We have used single-molecule spectroscopy to untangle conformational dynamics and internal chemistry in the hairpin ribozyme. The active site of the ribozyme is stably formed by docking two internal loops, but upon cleavage undocking is accelerated by two orders of magnitude. The markedly different kinetic properties allow us to differentiate cleaved and ligated forms, and thereby observe multiple cycles of internal cleavage and ligation of a ribozyme in a uniquely direct way. The position of the internal equilibrium is biased toward ligation, but the cleaved ribozyme undergoes several undocking events before ligation, during which products may dissociate. Formation of the stably docked active site, rapid undocking after cleavage, and a strong bias toward ligation should combine to generate a stable circular template for the synthesis of the viral (+) strand and thus ensure a productive replication cycle.
The nucleolytic ribozymes are among the simplest natural RNA catalysts1,
2. They generate site-specific cleavage by means of a transesterification reaction involving attack of a ribose 2' O on the adjacent 3' phosphate to generate a cyclic 2'3' phosphate and 5' hydroxyl group. The reverse ligation reaction may also be efficiently catalyzed in most nucleolytic ribozymes3,
4,
5.
The hairpin ribozyme6 comprises two internal loops that are present on adjacent arms of a four-way helical junction. Intimate association of these loops, called docking (or folding), is stabilized by divalent metal ions and generates the local environment in which catalysis occurs7,
8,
9. A minimal version of the ribozyme in which the four-way junction is replaced by a simple phosphodiester linkage is active10, but requires a 1,000-fold higher Mg2+ concentration to induce folding11.
Single-molecule fluorescence resonance energy transfer (FRET) studies have revealed that the natural (junction-containing) form of the ribozyme, while it is undocked, exhibits conformational fluctuations derived from the junction12,
13. Repeated juxtapositions of the loops accelerate docking by three orders of magnitude compared with the minimal form of the ribozyme14, ensuring that docking is substantially faster than cleavage. However, previous experiments12,
14 could not observe internal cleavage and ligation reactions directly. In the present work we studied catalytically competent hairpin ribozymes to disentangle folding and catalysis unambiguously. We found that the dynamics of the cleaved and ligated forms of the hairpin ribozyme are very different. This enables us to observe multiple cycles of cleavage and ligation in the same molecule, and to measure the rates of these conversions without uncertainties about conformational processes.
Results Constructs for single-molecule studies We carried out three different types of experiments on the four-way junction form of the hairpin ribozyme (Fig. 1).
Figure 1. Analysis of cleavage and ligation in the hairpin ribozyme.
The ribozyme is constructed by the hybridization of four strands labeled a−d, where the non-blue strand is the substrate. The four arms are labeled A−D. In species 1 the short substrate (green) generates a 3-bp terminal helix in arm A. A cleavage reaction creates species 2 after dissociation of the short 3' product strand, and results in a 5' cleavage product that is terminated by a cyclic phosphate, indicated by the red triangle. Species 3 is generated by annealing a 3' product (magenta) that forms a 7-bp terminal helix in arm A. A ligation reaction generates species 4, whereupon cycles of cleavage and ligation are possible.
In the simple cleavage experiment, we begin with species 1 in which the truncated 3' end of strand d limits the extent of the terminal helix of arm A to 3 base pairs (bp). Upon ribozyme cleavage, 3' product dissociation is rapid and does not affect apparent cleavage rates3. The remaining species 2 behaves like a simple junction, which exhibits rapid two-state dynamics that are easily distinguishable from those of the complete ribozyme12.
In the simple ligation experiment, we began with species 2, which has a cyclic 2'3' phosphate at the end of the retained 5' product of cleavage. We introduced a new 3' strand that can hybridize with the 5' end of strand a to form a 7-bp helix (species 3). This species can undergo a ligation reaction to generate species 4. The dynamics of docking of species 3 and 4 are easily distinguishable.
In the multiple cycles experiment we initiated folding and cleavage of species 4 by addition of Mg2+, to give species 3. Multiple cycles of cleavage and ligation can be observed as species 3 and 4 interconvert.
Simple cleavage experiment We immobilized species 1 in a buffer containing 0.5 mM EDTA and lacking Mg2+. We then obtained FRET time trajectories of single ribozymes while adding in buffers of various Mg2+ concentrations (Fig. 2). As was reported previously for 10 mM Mg2+ (ref. 12), addition of Mg2+ first induces docking, observed as an increase in FRET efficiency. Subsequently, cleavage occurs and the 3' product dissociates, marked by the onset of rapid two state fluctuations. These junction dynamics become faster at lower Mg2+ concentrations12,
13, and the two states cannot be clearly distinguished with the 100-ms integration time used here if the Mg2+ concentration is 2 mM (Fig. 2b).
(a) Schematic of experimental principle. We begin with the ribozyme-short substrate construct attached to the surface in its undocked conformation in the absence of divalent metal ions (Lu). The FRET efficiency is low because the fluorophores on the termini of the A and B helices are well separated. On addition of Mg2+, the complex undergoes a transition to the docked conformation (Ld), giving an increase in FRET. A cleavage reaction generates species Cd, in which the 5' product terminates with a cyclic 2'3' phosphate (red triangle). The 3' product held by 3 bp is rapidly lost by dissociation upon undocking. The remaining species exhibits fast structural dynamics equivalent to that of the four-way RNA junction (boxed in purple). (b) Sample intensity time traces of Cy3 donor (green) and Cy5 acceptor (red) signals obtained on addition of 2 mM Mg2+. The decrease in stability of the high-FRET conformation after 100 s is the result of cleavage and product release, leading to the emergence of the junction-like behavior. To reduce photobleaching, one data point of 0.1 s duration was recorded every second by means of a laser shutter. (c) Apparent rate of cleavage as a function of Mg2+ concentration for the dominant ribozyme population.
The inverse of the time between docking and the emergence of junction behavior is a measure of the apparent cleavage rate. At each Mg2+ concentration, the apparent cleavage rate was heterogeneous among molecules with at least two populations, with the dominant population (>80%) being faster. The apparent cleavage rate for the major population (kc,app) increased slightly with Mg2+ concentration (Fig. 2c), after correction for molecules photobleached before reaction (20%)12. The cleavage rate for the minor population could not be determined owing to photobleaching. Because the 3' product strand is closely associated with the ribozyme15, including the insertion its 5' terminal nucleotide G+1 into a pocket in loop B, we expect that the dissociation of the 3' product will require prior undocking14,
16. If undocking were slower than ligation, multiple cleavage and ligation events could occur before undocking and the apparent cleavage rate would be substantially lower than the internal cleavage rate. Conversely, if undocking were much faster than ligation, product release would follow a single cleavage event and the apparent cleavage rate would closely approximate the internal cleavage rate. To determine the rates of undocking and ligation, we studied a ribozyme with a longer substrate strand so that dissociation of the 3' cleavage product is largely prevented by base-pairing.
Multiple cycles experiment The ribozyme with a longer substrate strand switched between different docking-undocking kinetics in 1 mM Mg2+ (Fig. 3). Although the molecules remained stably docked for a majority of the time, at other times they exhibited rapid docking and undocking transitions, and single molecules alternated between these two modes (Fig. 3c). No such behavior was observed in noncleavable ribozymes12. The docking and undocking rates within the rapidly fluctuating mode are kCdock = 2.5 0.1 s-1 and kCundock,obs = 2.3 0.1) s-1 (Fig. 3d,e); these rates are about an order of magnitude slower than the junction dynamics under the same conditions12. Although it seemed likely that cycles of cleavage and ligation produced this complex behavior, we carried out experiments to verify this and assign the states unambiguously.
Figure 3. Multiple cleavage and ligation reactions.
(a) Schematic of experimental principle. We begin with a ribozyme with a 7-bp terminal helix of arm A (species Ld), so that after cleavage the 3' product remains annealed to the ribozyme. The cleaved ribozyme can undergo multiple docking-undocking transitions (CdCu) before ligating back to Ld. (b,c) Time traces of the apparent FRET efficiency, Eapp. Purple bars denote regions of rapid docking and undocking arising from the cleaved ribozyme corresponding to the ribozyme conformational changes shown in the purple box in a. (d) Histogram of the undocked state dwell time of the cleaved ribozyme (tCundocked) constructed from 82 molecules. A single-exponential decay fit gives the docking rate for the cleaved ribozyme, kCdock = 2.5 0.1 s-1. The first time bin was excluded from the fit because the experimental time resolution results in many events of this duration being missed. (e) Histogram of the docked state dwell time of the cleaved ribozyme (tCdocked), fitted by a single-exponential decay, giving an undocking rate of kCundock,obs = 2.3 0.1 s-1. As in the preceding histogram, the first bin was excluded from the fit.
Assignment of the ligated ribozyme When a solution of 1 mM Mg2+ solution was added to species 4, the ribozymes were observed to dock and to remain so typically for tens of seconds (Fig. 4a,b). Because the ribozymes were in the ligated form initially, we assign the stably docked mode to the ligated form. A fraction of molecules exhibited a period of rapid docking-undocking behavior before photobleaching, as observed in the multiple cycles experiment.
Figure 4. Assigning the cleaved and ligated states.
(a) Schematic of the principle of the experiment to identify the ligated form of the ribozyme. The ribozyme with the long substrate is immobilized in the absence of Mg2+ ions so that it is in the undocked state (Lu). Addition of Mg2+ induces docking (Ld). After cleavage, the ribozyme undocks and docks multiple times (CdCu, boxed in purple) before religating. (b) A sample Eapp time trace obtained during the experiment in a. Upon addition of 1 mM Mg2+ (blue arrow) the ribozyme docks (high FRET) and remains docked until it exhibits a brief period of rapid undocking and docking signifying a cleavage event (purple bar). (c) Schematic of the principle of the experiment to identify the cleaved form of the ribozyme. Species with the 5' cleavage product annealed but lacking the 3' cleavage product (Pu) are generated in situ. The long 3' product (500 nM) is pumped into the sample chamber in the presence of buffer including 1 mM Mg2+. This anneals to the ribozyme, giving a conformational equilibrium between undocked (Cu) and docked (Cd) species. Ligation generates species Ld. (d) A sample Eapp time trace obtained during the experiment in c, showing rapid docking-undocking (indicated by the purple bar) before a transition to the stably docked state. (e) A cumulative histogram showing the fraction of molecules ligated after the specified number of docking events. The histogram is fitted by a double exponential with decay constants of N1 = 2.2 and N2 = 11 docking events.
Assignment of the cleaved ribozyme To show that the bursts of rapid docking and undocking are due to the dynamics of the cleaved ribozyme, we induced cleavage in species 1 by addition of 1 mM Mg2+, generating species 2 (Fig. 4c). The junction-like structural transitions of this species are too fast to be resolved12, resulting in low FRET (Fig. 4d, first few seconds). At this point we added in a solution containing 1 mM Mg2+ and 500 nM of the long 3' product. Shortly thereafter we observed rapid docking and undocking followed by stable docking (Fig. 4d). We attribute the time lag between buffer exchange and initial docking mostly to the time taken for binding the long 3' product. Because the ribozymes are in the cleaved form immediately after product annealing, we conclude that the rapid dynamics are characteristic of the cleaved ribozyme. The rates determined from the initial transitions, kCdock = 2.6 0.2 s-1 and kCundock,obs = 2.4 0.2 s-1 (Supplementary Fig. 1 online), are comparable to the rates measured in the multiple cycles experiment, further supporting our interpretation.
On addition of the 3' product, 49 of 59 molecules switched to the stably docked state before photobleaching. Of these, 13 made a direct transition to the stably docked state; we interpret this to result from ligation reactions occurring during the first docking event. Excluding molecules that photobleached before ligation, we obtain a cumulative histogram (Fig. 4e) of the number of docking transitions observed before the stably docked state was achieved. A better agreement with the data can be obtained with a double-exponential fit with decay constants of 2.2 and 11 transitions than with a single exponential, suggesting that the ligation reaction rate is not homogeneous. The average number of docking events before ligation weighted by relative populations is 6.7 1.0.
Rapid undocking follows cleavage The preceding experiments allow us to explain the complex behavior observed in the multiple cycles experiment (Fig. 3). The ligated ribozyme is stably docked but undocks rapidly after cleavage. Because the 3' product remains bound, the cleaved ribozyme docks and undocks rapidly until ligation occurs. From this experiment we obtained an average time in the cleaved state of 8.1 0.7 s (Supplementary Fig. 2 and Supplementary Note online). From the simple ligation experiment we obtained a value of 5.6 0.4 s by multiplying the average number of docking events until ligation (6.7) and the average time for one docking-undocking cycle (1/2.5 + 1/2.3 s). We therefore estimate the apparent ligation rate to be between 1/8.1 = 0.12 s-1 and 1/5.6 = 0.18 s-1 (7.4−11 min-1). The internal ligation rate (kL), defined as the rate of ligation in a docked ribozyme, is about twice as large (0.24−0.34 s-1), because the cleaved ribozyme spends about half of its time in the docked state (Fig. 3d,e). We favor the latter value because in the multiple cycles experiment some cleavage events are missed (Supplementary Note online). Because the observed rate of undocking of the cleaved form is the sum of the rates of undocking and ligation, we obtain a corrected undocking rate kCundock = 2.0 s-1. Because undocking is much faster than ligation, multiple docking events are typically needed before ligation occurs. By the same reasoning, once cleavage occurs the molecule is more likely to undock than to religate and a majority of cleavage events can be detected as rapid docking and undocking.
The internal cleavage rate (kC) is 1.0 min-1 (0.017 s-1) in the presence of 1 mM Mg2+, as determined from the multiple cycles experiment (Supplementary Note online). Photobleaching in this experiment led to an underestimation of the time spent in the ligated state, and an overestimation of the rate of cleavage. However, the apparent cleavage rate obtained in the simple cleavage experiment will be close to the internal rate of cleavage because kCundock > kL and kCundockkc,app. Therefore, we favor the rate of 0.60 0.1 min-1 (0.010 s-1) (Fig. 2c) obtained in this experiment. We calculate an internal equilibrium constant between cleavage and ligation in 1 mM Mg2+ as Kint = kL / kC = 0.34 / 0.010 = 34, showing that the equilibrium is substantially biased towards ligation.
pH-dependence of ligation and cleavage rates We examined the dependence of the ligation rates on pH by carrying out the multiple cycles experiment. Docking and undocking within the cleaved form are substantially faster than ligation at all pH values (Supplementary Fig. 3 online). Whereas the apparent ligation rate peaks at pH 7, the internal ligation rate, obtained by dividing the apparent ligation rate by the fraction of time spent in the docked state, is independent of pH above pH 7.5, but reduces at lower pH values, being approximately three-fold slower at pH 6 (Fig. 5a). The data are consistent with a sensitivity of the ligation reaction to a group titrating with an apparent pKa of 6.2 0.1.
Figure 5. pH-dependence of ligation and cleavage rates.
(a) The pH-dependence of apparent and internal ligation rates, determined from single-molecule multiple cycles experiments. The internal ligation rate data are fitted by equation 1, yielding an apparent pKa of 6.2 0.1. (b) The pH-dependence of the apparent cleavage rate determined from ensemble kinetic studies. The fast component is shown fitted by equation 1, yielding an apparent pKa of 6.3 0.1.
We also measured the pH-dependence of the cleavage reaction in bulk solution, under conditions that were closely similar to those used in the single-molecule experiments, where we know that docking and undocking are not rate-limiting. These reactions required two rates to describe the data. A clear pH-dependence was observed for the fast cleavage rate (Fig. 5b), consistent with the titration of a group with an apparent pKa of 6.3 0.1. The slower rate of cleavage (0.02 min-1) did not exhibit the same pH-dependence, suggesting that the reaction of some molecules may be limited by a conformational change (Supplementary Fig. 4 online).
Cyclic phosphate accelerates undocking In single-molecule studies of the minimal form of the hairpin ribozyme, a 5' product that was terminated by a 3' phosphate was used to simulate the cleaved form of the ribozyme14. The undocking rates measured both for this construct and for the noncleavable ribozyme were 10-2 s-1. In contrast, our studies of the four-way junction form show that the undocking rate of the cleaved ribozyme with a cyclic phosphate is markedly accelerated compared with that of the ligated state.
To investigate this discrepancy we studied junction forms of the cleaved ribozyme in which the 5' product had either terminal 3' phosphate or hydroxyl groups. In both cases, we observed that undocking was almost an order of magnitude slower (kCundock = 0.28−0.34 s-1, Fig. 6) compared with the natural cleaved ribozyme (kCundock = 2.3 s-1). In addition, the rates of docking for these non-natural products were accelerated more than two-fold. This suggests that the loss of backbone continuity alone cannot account for the marked acceleration of undocking in the cleaved ribozyme and that even seemingly minor alterations of the products can affect the structural dynamics substantially.
Figure 6. Structural dynamics of cleaved, nonligatable ribozymes.
(a,b) Weighted dwell time histograms (158 molecules) for the docked (a) and undocked (b) states of the nonligatable ribozyme terminated at the 3' end of its 5' product with a hydroxyl group. Single-exponential fits give a docking rate constant of kOHdock = 6.8 0.5 s-1 and an undocking rate constant of kOHundock = 0.28 0.03 s-1. (c,d) Weighted dwell time histograms (74 molecules) for the docked (c) and undocked (d) states of the nonligatable ribozyme terminated at the 3' end of its 5' product with a phosphate group. Single-exponential fits give a docking rate of kPO4dock = 5.0 0.6 s-1 and an undocking rate of kPO4undock = 0.34 0.04 s-1. Because of the heterogeneity in these data, single exponentials provide poor fits at longer times and produce overestimates of rates. If the heterogeneity were to be fully accounted for, the difference between the undocking rates of ribozymes with natural and non-natural products would be larger than a factor of 10.
Discussion We have observed the internal cleavage and ligation reactions of a ribozyme for the first time. We clearly distinguished the cleaved and ligated forms through single-molecule spectroscopy, on the basis of their distinct structural dynamics. This enabled us to describe the kinetic pathway for the reaction of the natural form of the hairpin ribozyme (Fig. 7a).
Figure 7. Ribozyme dynamics and the replication cycle of viral satellite RNA.
(a) Summary of the rates for structural dynamics and ligation-cleavage reactions in 1 mM Mg2+. Docking and undocking rates within the ligated form cannot be determined reliably in the presence of 1 mM Mg2+ because most molecules remain docked until photobleaching occurs. (b) The role of the hairpin ribozyme in the tobacco ringspot viroid satellite RNA replication cycle. The circular (+) strand of the tobacco ringspot viral satellite is transcribed by an RNA-dependent RNA polymerase (RNAP) in a rolling circle process. The concatenated (-) strand transcript is cleaved into monomeric linear RNA by the action of the hairpin ribozyme. This RNA is cyclized by the ligation activity of the same ribozyme. The circular (-) strand RNA is then used as the template for the synthesis of the (+) strand RNA, which is processed by the hammerhead ribozyme.
The apparent ligation rate of 11 min-1 has been estimated in 1 mM Mg2+ at 20 °C. This rate is similar to those estimated previously in 2 mM Mg2+ at 30 °C (9.2 min-1)17 and in the intracellular conditions of yeast (4 min-1)18. The single-molecule approach revealed that the cleaved ribozyme is not stably docked under these conditions, and an internal ligation rate of kL = 21 min-1 was obtained from our data after taking into account the proportion of time the cleaved molecule spends in the docked state.
The simple cleavage experiment gave an apparent cleavage rate of 0.60 0.1 min-1 (0.010 s-1) in 1 mM Mg2+ at 20 °C. Because product dissociation is known to be rapid3, and we have shown that the undocking rate is substantially faster than cleavage and ligation, this rate should closely approximate the internal cleavage rate. This cleavage rate is similar to the apparent cleavage rates that were estimated previously in 2 mM Mg2+ at 30 °C (k = 1.3 min-1)17 as well as in the intracellular conditions of yeast (k = 0.7 min-1)19. The internal equilibrium constant between cleavage and ligation (Kint = kL / kC = 34) shows that the equilibrium is substantially biased towards ligation.
Our internal cleavage rate is considerably lower than that deduced for the minimal form (12 min-1)14; however in that work and subsequent studies with sequence variants20 the cleavage and ligation reactions were not observed directly, rather their rates were estimated using a model with several assumptions that were not independently verified. For instance, it was assumed that molecules with highly heterogeneous docking-undocking kinetics share a single cleavage rate and a single ligation rate. It was further assumed that docking-undocking kinetics measured from noncleavable mutants and nonligatable mutants are identical to those of catalytically competent ribozymes. However this assumption is questionable because we observed undocking rates that were reduced by at least a factor of 10 from nonligatable ribozymes.
In 1 mM Mg2+ the rates of docking and undocking of the cleaved form are 2.5 and 2.0 s-1, respectively. These are an order of magnitude slower than the corresponding rates for the four-way junction under the same conditions, indicating that the interaction between the loops is rate-limiting for docking. A previous study21 concluded that the transition state for the folding of the minimal form of the ribozyme resembles loosely associated loops. We cannot measure the docking-undocking dynamics of the ligated form accurately under these conditions, because the ribozyme seems to be stably folded during the observation time (1 min) that is limited by photobleaching. Undocking must therefore be accelerated by at least two orders of magnitude upon cleavage.
We have shown previously12 that in the ligated form of the natural ribozyme, the rate of docking is much faster than cleavage. Combining this with our measurements of the cleaved ribozyme leads us to conclude that the reaction of the natural ribozyme is not limited by the structural dynamics of docking and undocking under close to physiological conditions. Furthermore, the sensitivity to pH of the observed rates is consistent with the measurement of the rates of internal cleavage and ligation. The apparent pKa values of 6.3 and 6.2 observed for cleavage and ligation reactions, respectively, compare with those of 6.5 for cleavage and 5.6 for ligation measured previously22 in the presence of 10 mM Mg2+. Bases that could be responsible for the pH-dependence include A38, which could act as a general acid in the cleavage reaction8 and A10, which has exhibited pH-sensitivity in nucleotide analog interference mapping experiments23.
Only the cleaved ribozyme with a cyclic 2'3' phosphate exhibits the docking-undocking characteristics we have described above, and replacement with either 3' OH or 3' PO4 led to markedly different dynamic properties. Crystal structures have been solved of the hairpin ribozyme in the precursor form (noncleavable ligated), in a non-natural product form (5' product terminated by a 3' OH), in the natural product form, and as a transition state analog8,
15. These forms are almost identical, with one major difference in the stereochemistry of the ribose ring at the A1 position. Sugar pucker in the cyclic phosphate-containing product was found to be uniquely altered in this form15. It is possible that this leads to the observed altered dynamics.
The dynamic properties of the hairpin ribozyme are well suited to the biological role in the replication cycle of the tobacco ringspot virus satellite RNA. The (-) strand is produced by an RNA-dependent RNA polymerase using the (+) strand as a template in a rolling circle process, and the concatameric transcript is processed into monomeric units by the cleavage activity of the hairpin ribozyme (Fig. 7b)24,
25. Each cleavage reaction creates the 3' end of one monomer and the 5' end of the subsequent monomer. Although the cleavage reaction is relatively slow, once it occurs the rapid undocking of the cleaved ribozyme will facilitate dissociation of the monomers. The predicted secondary structure of the (-) strand indicates that the 3' product will form a helix of 6 bp (ref. 26). Such a product is estimated to dissociate from the minimal ribozyme with a rate of 0.3 s-1 in 10 mM Mg2+ (ref. 17) and this may occur more slowly in the natural form3. Product dissociation may therefore be a limiting factor in the replication cycle. However, this may also be influenced by factors not addressed in this study such as flanking RNA sequences and cellular proteins. After dissociation, the increase in translational entropy will favor the monomer forming a hairpin ribozyme in a unimolecular process. The internal equilibrium for cleavage and ligation then ensures the efficient production of a circular template for the synthesis of the (+) strand. Thus, the structural dynamics and internal equilibrium of the ribozyme facilitate a productive replication cycle.
Methods RNA preparation. RNA was synthesized using t-BDMS-phosphoramidite chemistry and deprotected and purified as described27, or purchased from Dharmacon and deprotected and purified according to the manufacturer's recommendations. The hairpin ribozyme was assembled from oligonucleotides of the following sequences (all are written 5'3', with deoxyribonucleotides in lowercase and ribonucleotides in uppercase): a strand, Cy3-cCGACAGAGAAGUCAACCAGAGAAACACACUUGCGg; b strand, Cy5-cCGCAAGUGGUAUAUUACCUGGUACGCGUUCACGg; c strand, biotin-cCGUGAACGCGUGGUGCGAAUCGg.
The substrate strand d had the following sequences: ligated form (giving 10 nt 3' product), cCGAUUCGCACCUGACAGUCCUGUCGg; ligated form (giving 6 nt 3' product), cCGAUUCGCACCUGACAGUCCUG.
The cleaved form required two oligonucleotides to form strand d. The 3' strand was GUCCUGUCGg in each case, whereas the 5' strand was cCGAUUCGCACCUGACA, where the nature of the 3' terminus varies with the experiment as detailed in the text. The 5' product with a 3' phosphate was synthesized from a precursor oligonucleotide with the sequence cCGAUUCGCACCUGACAG by periodate oxidation and -elimination of the 3'-terminal guanosine28, and was purified by gel electrophoresis.
Each construct was assembled from a mixture of component strands with a molar ratio of 0.8:1.2:1:1.2 (a/b/c/d), except that a two-fold excess of the oligonucleotides comprising strand d was used when assembling the cleaved form. The mixture was annealed by heating to 80 °C in 10 mM HEPES, pH 7.5, 50 mM NaCl, and allowing it to cool slowly to room temperature.
Single-molecule spectroscopy. Single-molecule fluorescence measurements were made using a wide-field prism-type total internal reflection microscope with 100-ms time resolution as described12,
13. The ribozyme molecules were attached to the streptavidin coated quartz surface via a biotin conjugated to the 5' terminus of arm C. Perturbation due to surface tethering must be insignificant because we obtained identical folding kinetics including heterogeneity from ribozymes encapsulated in phospholipid vesicles29. Cleavage experiments were done using a flow cell coupled to a syringe pump. Unless otherwise specified, measurements were made at 20 °C in 10 mM HEPES, pH 7.5, 50 mM NaCl, using an oxygen scavenger system30 (6% (w/v) glucose, 1% (v/v) 2-mercaptoethanol, 0.1 mg ml-1 glucose oxidase, 0.02 mg ml-1 catalase) with specified amounts of MgCl2.
Determination of rates by dwell-time analysis. After correcting for donor leakage into the acceptor channel and the direct excitation of the acceptor, time traces of the apparent FRET efficiency Eapp were calculated using Eapp = IA / (IA + ID) where IA and ID are the acceptor and donor intensities, respectively. Histograms of dwell times of individual states were generated and fitted by exponential decay functions to obtain rate constants. Details of the calculation of the rates of cleavage and ligation are given in the relevant sections of the text and Supplementary Note online. All errors reported here denote single standard deviations.
Weighted histograms were used to obtain the docking and undocking rates of the ribozyme with nonligatable 5' and 3' cleavage products because the population was heterogeneous. Treating each dwell time equally would lead to an over-representation of quickly fluctuating molecules because they undergo a larger number of transitions before photobleaching. To avoid such bias, dwell times from each molecule were weighted by a factor inversely proportional to the number of transitions observed for that molecule.
pH-dependence of ligation and cleavage. The pH-dependence of ligation was determined by doing the single-molecule multiple cycles experiment as described above, except that 10 mM HEPES, pH 7.5, was replaced with 10 mM of the buffers CHES (pH 9.5), Tris (pH 8−9), HEPES (pH 6.5−8) and MES (pH 6.0−6.5).
Cleavage assays in bulk solution were done using the three ribozyme strands listed above (except that no fluorophores or biotin were attached to the 5' ends) and a radioactively labeled short substrate strand. Assays were done under single-turnover conditions at 25 °C in solutions containing 50 mM NaCl, 1 mM MgCl2 and 10 mM of buffer. The buffers used were acetate (pH 5.0−5.5), MES (pH 5.5−6.75), HEPES (pH 6.75−8.0) and TAPS (pH 8.0−9.0). Where pH ranges overlap, experiments with alternative buffers showed no substantial difference in cleavage rates. Cleavage was initiated by addition of MgCl2 and aliquots removed at various times, terminated in formamide-EDTA and run on denaturing polyacrylamide gels to determine the extent of reaction. Reaction time courses exhibited biphasic kinetics. The data reported at each pH are the average and s.d. of between three and six independent assays.
Estimates of the pKa of titratable groups were obtained by fitting the observed rates of ligation or cleavage (kobs) to equation (1):
where kmax and kmin are the maximum and minimum observed rates, respectively. The uncertainties reported are the asymptotic standard errors of the fitted parameters.
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Acknowledgments Funding was provided by the US National Science Foundation (NIH) (PHY-0134916, DBI-0215869, T.H.), by the US National Institutes of Health (GM065367, T.H.), and by Cancer Research-UK (D.M.J.L.). M.K.N. was partially supported by the NIH molecular biophysics training grant (T32GM008276).
Competing interests statement:
The authors declare that they have no competing financial interests.
2 mM (
100 s is the result of cleavage and product release, leading to the emergence of the junction-like behavior. To reduce photobleaching, one data point of 0.1 s duration was recorded every second by means of a laser shutter. (c) Apparent rate of cleavage as a function of Mg2+ concentration for the dominant ribozyme population.
0.1 s-1 and kCundock,obs = 2.3 
Cu) before ligating back to Ld. (b,c) Time traces of the apparent FRET efficiency, Eapp. Purple bars denote regions of rapid docking and undocking arising from the cleaved ribozyme corresponding to the ribozyme conformational changes shown in the purple box in a. (d) Histogram of the undocked state dwell time of the cleaved ribozyme (tCundocked) constructed from 82 molecules. A single-exponential decay fit gives the docking rate for the cleaved ribozyme, kCdock = 2.5 
kc,app. Therefore, we favor the rate of 0.60 
3', with deoxyribonucleotides in lowercase and ribonucleotides in uppercase): a strand, Cy3-cCGACAGAGAAGUCAACCAGAGAAACACACUUGCGg; b strand, Cy5-cCGCAAGUGGUAUAUUACCUGGUACGCGUUCACGg; c strand, biotin-cCGUGAACGCGUGGUGCGAAUCGg.
-elimination of the 3'-terminal guanosine
