Observing the base-by-base search for native structure along transition paths during the folding of single nucleic acid hairpins.

Biomolecular folding involves searching among myriad possibilities for the native conformation, but the elementary steps expected from theory for this search have never been detected directly. We probed the dynamics of folding at high resolution using optical tweezers, measuring individual trajectories as nucleic acid hairpins passed through the high-energy transition states that dominate kinetics and define folding mechanisms. We observed brief but ubiquitous pauses in the transition states, with a dwell time distribution that matched microscopic theories of folding quantitatively. The sequence dependence suggested that pauses were dominated by microbarriers from nonnative conformations during the search by each nucleotide residue for the native base-pairing conformation. Furthermore, the pauses were position dependent, revealing subtle local variations in energy-landscape roughness and allowing the diffusion coefficient describing the microscopic dynamics within the barrier to be found without reconstructing the shape of the energy landscape. These results show how high-resolution measurements can elucidate key microscopic events during folding to test fundamental theories of folding.

Structural dynamics of single SARS-CoV-2 pseudoknot molecules reveal topologically distinct conformers.

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.

Probing microscopic conformational dynamics in folding reactions by measuring transition paths.

Transition paths comprise those parts of a folding trajectory where the molecule passes through the high-energy transition states separating folded and unfolded conformations. The transition states determine the folding kinetics and mechanism but are difficult to observe because of their brief duration. Single-molecule experiments have in recent years begun to characterize transition paths in folding reactions, allowing the microscopic conformational dynamics that occur as a molecule traverses the energy barriers to be probed directly. Here we review single-molecule fluorescence and force spectroscopy measurements of transition-path properties, including the time taken to traverse the paths, the local velocity along them, the path shapes, and the variability within these measurements reflecting differences between individual barrier crossings. We discuss how these measurements have been related to theories of folding as diffusion over an energy landscape to deduce properties such as the diffusion coefficient, and how they are being combined with simulations to obtain enhanced atomistic understanding of folding. The richly detailed information available from transition path measurements holds great promise for improved understanding of microscopic mechanisms in folding.

Measuring the average shape of transition paths during the folding of a single biological molecule.

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(t|τ)〉 τ Whereas 〈t(x)〉 was close to straight, with only a subtle curvature, 〈x(t|τ)〉 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(t|τ)〉 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.

Transition-path properties for folding reactions in the limit of small barriers.

Transition paths are of great interest because they encapsulate information about the mechanisms of barrier-crossing reactions. Analysis of experiments measuring biomolecular folding reactions has relied on expressions for properties of transition paths such as transition-path times and velocities that hold in the limit of large harmonic barriers, but real molecules often have relatively small barriers. Recent theoretical work presented more general expressions for transition-path properties. Here we extend this work, deriving expressions from the general case that can be applied to small harmonic barriers. We first compared the performance of small-barrier, large-barrier, and general solutions when applied to simulated transitions, focusing on improvements in estimates of the diffusion coefficient determined from transition times and velocities. We then applied these expressions to experimental data from force spectroscopy measurements of DNA hairpins. We found that the low-barrier approximation and exact solution reduced or resolved the small but systematic inconsistencies that had arisen from assuming large harmonic barriers, demonstrating the practical utility of the new equations for analyzing experimental data.

Measuring the Local Velocity along Transition Paths during the Folding of Single Biological Molecules.

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.

Testing Kinetic Identities Involving Transition-Path Properties Using Single-Molecule Folding Trajectories.

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.