Atomic force microscopes and optical tweezers are widely used to probe the mechanical properties of individual molecules and molecular interactions, by exerting mechanical forces that induce transitions such as unfolding or dissociation. These transitions often occur under nonequilibrium conditions and are associated with hysteresis effects-features usually taken to preclude the extraction of equilibrium information from the experimental data. But fluctuation theorems 1-5 allow us to relate the work along nonequilibrium trajectories to thermodynamic free-energy differences. They have been shown to be applicable to single-molecule force measurements 6 and have already provided information on the folding free energy of a RNA hairpin 7,8 . Here we show that the Crooks fluctuation theorem 9 can be used to determine folding free energies for folding and unfolding processes occurring in weak as well as strong nonequilibrium regimes, thereby providing a test of its validity under such conditions. We use optical tweezers 10 to measure repeatedly the mechanical work associated with the unfolding and refolding of a small RNA hairpin 11 and an RNA three-helix junction 12 . The resultant work distributions are then analysed according to the theorem and allow us to determine the difference in folding free energy between an RNA molecule and a mutant differing only by one base pair, and the thermodynamic stabilizing effect of magnesium ions on the RNA structure.The Crooks fluctuation theorem 9 (CFT) predicts a symmetry relation in the work fluctuations associated with the forward and reverse changes a system undergoes as it is driven away from thermal equilibrium by the action of an external perturbation. This theorem applies to processes that are microscopically reversible, and its experimental evaluation in small systems is crucial to understand better the foundations of nonequilibrium physics 13 . A consequence of the CFT is Jarzynski's equality 14 , which relates the equilibrium free-energy difference ΔG between two equilibrium states to an exponential average (denoted by angle brackets) of the work done on the system, W, taken over an infinite number of repeated none-quilibrium experiments, exp The equality has been developed 6 into a formalism that allows us to use nonequilibrium single-molecule pulling experiments to reconstruct free-energy profiles or potentials of mean force 15 along reaction coordinates. Experimental testing of Jarzynski's equality in single-molecule force experiments 16 used the P5ab RNA hairpin 7,8 , which can be folded and unfolded quasi-reversibly. But for processes that occur far from equilibrium, the applicability of Jarzynski's equality is hampered by large statistical uncertainties that arise from the sensitivity of the exponential average to rare events 17,18 (low values of W). Moreover, although the equality 〈W〉 = ΔG holds for processes occurring near equilibrium, spatial drift in the experimental system usually makes it difficult in practice to extract unfolding free energies using...

Mechanical unfolding and refolding of single RNA molecules have previously been observed in optical traps as sudden changes in molecular extension. Two methods have been traditionally used: "force-ramp", with the applied force continuously changing, and "hopping". In hopping experiments the force is held constant and the molecule jumps spontaneously between two different states. Unfolding/refolding rates are measured directly, but only over a very narrow range of forces. We have now developed a force-jump method to measure the unfolding and refolding rates independently over a wider range of forces. In this method, the applied force is rapidly stepped to a new value and either the unfolding or refolding event is monitored through changes in the molecular extension. The force-jump technique is compared to the force-ramp and hopping methods by using a 52-nucleotide RNA hairpin with a three-nucleotide bulge, i.e., the transactivation response region RNA from the human immunodeficiency virus. We find the unfolding kinetics and Gibbs free energies obtained from all three methods to be in good agreement. The transactivation response region RNA hairpin unfolds in an all-or-none two-state reaction at any loading rate with the force-ramp method. The unfolding reaction is reversible at small loading rates, but shows hysteresis at higher loading rates. Although the RNA unfolds and refolds without detectable intermediates in constant-force conditions (hopping and force-jump), it shows partially folded intermediates in force-ramp experiments at higher unloading rates. Thus, we find that folding of RNA hairpins can be more complex than a simple single-step reaction, and that application of several methods can improve understanding of reaction mechanisms.

We apply Kramers theory to investigate the dissociation of multiple bonds under mechanical force and interpret experimental results for the unfolding and refolding force distributions of an RNA hairpin pulled at different loading rates using laser tweezers. We identify two different kinetic regimes depending on the range of forces explored during the unfolding and refolding process. The present approach extends the range of validity of the two-states approximation by providing a theoretical framework to reconstruct free-energy landscapes and identify force-induced structural changes in molecular transition states using single molecule pulling experiments. The method should be applicable to RNA hairpins with multiple kinetic barriers.

The nuclear receptor retinoid acid receptor-related orphan receptor γt (RORγt) is a master regulator of the Th17/IL-17 pathway that plays crucial roles in the pathogenesis of autoimmunity. RORγt has recently emerged as a highly promising target for treatment of a number of autoimmune diseases. Through high-throughput screening, we previously identified several classes of inverse agonists for RORγt. Here, we report the crystal structures for the ligand-binding domain of RORγt in both apo and ligand-bound states. We show that apo RORγt adopts an active conformation capable of recruiting coactivator peptides and present a detailed analysis of the structural determinants that stabilize helix 12 (H12) of RORγt in the active state in the absence of a ligand. The structures of ligand-bound RORγt reveal that binding of the inverse agonists disrupts critical interactions that stabilize H12. This destabilizing effect is supported by calculations and experimentally by a normalized crystallographic B-factor analysis. Of note, the H12 destabilization in the active state shifts the conformational equilibrium of RORγt toward an inactive state, which underlies the molecular mechanism of action for the inverse agonists reported here. Our findings highlight that nuclear receptor structure and function are dictated by a dynamic conformational equilibrium and that subtle changes in ligand structures can shift this equilibrium in opposite directions, leading to a functional switch from agonists to inverse agonists.

UV melting curves of mono- and di-2‘-hydroxylated cytosine tetrads were recorded. The substitution of one DNA residue by RNA decreased the melting temperature (T m) by roughly 6.5 °C. In sequences with two RNA residues, strong positional effects were observed. Juxtaposition of the two d-ribose sugars in the tetrad incurred an additional loss of 6 °C in tetrad stability and decreased the T m by 19 °C from that of the parent compound, d(TCCCCC)4. The effect of increasing the number of cytosines on tetrad stability was also measured. Addition (or removal) of one cytosine-protonated cytosine base-pair from the tetrad increased (or decreased) the T m by roughly 9 °C. Thus, the penalty of adding an RNA residue is equal to or greater than the benefit of the additional base-pair. This implies that the stability of RNA cytosine tetrads should not rise with increasing length and that thermal transitions previously observed in poly(rC) correspond to duplex structures.

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We have used laser tweezers to unfold single RNA molecules at room temperature and in physiological-type solvents. The forces necessary to unfold the RNAs are over the range 10-20 pN, forces that can be generated by cellular enzymes. The Gibbs free energy for the unfolding of TAR (transactivation-responsive) RNA from HIV was found to be increased after the addition of argininamide; the TAR hairpin was stabilized. The rate of unfolding was decreased and the rate of folding was increased by argininamide.

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