Pan T. X. Li *, Carlos Bustamante *^{, 1, 2}, and Ignacio Tinoco Jr. *¶

Departments of *Chemistry and ¹Physics and Molecular and Cell Biology, and ²Howard Hughes Medical Institute, University of California, Berkeley, CA 94720

¶To whom correspondence should be addressed.
Ignacio Tinoco Jr., E-mail: intinoco@lbl.gov

Author contributions: P.T.X.L., C.B., and I.T. designed research; P.T.X.L. performed research; P.T.X.L. and I.T. analyzed data; and P.T.X.L. and I.T. wrote the paper.

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.

Tertiary interactions enable RNA to form long-range contacts and thereby form complex structures. However, thermodynamic and kinetic information for these interactions is scarce (1). Recent developments in single-molecule techniques allow a close look at the folding of individual RNA molecules (2–4). Particularly, the application of force to single-ribozyme molecules by optical tweezers (3) revealed the detailed unfolding pathways of this 390-nt RNA in nondenaturing solutions at physiological temperatures. It remains a challenge, however, to study the kinetics of individual steps in folding an RNA with complicated tertiary structures.

A kissing interaction, a basic type of RNA tertiary contact, is the base-pairing formed by complementary sequences in the apical loops of two hairpins (5). Intramolecular kissing complexes have been found in many RNA structures, ranging from 75-nt tRNAs (6, 7) to megadalton ribosomes (8); intermolecular kissing interactions also are critical for many biological processes (reviewed in ref. 5), such as dimerization of retroviral genomic RNAs (9, 10). The simplest kissing interaction is formed between a pair of hairpins each with a GACG tetraloop (11). The third and fourth nucleotides in the loop form two G·C base pairs with their counterparts from the other hairpin. This minimal kissing interaction was initially found in the genomic RNA of Moloney murine leukemia virus (MMLV), an extensively studied retrovirus (12) and one of the most used vectors for gene therapy (13). The 5' UTR of the MMLV genomic RNA contains four closely spaced stem loops (SL-A - SL-D) (14), each of which is capable of forming a kissing interaction with its counterpart in another copy of the genomic RNA (11, 15, 16). This region, including the two hairpins with GACG loops (SL-C and SL-D), serves both as the RNA dimerization initiation site (DIS) and as the RNA encapsidation signal ({psi}) (17, 18).

The kissing hairpins are evolutionarily conserved in the DIS region of retroviruses, and mutational disruption of the kissing usually compromises the viral packaging, viability, and infectivity (9). However, because these homodimeric kissing complexes are structurally rearranged into more stable extended duplexes in the mature viral particle (9, 10), they are frequently labeled as labile or metastable dimer intermediates. So how stable are the kissing complexes? To address this question, we used an optical tweezers technique to test the mechanical stability of a minimal kissing complex.

Based on the kissing complexes formed by SL-C and SL-D hairpins (11, 16), we designed an RNA (KC30) containing two hairpins linked by 30 A-rich nucleotides (Fig. 1). The two hairpins, each with a GACG loop, can form an intramolecular kissing complex. The linker between the hairpins allowed refolding of the kissing complex after the RNA unkissed such that a kissing complex can be repeatedly unfolded and refolded many times. To avoid adding strain to the kissing structure, the linker was designed to avoid secondary structure; it was roughly twice as long as the end-to-end distance of the kissing hairpins. We assume that the helical axes of the two hairpins are parallel to the direction of applied force, in contrast to the unzipping of a hairpin, during which the axis of the hairpin is perpendicular to the force (1). The KC30 RNA, flanked by two ~500-bp DNA/RNA handles, was tethered to two micrometer-sized polystyrene beads through affinity interactions (2) (Fig. 1). The two beads were held by a dual-beam optical trap and a micropipette, respectively (2, 19). Movement of the micropipette changed the extension of the molecule and generated tension. The folding reaction was studied at 22°C in a flow chamber containing a buffer of 10 mM Hepes (pH 8.0) and 250 mM KCl, in which the structure of the minimal kissing complex formed by a pair of unlinked hairpins was determined (3).

Fig. 1. Experimental setup.

Fig. 1. Experimental setup.

KC30 RNA contains two hairpins linked by 30 A-rich nucleotides. The GACG loops of the two hairpins can form a kissing complex. This RNA is flanked by double-stranded DNA/RNA handles, through which the entire molecule can be tethered between two microspheres by affinitive interactions. The streptavidin-coated bead was held by a force-measuring trap (28). The digoxigenin-coated bead was mounted on a micropipette. By moving the piezoelectric flexure stage on which the micropipette was attached, force was exerted on the RNA in the direction shown by the arrows. The drawing is not to scale.

In force-ramp experiments, an RNA molecule was repeatedly stretched and relaxed. When the double-stranded handles alone were pulled, the force increased monotonically with extension (2), as typically described by a worm-like-chain interpolation formula (20). Unfolding an RNA structure suddenly increased the extension of the molecule, resulting in a "rip" on the force–extension curve. Similarly, a "zip" that decreased the extension indicated a folding step. Such changes in the extensions caused the trapped bead to quickly move either toward or away from the center of the trap, thus altering the force. Therefore, in the force–extension curves, both rip and zip transitions have negative slopes, in sharp contrast to the elastic stretching of the handles. After the RNA was unfolded into a single strand, the force again increased monotonically with the extension to ~60 pN (2, 3, 21).

Several transitions were observed in the force–extension curves of KC30 RNA (Fig. 2a–c). To relate these transitions to the structural changes, we pulled individual hairpins and a pair of hairpins that cannot form kissing interactions (Fig. 2 d–f). Hairpin 1, containing 11 base pairs and a tetraloop, unfolds and refolds several times between 16 and 20 pN with a change in extension, DX, of ~9–10 nm. The value of DX is consistent with the value estimated from a worm-like-chain model (20) using a persistence length of 1 nm and a contour length of 0.59 nm per nucleotide (2). The many unfolding/refolding transitions within a few piconewtons indicates the bistability of the hairpin: Free energies of unfolded and folded states at these forces are very close, and the kinetic barrier between the two states is low. Such quick transitions between the two states was previously termed "hopping" (2). The transition force of hairpin 2 ranges from 14 to 18 pN. DX for unfolding this hairpin with seven base pairs is ~4–5 nm. The equilibrium force, F1/2, at which unfolding and refolding rates are equal, is 17.6 ± 0.1 pN for hairpin 1 and 16.0 ± 0.1 pN for hairpin 2. In the two-hairpin KC30AA RNA, the apical loop of hairpin 2 was mutated from GCAG to GAAA. As expected, formation of the two hairpins but not the kissing interaction was observed in the folding of this RNA.

Fig. 2. Force–extension curves of KC30 RNA and its mutants.

Fig. 2. Force–extension curves of KC30 RNA and its mutants.

(a–c) The typical trajectories of KC30 RNA. Three types of unfolding (blue) curves were observed, but all refolding (green) follow the same pathway.

(d–f) The unfolding/refolding curves of hairpin 1, hairpin 2, and KC30AA RNA. KC30AA RNA is identical to KC30, except the apical loop of hairpin 2 is mutated to GAAA to prevent the formation of the kissing interaction.

The experiments on the individual hairpins and the mutant lacking the complementary loops make the transitions on the force–extension curves of KC30 RNA interpretable (Fig. 2 a–c). When force was relaxed from 30 pN (green curves), the two hairpins formed first between 20 and 14 pN. The third transition with DX of ~7 nm, which occurred at 5–10 pN, represents the kissing interaction between the two hairpins. On extension, three types of force–extension curves were observed. The first type of curve displays three transitions: a rip of ~10 nm at ~7–17 pN followed by unfolding of the two hairpins. This first rip indicates the unkiss, i.e., the disruption of the kissing interaction. The second type of unfolding curve shows only two transitions: In the first one, the kiss and hairpin 2 appear to be unfolded in a single step (15–20 nm, double transition); DX of the second transition is similar to the unfolding of hairpin 1. Only a single, big rip appears in the third type of unfolding trajectory. The DX of this rip (~30 nm) is consistent with the entire RNA being unfolded in a single step (triple transition). To confirm the unkiss and kissing transitions, we repeated the pulling experiments but only relaxed the force to >10 pN to prevent the kissing. As expected, such trajectories show only the folding and unfolding of the two hairpins, similar to the KC30AA mutant (data not shown). This observation clearly indicates that the kissing interaction only occurs after the formation of the hairpins (Fig. 3a).

Fig. 3. Three types of unfolding trajectories of KC30 RNA.

Fig. 3. Three types of unfolding trajectories of KC30 RNA.

(a) Unfolding and refolding pathways. The first apparent transition can contain one, two, or three steps.

(b) Distribution of the three types of transition forces at 1.3 pN/s. Totally, 102 observations were split into unkiss alone (+), double transition (circles), and triple transition (blacksquares).

(c) Percentage of the three types of unfolding trajectories: three-step unfolding with an unkiss transition (light gray), two-step unfolding with a double transition (black), and one-step unfolding with a triple transition (dark gray). Each column summarizes the results of at least 100 trajectories.

In contrast, in all three types of mechanical unfolding curves of KC30 RNA, the first transition always includes the unkiss, suggesting that the hairpins cannot be unfolded before the kissing interaction is disrupted. The unfolding trajectories can be explained by a kinetic mechanism (Fig. 3a) with two premises: The unkiss is always the first unfolding step, and the unkiss occurs over a large range of the force. Therefore, the occurrence of the three types of unfolding trajectories is determined by the unkiss. Because the kissing interaction broke at forces <16 pN, both hairpins remained intact, and the unfolding appears to take three steps. When the RNA unkissed at forces >16 pN, hairpin 2 became unstable and quickly unfolded; the first unfolding step appears as a double-transition. If the kissing interaction survived until force was raised above F1/2 of hairpin 1, an apparent triple transition, in which two hairpins unfold right after the unkiss, occurred. Force distribution of the first unfolding transition categorized by the three types (Fig. 3b) is consistent with this kinetic scheme.

When pulled faster, RNA structures tend to break at higher forces (2, 22). At higher loading rates, KC30 RNA unkisses at higher forces such that three-step unfolding becomes rare and that occurrence of the triple transition is more likely. This trend is clearly shown in Fig. 3c. At 0.7 pN/s, >70% of the trajectories are three-step. However, the occurrence of this type drops quickly as the loading rate increases. At loading rates of 1.3 pN/s or higher, most trajectories show a single triple transition. The two-step curves always represent a small fraction of total trajectories, first increasing to ~20% at 1.3 pN/s, then decreasing as the loading rate increases.

Therefore, force distribution of the first unfolding transition effectively reflects the kinetics of the unkiss. To extract kinetic parameters of the unkiss, all of the first rip forces at 1.3 pN/s were pooled and analyzed by using the following equation (22):

where N(F, r) is the fraction of folded molecule at force F and loading rate r; A is the apparent rate constant at zero force (2, 21); XFormula is the distance from the initial structure to the transition state; kB is the Boltzmann constant; and T is the temperature. We obtained XFormula of 0.78 ± 0.04 nm for breaking the kissing interaction. Analyses of the force distributions collected at different loading rates yield similar results (data not shown). From the force-ramp experiments of the individual hairpins, we also obtained that the X{ddagger} for disrupting hairpins 1 and 2 are 6.3 ± 0.3 nm and 4.2 ± 0.2 nm, respectively (Table 1, which is published as supporting information on the PNAS web site). Noticeably, X_unkiss for breaking the kissing interaction is significantly smaller than that for unfolding hairpins. The difference in X_unkiss also is reflected in the rip force distribution because the value of X{ddagger} is inversely correlated to the width of the rip's force distribution. Most rips of hairpins 1 and 2 occurred within a force range of 3 pN. In contrast, the unkiss force ranges from 7 to 30 pN at 1.3 pN/s (Fig. 3b).

The value of X{ddagger} also reflects how the rate constant changes with force. Eq. 1 was derived with the assumption that the dependence of the rate constant, k(F), on force can be described by an Arrehnius-like equation (23):

For hairpins 1 and 2 with XFormula of ~4–6 nm, the unfolding rate constants rapidly increase with the force. From a narrow force range of ~1–2 pN, such structural transitions occur either too fast or too slow to be detected. However, the small XFormula indicates that the rate constant of the unkiss transition can be measured over a wide range of force.

Unkiss and Kissing Kinetics Measured by Force Jump

To verify this unusual force dependence of the unfolding kinetics, we measured the unkissing rate constants at forces ranging from 13.5 to 30 pN by using a force-jump method (24). The applied force was rapidly stepped to a new value and the structural transitions were monitored through changes in the molecular extension. The rate constants of these transitions can be obtained from the lifetimes of the unreacted species. In a typical experiment (Fig. 4), force was quickly raised from 3 pN to a set force and held constant. The extension of the molecule remained constant until the unfolding occurred. For instance, the extension increased ~30 nm upon a triple transition at >20 pN. After being raised to 30 pN or higher, the force was kept constant for a few seconds to ensure that the RNA became single-stranded, before it was ramped down to ~13–14 pN. The refolding of the two hairpins during the ramp was indicated by the small zips in the extension. The force was then dropped to ~7–8 pN to allow the kissing interaction between the hairpin loops, which was indicated by a decrease of the extension of ~7–8 nm. After the kissing complex formed, the force was ramped down to 3 pN before starting another cycle of experiments.

Fig. 4. Unkiss and kissing transitions monitored at constant forces.

Fig. 4. Unkiss and kissing transitions monitored at constant forces.

(Upper) In a typical force-jump experiment, force was first quickly stepped from 3 to 22 pN.

(Lower) When a triple transition occurred, extension of the molecule increased by ~30 nm. The force was then raised to 30 pN before being ramped to 14 pN. Next, the force was dropped rapidly to 8 pN.

(Inset) The kissing shortens the extension by ~7–8 nm. The detect position reflects the change in the molecular extension.

By using this approach, we followed the unfolding of KC30 RNA at various forces. As set force increased, the first unfolding transition changed from the unkiss alone to a double transition, and then to a triple transition (Fig. 5). At forces ranging from 13.5 to 15 pN, DX of the first transition was ~10 nm, consistent with the unkiss alone. The two hairpins were intact until the force was further raised (data not shown). When the force was held constant between 15.5 and 17 pN, DX of the first unfolding transition was ~13–20 nm, suggesting that hairpin 2 unfolded along with the unkiss. When the force was subsequently ramped up, hairpin 1 was unfolded at between 17 and 20 pN. The triple transition with DX of ~30 nm was observed at forces of >17 pN. By using the worm-like-chain interpolation formula (20), we calculated DX for the three types of the unfolding transitions (Fig. 5d). The measured values of DX for each type of transition match the predicted values.

Fig. 5. Step size of the first unfolding transition.

Fig. 5. Step size of the first unfolding transition.

(a–c) When KC30 RNA was unfolded at constant forces, the first transitions were unkiss alone, double transition, or triple transition.

(b) At ~16 pN, after the double transition, extension of the molecule hopped frequently, indicating the reversible unfolding of hairpin 2.

(c) Similarly, hairpin 1 hopped at 17.7 pN once the triple transition occurred.

(d) DX of the first unfolding transition as a function of force. Each value represents at least 100 observations. {blacktriangleup}, bullet, and {blacksquare} represent unkiss alone, double transition, or triple transition, respectively. Dashed curves are DX calculated by using the worm-like-chain interpolation formula (20). In these calculations, the persistence and contour length of a single strand are 1 nm and 0.59 nm per nucleotide, respectively; and the contour length of each base pair in the hairpin was assumed to be 0.3 nm.

The force regions at which the three types of unfolding occurred are consistent with the force-dependent kinetics of disrupting individual structures (Fig. 5d). The double transition occurred in the same force region that hairpin 2 unfolds, but hairpin 1 remains stable. The unkiss alone takes place below this force range, whereas the triple transition occurred at forces no less than the unfolding force of hairpin 1. The rate-limiting effect of the unkiss step in the unfolding is most evident in the unfolding traces at ~16 pN and at 17.7 pN. At ~16 pN, only after the double transition, the extension of the molecule hops back and forth with a DX of ~6 nm, indicating the hopping of hairpin 2 (Fig. 5b). At 17.7 pN, hairpin 1 hops once the triple transition occurred (Fig. 5c). The hopping rates of the hairpins at these forces were visibly fast, whereas the both the double and triple transition, rate-limited by the unkiss, took seconds to occur.

Over 100 observations of the lifetimes of the kissing complex at each force were pooled to generate the probability that the RNA had not yet unfolded at a given time. This probability decays as a single exponential function of time, indicating first-order kinetics for the unkiss. The average lifetime of the kissing complex ranges from 1.6 s at 30 pN to 23 s at 13.5 pN (Fig. 6). By fitting the data to Eq. 2, we obtained XFormula of 0.65 ± 0.8 nm, very similar to the value derived from the force-ramp experiments.

Fig. 6. Rate constant in unfolding/refolding KC30 RNA.

Fig. 6. Rate constant in unfolding/refolding KC30 RNA.

First-order rate constants of unkiss and kissing were obtained from at least 100 observations of lifetimes. {blacktriangleup}, bullet, and {blacksquare} represent unkiss alone, double transition, or triple transition, respectively. {diamondsuit} indicates the kissing. Dashed lines are fits to Eq. 2. Unfolding and refolding rates of hairpins 1 and 2 (Table 1) were estimated from the results of force-ramp experiments (2, 22). For hairpin 1, lnkf->u = (1.46 ± 0.07)F – (23.9 ± 0.3) and lnku->f = (–1.36 ± 0.06)F + (25.4 ± 0.3). For hairpin 2, lnkf->u = (1.02 ± 0.05)F – (15.3 ± 0.3) and lnku->f = (–1.35 ± 0.06)F + (24.4 ± 0.3). Hopping rates at F1/2 for both hairpins are consistent with these extrapolations (data not shown).

Because the kissing occurred at ~7–8 pN, the hairpins could not form the kissing interaction again once the kissing is disrupted at higher force. Under such conditions, the hopping of each of the two hairpins can be monitored at their transition forces. The unfolding and refolding rates of the hairpins near their F1/2 values are the same as those of the individual hairpins within experimental error. Disruption of tertiary interactions is often irreversible (3). It is therefore possible to use the force-jump method to selectively break certain interactions and measure the rate constant of a specific step. In a recent study, a similar approach was used in atomic force microscopy to study the steps in unfolding a protein (25). As demonstrated here, implementation of the force-jump method on the optical tweezers also makes it feasible to dissect complicated kinetics of folding a multidomain RNA.

This technique can also be used to measure the rate constant of the kissing, which occurred only after the formation of the hairpins (Fig. 4). We measured the kissing interaction at forces between 7.5 and 8.5 pN. At each force, the folding appears to follow first-order kinetics. The rate constant of the kissing increases as the force declines, as expected. We obtained a XFormula of 4 ± 1 nm by using Eq. 2. For a simple hairpin that folds reversibly without stable intermediate, X{ddagger} indicates the position of a single transition state along the reaction coordinate; the sum of XFormula and XFormula should equal DX, the change in the extension upon unfolding (21). However, the sum of XFormula and XFormula is only ~5 nm, well short of the DX of kissing ~7–8 nm). This observation suggests that the kissing and unkiss transitions involve multiple steps and that the transition states for the forward and reverse reaction are different.

The folding free energy for the kissing interaction can be estimated from the force dependence of the unkiss and kissing rate constants (Fig. 6). The rates become equal at ~0.02 s–1 when extrapolated to 9.9 ± 0.2 pN. Both the worm-like-chain model (20) and experimental data give DX of 8.6 nm when the kissing complex is unfolded into two hairpins at this force (Fig. 5d). Hence, DG10.2 pN 22°C, which equals the reversible mechanical work to unfold the kissing interaction at this F1/2, is 85 ± 2 pN·nm. After correction for stretching the single-stranded linker to F1/2 (2, 21), DG0pN 22°C 250 mM KCl, the kissing free energy at zero force, is 48 ± 2 pN·nm or 29 ± 1 kJ·mol–1, comparable with a DG0pN 37°C 100 mM NaCl of 27 kJ·mol–1 for the homodimeric minimal kissing complex measured by thermal melting (11). We also estimated the folding energy of hairpins 1 and 2 at zero force and 22°C as 69 ± 11 and 41 ± 10 kJ·mol–1, respectively (Table 1).

Discussion

Because the unkiss rate constant increases slowly with force at forces of >20 pN, under our experimental setup the unkissing rate is significantly slower than the unfolding rate of the hairpins. Under these forces, the unfolding rates of the two hairpins in the intact kissing complex are solely dependent on the rate-limiting unkiss step (Fig. 7a); the effective kinetic barrier for unfolding the hairpins corresponds to the unkiss. Clearly, the kissing interaction significantly increases the kinetic stability of the two hairpins at high forces.

Fig. 7. Rate-limiting effect of the unkiss.

Fig. 7. Rate-limiting effect of the unkiss.

(a) At high forces, the effective kinetic barrier for the overall unfolding is the one to break the kissing.

(b) When a triple transition occurs at high force (blue), the first part of the rip is to unkiss; the rest is the unfolding of the hairpins. The area under the rip for unfolding the hairpins (green) equals the mechanical work done to unfold the two hairpins in the kissing complex, which is significantly larger than the mechanical work to fold the hairpins (orange areas). This difference and the hysteresis between the unfolding and refolding curves reflect the enhanced kinetic stability of the hairpins imposed by the rate-limiting kissing interaction.

Such enhancement of the kinetic stability also is reflected by the hysteresis between the unfolding and refolding force–extension curves (Figs. 2 b and c and 7b). Particularly in the triple-transition curves, as force increased the hairpins were unfolded along with the kissing interaction at much higher forces than their normal unfolding forces. The unfolding forces of the hairpins is determined by the unkiss force. The hairpins do not experience the unzipping force until the kissing interaction is disrupted. The hysteresis between the unfolding and refolding of the hairpins represents the extra mechanical work required to unfold them in the presence of the kissing interaction (Fig. 7b). This phenomenon is more pronounced at higher loading rates, under which single-step trajectories are dominant and unkiss forces are higher.

Our results provide an example that tertiary interaction enhances the kinetic stability of an RNA by blocking the transmission of force to interior domains. The unfolding and refolding force–extension curves of L-21 ribozyme also display a large hysteresis (3). In that case, the rips were mapped to single-step unfolding of individual domains consisting of both secondary and tertiary structures. Some rips occurred as high as 25 pN and were possibly rate-limited by disrupting tertiary contacts. The refolding transitions, consisting of a series of small transitions, were not assigned. We now think that a large plateau at ~10–15 pN on the force–extension curve likely represents sequential folding of secondary structures and that some zip-like transitions at lower force indicate formation of tertiary interactions. The hierarchy in RNA folding (1) demonstrated in this work probably also applies to the mechanical unfolding/folding of L-21 ribozyme and other RNAs.

In the simplest scenario, disruption of the kissing interaction must involve two steps (Fig. 8, which is published as supporting information on the PNAS web site). First, the two kissing G·C pairs break, and then the two hairpins are pulled apart and the linker is stretched to an extension at which the tension matches the applied force, yielding most of the observable DX. The first step is presumably rate-limiting; consistently, XFormula is significantly smaller than DX, indicating that the position of the transition state is close to the kissing complex. The conformational change of the RNA at the transition state is projected on the end-to-end extension as XFormula. The value of XFormula of ~0.7 nm is roughly equivalent to the length of 2 bp. This value suggests two features of the unkiss: First, under tension, the helix axis of two kissing base pairs is nearly parallel to the direction of applied force; second, both kissing base pairs are broken at the transition state. The end-to-end distance of the molecule is therefore extended by 2 bp (Fig. 9, which is published as supporting information on the PNAS web site). Consistent with these suggestions, the kissing base pairs and the two stems are stacked coaxially in the NMR structure and the phosphate-to-phosphate distance of the two kissing base pairs is ~0.7 nm (11) (Fig. 10, which is published as supporting information on the PNAS web site).

The small value of XFormula, 0.7 nm, means that the unkiss rate constant is very insensitive to force, as compared with the rate constants of the hairpins. The minimal kissing interaction shows slow unfolding rates of ~0.05–0.5 s^-1 over a broad force range from 13 to 30 pN (Fig. 6). In contrast, unfolding and refolding rates of the hairpins change rapidly with the force. As a result, the two kissing base pairs can survive a few seconds at 30 pN, whereas the lifetimes for the hairpins are on the order of microseconds at this force. Such an unusual mechanical stability of this minimal kissing complex again indicates that both kissing base pairs are broken simultaneously. Force, as a vector, affects molecular structure depending on its direction. Hence, the geometry of the molecule relative to the direction of applied force affects the mechanical stability. For instance, when a single piece of double-stranded l-DNA was stretched from opposite ends, a overstretching transition occurred at ~65 pN (19); however, when the l-DNA was unzipped from the 5' and 3' termini at the same end, dissociation of the helix occurred at ~15 pN (26). Unfolding of a hairpin is similar to unzipping the l-DNA because in both cases the direction of force is perpendicular to the structure and causes the ripping fork to proceed by breaking base pairs sequentially (Fig. 11, which is published as supporting information on the PNAS web site). According to our hypothesis of kissing loops described above, the force is parallel to the axis of the kissing base pairs, similar to the geometry in stretching the l-DNA from the opposite ends. Under such shearing force, multiple base pairs need to break simultaneously to cause a structural transition; therefore, more resistance to the mechanical perturbation is expected.

We have observed that the sum of XFormula and XFormula is smaller than DX. These observations suggest that the transition state of the kissing is different from that of the unkiss. The kissing rate constant is determined both by the strength of the interaction and by the distance between the two loops. The latter is controlled by the tension and the length of the single-stranded linker. We notice that the apparent XFormula is roughly half of DX (Fig. 6), indicating that intramolecular diffusion plays an important role in determining the kissing rate.

In summary, we have found that this minimal kissing complex has characteristics distinct from those of secondary structures: the two kissing base pairs broken simultaneously by force, small XFormula and a nearly force-independent unfolding rate constant, relatively high mechanical stability, and increased folding irreversibility as indicated by the hysteresis between forward and reverse reactions. The hierarchy of RNA force folding is evident. Breaking the tertiary contact is the first unfolding step and becomes rate-limiting at high force; the kissing interaction forms last, only after the hairpins have folded. Further investigations are required to test whether these features are general to RNA tertiary structures.

Is the mechanical property of this RNA kissing complex important to the dimerization of retroviral RNAs? One clue comes from evolution. The kissing hairpins are found in all characterized retroviral DIS region. For instance, DIS of Moloney murine sarcoma virus contains two kissing hairpins with GACG loops (27). As we demonstrate here, even a minimal kissing complex with two G·C pairs is mechanically stable at 22°C, consistent with previous results from thermal melting and NMR studies (11). The presence of multiple kissing complexes surely increases the stability of RNA dimers and can speed the dimerization (18).

However, several "kissable" hairpins with the same loop can cause mismatch problems. In MMLV, the DIS/{psi} region contains four kissable hairpins, two of each kind (Fig. 12, which is published as supporting information on the PNAS web site). In the mature virus, the viral RNA dimer eventually evolves into a mature form, in which the first two kissing complexes (formed by SL-A and SL-B) are converted into extended duplexes and the other two kissing complexes may or may not exist in the final dimer (9, 10). However, mismatched kissing interactions, such as the one with SL-C from one RNA kissing SL-D from another strand, can also be formed. The mismatched kissing interactions in such dimers have to be disrupted before the mature dimer can be formed. We hypothesize that the relatively force-insensitive unkiss rate provides the minimal kissing complex almost constant stability over a large range of force; yet, even at low force, this structure is breakable in minutes, allowing it to form the correct kissing pairs or be rearranged into a mature duplex structure. The mechanism by which viruses solve this mismatch problem is a question for future research.

Materials and Methods

Preparation of RNA.

All four RNAs were cloned into pBR322 vector between the EcoRI and HindIII sites. Both KC30 and KC30AA RNA contain a 30-nt linker between the two hairpins. The linker sequence is 5'-AAAAA UAUCG AAAAA AATAC CAAAA AAAAA-3'. Hairpin 2 in KC30AA RNA contains an apical loop of GAAA. The plasmids were used as a template for PCR to produce a ~1.2-kb DNA containing the inserted sequence and two flanking "handles" ~500 bp long. This DNA also had a T7 promoter to be used as a template for in vitro transcription of the RNA with handles. DNA molecules with sequence complementary to the handles were also generated by PCR. Then the RNA and two DNA handles were annealed. The DNA handle upstream of the kissing structure was biotinylated at the 3' end, and the downstream DNA handle contained a digoxigenin group at the 5' terminus. Through affinity interactions, the annealed molecule can be attached to a pair of beads coated with streptavidin and antidigoxigenin antibody, respectively (Fig. 1).

Optical Tweezers.

Dual-beam optical tweezers (28) were used to study the folding of the kissing RNA. In a flow chamber, the streptavidin-coated bead was held by a force-measuring optical trap. The antidigoxigenin-coated bead was mounted on the tip of a micropipette by suction. The position of the micropipette was controlled by a piezoelectric flexure stage. By moving the micropipette, the extension of the molecule was changed, which induced tension on the molecule. Change in the extension of the molecule was measured by the relative movement of the trapped bead and the piezoelectric flexure stage.

Folding Experiments.

All unfolding/refolding experiments were done at 22°C in 10 mM Hepes, pH 8.0/250 mM KCl/1 mM EDTA/0.05% NaN3. In the force-ramp experiments, the piezoelectric flexure stage was moved in one dimension at a constant rate (nm/s), which generated a roughly constant loading rate (pN/s) between 3–30 pN. The force-jump experiments used a feedback control to maintain constant force (24). Force and extension of the molecule were recorded at a rate of 100 Hz.

Fig. 8. Simplest kinetic schemes for disruption and formation of a kissing complex involve an intermediate in which kissing base pairs are broken, but the two hairpins are closed. In unfolding, the two unkissed hairpins are then pulled away, yielding an observable DX (>10 nm). The rate-limiting substep in the unfolding is obviously the breaking of the kissing base pairs.

For simplicity, a 2D model is drawn here. In this model, we propose that the kissing helix is more or less parallel to the stem helixes. Breaking the two kissing base pairs would extend the entire molecule by 2 bp, which could count for X^‡_unkiss of 0.7 nm.

1. Kim C, Tinoco I, Jr (2000) Proc Natl Acad Sci USA 97:9396-9401.

F is force in piconewtons.

We thank Ms. Maria Manosas, Mr. Jeff Vieregg, Dr. Gang Chen, and Dr. Felix Ritort for critically reading the manuscript. This work is supported by National Institutes of Health Grants GM-10840 (to I.T.) and GM-32543 (to C.B.).

Footnotes

Abbreviations: MMLV, Moloney murine leukemia virus; DIS, dimerization initiation site; SL, stem loop.

¶To whom correspondence should be addressed. E-mail: intinoco@lbl.gov

Author contributions: P.T.X.L., C.B., and I.T. designed research; P.T.X.L. performed research; P.T.X.L. and I.T. analyzed data; and P.T.X.L. and I.T. wrote the paper.

The authors declare no conflict of interest.

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NetworkEditor's Perspective: "RNA-RNA Kissing bonds are selective and strong".

This unique study by Pan T. X. Li, Carlos Bustamante, and Ignacio Tinoco Jr. reveals that the RNA-RNA minimal kissing complex is highly selective and especially stable. Similar studies of the DNA-DNA kissing complex of interphase mammalian chromosomes are in progress.

Frenster JH, and Hovsepian JA, "Kissing Chromosomes and Paired Sense-Antisense RNA Synthesis".

Kioussis D, "Gene regulation: Kissing Chromosomes",  Nature vol. 435, no. 7042, pp. 579-580 (June 2,  2005).  http://www.nature.com/nature/journal/v435/n7042/full/435579a.html

1. Changbong Hyeon and Dave Thirumalai
    Mechanical unfolding of RNA: From hairpins to structures with internal multiloops
Biophys. J. BioFAST: October 6, 2006. doi:10.1529/biophysj.106.093062
http://www.biophysj.org/cgi/content/abstract/biophysj.106.093062v1

2. Gregory J Gemmen, Rachel Millin, and Douglas E Smith
    Dynamics of single DNA looping and cleavage by Sau3AI and effect of tension applied to the DNA
Biophys. J. BioFAST: September 8, 2006. doi:10.1529/biophysj.106.088518
http://www.biophysj.org/cgi/content/abstract/biophysj.106.088518v1

3. Li, PTX, Collin, D, Smith, S, Bustamante, C & Tinoco, I Jr., Biophysical J. vol. 90, no. 1, pp. 250-260 (January, 2006), "Probing the Mechanical Folding Kinetics of TAR RNA by Hopping, Force-Jump, and Force-Ramp Methods".   http://www.biophysj.org/cgi/content/abstract/90/1/250?

4. Frenster JH, and Hovsepian JA, "Kissing Chromosomes and Paired Sense-Antisense RNA Synthesis".

5. Frenster JH, and Hovsepian JA, "Activator RNA Initiation of the DNA Transcription Bubble".

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