Real-Time Control of the Energy Landscape by Force Directs the Folding of RNA Molecules

Real-time control of the energy landscape by force directs the folding of RNA molecules

Pan T. X. Li*†§, Carlos Bustamante*¶ʈ, and Ignacio Tinoco, Jr.*§

Departments of *Chemistry and ¶Physics and Molecular and Cell Biology, ʈHoward Hughes Medical Institute, University of California, Berkeley, CA 94720

Contributed by Ignacio Tinoco, Jr., March 9, 2007 (sent for review January 30, 2007) The rugged folding-energy landscapes of RNAs often display many a competing minima. How do RNAs discriminate among competing b G G U G C A conformations in their search for the native state? By using optical laser trap C G FF G C FU A U tweezers, we show that the folding-energy landscape can be G C U manipulated to control the fate of an RNA: individual RNA mole- C Handle A UA U G C cules can be induced into either native or misfolding pathways by XF RNA A U C G C G modulating the relaxation rate of applied force and even be Handle B U A X G C A U redirected during the folding process to switch from misfolding to U A U A G C native folding pathways. Controlling folding pathways at the G U U A single-molecule level provides a way to survey the manifold of C G U G C G folding trajectories and intermediates, a capability that previously G C 5'- G C -3' was available only to theoretical studies. micropipette TAR mechanical force ͉ misfolding ͉ optical tweezers ͉ RNA folding ͉ c single-step multiple-steps misfolding single molecule start 20 rip rip rip ecroF )Np( ecroF )Np(

he folding of a macromolecule can be thought of as a biased s e t 15 a diffusion over an energy surface that describes the thermo- i T d e dynamic and kinetic constraints of possible intramolecular in- mr 10 zip etn rescue teractions. RNAs differ from proteins in the nature, strength, i ec r specificity, and degeneracy of the interactions that stabilize their zip oF 5 native structures. Whereas proteins are made of 20 amino acids, 20 nm it takes only 4 nucleotides to build RNAs. This simpler compo- 0 sition, endowed with robust base-pairing rules, greatly increases Extension the promiscuity of interactions between any given nucleotide and Fig. 1. Optical-tweezers assay for studying folding, misfolding, and rescue of the rest of the RNA structure. These RNA–protein differences TAR RNA. (a) Experimental design. RNA hairpin TAR, flanked by dsDNA/RNA are reflected in the topography of the energy surface over which handles, is tethered to two microspheres (11). One microsphere is held by a the molecules diffuse in their search for the native structure: the force-measuring trap, and the other is held on a micropipette. By moving the energy surfaces of RNAs are significantly more rugged than micropipette, tension (F) is exerted on the molecule, and the change in those of proteins, containing many competing local minima extension (X) is measured (13). (b) Native structure of TAR. (c) Three types of (1–4). Even relatively small RNAs, such as tRNA (4–6), tend to force-extension curves for TAR RNA. In each experiment, force was first relaxed from 20 to 1 pN (red) and then was raised back to 20 pN (blue). fold into stable alternate secondary structures with energies only ϭ Unfolding is indicated by rips that increase the extension, whereas folding and a few kilocalories (1 kcal 4.18 kJ on first use) per mole apart rescue are indicated by zips that shorten the extension. The arrows point to (4). Once trapped kinetically in a secondary structure with the fluctuations/intermediates on refolding. suboptimal folding energy, it is difficult for an RNA molecule to reach its native structure (1). The promiscuous nature of secondary interactions in RNA begs loading and unloading rate, respectively). Significantly, the applied answers for three questions: How do RNAs find their native tension slows the hairpin folding kinetics from an order of 106 sϪ1 structure? How do they avoid the kinetic traps on their rugged at zero force (14) to a more measurable range from 102 to 10Ϫ2 sϪ1 folding-energy landscape? And, how can RNAs switch between at its transition force such that the process of the folding can be alternate structures in response to changes in the cellular environ- monitored in real time. The force (F)-dependent un/refolding rate ment, as happens, for example, during transcription attenuation in constant (kF) can be described by an Arrhenius-type equation (15): bacteria (7)? To address these questions, we need to follow the ϭ ϩ ‡͞ folding trajectories of RNA molecules as they diffuse over their ln kF ln k0 FX kBT, [1] energy landscape in search of stable conformations. Because of the where k0 is the apparent rate constant of the mechanical structural polymorphism and manifold pathways of RNA, single- unfolding process at zero force, and k T is Boltzmann’s constant molecule approaches (8–12) are particularly useful for answering B these questions by identifying folding intermediates and distinguish- BIOPHYSICS ing native pathways from those that misfold. Author contributions: P.T.X.L., C.B., and I.T. designed research; P.T.X.L. performed research; Here we use optical tweezers to unfold and control the refolding P.T.X.L. and I.T. analyzed data; and P.T.X.L., C.B., and I.T. wrote the paper. of single RNA molecules by force (11, 13). Two micrometer-sized The authors declare no conflict of interest. beads are attached to the ends of an RNA molecule and are Abbreviation: TAR, transactivation response region. manipulated by optical tweezers to exert force on the RNA (Fig. †Present address: Department of Biological Sciences, University at Albany, State University 1a). The unfolding and refolding of the RNA molecule, induced by of New York, Albany, NY 12222. controlled application of force, is monitored by nanometer changes §To whom correspondence may be addressed. E-mail: [email protected] or panli@ in the end-to-end distance of the molecule. In a typical ‘‘pulling’’ albany.edu. experiment, force is increased or decreased at a fixed rate (the © 2007 by The National Academy of Sciences of the USA

www.pnas.org͞cgi͞doi͞10.1073͞pnas.0702137104 PNAS ͉ April 24, 2007 ͉ vol. 104 ͉ no. 17 ͉ 7039–7044 Downloaded by guest on September 27, 2021 60 a 40 b 35 50 30 e

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r 30 20 o f uc siM cO 15 20 10 10 5 0 0 3 4 5 6 7 8 9 10 11 12 15 20 25 30 35 40 number of ss nucleotides paired Unloading Rate (pN/s)

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2 -1.5

0 -2 5 6 7 8 9 10 11 12 13 8 8.5 9 9.5 10 10.5 11 Rescue Force (pN) Rescue Force (pN)

Fig. 2. Misfolding and rescue of TAR RNA. (a) Histogram of the decrease in end-to-end distance, ⌬Xrescue, in the rescue. ⌬Xrescue was converted to the number of single-stranded nucleotides that become paired in the rescue. (b) Fraction of misfolded trajectories as a function of unloading rates. Between 122 and 324 total trajectories were collected at each unloading rate. (c) Histogram of the rescue forces in the force-ramp experiment at an unloading rate of 11.2 pN/s followed by a loading rate of 2 pN/s. The rescue force was deﬁned as the force at which the rescue transition starts. (d) The rescue-force distribution in c is ﬁtted to Eq. ‡ Ϯ 2, yielding an Xrescue1 of 6 1 nm.

times temperature in Kelvin. X‡, the distance to the transition at Ϸ13–16 pN. In contrast, when the tension on the molecule was state, is positive for unfolding and negative for refolding. Hence, allowed to relax at a rate of 1.5 pN/s, Ͼ95% of the refolding curves we can control the un/refolding rate constants by manipulating show multiple-step refolding, displaying a decreasing extension with the tension on a molecule. characteristic fluctuations (Fig. 1c, black arrows) followed by a When an RNA molecule is pulled and relaxed very slowly such small zip. This zip corresponds to the folding of an average of 26 nt, that the process is thermodynamically reversible, simple hairpins which is half the value for the refolding of the entire molecule. are often seen to unfold and refold cooperatively in a single step Subsequent pulling of such molecules displayed unfolding charac- (11, 16–21). One example is the 52-nt HIV transactivation teristics similar to those observed in the slow relaxation curves, response region (TAR) RNA (22), which folds into a 21-bp indicating that these RNAs had folded into the native structure. The hairpin with a 3-nt bulge (Fig. 1b) (23). The equilibrium force back-and-forth oscillations in the force-extension curve before the zip are likely successive refolding and unfolding events as the (F1/2), at which its unfolding and refolding rates are equal, is 12.4 pN in 100 mM KCl, pH 8, at 22°C (19). When the force is held molecule moves into and out of alternative, competing folding pathways. Once an RNA molecule, following this search process, constant at or near the F1/2 value, an individual TAR molecule can be seen to transit between folded and unfolded states folds into intermediate structures that contain only native contacts, without detectable intermediates. At forces 1 pN below or above the remaining helix can form cooperatively, as manifested by the observed zip. the F , the molecule mainly stays in the folded or unfolded 1/2 At unloading rates Ͼ2 pN/s, we observed another type of state. These observations are consistent with a two-step folding relaxation curve that showed no zipping at all; at low force the process in which the refolding occurs through a nucleation step: extension of the RNA never returned to that of the native hairpin formation of the loop-closing first base pair followed by a (Fig. 1c, misfolding). When the force on the molecule was subse- helix-propagation process (24–26). quently increased, the extension of the RNA increased monoton- To explore the possibility of alternative folding pathways, indi- ically, retracing the relaxation curve until a zip transition suddenly vidual TAR molecules were stretched and relaxed repeatedly at shortened the end-to-end distance of the molecule, against the approximately fixed loading and unloading rates (pN/s). In a typical increasing force. This transition, not observed previously, is a Ͻ cycle, the force was first ramped down from 20 to 2pN(Fig.1c, refolding event in that the extension of the molecule is shortened, red) before it was increased again to 20 pN (blue). These experi- yet it occurs as the force is increasing, which normally causes ments revealed three different types of trajectories, each associated unfolding. The magnitude of this zip shows a broad distribution with with distinctive refolding characteristics: single-step refolding, mul- a mean of Ϸ30 single-stranded nucleotides becoming paired (Fig. tiple-step refolding, and misfolding. The single-step refolding 2a), indicating that a range of partially folded structures existed mostly occurs at force relaxation rates Ͻ1 pN/s. In this case the before the transition. As the force was further raised, the force- force-extension curve displays a single transition (zip) at 10–13 pN extension curve always showed a rip similar to the unfolding of the with a decrease in extension of Ϸ17 nm. This behavior is consistent native hairpin. We conclude that the structures at low force are with a single-step refolding process from a single strand to the native misfolded, and that the application of force allowed the RNA structure. When pulled, the natively folded TAR always displayed molecules to form the native hairpin in the zip transition. Accord- a sudden length increase of Ϸ18 nm that appeared as a single rip ingly, we term this zip a ‘‘rescue’’ transition.

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start 01 mn ro force 18 f force ecrof reached 16 released )Np( ecroF )Np( noisnetxE 14 rescued set force 12 released 10 ∆Xrescue 8 6 set force misfolded 4 reached 20 nm 2 lifetime 0 755 756 757 758 759 760 761 762 Extension (nm) Time (s)

4 c 35 d TAR∆b 3 30 gn

2 TAR id 25 l

e of gnid c 1 eu n k nl k n 20 c u erruccO s lo 0 e dloferf 15 R n RAT gniu -1 lofer 10 -2 gnid 5 -3 0 15 20 25 30 35 40 -4 7.5 10.0 12.5 15.0 17.5 number of nucleotides rescued Force (pN)

Fig. 3. Rescue at constant force. (a) The experiment took two steps: (1) the force was decreased from 20 to 9.5 pN at a rate of 11 pN/s and held constant (black) (the rescue is indicated by a zip), and (2) after the rescue occurred, the force was lowered to 1 pN (black) and then raised to 20 pN to check the folded structure (gray). (b) Time trace of the extension at the rescue force. (c) Histogram of ⌬Xrescue in the number of single-stranded nucleotides paired at rescue. (d) Rescue-rate constants (Œ) as a function of force. Unfolding (■) and refolding (F) rates of TAR were measured by force jump (19). Unfolding (E) and refolding (ᮀ) rates of TAR⌬b were measured by constant force experiments. The standard deviation of each point is Ͻ10% of the mean. Solid lines are best least squares ﬁt to Eq. 1.

The faster the force is decreased, the more likely a molecule Which steps in the folding process of the native hairpin are becomes trapped into a variety of stable misfolded structures perturbed by the fast force relaxation? High force favors the with less base pairs and longer end-to-end distances than the longer single-strand forms over base-paired structures. As the native hairpin, as shown by the increase in frequency of mis- force is relaxed, new intramolecular contacts and partly folded folding with increasing force relaxation rates (Fig. 2b). Rescue structures become accessible to the molecule. The effect of occurred between 6 and 12 pN at a loading rate of 2 pN/s (Fig. relaxing the force, therefore, is to expand and change continu- 2c). The low threshold of the transition force argues against the ously the topography of the energy surface over which the idea that the prerescue structures are on-pathway folding inter- molecules can diffuse. The folding of a hairpin involves nucle- mediates. If they were so, one would expect them to fold quickly ation and helix formation, both of which are influenced by force. at Ͻ6 pN, given that the RNA folds into the native hairpin in Formation of the first base pair closing the native loop has to seconds even at Ϸ12 pN (19). To further rule out this possibility, compete with many other possible loop-closing base pairs. When we kept the misfolded structures at zero tension for 30 min. the molecule is allowed to equilibrate, either at constant force Subsequent pulls showed the characteristic zip–rip signature (in that order), clearly indicating that these nonnative structures are Ͼ G G stable at low forces and that forces 6 pN are required for their U G C A conversion to the native hairpin. Such forces were needed to C G TAR∆b G C A U break the nonnative interactions that trapped the RNA struc- G C A U G C ture, allowing the molecule to search for its correct folding 25 A U e C G cro C G pathway and effectively rescuing it from the misfolded state. A G C F Assuming that the rate-liming step in the rescue is disruption A U

)Np( ecroF )Np( U A 20 U A of nonnative base pairs, we can determine the kinetics for rescue. G C G U U A The distribution of rescue forces was fitted to the following C G U G C G equation (27), 15 G C G C A A ‡ C C ͕ ͓ ͑ ͔͖͒ ϭ ͓ ͑ ͔͒ A A ln r ln 1/M F, r ln A/ Xrescue1/kBT 5' 3' 10 BIOPHYSICS ϩ ͑ ‡ ͒ Xrescue1/kBT F, [2] e cro where [M(F, r)] is the fraction of misfolded molecule at each 5 F force (F), and the loading rate is (r); A is a factor reflecting both 20 nm the rescue-rate constant at zero force and instrumental effects 0 ‡ (11); and Xrescue1 represents the average distance to the transi- Extension (nm) tion state of the native fold from the misfolded structures. We ‡ Ϯ obtained Xrescue1 of 6 1 nm (Fig. 2d) from fitting the data Fig. 4. The force-extension curve of TAR⌬b shows no misfolding at an shown in Fig. 2c to Eq. 2. unloading rate of 20 pN/s.

Li et al. PNAS ͉ April 24, 2007 ͉ vol. 104 ͉ no. 17 ͉ 7041 Downloaded by guest on September 27, 2021 dicted by the mfold program (29), several stable ones contain a b A c A C Ј C G G C nonnative base pairs formed by the first 5 nt at the 5 end (Fig. C A A U A A 5). We designed a mutant hairpin, TAR2, in which the second G C U G TAR A U U A (G⅐C) and fourth (U⅐A) base pairs from the end of the native U G G U U A G C helix were interchanged to specifically destabilize the hypothet- G U U G G G C C G ical misfolded structures. In addition, other alternative struc- U G G C U U A C A C G tures of this mutant are predicted to be less stable than those of U G G C G G C G C C G TAR. Consistent with this prediction, this mutant RNA refolds G C U A U U A '5 G without misfolding at unloading rates up to 21 pN/s. This G C C G U G C Ј C G U observation strongly implicates the nucleotides at the 5 end in C U UA U '5 the formation of the nonnative base-pairing in the misfolded G C '3 A U structures. Thus, a combination of the bulge-closing slow step in C G '3 C G the native helix formation and metastable misfolded structures A G C allow alternative folding pathways to compete kinetically at fast A U A A C C G U A e G C force relaxation. d C A U A A U A A G The three types of force-extension curves of TAR shown in Fig. G C G C U ϩ G U A U U A 1c have also been observed in various concentrations of K and U A U G G U 2ϩ C G U A G C Mg . Transition forces, including unfolding/refolding, misfolding, 4th U G G U U C G G C C G and rescue, are affected by the type and concentration of the cation. A 2nd G C G C U G ϩ 2ϩ G C G C G As expected, increasing K and Mg increases the stability and '5 3 U G U C ' C G G C folding rates of the native hairpin and decreases the unfolding rates. G A '5 U 2ϩ C G G The thermodynamic stability of TAR in 10 mM Mg is similar to U C ϩ G U that in1MK (data not shown). We have not systematically C U 5' investigated the effects of ionic conditions on the occurrence of 3 ' misfolding, but specific effects of different cations are likely. '3 How can a misfolded RNA molecule escape from the kinetic trap and find its minimum energy structure? To gain insight into Fig. 5. Hypothetical misfolded intermediates of TAR. (a) Native hairpin of TAR (Ϫ31.3 kcal/mol). In the TAR2 mutant, the second and fourth base pair this question, we monitored the structural evolution of misfolded from the bottom of the helix (arrows) were switched. (b and c) The 5Ј end of RNAs to the native fold. First, force was decreased on an TAR can form stable alternative structures [Ϫ11.4 (b) and Ϫ11.3 (c) kcal/mol]. unfolded molecule from 20 pN to between 7 and 9.5 pN at a rate The rest of the sequence is represented by a gray bar. (d and e) In TAR2, the of Ϸ11 pN/s to induce misfolding; in nearly half of the trajec- same intermediate structures shown in b and c were greatly destabilized [Ϫ4.2 tories, the molecule was not completely folded when the set force (d) and Ϫ0.5 (e) kcal/mol]. was reached. Then, the force was held constant until the native fold was reached, which was indicated by a decrease in extension (Fig. 3a). Typically, the extension of the misfolded structures near its F1/2 or when the force is relaxed very slowly relative to remained relatively constant for a few seconds until a zipping the rate of forming the correct base pairs, the single strand folds event occurred (Fig. 3b). The decrease in extension of this zip, into the native hairpin by sequentially base-pairing from the ⌬Xrescue2, shows a broad distribution (Fig. 3c), indicating that native loop; the refolding appears to be two-state. In contrast, many different partially folded structures, with an average of when the force is relaxed fast, alternative loop closures and 10 Ϯ 3 bp, had formed after the fast force relaxation. At the nonnative base pairings become accessible to the molecule rescue forces, the single strand would fold into the native hairpin before the native contacts form. As the force continues to in milliseconds or less, yet lifetimes of these partially folded decrease fast, some of these nonnative loop closures will not have structures are at least tens of seconds (Fig. 3d), indicating that sufficient time to open but instead lead to propagation of these structures must be off-pathway, misfolded species. After nonnative helices at lower forces. Such a structural evolution is the zipping, the extension varied little up to 5 min, indicating that reflected by the fluctuations displayed in the multiple-step the native hairpin is stable at this force and that the mechanical refolding trajectories. Probabilities of both forming and unfold- rescue of the native structure from the metastable structures is ing of these misfolded structures depend on the instantaneous irreversible. Subsequent pulling verified the native folding (Fig. value of the force. When the force is decreased faster than the 3a, gray curve). rate at which misfolded structures can unfold, the molecule The lifetimes of the misfolded structures at each force fit a single becomes kinetically trapped in metastable states. exponential distribution, from which we calculated the rescue-rate To reduce or avoid misfolding, the topography of the energy constant at force F, krescue2(F). The force dependence of the ‡ landscape needs to be modified in such a way that the channels rescue-rate constant is fitted to Eq. 1, in which Xrescue2 represents leading to the native fold become more favorable than alternate the average distance to the transition state of the native fold from pathways. This situation can be achieved by engineering the mo- the misfolded structures. The rescue rate increases with the force, ‡ Ϯ lecular structure such that the correct folding is speeded up and/or yielding a positive value of Xrescue2 (4.9 0.8 nm; Fig. 3d), formation of the misfolded structures is slowed. To test these characteristic of a helix-unfolding transition (30). This value also ‡ hypotheses, we measured misfolding of two mutant TAR hairpins. agrees with the Xrescue1 obtained from pulling experiments (Fig. 2d). First, we tried to facilitate the correct folding. In the native structure Rescue below 7 pN took at least a few minutes and was rarely (Fig. 1b), formation of the bulge-closing base pair is energetically observed, consistent with the rescue-force distribution observed in unfavorable (28) and is a slow step in the helix formation. To the force-ramp experiments (Fig. 2b). However, between 9.5 and 11 eliminate this slow step, we constructed a mutant hairpin, TAR⌬b, pN, both the native folding rate and the rescue rate are so fast that in which the 3-nt bulge is deleted. As predicted, the bulgeless misfolded structures are practically not observable. mutant is more stable than TAR, with an F1/2 of Ϸ16 pN. Moreover, In a classic study of RNA misfolding, the activity of a TAR⌬b folds faster than TAR by four orders of magnitude (Fig. misfolded tRNA was restored by heating the sample in the 3d) and shows no misfolding (Fig. 4). presence of Mg2ϩ (6). Presumably, raising the temperature, just Next, we tried to reduce the alternative folding by destabilizing as increasing the force, disrupts the nonnative conformation and the misfolded structures. Among the nonnative structures pre- thereby allows correct folding. Here, the rescue rate was raised

7042 ͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0702137104 Li et al. Downloaded by guest on September 27, 2021 by increasing the force applied to the molecule, confirming that process through the participation of specialized proteins (34–40). the rate-limiting step in the rescue is the disruption of incorrect, The mechanism by which RNA chaperone proteins facilitate cor- trapped structures. An important question, then, is: Must the rect RNA folding remains unclear (3, 41). The results presented trapped molecule unfold completely to gain access to the native above suggest two possible scenarios. Proteins may simply facilitate fold? If, during rescue, the misfolded RNAs were first unfolded the attainment of the folded structure by binding to specific regions into a single strand, the extension would increase by Ϸ10 nm on of the unfolded structure and sterically interfering with the forma- average. However, such an unfolding step was not observed tion of alternative competing pathways on the folding-energy before the rescue zip (Fig. 3). To further investigate the nature surface. Alternatively, motor proteins, such as helicases (17), gen- of the molecular rearrangements that take place during rescue, erate and apply force to actively induce the mechanical disruption we characterized the fluctuations of the molecular extension in of RNA molecules trapped in nonnative folds in the cell. The the constant-force rescue experiments. The root-mean-square methods described here make it possible to investigate the mech- deviation of the molecular extension before the appearance of anisms used by proteins or other molecular components to steer the zip is 0.7 Ϯ 0.2 nm, just slightly higher than the value and facilitate the attainment of the native fold through the rugged observed after the native hairpin formed (0.5 Ϯ 0.1 nm). The RNA landscapes. lack of a distinctive unfolding step suggests that a series of partial unfolding and refolding events in small steps are responsible for Materials and Methods gradually converting the RNA into an on-pathway intermediate, RNA Preparation. The RNA samples were prepared as described at which time the zipping transition occurred. It is notable that previously (19). The entire RNA, the hairpin with flanking in the multiple-step refolding observed at high relaxation rates, handles (500 nt each), was transcribed from plasmid template by many small-step unfolding/refolding transitions occur before the T7 RNA polymerase. Two Ϸ500-bp dsDNA handles correspond- final zip (Fig. 1c). Taken together these observations suggest that ing to the regions flanking the hairpin were amplified by PCRs the structural rearrangements that lead the molecule from and modified by either biotin or digoxigenin at each of the misfolded structures to the native state occur through pathways termini. The DNA handles were annealed to the RNA. Properly made up of multiple small unfolding/refolding steps and not annealed molecules can be tethered between two microspheres through a path that requires the complete unfolding of the RNA. coated with streptavidin and anti-digoxigenin antibody, respec- A similar mechanism has been proposed for the conformational tively (11) (Fig. 1a). switch of a ribozyme (31). We have shown how direct mechanical manipulation can be used Optical Tweezers. Dual-beam optical tweezers (13) were used to to control the folding pathway of a single molecule. In particular, we study the RNA folding. The streptavidin-coated bead was placed showed that decreasing the force applied to the molecule can be on a micropipette mounted on a piezoelectric flexture stage. The used to change, in real time, the number of configurations acces- anti-digoxigenin antibody-coated bead was held by the optical sible to the molecule; lowering the force increases the number of trap. Force is determined by the displacement of the trapped structures and interactions accessible to the molecule. Moreover, by bead from the center of the trap. The change in the extension of controlling the rate at which the force is relaxed, we effectively the molecule results from the movement of both the trapped modify the folding-energy landscape (15, 21, 32) and the alternative bead and the bead on the micropipette. pathways over which the molecule diffuses in its search for the native state. The relaxation rate, then, is the control parameter that Manipulation of Single Molecules. In the force-ramp experiments, determines how many and how fast these pathways become acces- the piezoelectric stage moved the micropipette at a constant rate sible to the molecule, the degree of kinetic competition between (nm/s), which changed the tension on the RNA with an approx- these pathways, and, just as importantly, how long the molecule is imately constant (un)loading rate (pN/s) between 3 and 20 pN. allowed to follow a particular pathway before other competing When constant force was implemented, a feedback mechanism paths become available. using a proportional, integrative, and differential algorithm was As shown here in the case of TAR, by direct manipulation and used to maintain the tension. In all experiments, force and modification of the force applied to the molecule, it is possible extension were recorded at 100 Hz. to suddenly ‘‘tilt’’ the energy landscape of the molecule, increasing its chance to attain off-pathway states and even allow the Folding Condition. The folding was studied in 10 mM Hepes (pH molecule to switch back to the on-pathway amid the folding. We 8.0), 100 mM KCl, and 0.1 mM EDTA; 0.05% NaN3 was added to know of no other experimental method that permits such control prevent the growth of bacteria. All folding reactions were studied over the detailed kinetics of refolding of a molecule in real time. at 22°C. Combined with mutagenesis, we have characterized here what Conversion of ⌬X. To compare the increase in end-to-end exten- the crucial elements are in TAR that favor misfolding (i.e., the sion, ⌬X, at different forces, each ⌬X is converted to the number three-base bulge and the sequence at the 5Ј end). More elaborate of single-stranded ribonucleotides at the corresponding force. schemes of force relaxation interspersed with constant force The conversion is calculated by using the worm-like-chain events could be used to characterize the molecular processes interpolation formula (42) with a single-stranded RNA contour leading to various intermediates, to trapping, and to structural length of 0.59 nm/nt and persistent length of 1 nm. rearrangement of the RNA. To maintain cellular homeostasis, living cells must ensure the We thank Ms. Maria Manosas, Mr. Jeff Vieregg, Dr. Gang Chen, and Dr. proper folding of millions of copies of RNAs. Deletion of RNA Felix Ritort for critical reading of the manuscript. We thank Dr. Laurent BIOPHYSICS chaperones has been implicated in cell death after UV irradiation Lacroix for sharing thermal melting data. This work is supported by and in autoimmune disease (33). Mounting evidence, accumulated National Institutes of Health Grants GM-10840 (to I.T.) and GM-32543 in recent years, suggests that RNA folding in vivo is an assisted (to C.B.).

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