Probing Position-Dependent Diffusion in Folding Reactions Using Single-Molecule Force Spectroscopy.

Folding of proteins and nucleic acids involves a diffusive search over a multidimensional conformational energy landscape for the minimal-energy structure. When examining the projection of conformational motions onto a one-dimensional reaction coordinate, as done in most experiments, the diffusion coefficient D is generally position dependent. However, it has proven challenging to measure such position-dependence experimentally. We investigated the position-dependence of D in the folding of DNA hairpins as a simple model system in two ways: first, by analyzing the round-trip time to return to a given extension in constant-force extension trajectories measured by force spectroscopy, and second, by analyzing the fall time required to reach a given extension in force jump measurements. These methods yielded conflicting results: the fall time implied a fairly constant D, but the round-trip time implied variations of over an order of magnitude. Comparison of experiments with computational simulations revealed that both methods were strongly affected by experimental artifacts inherent to force spectroscopy measurements, which obscured the intrinsic position-dependence of D. Lastly, we applied Kramers's theory to the kinetics of hairpins with energy barriers located at different positions along the hairpin stem, as a crude probe of D at different stem positions, and we found that D did not vary much as the barrier was moved along the reaction coordinate. This work underlines the difficulties faced when trying to deduce position-dependent diffusion coefficients from experimental folding trajectories.

Direct observation of transition paths during the folding of proteins and nucleic acids.

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.

Reconstructing folding energy landscape profiles from nonequilibrium pulling curves with an inverse Weierstrass integral transform.

The energy landscapes that drive structure formation in biopolymers are difficult to measure. Here we validate experimentally a novel method to reconstruct landscape profiles from single-molecule pulling curves using an inverse Weierstrass transform (IWT) of the Jarzysnki free-energy integral. The method was applied to unfolding measurements of a DNA hairpin, replicating the results found by the more-established weighted histogram (WHAM) and inverse Boltzmann methods. Applying both WHAM and IWT methods to reconstruct the folding landscape for a RNA pseudoknot having a stiff energy barrier, we found that landscape features with sharper curvature than the force probe stiffness could not be recovered with the IWT method. The IWT method is thus best for analyzing data from stiff force probes such as atomic force microscopes.

Transition path times for nucleic Acid folding determined from energy-landscape analysis of single-molecule trajectories.

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.

Programmed -1 frameshifting efficiency correlates with RNA pseudoknot conformational plasticity, not resistance to mechanical unfolding.

Programmed -1 frameshifting, whereby the reading frame of a ribosome on messenger RNA is shifted in order to generate an alternate gene product, is often triggered by a pseudoknot structure in the mRNA in combination with an upstream slippery sequence. The efficiency of frameshifting varies widely for different sites, but the factors that determine frameshifting efficiency are not yet fully understood. Previous work has suggested that frameshifting efficiency is related to the resistance of the pseudoknot against mechanical unfolding. We tested this hypothesis by studying the mechanical properties of a panel of pseudoknots with frameshifting efficiencies ranging from 2% to 30%: four pseudoknots from retroviruses, two from luteoviruses, one from a coronavirus, and a nonframeshifting bacteriophage pseudoknot. Using optical tweezers to apply tension across the RNA, we measured the distribution of forces required to unfold each pseudoknot. We found that neither the average unfolding force, nor the unfolding kinetics, nor the parameters describing the energy landscape for mechanical unfolding of the pseudoknot (energy barrier height and distance to the transition state) could be correlated to frameshifting efficiency. These results indicate that the resistance of pseudoknots to mechanical unfolding is not a primary determinant of frameshifting efficiency. However, increased frameshifting efficiency was correlated with an increased tendency to form alternate, incompletely folded structures, suggesting a more complex picture of the role of the pseudoknot involving the conformational dynamics.

Single-molecule force spectroscopy of the add adenine riboswitch relates folding to regulatory mechanism.

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.

Direct observation of hierarchical folding in single riboswitch aptamers.

Riboswitches regulate genes through structural changes in ligand-binding RNA aptamers. With the use of an optical-trapping assay based on in situ transcription by a molecule of RNA polymerase, single nascent RNAs containing pbuE adenine riboswitch aptamers were unfolded and refolded. Multiple folding states were characterized by means of both force-extension curves and folding trajectories under constant force by measuring the molecular contour length, kinetics, and energetics with and without adenine. Distinct folding steps correlated with the formation of key secondary or tertiary structures and with ligand binding. Adenine-induced stabilization of the weakest helix in the aptamer, the mechanical switch underlying regulatory action, was observed directly. These results provide an integrated view of hierarchical folding in an aptamer, demonstrating how complex folding can be resolved into constituent parts, and supply further insights into tertiary structure formation.