Recent advances in statistical mechanical theory can be used to solve a fundamental problem in experimental thermodynamics. In 1997, Jarzynski proved an equality relating the irreversible work to the equilibrium free energy difference, DeltaG. This remarkable theoretical result states that it is possible to obtain equilibrium thermodynamic parameters from processes carried out arbitrarily far from equilibrium. We test Jarzynski's equality by mechanically stretching a single molecule of RNA reversibly and irreversibly between two conformations. Application of this equality to the irreversible work trajectories recovers the DeltaG profile of the stretching process to within k(B)T/2 (half the thermal energy) of its best independent estimate, the mean work of reversible stretching. The implementation and test of Jarzynski's equality provides the first example of its use as a bridge between the statistical mechanics of equilibrium and nonequilibrium systems. This work also extends the thermodynamic analysis of single molecule manipulation data beyond the context of equilibrium experiments.

Helicases are a ubiquitous class of enzymes involved in nearly all aspects of DNA and RNA metabolism. Despite recent progress in understanding their mechanism of action, limited resolution has left inaccessible the detailed mechanisms by which these enzymes couple the rearrangement of nucleic acid structures to the binding and hydrolysis of ATP 1,2 . Observing individual mechanistic cycles of these motor proteins is central to understanding their cellular functions. Here we follow in real time, at a resolution of two base pairs and 20 ms, the RNA translocation and unwinding cycles of a hepatitis C virus helicase (NS3) monomer. NS3 is a representative superfamily-2 helicase essential for viral replication 3 , and therefore a potentially important drug target 4 . We show that the cyclic movement of NS3 is coordinated by ATP in discrete steps of 11 ± 3 base pairs, and that actual unwinding occurs in rapid smaller substeps of 3.6 ± 1.3 base pairs, also triggered by ATP binding, indicating that NS3 might move like an inchworm 5,6 . This ATP-coupling mechanism is likely to be applicable to other non-hexameric helicases involved in many essential cellular functions. The assay developed here should be useful in investigating a broad range of nucleic acid translocation motors.NS3 is a key component of the hepatitis C virus (HCV) RNA replication machinery and lies in a membrane-bound complex with other proteins 7,8 . NS3 is an NTPase with 3′ to 5′ helicase activity 9,10 , and it has been structurally characterized in various contexts 11 . We have developed a single-molecule 12-16 assay for directly following the movement of full-length NS3 on its RNA substrate. Specifically, we use optical tweezers to apply a constant tension between two beads attached to the ends of a 60-base-pair (bp) RNA hairpin (Fig. 1a) and monitor the end-to-end distance change of the RNA as it is unwound by NS3. To establish the basis for interpretation of the enzymatic activity, we initially characterize the mechanical unfolding of the substrate in the absence of enzyme. The substrate unfolds at a force of 20.4 ± 0.2 pN (Fig. 1b). When the substrate is held at a constant force below 19 pN with the Reprints and permissions information is available at npg.nature.com/reprintsandpermissions. The authors declare no competing financial interests. Correspondence and requests for materials should be addressed to C.B. (carlos@alice.berkeley.edu).. * These authors contributed equally to this work.Supplementary Information is linked to the online version of the paper at www.nature.com/nature. To follow NS3-catalysed unwinding, we flow NS3 (1-90 nM) and ATP (0.05-1 mM) together in buffer U (see Methods). We then hold the RNA substrate at a constant force of between 5 and 17 pN. NS3 loads on its substrate by means of a 3 ′ single-stranded RNA loading site. As NS3 unwinds the hairpin, the bead separation increases so as to hold the force on the molecule constant (Fig. 1b). The bead separation can be converted, at that force, into the number of RNA base ...

Mechanical unfolding trajectories for single molecules of the Tetrahymena thermophila ribozyme display eight intermediates corresponding to discrete kinetic barriers that oppose mechanical unfolding with lifetimes of seconds and rupture forces between 10 and 30 piconewtons. Barriers are magnesium dependent and correspond to known intra-and interdomain interactions. Several barrier structures are "brittle," breakage requiring high forces but small (1 to 3 nanometers) deformations. Barrier crossing is stochastic, leading to variable unfolding paths. The response of complex RNA structures to locally applied mechanical forces may be analogous to the responses of RNA during translation, messenger RNA export from the nucleus, and viral replication.Numerous cellular processes, such as the translocation of mRNA through the ribosome and the action of RNA helicases and of RNA-dependent RNA polymerases, involve mechanical deformation and unfolding of RNA. Although the structure of RNAs and their folding thermodynamics and kinetics have been the focus of considerable inquiry, it has proven difficult to investigate their molecular responses to mechanical forces. Here, we use optical tweezers (1-3) to determine the strength and location of kinetic barriers opposing the unfolding of single molecules (4, 5) of the L-21 derivative of the Tetrahymena thermophila ribozyme (6-8), a 390-nucleotide (nt) catalytic RNA (Fig. 1A) whose three-dimensional structure (9), independently folding domains (10), intra-and interdomain contacts (11), and Mg 2+ -mediated tertiary interactions are well established. Figure 1B shows a typical force/extension curve obtained by unfolding and refolding a ribozyme molecule in Mg 2+ . The unfolding curve (black) shows six transitions corresponding to successive unfolding events. Thus, RNA unfolding in the presence of Mg 2+ and at loading rates of 3 to 5 pN s −1 is a "stick-slip" process (12): Unfolding temporarily arrests at kinetic barriers (arrows in Fig. 1B) until they yield, leading to a sudden increase in the extension of the RNA and a drop in the force. We refer to these features as "rips" and interpret them as the ‡To whom correspondence should be addressed.

The mitotic spindle assembles to a steady-state length at metaphase through the integrated action of molecular mechanisms that generate and respond to mechanical forces. While molecular mechanisms that produce force have been described, our understanding of how they integrate with each other, and with the assembly-disassembly mechanisms that regulate length, is poor. We review current understanding of the basic architecture and dynamics of the metaphase spindle, and some of the elementary force producing mechanisms. We then discuss models for force integration, and spindle length determination. We also emphasize key missing data that notably includes absolute values of forces, and how they vary as a function of position, within the spindle.