Report

Reversible Unfolding of Single RNA Molecules by Mechanical Force

See allHide authors and affiliations

Science  27 Apr 2001:
Vol. 292, Issue 5517, pp. 733-737
DOI: 10.1126/science.1058498

Abstract

Here we use mechanical force to induce the unfolding and refolding of single RNA molecules: a simple RNA hairpin, a molecule containing a three-helix junction, and the P5abc domain of theTetrahymena thermophila ribozyme. All three molecules (P5abc only in the absence of Mg2+) can be mechanically unfolded at equilibrium, and when kept at constant force within a critical force range, are bi-stable and hop between folded and unfolded states. We determine the force-dependent equilibrium constants for folding/unfolding these single RNA molecules and the positions of their transition states along the reaction coordinate.

RNA molecules must fold into specific three-dimensional shapes to perform catalysis. However, bulk studies of folding are often frustrated by the presence of multiple species and multiple folding pathways, whereas single-molecule studies can follow folding/unfolding trajectories of individual molecules (1). Furthermore, in mechanically induced unfolding, the reaction can be followed along a well-defined coordinate, the molecular end-to-end distance (x).

We studied three types of RNA molecules representing major structural units of large RNA assemblies. P5ab (Fig. 1A) is a simple RNA hairpin that typifies the basic unit of RNA structure, an A-form double helix. P5abcΔA has an additional helix and thus a three-helix junction. Finally, P5abc is comparatively complex and contains an A-rich bulge, enabling P5abc to pack into a stable tertiary structure (a metal-ion core) in the presence of Mg2+ ions (2 9).

Figure 1

(A) Sequence and secondary structure of the P5ab, P5abcΔA, and P5abc RNAs. The five green dots represent magnesium ions that form bonds (green lines) with groups in the P5c helix and the A-rich bulge (3). (B) RNA molecules were attached between two 2-μm beads with ∼500–base pair RNA:DNA hybrid handles.

The individual RNA molecules were attached to polystyrene beads by RNA/DNA hybrid “handles” (Fig. 1B) (10). One bead was held in a force-measuring optical trap, and the other bead was linked to a piezo-electric actuator through a micropipette (11,12). When the handles alone were pulled, the force increased monotonically with extension (Fig. 2A, red line), but when the handles with the P5ab RNA were pulled, the force-extension curve was interrupted at 14.5 pN by an ∼18-nm plateau (black curve), consistent with complete unfolding of the hairpin. The force of 14.5 pN is similar to that required to unzip DNA helices (13, 14). P5ab switched from the folded to the unfolded state, and vice-versa, in less than 10 ms and without intermediates. Forward and reverse curves nearly coincided, indicating thermal equilibrium. The variation of folding/unfolding force (SD 0.4 pN) reflects the stochastic nature of a thermally facilitated process. Indeed, a plot of the fraction unfolded versus force (Fig. 2B, dots) is fit well by the statistics of a two-state system in an external field at finite temperature (solid line). From this analysis, P5ab's unfolding free energy (ΔG) is 193 ± 6 kJ mol−1 (12, 15). A second, independent, measure of P5ab's ΔG is the average area under the reversible folding/unfolding plateau, which equals the potential of mean force of folding and yields a ΔG of 157 ± 20 kJ mol−1. After correction for the free energy reduction of the unfolded state due to tethering (calculated to be 44 ± 10 kJ mol−1) (12), these values compare well with the predicted ΔG of unfolding untethered P5ab calculated with the mfold free energy–minimization method (ΔG sigmoid = 149 ± 16; ΔG 〈area〉 = 113 ± 30; ΔG mfold = 147 kJ mol−1) (12, 16).

Figure 2

(A) Force-extension curves of the RNA-DNA handles without an insert (red) and with the P5ab RNA (black) in 10 mM Mg2+. Stretching and relaxing curves are superimposed. Inset, detail of force-extension trace showing hopping. Right inset, force-extension curves for the RNA hairpin without Mg2+. (B) Probability of opening versus force in Mg2+was obtained by summing a normalized histogram of hairpins opened versus force. Data are from 36 consecutive pulls of one molecule. Solid line, probability p(E) of a two-state system:p(E) = 1 (1 +e E/kBT). Best-fit (least squares) values, ΔG(F 1/2) = 193 ± 6 kJ mol−1, Δx = 22 ± 1 nm (12). (C) Length versus time traces of the RNA hairpin at various constant forces in 10 mM Mg2+. (D) The logarithm of the equilibrium constant in Mg2+ plotted as a function of force (error bar = 1 SD). (E) Detail of the stretching (blue) and relaxing (green) force-extension curves of the P5abcΔA molecule taken at low and high loading rates in 10 mM Mg2+.

Several force-extension traces showed the molecule's extension jumping between two values when the force was within ∼1 pN of the unfolding plateau (Fig. 2A, left inset). We investigated this bi-stability by imposing a constant force on the molecule with feedback-stabilized optical tweezers capable of maintaining a preset force within ±0.05 pN by moving the beads closer or further apart. Then, the end-to-end distance of the P5ab hairpin hopped back and forth by ∼18 nm, signaling the repeated folding and unfolding of a single RNA molecule. As in the pulling experiments, transitions between the two states were unresolvably fast (<10 ms) and without intermediates. By increasing the pre-set force, it was possible to tilt the folded⇔unfolded equilibrium toward the unfolded state and thus directly to control the thermodynamics and kinetics of RNA folding in real time (Fig. 2C). As the force was increased, the molecule spent more time in the extended open form and less time in the short folded form.

Whether hopping can be observed with a particular type of RNA depends on the time resolution of the instrument, its drift rate, and the kinetic barrier to folding/unfolding as determined by the potential energy surface of the molecule (12). In the instrument we used, hopping could be observed for rates between approximately 0.05 Hz and 20 Hz.

A ratio of the average lifetimes of the molecule in the two states yields the equilibrium constant K(F) for folding/unfolding at that force (Fig. 2D). Linear extrapolation ofK(F) to zero force, and correction for free energy reduction due to tethering (as above), yields a ΔG of 156 ± 8 kJ mol−1, which coincides with the ΔG values obtained from stretching and the predicted value. Therefore, three different methods of measuring P5ab's unfolding ΔG give similar results: (i) the fit to the distribution of opening forces, (ii) the average area under the folding/unfolding plateau, and (iii) the ratio of folded and unfolded lifetimes.

The sensitivity of RNA hopping to external force is determined by the force-dependent length difference between the unfolded and folded forms, Δx(F). In particular, an expression analogous to the van't Hoff formula holds: d lnK (F)/dF = Δx(F)/kBT(17). Indeed, the slope of the ln Kversus F plot (Fig. 2D) multiplied by kBTis 23 ± 4 nm, and the Δx(F 1/2) value thus obtained is within experimental error of the value from the length-time trace (18 ± 2 nm, Table 1) (18).

Table 1

Force-extension and constant force measurements.

View this table:

P5ab's folding kinetics in Mg2+ were determined from the force-dependent average lifetimes of the folded and unfolded forms, 〈τf〉 and 〈τu〉 (Fig. 2C). The logarithm of the mechanical folding/unfolding rate appears to be a linear function of external force, with kf→u increasing from 0.5 s−1 to 30 s−1 with force, andku→f decreasing from 30 s−1 to 0.4 s−1 (Table 1) (12). These rate constants then can be fit to Arrhenius-like expressions of the form:Embedded Image(1)where km represents the contribution of handle and bead fluctuations to the absolute rates (19), k 0 is the RNA's unfolding rate at zero force, and Δx f→u is the thermally averaged distance between the folded state and the transition state along the direction of force (20). A similar expression holds for the reverse reaction. Consistent with the predicted shape of P5ab's free energy curve along the reaction coordinate (12), the position of P5ab's transition state on the reaction coordinate determined from the slope of the lnk versus F plots is equidistant from the unfolded and folded states: Δx u→f = 11.5 nm, and Δx f→u = 11.9 nm. By contrast, the transition state for mechanical unfolding of certain protein domains, e.g., titin immunoglobulin, is closer to the native state (∼0.3 nm) than the denatured state (between 2 and 8 nm) (21, 22). These positioning differences may reflect the absence of nonlocal (tertiary) contacts in the P5ab hairpin and the dependence of the stability of the protein-folded state on nonlocal interactions.

Removal of Mg2+ lowers the average force of folding/unfolding in pulling experiments from 14.5 to 13.3 pN, thus reducing the ΔG 〈area〉 by 8%. It does not, however, affect the transition state position on the reaction coordinate (Table 1). Mg2+ thus slightly stabilizes the P5ab hairpin, presumably through nonspecific ionic shielding of phosphate repulsions (23, 24).

Having explored the simplest RNA structural unit, we characterized the mechanical behavior of a helix junction. The P5abcΔA three-helix junction (Fig. 1A) also hopped between two states when held at constant force in Mg2+ and EDTA (Table 1). However, a force-hysteresis of ∼1.5 pN was observed in the force-extension curves in both ionic conditions, indicating a loading rate faster than the slowest relaxation process of the molecule. Thermodynamic equilibrium, as marked by coincident stretch and relax curves, was attained when loading rates (20) were reduced to ≤1 pN s−1 (Fig. 2E). The rates of P5abcΔA's folding/unfolding are smaller than those of P5ab, despite identical effective transition state location, presumably because two hairpins must nucleate, and therefore, two kinetic barriers, representing two transition states, must be crossed to fold P5abcΔA. Similarly, two helices must be opened sequentially to unfold P5abcΔA. The overall activation barrier for P5abcΔA folding/unfolding is therefore larger than that of P5ab, slowing its kinetics.

Although helices and their combinations are fundamental units of RNA structure, they are not sufficient for three-dimensional organization. Consequently, we investigated Mg2+-dependent tertiary contacts using the P5abc RNA, whose structure is stabilized by Mg2+ ions that form a metal-ion core between the P5c helix and the A-rich bulge (Fig. 1A) (3).

As shown in Fig. 3A, the tertiary interactions formed in Mg2+ lead to substantial curve hysteresis (loading rate: 3 pN s−1). Forces as high as 22 pN are needed before the molecule suddenly unfolds (blue curves), displaying a “molecular stick-slip” or “ripping” behavior (25). Typically, the molecule unfolds suddenly at a high force (19 ± 3 pN, 96% of curves, n = 150, Fig. 3A, blue arrow). Rarely (4% of curves), unfolding is interrupted after 13 nm, and the force then rises again until a second rip (inset, red stars) completes unfolding. The two-step unfolding reveals two distinct kinetic barriers to mechanical unfolding of P5abc in Mg2+. Considering the ionic requirements of those barriers (see below), and their absence in the P5ab and P5abcΔA curves, we assign them to Mg2+-dependent tertiary interactions among the P5c helix, the A-rich bulge, and the rest of the molecule. Because it is not preceded by other unfolding, the first rip must represent opening of P5a followed by rip propagation through the entire RNA structure (Fig. 3F, most probable path, blue arrow). Unfolding is sometimes interrupted by the second barrier, probably located at the base of the P5b helix (Fig. 3F, rare path, red arrow). Consistent with the slow kinetics of P5abc in Mg2+ (Fig. 3A), these molecules do not hop when held at constant force; rather, they unfold suddenly and do not refold for the duration of the experiment (5 min, Fig. 3E).

Figure 3

(A) Stretch (blue) and relax (green) force-extension curves for P5abc in 10 mM Mg2+. Inset, detail of P5abc stretching curves showing unfolding intermediates (red stars). (B) Comparison of P5abc force-extension curves in the presence and absence of Mg2+. (C) The force-distribution of unfolding of the first kinetic barrier at loading rates of 1 and 10 pN s−1. Best fit (least squares) values, Δx f→u = 1.6 ± 0.1 nm,k 0 = 2 × 10−4s−1. (D) Length versus time traces for P5abc in EDTA (12). (E) Length versus time traces of P5abc in 10 mM Mg2+. (F) Model for P5abc's unfolding by force in Mg2+.

Removal of Mg2+ removes the kinetic barriers, and folding/unfolding becomes reversible. Unfolding then begins at 7 pN (Fig. 3B), showing that in EDTA the A-rich bulge destabilizes P5abc. The refolding curves in Mg2+ and EDTA coincide, except for an offset of 1.5 pN due to charge neutralization (Fig. 3B, green curves). In contrast to the all-or-none behavior of P5ab, refolding of P5abc both with and without Mg2+ has intermediates: the force curve inflects gradually between 14 and 11 pN (Fig. 3B, black stars) and this inflection is followed by a fast (<10 ms) hop without intermediates at 8 pN (green arrows). The cooperativity of mechanically induced folding/unfolding is determined by the shape of the free-energy surface along the reaction coordinate and, thus, by the RNA sequence (12).

The different widths of the two transitions and their force-separation suggest that the inflection (Fig. 3B, stars) marks folding of the P5b/c helices, whereas the hop (Fig. 3B, arrows) marks P5a helix formation. The folding/unfolding of P5a as compared with P5b/c can be resolved in constant-force experiments. Now, although the molecule hops (Fig. 3D), the average length of its hops (∼17-nm) is only about two-thirds the expected value, and a second type of hop is occasionally observed (red arrow) (12). Evidently, in EDTA P5abc hops between partially folded states, with the ∼17 nm transitions presumably representing folding/unfolding of the P5a helix and parts of the three-helix junction.

To measure P5abc's unfolding kinetics in Mg2+, we determined the probability that the molecule will be unfolded (ripped) at a given force from a series of unfolding curves like Fig. 3A (blue). From these data, the unfolding rate and the position of the transition state of the first barrier were obtained using (20):Embedded Image(2)In the high-force limit (>3 pN), this expression may be simplified to the following:Embedded Image(3)where N is the fraction folded,r is the loading rate (pN s−1),k 0 is the zero-force opening rate, and b= Δx/kBT. Plots of the ln [rln (1/N)] versus force for the first barrier at loading rates of 1 and 10 pN s−1 are shown in Fig. 3C. A fit of the data in Fig. 3C yields a distance of 1.6 ± 0.1 nm from the folded to the transition state (Δx f→u ) along the reaction coordinate, and an apparent k 0 of 2 × 10−4 s−1. Thus the A-rich bulge, in the presence of Mg2+, converts an RNA with a Δx f→u of 12 nm (P5abcΔA), into one with a transition distance similar to those of globular proteins. Apparently, the nonlocal contacts in hydrophobic and electrostatic cores of proteins and RNAs, respectively, are responsible for their cooperative unfolding behavior under locally applied mechanical forces.

How does the metal-ion core stabilize P5abc against mechanical unfolding? The ΔG of opening P5abc's tertiary contact is about 80 kJ mol−1 smaller than the ΔG of opening the P5ab and P5abcΔA helices (zero-force rate: 10−4 versus 10−18,Table 1). Why then is opening P5abc's tertiary contact, and not its helices, rate limiting to mechanical unfolding? At any finite pulling rate, and for a given ΔG , the average force required to commence unfolding is inversely proportional to Δx f→u , which, for the tertiary contact, is 7 times as short as for a helix. P5abc in Mg2+is consequently a “brittle” structure that resists mechanical deformation but fractures once deformed slightly. Conversely, the P5ab helix is compliant and unfolds reversibly under mechanical force.

Unlike the secondary structural elements of proteins, those of RNA are independently stable. The free energies of secondary and tertiary interactions of RNA may therefore be additive and separable. By revealing these free energies, mechanical and fluorescence studies (1) of individual RNAs will help develop an aufbaualgorithm for RNA folding (26). Mechanical studies permit uninterrupted access (lasting minutes to hours) to the kinetic and thermodynamic properties of single polymers; investigation of folding/unfolding in physiological ionic strengths and temperatures; and determination of the effects of ions, drugs, and proteins on RNA structure (27).

  • * To whom correspondence should be addressed. E-mail: carlos{at}alice.berkeley.edu

  • * To whom correspondence should be addressed. E-mail: jliphard{at}alice.berkeley.gov or JTLiphardt{at}lbl.gov

REFERENCES AND NOTES

View Abstract

Navigate This Article