Search

We investigate the work dissipated during the irreversible unfolding of single molecules by mechanical force, using the simplest model necessary to represent experimental data. The model consists of two levels (folded and unfolded states) separated by an intermediate barrier. We compute the probability distribution for the dissipated work and give analytical expressions for the average and variance of the distribution. To first order, the amount of dissipated work is directly proportional to the rate of application of force (the loading rate) and to the relaxation time of the molecule. The model yields estimates for parameters that characterize the unfolding kinetics under force in agreement with those obtained in recent experimental results. We obtain a general equation for the minimum number of repeated experiments needed to obtain an equilibrium free energy, to within [k.sub.B]T, from nonequilibrium experiments by using the Jarzynski formula. The number of irreversible experiments grows exponentially with the ratio of the average dissipated work, [W.sub.dis] to [k.sub.B]T.

The movement of ribosomes on mRNA is often interrupted by secondary structures that present mechanical barriers and play a central role in translation regulation. We investigate how ribosomes couple their internal conformational changes with the activity of translocation factor EF-G to unwind mRNA secondary structures using high-resolution optical tweezers with single-molecule fluorescence capability. We find that hairpin opening occurs during EF-G-catalyzed translocation and is driven by the forward rotation of the small subunit head. Modulating the magnitude of the hairpin barrier by force shows that ribosomes respond to strong barriers by shifting their operation to an alternative 7-fold-slower kinetic pathway prior to translocation. Shifting into a slow gear results from an allosteric switch in the ribosome that may allow it to exploit thermal fluctuations to overcome mechanical barriers. Finally, we observe that ribosomes occasionally open the hairpin in two successive sub-codon steps, revealing a previously unobserved translocation intermediate., (Copyright © 2019 Elsevier Inc. All rights reserved.)

In recent years, highly stable optical tweezers systems have enabled the characterization of the dynamics of molecular motors at very high resolution. However, the motion of many motors with angstrom-scale dynamics cannot be consistently resolved due to poor signal-to-noise ratio. Using an acousto-optic deflector to generate a "time-shared" dual-optical trap, we decreased low-frequency noise by more than one order of magnitude compared with conventional dual-trap optical tweezers. Using this instrument, we implemented a protocol that synthesizes single base-pair trajectories, which are used to test a Large State Space Hidden Markov Model algorithm to recover their individual steps. We then used this algorithm on real transcription data obtained in the same instrument to fully uncover the molecular trajectories of Escherichia coli RNA polymerase. We applied this procedure to reveal the effect of pyrophosphate on the distribution of dwell times between consecutive polymerase steps., Competing Interests: Conflict of interest statement: C.B. and D.J.K. are collaborating on a forthcoming book., (Copyright © 2018 the Author(s). Published by PNAS.)

Programmed -1 ribosomal frameshifting (-1PRF) is tightly regulated by messenger RNA (mRNA) sequences and structures in expressing two or more proteins with precise ratios from a single mRNA. Using single-molecule fluorescence resonance energy transfer (smFRET) between (Cy5)EF-G and (Cy3)tRNALys, we studied the translational elongation dynamics of -1PRF in the Escherichia coli dnaX gene, which contains three frameshifting signals: a slippery sequence (A AAA AAG), a Shine-Dalgarno (SD) sequence and a downstream hairpin. The frameshift promoting signals mostly impair the EF-G-catalyzed translocation step of the two tRNALys and the slippery codons from the A- and P- sites. The hairpin acts as a road block slowing the translocation rate. The upstream SD sequence together with the hairpin promotes dissociation of futile EF-G and thus causes multiple EF-G driven translocation attempts. A slippery sequence also helps dissociation of the EF-G by providing alternative base-pairing options. These results indicate that frameshifting takes place during the repetitive ribosomal conformational changes associated with EF-G dissociation upon unsuccessful translocation attempts of the second slippage codon from the A- to the P- sites., (© The Author(s) 2016. Published by Oxford University Press on behalf of Nucleic Acids Research.)

My personal view of ethical behavior as a scientific researcher in an academic environment is presented. I discuss the behavior of a graduate student, a postdoctoral, and a professor. Ethical behavior in teaching, choosing a research project, publishing papers, and obtaining a job is discussed., (© 2014 Wiley Periodicals, Inc.)

Protein synthesis rates can affect gene expression and the folding and activity of the translation product. Interactions between the nascent polypeptide and the ribosome exit tunnel represent one mode of regulating synthesis rates. The SecM protein arrests its own translation, and release of arrest at the translocon has been proposed to occur by mechanical force. Using optical tweezers, we demonstrate that arrest of SecM-stalled ribosomes can indeed be rescued by force alone and that the force needed to release stalling can be generated in vivo by a nascent chain folding near the ribosome tunnel exit. We formulate a kinetic model describing how a protein can regulate its own synthesis by the force generated during folding, tuning ribosome activity to structure acquisition by a nascent polypeptide., (Copyright © 2015, American Association for the Advancement of Science.)

Programmed ribosomal frameshifting produces alternative proteins from a single transcript. -1 frameshifting occurs on Escherichia coli's dnaX mRNA containing a slippery sequence AAAAAAG and peripheral mRNA structural barriers. Here, we reveal hidden aspects of the frameshifting process, including its exact location on the mRNA and its timing within the translation cycle. Mass spectrometry of translated products shows that ribosomes enter the -1 frame from not one specific codon but various codons along the slippery sequence and slip by not just -1 but also -4 or +2 nucleotides. Single-ribosome translation trajectories detect distinctive codon-scale fluctuations in ribosome-mRNA displacement across the slippery sequence, representing multiple ribosomal translocation attempts during frameshifting. Flanking mRNA structural barriers mechanically stimulate the ribosome to undergo back-and-forth translocation excursions, broadly exploring reading frames. Both experiments reveal aborted translation around mutant slippery sequences, indicating that subsequent fidelity checks on newly adopted codon position base pairings lead to either resumed translation or early termination., (Copyright © 2015 Elsevier Inc. All rights reserved.)

Ribosomal frameshifting occurs when a ribosome slips a few nucleotides on an mRNA and generates a new sequence of amino acids. Programmed -1 ribosomal frameshifting (-1PRF) is used in various systems to express two or more proteins from a single mRNA at precisely regulated levels. We used single-molecule fluorescence resonance energy transfer (smFRET) to study the dynamics of -1PRF in the Escherichia coli dnaX gene. The frameshifting mRNA (FSmRNA) contained the frameshifting signals: a Shine-Dalgarno sequence, a slippery sequence, and a downstream stem loop. The dynamics of ribosomal complexes translating through the slippery sequence were characterized using smFRET between the Cy3-labeled L1 stalk of the large ribosomal subunit and a Cy5-labeled tRNA(Lys) in the ribosomal peptidyl-tRNA-binding (P) site. We observed significantly slower elongation factor G (EF-G)-catalyzed translocation through the slippery sequence of FSmRNA in comparison with an mRNA lacking the stem loop, ΔSL. Furthermore, the P-site tRNA/L1 stalk of FSmRNA-programmed pretranslocation (PRE) ribosomal complexes exhibited multiple fluctuations between the classical/open and hybrid/closed states, respectively, in the presence of EF-G before translocation, in contrast with ΔSL-programmed PRE complexes, which sampled the hybrid/closed state approximately once before undergoing translocation. Quantitative analysis showed that the stimulatory stem loop destabilizes the hybrid state and elevates the energy barriers corresponding to subsequent substeps of translocation. The shift of the FSmRNA-programmed PRE complex equilibrium toward the classical/open state and toward states that favor EF-G dissociation apparently allows the PRE complex to explore alternative translocation pathways such as -1PRF.

Life at Berkeley for the past 57 years involved research on the thermodynamics, kinetics, and spectroscopic properties of RNA to better understand its structures, interactions, and functions. We (myself and all the graduate students and postdocs who shared in the fun) began with dinucleoside phosphates and slowly worked our way up to megadalton-sized RNA molecular motors. We used UV absorption, circular dichroism, circular intensity differential scattering, fluorescence, NMR, and single-molecule methods. We learned a lot and had fun doing it.

Translation of messenger RNA by a ribosome occurs three nucleotides at a time from start signal to stop. However, a frameshift means that some nucleotides are read twice or some are skipped, and the following sequence of amino acids is completely different from the sequence in the original frame. In some messenger RNAs, including viral RNAs, frameshifting is programmed with RNA signals to produce specific ratios of proteins vital to the replication of the organism. The mechanisms that cause frameshifting have been studied for many years, but there are no definitive conclusions. We review ribosome structure and dynamics in relation to frameshifting dynamics provided by classical ensemble studies, and by new single-molecule methods using optical tweezers and FRET., (Copyright © 2013 Wiley Periodicals, Inc.)

The sequence and secondary structure of the 5'-end of mRNAs regulate translation by controlling ribosome initiation on the mRNA. Ribosomal protein S1 is crucial for ribosome initiation on many natural mRNAs, particularly for those with structured 5'-ends, or with no or weak Shine-Dalgarno sequences. Besides a critical role in translation, S1 has been implicated in several other cellular processes, such as transcription recycling, and the rescuing of stalled ribosomes by tmRNA. The mechanisms of S1 functions are still elusive but have been widely considered to be linked to the affinity of S1 for single-stranded RNA and its corresponding destabilization of mRNA secondary structures. Here, using optical tweezers techniques, we demonstrate that S1 promotes RNA unwinding by binding to the single-stranded RNA formed transiently during the thermal breathing of the RNA base pairs and that S1 dissociation results in RNA rezipping. We measured the dependence of the RNA unwinding and rezipping rates on S1 concentration, and the force applied to the ends of the RNA. We found that each S1 binds 10 nucleotides of RNA in a multistep fashion implying that S1 can facilitate ribosome initiation on structured mRNA by first binding to the single strand next to an RNA duplex structure ("stand-by site") before subsequent binding leads to RNA unwinding. Unwinding by multiple small substeps is much less rate limited by thermal breathing than unwinding in a single step. Thus, a multistep scheme greatly expedites S1 unwinding of an RNA structure compared to a single-step mode.

Proteins are synthesized by the ribosome and generally must fold to become functionally active. Although it is commonly assumed that the ribosome affects the folding process, this idea has been extremely difficult to demonstrate. We have developed an experimental system to investigate the folding of single ribosome-bound stalled nascent polypeptides with optical tweezers. In T4 lysozyme, synthesized in a reconstituted in vitro translation system, the ribosome slows the formation of stable tertiary interactions and the attainment of the native state relative to the free protein. Incomplete T4 lysozyme polypeptides misfold and aggregate when free in solution, but they remain folding-competent near the ribosomal surface. Altogether, our results suggest that the ribosome not only decodes the genetic information and synthesizes polypeptides, but also promotes efficient de novo attainment of the native state.

Nonhexameric helicases use adenosine triphosphate (ATP) to unzip base pairs in double-stranded nucleic acids (dsNAs). Studies have suggested that these helicases unzip dsNAs in single-base pair increments, consuming one ATP molecule per base pair, but direct evidence for this mechanism is lacking. We used optical tweezers to follow the unwinding of double-stranded RNA by the hepatitis C virus NS3 helicase. Single-base pair steps by NS3 were observed, along with nascent nucleotide release that was asynchronous with base pair opening. Asynchronous release of nascent nucleotides rationalizes various observations of its dsNA unwinding and may be used to coordinate the translocation speed of NS3 along the RNA during viral replication.

The ribosome translates the genetic information encoded in messenger RNA into protein. Folded structures in the coding region of an mRNA represent a kinetic barrier that lowers the peptide elongation rate, as the ribosome must disrupt structures it encounters in the mRNA at its entry site to allow translocation to the next codon. Such structures are exploited by the cell to create diverse strategies for translation regulation, such as programmed frameshifting, the modulation of protein expression levels, ribosome localization and co-translational protein folding. Although strand separation activity is inherent to the ribosome, requiring no exogenous helicases, its mechanism is still unknown. Here, using a single-molecule optical tweezers assay on mRNA hairpins, we find that the translation rate of identical codons at the decoding centre is greatly influenced by the GC content of folded structures at the mRNA entry site. Furthermore, force applied to the ends of the hairpin to favour its unfolding significantly speeds translation. Quantitative analysis of the force dependence of its helicase activity reveals that the ribosome, unlike previously studied helicases, uses two distinct active mechanisms to unwind mRNA structure: it destabilizes the helical junction at the mRNA entry site by biasing its thermal fluctuations towards the open state, increasing the probability of the ribosome translocating unhindered; and it mechanically pulls apart the mRNA single strands of the closed junction during the conformational changes that accompany ribosome translocation. The second of these mechanisms ensures a minimal basal rate of translation in the cell; specialized, mechanically stable structures are required to stall the ribosome temporarily. Our results establish a quantitative mechanical basis for understanding the mechanism of regulation of the elongation rate of translation by structured mRNAs., (©2011 Macmillan Publishers Limited. All rights reserved)

The last 15 years have witnessed the development of tools that allow the observation and manipulation of single molecules. The rapidly expanding application of these technologies for investigating biological systems of ever-increasing complexity is revolutionizing our ability to probe the mechanisms of biological reactions. Here, we compare the mechanistic information available from single-molecule experiments with the information typically obtained from ensemble studies and show how these two experimental approaches interface with each other. We next present a basic overview of the toolkit for observing and manipulating biology one molecule at a time. We close by presenting a case study demonstrating the impact that single-molecule approaches have had on our understanding of one of life's most fundamental biochemical reactions: the translation of a messenger RNA into its encoded protein by the ribosome.

Many viruses use programmed -1 ribosomal frameshifting to express defined ratios of structural and enzymatic proteins. Pseudoknot structures in messenger RNAs stimulate frameshifting in upstream slippery sequences. The detailed molecular determinants of pseudoknot mechanical stability and frameshifting efficiency are not well understood. Here we use single-molecule unfolding studies by optical tweezers, and frameshifting assays to elucidate how mechanical stability of a pseudoknot and its frameshifting efficiency are regulated by tertiary stem-loop interactions. Mechanical unfolding of a model pseudoknot and mutants designed to dissect specific interactions reveals that mechanical stability depends strongly on triplex structures formed by stem-loop interactions. Combining single-molecule and mutational studies facilitates the identification of pseudoknot folding intermediates. Average unfolding forces of the pseudoknot and mutants ranging from 50 to 22 picoNewtons correlated with frameshifting efficiencies ranging from 53% to 0%. Formation of major-groove and minor-groove triplex structures enhances pseudoknot stem stability and torsional resistance, and may thereby stimulate frameshifting. Better understanding of the molecular determinants of frameshifting efficiency may facilitate the development of anti-virus therapeutics targeting frameshifting.

In the cell, proteins are synthesized by ribosomes in a multi-step process called translation. The ribosome translocates along the messenger RNA to read the codons that encode the amino acid sequence of a protein. Elongation factors, including EF-G and EF-Tu, are used to catalyze the process. Recently, we have shown that translation can be followed at the single-molecule level using optical tweezers; this technique allows us to study the kinetics of translation by measuring the lifetime the ribosome spends at each codon. Here, we analyze the data from single-molecule experiments and fit the data with simple kinetic models. We also simulate the translation kinetics based on a multi-step mechanism from ensemble kinetic measurements. The mean lifetimes from the simulation were consistent with our experimental single-molecule measurements. We found that the calculated lifetime distributions were fit in general by equations with up to five rate-determining steps. Two rate-determining steps were only obtained at low concentrations of elongation factors. These analyses can be used to design new single-molecule experiments to better understand the kinetics and mechanism of translation.

An RNA kissing complex formed by the dimerization initiation site plays a critical role in the survival and infectivity of human immunodeficiency virus. Two dimerization initiation site kissing sequences, Mal and Lai, have been found in most human immunodeficiency virus 1 variants. Formation and stability of these RNA kissing complexes depend crucially on cationic conditions, particularly Mg 2+. Using optical tweezers, we investigated the mechanical unfolding of single RNA molecules with either Mal-type (GUGCAC) or Lai-type (GCGCGC) kissing complexes under various ionic conditions. The force required to disrupt the kissing interaction of the two structures, the rip force, is sensitive to concentrations of KCl and MgCl2; addition of 3 mM MgCl2 to 100 mM KCl changes the rip force of Mal from 21 +/- 4 to 46 +/- 3 pN. From the rip force distribution, the kinetics of breaking the kissing interaction is calculated as a function of force and cation concentration. The two kissing complexes have distinct unfolding transition states, as shown by different values of deltaX(++), which is the distance from the folded structure to the unfolding transition state. The deltaX(++) of Mal is approximately 0.6 nm smaller than that of Lai, suggesting that fewer kissing base pairs are broken at the transition state of the former, consistent with observations that the Lai-type kissing complex is more stable and requires significantly more force to unfold than the Mal type. More importantly, neither K+ nor Mg 2+ significantly changes the position of the transition state along the reaction coordinate. However, increasing concentrations of cations increase the kinetic barrier. We derived a cation-specific parameter, m, to describe how the height of the kinetic barrier depends on the concentration of cations. Our results suggest that Mg 2+ greatly slows down the unfolding of the kissing complex but has moderate effects on the formation kinetics of the structure.

The pseudoknot is an important RNA structural element that provides an excellent model system for studying the contributions of tertiary interactions to RNA stability and to folding kinetics. RNA pseudoknots are also of interest because of their key role in the control of ribosomal frameshifting by viral RNAs. Their mechanical properties are directly relevant to their unfolding by ribosomes during translation. We have used optical tweezers to study the kinetics and thermodynamics of mechanical unfolding and refolding of single RNA molecules. Here we describe the unfolding of the frameshifting pseudoknot from infectious bronchitis virus (IBV), three constituent hairpins, and three mutants of the IBV pseudoknot. All four pseudoknots cause -1 programmed ribosomal frameshifting. We have measured the free energies and rates of mechanical unfolding and refolding of the four frameshifting pseudoknots. Our results show that the IBV pseudoknot requires a higher force than its corresponding hairpins to unfold. Furthermore, its rate of unfolding changes little with increasing force, in contrast with the rate of hairpin unfolding. The presence of Mg(2+) significantly increases the kinetic barriers to unfolding the IBV pseudoknot, but has only a minor effect on the hairpin unfolding. The greater mechanical stability of pseudoknots compared to hairpins, and their kinetic insensitivity to force supports the hypothesis that -1 frameshifting depends on the difficulty of unfolding the mRNA.

Understanding how RNA folds and what causes it to unfold has become more important as knowledge of the diverse functions of RNA has increased. Here we review the contributions of single-molecule experiments to providing answers to questions such as: How much energy is required to unfold a secondary or tertiary structure? How fast is the process? How do helicases unwind double helices? Are the unwinding activities of RNA-dependent RNA polymerases and of ribosomes different from other helicases? We discuss the use of optical tweezers to monitor the unfolding activities of helicases, polymerases, and ribosomes, and to apply force to unfold RNAs directly. We also review the applications of fluorescence and fluorescence resonance energy transfer to measure RNA dynamics.

Using optical tweezers, we have measured the effect of monovalent cation concentration and species on the folding free energy of five large (49-124 nt) RNA hairpins, including HIV-1 TAR and molecules approximating A.U and G.C homopolymers. RNA secondary structure thermodynamics are accurately described by a model consisting of nearest-neighbor interactions and additive loop and bulge terms. Melting of small (<15 bp) duplexes and hairpins in 1 M NaCl has been used to determine the parameters of this model, which is now used extensively to predict structure and folding dynamics. Few systematic measurements have been made in other ionic conditions or for larger structures. By applying mechanical force, we measured the work required to fold and unfold single hairpins at room temperature over a range of cation concentrations from 50 to 1000 mM. Free energies were then determined using the Crooks fluctuation theorem. We observed the following: (1) In most cases, the nearest-neighbor model accurately predicted the free energy of folding at 1 M NaCl. (2) Free energy was proportional to the logarithm of salt concentration. (3) Substituting potassium ions for sodium slightly decreased hairpin stability. The TAR hairpin also misfolded nearly twice as often in KCl, indicating a differential kinetic response. (4) Monovalent cation concentration affects RNA stability in a sequence-dependent manner. G.C helices were unaffected by changing salt concentration, A.U helices were modestly affected, and the hairpin loop was very sensitive. Surprisingly, the U.C.U bulge of TAR was found to be equally stable in all conditions tested. We also report a new estimate for the elastic parameters of single-stranded RNA.

RNA unfolding and folding reactions in physiological conditions can be facilitated by mechanical force one molecule at a time. By using force-measuring optical tweezers, we studied the mechanical unfolding and folding of a hairpin-type pseudoknot in human telomerase RNA in a near-physiological solution, and at room temperature. Discrete two-state folding transitions of the pseudoknot are seen at approximately 10 and approximately 5 piconewtons (pN), with ensemble rate constants of approximately 0.1 sec(-1), by stepwise force-drop experiments. Folding studies of the isolated 5'-hairpin construct suggested that the 5'-hairpin within the pseudoknot forms first, followed by formation of the 3'-stem. Stepwise formation of the pseudoknot structure at low forces are in contrast with the one-step unfolding at high forces of approximately 46 pN, at an average rate of approximately 0.05 sec(-1). In the constant-force folding trajectories at approximately 10 pN and approximately 5 pN, transient formation of nonnative structures were observed, which is direct experimental evidence that folding of both the hairpin and pseudoknot takes complex pathways. Possible nonnative structures and folding pathways are discussed.

RNA helicases regulate virtually all RNA-dependent cellular processes. Although much is known about helicase structures, very little is known about how they deal with barriers in RNA and the factors that affect their processivity. The hepatitis C virus encodes NS3, an RNA helicase that is essential for viral RNA replication. We have used optical tweezers to determine at the single-molecule level how the local stability of the RNA substrate affects the enzyme rate of strand separation, whether separation occurs by an active or a passive mechanism, and whether processivity is affected. We show that sequence barriers in RNA modulate NS3 activity. NS3 processivity depends on barriers ahead of the opening fork. Our results rule out a model where NS3 passively waits for the thermal fraying of double-stranded RNA. Instead, we find that NS3 destabilizes the duplex before separating the strands. Failure to do so before a strong barrier leads to helicase dissociation and limits the processivity of the enzyme.

Experimental variables of optical tweezers instrumentation that affect RNA folding/unfolding kinetics were investigated. A model RNA hairpin, P5ab, was attached to two micron-sized beads through hybrid RNA/DNA handles; one bead was trapped by dual-beam lasers and the other was held by a micropipette. Several experimental variables were changed while measuring the unfolding/refolding kinetics, including handle lengths, trap stiffness, and modes of force applied to the molecule. In constant-force mode where the tension applied to the RNA was maintained through feedback control, the measured rate coefficients varied within 40% when the handle lengths were changed by 10-fold (1.1-10.2 Kbp); they increased by two- to threefold when the trap stiffness was lowered to one-third (from 0.1 to 0.035 pN/nm). In the passive mode, without feedback control and where the force applied to the RNA varied in response to the end-to-end distance change of the tether, the RNA hopped between a high-force folded-state and a low-force unfolded-state. In this mode, the rates increased up to twofold with longer handles or softer traps. Overall, the measured rates remained with the same order-of-magnitude over the wide range of conditions studied. In the companion article on pages 3010-3021, we analyze how the measured kinetics parameters differ from the intrinsic molecular rates of the RNA, and thus how to obtain the molecular rates.

The rugged folding-energy landscapes of RNAs often display many competing minima. How do RNAs discriminate among competing conformations in their search for the native state? By using optical tweezers, we show that the folding-energy landscape can be manipulated to control the fate of an RNA: individual RNA molecules can be induced into either native or misfolding pathways by modulating the relaxation rate of applied force and even be redirected during the folding process to switch from misfolding to native folding pathways. Controlling folding pathways at the single-molecule level provides a way to survey the manifold of folding trajectories and intermediates, a capability that previously was available only to theoretical studies.

Single-molecule methods have made it possible to apply force to an individual RNA molecule. Two beads are attached to the RNA; one is on a micropipette, the other is in a laser trap. The force on the RNA and the distance between the beads are measured. Force can change the equilibrium and the rate of any reaction in which the product has a different extension from the reactant. This review describes use of laser tweezers to measure thermodynamics and kinetics of unfolding/refolding RNA. For a reversible reaction the work directly provides the free energy; for irreversible reactions the free energy is obtained from the distribution of work values. The rate constants for the folding and unfolding reactions can be measured by several methods. The effect of pulling rate on the distribution of force-unfolding values leads to rate constants for unfolding. Hopping of the RNA between folded and unfolded states at constant force provides both unfolding and folding rates. Force-jumps and force-drops, similar to the temperature jump method, provide direct measurement of reaction rates over a wide range of forces. The advantages of applying force and using single-molecule methods are discussed. These methods, for example, allow reactions to be studied in non-denaturing solvents at physiological temperatures; they also simplify analysis of kinetic mechanisms because only one intermediate at a time is present. Unfolding of RNA in biological cells by helicases, or ribosomes, has similarities to unfolding by force.

By using optical tweezers, we have investigated the mechanical unfolding of a minimal kissing complex with only two G.C base pairs. The loop-loop interaction is exceptionally stable; it is disrupted at forces ranging from 7 to 30 pN, as compared with 14-20 pN for unfolding hairpins of 7 and 11 bp. By monitoring unfolding/folding trajectories of single molecules, we resolved the intermediates, measured their rate constants, and pinpointed the rate-limiting steps. The two hairpins unfold only after breaking the intramolecular kissing interaction, and the kissing interaction forms only after the folding of the hairpins. At forces that favor the unfolding of the hairpins, the entire RNA structure is kinetically stabilized by the kissing interaction, and extra work is required to unfold the metastable hairpins. The strong mechanical stability of even a minimal kissing complex indicates the importance of such loop-loop interactions in initiating and stabilizing RNA dimers in retroviruses.

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. 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, and therefore a potentially important drug target. 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. 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.

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.

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 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 and have already provided information on the folding free energy of a RNA hairpin. Here we show that the Crooks fluctuation theorem 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 to measure repeatedly the mechanical work associated with the unfolding and refolding of a small RNA hairpin and an RNA three-helix junction. 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.

Two methods of temperature control of a dual-beam optical-tweezers system are compared. In the first method, we used a 975 nm infrared laser to raise the temperature 5.6 degrees C/100 mW in a nonheating (830 nm) optical trap. The temperature increment logarithmically decreases toward the periphery of the heating beam, causing a fluid convection of 8 mum/s inside a 180 microm thick microchamber. In the second method, heating or cooling fluid was pumped through copper jackets that were placed on the water immersion objectives on both sides of the microchamber to control its temperature from 4.5 degrees C to 68 degrees C. The temperature controlled by the second method was both stable and homogeneous, inducing little fluid convection that would disturb single-molecule applications. An analysis of the power spectrum of the thermal force on a trapped bead showed no detectable vibration due to the liquid circulation. In both methods, force was measured directly by sensors of the momentum flux of light, independent of environmental disturbances including refractive index changes that vary with temperature. The utility of the second method was demonstrated in single-molecule experiments by measuring the mechanical stretch of a 41 kbp lambda double-stranded DNA at temperatures ranging from 8.4 degrees C to 45.6 degrees C.

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.

Single-molecule studies of RNA folding and unfolding are providing impressive details of the intermediates that occur and their rates of interconversion. The folding and unfolding of RNA are controlled by varying the concentration of magnesium ions and measuring fluorescence energy transfer, or by applying force to the RNA and measuring the end-to-end distance. The hierarchical nature of RNA folding - first secondary structure, then tertiary structure - makes the process susceptible to analysis and prediction.

The effect of force on the thermodynamics and kinetics of reactions is described. The key parameters are the difference in end-to-end distance between reactant and product for thermodynamics, and the distance to the transition state for kinetics. I focus the review on experimental results on force unfolding of RNA. Methods to measure Gibbs free energies and kinetics for reversible and irreversible reactions are described. The use of the worm-like-chain model to calculate the effects of force on thermodynamics and kinetics is illustrated with simple models. The main purpose of the review is to describe the simple experiments that have been done so far, and to encourage more people to enter a field that is new and full of opportunities.

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.

The usual variables chemists use to affect a chemical reaction are temperature and pressure. We consider here an additional variable: force, F. By attaching a molecule to the tip of a cantilever of an atomic force microscope, or to a bead in a laser light trap, we can control the force on a single molecule. This mechanical force can drive a reaction to completion, or stabilize the reactants. Force changes the thermodynamic stability of a molecule; it can thus increase or decrease the free energy change for the reaction. Force can also speed or slow rates of reactions; it changes the free energy of activation of the reaction., (Copyright 2002 Elsevier Science B.V.)

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.

The Watson-Crick double helix of DNA was first revealed in 1953. Since then a wide range of physical chemical methods have been applied to DNA and to its more versatile relative RNA to determine their structures and functions. My major goal is to predict the folded structure of any RNA from its sequence. We have used bulk and single-molecule measurements of thermodynamics and kinetics, plus various spectroscopic methods (UV absorption, optical rotation, circular dichroism, circular intensity differential scattering, fluorescence, NMR) to approach this goal.