stimulates programmed ribosomal frameshifting in SARS-CoV-2 is a possible drug target. To understand how it responds to mechanical tension applied by ribosomes, thought to play a key role during frameshifting, we probe its structural dynamics using optical tweezers. We find that it forms multiple structures: two pseudoknotted conformers with different stability and barriers, and alternative stem-loop structures. The pseudoknotted conformers have distinct topologies, one threading the 5′ end through a 3-helix junction to create a knot-like fold, the other with unthreaded 5′ end, consistent with structures observed via cryo-EM and simulations. Refolding of the pseudoknotted conformers starts with stem 1, followed by stem 3 and lastly stem 2; Mg2+ ions are not required, but increase pseudoknot mechanical rigidity and favor formation of the knot-like conformer. These results resolve the SARS-CoV-2 frameshift signal folding mechanism and highlight its conformational heterogeneity, with important implications for structure-based drug-discovery efforts.

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Transition paths represent the parts of a reaction where the energy barrier separating products and reactants is crossed. They are essential to understanding reaction mechanisms, yet many of their properties remain unstudied. Here, we report measurements of the average shape of transition paths, studying the folding of DNA hairpins as a model system for folding reactions. Individual transition paths were detected in the folding trajectories of hairpins with different sequences held under tension in optical tweezers, and path shapes were computed by averaging all transitions in the time domain, 〈t(x)〉, or by averaging transitions of a given duration in the extension domain, 〈x(tjτ)〉 τ . Whereas 〈t(x)〉 was close to straight, with only a subtle curvature, 〈x(tjτ)〉 τ had more pronounced curvature that fit well to theoretical expectations for the dominant transition path, returning diffusion coefficients similar to values obtained previously from independent methods. Simulations suggested that 〈t(x)〉 provided a less reliable representation of the path shape than 〈x(tjτ)〉 τ , because it was far more sensitive to the effects of coupling the molecule to the experimental force probe. Intriguingly, the path shape variance was larger for some hairpins than others, indicating sequence-dependent changes in the diversity of transition paths reflective of differences in the character of the energy barriers, such as the width of the barrier saddle-point or the presence of parallel paths through multiple barriers between the folded and unfolded states. These studies of average path shapes point the way forward for probing the rich information contained in path shape fluctuations. energy landscapes | diffusive reactions | DNA hairpins | optical tweezers T ransition paths involve those segments of a reaction during which the energy barrier between reactants and products is crossed (1, 2). They represent the most interesting part of any reaction because they exclude the nonproductive fluctuations, focusing only on the productive portions of the trajectories (Fig. 1). In particular, the high-energy states occupied along the transition paths dominate the reaction kinetics and effectively encode the reaction mechanism. Transition paths are especially interesting for understanding the folding of biological molecules like proteins and nucleic acids, because of the variety and complexity of possible mechanisms. They are technically challenging to measure in folding reactions, however, because they can only be observed in single molecules and have a very brief duration. As a result, it has only recently become possible to measure transition path properties directly (3). Work to date using fluorescence and force spectroscopy has probed properties such as the average transition path time for proteins and nucleic acids (4-8), the variations in transit times for individual transitions (9, 10), the occupancy statistics within transition paths (11,12), the distribution of velocities along the transition paths (13), and the agreement between expe...

Recent advances in single-molecule assays have allowed individual transition paths during the folding of single molecules to be observed directly. We used the transition paths of DNA hairpins having different sequences, measured with high-resolution optical tweezers, to test theoretical relations between the properties of the transition paths and the folding kinetics. We showed that folding and unfolding rates were related to the average transition-path times, as expected from theory, for all hairpins studied. We also found that the probability distribution of transition-path occupancies agreed with the profile of the average velocity along the transition paths for each of the hairpins, as expected theoretically. Finally, we used the latter result to show that the committor probability recovered from the velocity profile matches the committor measured empirically. These results validate the proposed kinetic identities.