Transition paths, the fleeting trajectories through the transition states that dominate the dynamics of biomolecular folding reactions, encapsulate the critical information about how structure forms. Owing to their brief duration, however, they have not previously been observed directly. We measured transition paths for both nucleic acid and protein folding, using optical tweezers to observe the microscopic diffusive motion of single molecules traversing energy barriers. The average transit times and the shapes of the transit-time distributions agreed well with theoretical expectations for motion over the one-dimensional energy landscapes reconstructed for the same molecules, validating the physical theory of folding reactions. These measurements provide a first look at the critical microscopic events that occur during folding, opening exciting new avenues for investigating folding phenomena.

Riboswitches regulate gene expression via ligand binding to an aptamer domain which induces conformational changes in a regulatory expression platform. By unfolding and refolding single add adenine riboswitch molecules in an optical trap, an integrated picture of the folding was developed and related to the regulatory mechanism. Force-extension curves (FECs) and constant-force folding trajectories measured on the aptamer alone revealed multiple partially-folded states, including several misfolded states not on the native folding pathway. All states were correlated to key structural components and interactions within hierarchical folding pathways. FECs of the full-length riboswitch revealed that the thermodynamically stable conformation switches upon ligand binding from a structure repressing translation to one permitting it. Along with rapid equilibration of the two structures in the absence of adenine, these results support a thermodynamically-controlled regulatory mechanism, in contrast with the kinetic control of the closely-related pbuE adenine riboswitch. Comparison of the folding of these riboswitches revealed many similarities arising from shared structural features but also essential differences related to their different regulatory mechanisms.

Free-energy-landscape formalisms provide the fundamental conceptual framework for physical descriptions of how proteins and nucleic acids fold into specific three-dimensional structures 1,2 . Although folding landscapes are difficult to measure experimentally, recent theoretical work by Hummer and Szabo 3 has shown that landscape profiles can be reconstructed from non-equilibrium single-molecule force spectroscopy measurements using an extension of the Jarzynski equality 4 . This method has been applied to simulations 5,6 and experiments 7,8 but never validated experimentally. We tested it using force-extension measurements on DNA hairpins with distinct, sequence-dependent folding landscapes. Quantitative agreement was found between the landscape profiles obtained from the non-equilibrium reconstruction and those from equilibrium probability distributions 9 . We also tested the method on a riboswitch aptamer with three partially folded intermediate states, successfully reconstructing the landscape but finding some states difficult to resolve owing to low occupancy or overlap of the potential wells. These measurements validate the landscape-reconstruction method and provide a new test of non-equilibrium work relations.Folding-landscape formalisms have broad applications in biophysics, from improving predictive structural models and protein engineering 10,11 to providing crucial insights into biomolecular structure, dynamics, function and disease 12,13 . Specific characteristics of folding landscapes, such as the roughness of the free-energy surface 14 or the properties of partially folded intermediate 15 and transition states 16 , including how they are altered by temperature changes, solvent substitutions or mutations 17 , have been widely studied by experiment and theory. However, it has proven remarkably challenging to go beyond such isolated features and measure the entire profile of the free-energy landscape along the reaction coordinate.Single-molecule force spectroscopy provides a unique window into folding reactions because of its ability to measure properties of the free-energy landscape. In single-molecule force spectroscopy, a single molecule is held under mechanical tension by a spring-like force probe such as an optical trap or atomic force microscope, and the end-to-end extension of the molecule is recorded while the molecule folds/unfolds under the influence of the denaturing force (Fig. 1a). By this means, the folding energies and rates, partially folded intermediates and similar characteristics may be explored 18 . Measurements can be made either in the equilibrium regime (for example, by maintaining a constant force using an active 19 1 Department of Physics, University of Alberta, 11322-89 Ave, Edmonton AB, T6G 2G7, Canada, 2 National Institute for Nanotechnology, 11421 Saskatchewan Dr, Edmonton AB, T6G 2M9, Canada. † These authors contributed equally to this work. *e-mail: Michael.woodside@nrc-cnrc.gc.ca. or passive 20 force clamp) or in the non-equilibrium regime (for example, by ramping the ...

The duration of structural transitions in biopolymers is only a fraction of the time spent searching diffusively over the configurational energy landscape. We found the transition time, τ(TP), and the diffusion constant, D, for DNA and RNA folding using energy landscapes obtained from single-molecule trajectories under tension in optical traps. DNA hairpins, RNA pseudoknots, and a riboswitch all had τ(TP)~10 μs and D~10(-13-14) m(2)/s, despite widely differing unfolding rates. These results show how energy-landscape analysis can be harnessed to characterize brief but critical events during folding reactions.