Direct Observation of Folding Energy Landscape of RNA Hairpin at

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Direct Observation of Folding Energy Landscape of RNA Hairpin at Mechanical Loading Rates Huizhong Xu,†,^ Benjamin Plaut,§,⊥ Xiran Zhu,‡ Maverick Chen,‡ Udit Mavinkurve,∥,# Anindita Maiti,∥,# Guangtao Song,∥ Krishna Murari,∥,∇ and Maumita Mandal*,†,∥,○ †

Department of Physics, ‡Department of Mathematical Sciences, §Department of Computer Science, and ∥Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States ABSTRACT: By applying a controlled mechanical load using optical tweezers, we measured the diffusive barrier crossing in a 49 nt long P5ab RNA hairpin. We find that in the free-energy landscape the barrier height (G‡) and transition distance (x‡) are dependent on the loading rate (r) along the pulling direction, x, as predicted by Bell. The barrier shifted toward the initial state, whereas ΔG‡ reduced significantly from 50 to 5 kT, as r increased from 0 to 32 pN/s. However, the equilibrium work (ΔG) during strand separation, as estimated by Crook’s fluctuation theorem, remained unchanged at different rates. Previously, helix formation and denaturation have been described as two-state (F ↔ U) transitions for P5ab. Herein, we report three intermediate states I1, I, and I2 located at 4, 11, and 16 nm respectively, from the folded conformation. The intermediates were observed only when the hairpin was subjected to an optimal r, 7.6 pN/s. The results indicate that the complementary strands in P5ab can zip and unzip through complex routes, whereby mismatches act as checkpoints and often impose barriers. The study highlights the significance of loading rates in force-spectroscopy experiments that are increasingly being used to measure the folding properties of biomolecules.

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initial base pairing of three to five nucleotides (nts), followed by an enthalpy-driven base stacking of two complementary strands; however, there is no direct evidence to show the nucleation event that initiates the early folding process. Besides, an accurate determination of the barrier position and the height along the folding reaction coordinate of a molecule continues to be a challenge. In the absence of any direct evidence, the nature of the activation barrier is mostly assumptive and hence do not advance our current understanding of the RNA folding problem. Furthermore, the role of mismatches in the RNA hairpin energy landscape is yet to be fully discussed. Such studies can provide valuable information on the barrier properties that largely dictate the zipping and unzipping of the helix strands. Recent single-molecule fluorescence and force-spectroscopy measurements have enabled direct measurements of the activation barrier in the folding of proteins16−19 and nucleic acids.20−23 The approaches have revealed crucial folding properties of the biomolecules that were not observed before, using traditional biochemical methods. Interestingly, helix folding has been studied in much greater details in dsDNA molecules than in ssRNA. This could primarily be caused by the flexible single-stranded RNA chain that can adopt various conformations under physiological ionic conditions; however, it

INTRODUCTION RNA hairpins are more versatile in structure and function than their DNA counterparts.1−3 Despite various sizes and lengths, all naturally occurring hairpins must fold into their native stemloop conformation to perform their biological activities. This journey from an unfolded to a folded conformation is decided by the free-energy landscape of the molecule. Therefore, a complete illustration of the folding reaction requires a thorough knowledge of the intermediate states and the native conformation, in addition to the barrier and checkpoints. The folding algorithm developed by Zuker and colleagues is a popular model for predicting RNA secondary structures at 1 M NaCl concentration.4 In silico and UV-melting studies support a two-state helix progression.5−7 Temperature-jump and calorimetric methods have provided important insights into the folding energy landscapes of small synthetic RNA hairpins that range from 3 to 5 bp;7,8 however, because of a limited resolution of these techniques, the kinetic rates of the early events in the hairpin folding are unclear. In short DNA hairpins (3−5 bp stem with variable loop sizes from 4 to 30 nt poly dA or poly dT), it has been shown by fluorescence correlation spectroscopy that the folding may be three-state with a stable long-lived intermediate state.9−14 Here, the conversion from the intermediate to the hairpin state occurred with a slow time scale. Recently, relaxation kinetics was measured by laser Tjump (or ion-jump) experiments that further strengthened the possibility of multistate folding.15 It is generally accepted that the helix progression in DNA/RNA occurs by nucleation of an © XXXX American Chemical Society

Received: October 13, 2016 Revised: February 13, 2017

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DOI: 10.1021/acs.jpcb.6b10362 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B

Figure 1. Effect of loading rate on the P5ab hairpin denaturation and renaturation. (a) Schematic representation of the dual-beam optical tweezers setup. (b) The sequence and the secondary structure of the P5ab hairpin. (c) Force−extension curve (FEC) fitted with eq 1 shows two-state F ↔ U transition, where F and U stand for the folded and unfolded conformations, respectively. (d, e) Probability distribution for rupture (Fu) and refolding (Ff) forces at 1.8 pN/s (n = 91 traces), 7.6 pN/s (n = 154 traces), 14.7 pN/s (n = 179 traces), and 28.4 pN/s (n = 114 traces). The dashed lines represent the actual counts. The solid lines represent the fitted curves following eqs 4 and 5 for rupture and refolding transitions, respectively. The arrows represent the shift in the average unfolding or refolding force with increasing r. (f) Extension histogram (dashed line) fitted with a single Gaussian (solid line) during unfolding of P5ab. The mean unfolding distances are indicated against each distribution.

such as bulges act as checkpoints, which can significantly alter the path for helix progression.

is often difficult to separate the conformers from the native state. We have undertaken the challenge to practically measure the folding routes, intermediate states, and barrier properties in the formation of the A-form RNA helix in physiological salt concentrations, using custom-built high-resolution optical tweezers. Our counter-propagating dual-beam optical tweezers instrument is based on the previous designs24,25 that can detect a linear distance of 1 nm at sub-piconewton forces (±0.15 pN) with high accuracy and precision. Figure 1a shows a schematic representation of our experimental setup. We employed the 49 nt P5ab RNA hairpin (Figure 1b) that forms a part of the P4− P6 domain in the group I intron of Tetrahymena thermophila.26,27 The P5ab and P5abc helical domains serve as model hairpin systems that have been extensively studied by several biochemical, biophysical, theoretical, and force-spectroscopy methods.20,22,26−29 The results obtained until now have indicated that P5ab is a two-state folder that collapses to the native hairpin (U → F) unhindered. In a recent theoretical study, an intermediate state has been identified from constantforce (CF) equilibrium experiments, which was not observed previously in the P5ab folding pathway.30 Here, in this study, we have identified multiple short-lived intermediate states (I1, I, and I2) in the unfolding and folding routes of P5ab. The results from the constant-speed (CS) and CF experiments suggest that the 49 nt P5ab hairpin undertakes a complex folding pathway rather than a two-state folding pathway. The data further emphasizes that the hairpin sequence and the structural defects

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EXPERIMENTAL SECTION Hairpin Sequence. All single-molecule assays were performed on the P5ab RNA hairpin with the following sequence: 5′-CCGUUCAGUACCAAGUCUCAGGGGAAACUUUGAGAUGGGGUGCUGACGG. Synthesizing RNA Hairpin for Single-Molecule Experiments. For our single-molecule experiments, we generated a dsDNA fragment corresponding to the P5ab hairpin sequence by polymerase chain reaction (PCR). Primers were purchased from Integrated DNA Technologies Inc. The DNA fragment was cloned into the pBR322 plasmid between EcoRI and HindIII restriction sites. The integrity of the recombinant DNA was confirmed by sequencing (Genewiz Inc.). Next, using the cloned DNA as a template, we PCR-amplified a 1100 bp DNA fragment that comprises the required hairpin insert and flanking regions (533 and 599 bp on each side of the insert). The forward primer contained a T7 promoter sequence to allow in vitro transcription by T7 polymerase. Separately, the flanking regions were PCR-amplified, which served as Handle A (533 bp) and Handle B (599 bp), respectively. To facilitate attachments with the microsphere beads, the handles were modified appropriately at one of the termini. Thus, Handle A was modified to incorporate digoxigenin-11-dUTP (Roche) to B


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various states. Data is plotted as extension versus time trace, as shown in Figure 6b. In our tweezers instrument, the preset force is maintained through a feedback control loop that operates at 4 kHz. The preset force fluctuated within ±0.15 pN (standard deviation) from the mean. The data was collected at 4 kHz and filtered with a 300-point moving average. Determination of the Pre-Exponential Factor, A0. We

establish connectivities with the antidigoxigenin (ADig)-coated beads (4.0−4.9 μm; Spherotech). Handle B was modified with 5′-biotin to facilitate attachments with the streptavidin (SA)coated beads (1.5−1.9 μm; Spherotech). The in vitro transcribed RNA (∼1100 nt) was then annealed with the DNA handles (10:1 mass ratio) in a buffer containing 83% formamide solution, 1 mM ethylenediaminetetraacetic acid, 42 mM PIPES, and 620 mM NaCl. The annealing reaction was carried out at 85 °C, 10 min; 62 °C, 2 h, and 52 °C, 2 h. The annealed mixture containing the required construct was ethanol-precipitated and used for single-molecule experiments. Establishing Single-Molecule Attachments in Optical Tweezers. In a typical experiment, ADig beads were incubated with a diluted stock of annealed P5ab RNA constructs in 1 mL buffer at room temperature for 15 min. The buffer contained 10 mM Tris−HCl, pH 7.5, 250 mM NaCl, and 3 mM MgCl2. The RNA-coated ADig beads were flown into the microfluidics chamber to trap one bead in the counter-propagating laser beams. Next, we moved the trap with the ADig bead toward the SA bead, which was held on a micropipette through suction. The close vicinity enabled a single molecule to attach with the SA bead. To assess that a single tether held the two beads together, the force−extension trajectory was fitted to a wormlike-chain (WLC) equation (eq 1).31−34 Additionally, we measured the overstretch transition in the graphical user interface. A single-molecule connectivity displayed an overstretch transition around 60−65 pN. Multiple tethers often resisted forces up to 90 pN or higher. Besides, such connectivities could not be fitted with the WLC equation. CS and CF Experiments. We recently built a counterpropagating dual-beam optical tweezers (λ = 845 nm) instrument as previously described,24,25 which can measure sub-piconewton forces and 1 nm distance with high accuracy and precision. The instrumental resolution and details have been described elsewhere.53 Briefly, the force calibration was done by Stoke’s law. The trap stiffness (κ = 0.046 pN/nm) was determined by power spectrum following the method described by Berg-Sørensen and Flyvbjerg.35 The calibrated force was further ascertained by overstretching a dsDNA molecule that showed a typical “S-shaped” trajectory between 63 and 65 pN.24,25,32 In this article, we applied an external load to a single P5ab molecule in two ways, namely, CS (or force-ramp) and CF. Typically, in the CS method, the hairpin is stretched and relaxed between 1 and 30 pN by moving the trap at a controlled speed. Data was recorded at 400 Hz and plotted, without any further averaging, as FECs (shown in Figure 1c). We used four different pulling speeds (v nm/s), namely, 50, 200, 400, and 800 nm/s. The corresponding loading rates were calculated by the methods described in the Results section. All FECs were fitted with a serial WLC equation (eq 1)31,32 F=

−2 kBT ⎡ 1 ⎛ x F⎞ 1 x F⎤ ⎢ ⎜1 − + ⎟ − + − ⎥ P ⎣4⎝ L K⎠ 4 L K⎦

(

used relationship A 0 = k u(F ) exp

ΔGu‡(F ) kBT

) to determine the

pre-exponential factor, A0. In the above relation, ku is the rate constant, kB is the Boltzmann constant, T is the temperature, and ΔG‡u(F) is the barrier height during the unfolding reaction. From CF data, we measured the equilibrium rate constant as ku = 10.0 ± 1.2 s−1 and ΔGu‡ = 7.6 ± 0.5 kBT. Using these values, A0 was determined to be 104.3±0.2 s−1, which agrees with the preexponential values reported earlier ranging from 103 to 107 s−1.17,21 Determination of ΔG from Crooks Fluctuation Theorem (CFT). According to CFT,36 the ratio of the probability distribution of the work done along the forward direction, PF(W), and the reverse direction, PR(−W), can be defined as ⎛ W − ΔG ⎞ PF(W ) ⎟ = exp⎜ ⎝ kT ⎠ PR ( −W )

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where the Gibbs free energy, ΔG, is the difference between the initial and the final state. Jarzynski’s equality (JE) allows the estimation of the free energy from an irreversible work done (W) given by the relationship,

( W)

exp( −ΔG /kT ) = limN →∞⟨exp − kT ⟩N , where ⟨ ⟩ represents

the average of N traces. As CFT utilizes information from both the forward and reverse processes, it allows for faster convergence; hence, it is more predictive than Jarzynski’s equilibrium.37,38 Hence, in this study, we used CFT analyses to deduce work done at different loading rates. Only for the optimal loading rate of 7.6 pN/s, we compared CFT and JE. Data Analysis. All data sets are represented as mean ± standard error. The number of traces (n) for each experiment is indicated in Table 1 or otherwise mentioned in the text as necessary. The number of traces analyzed in the calculation of work done is indicated in Figure 5. Table 1. Calculation of r from Mechanical Pulling Assay loading rate (r) (pN/s) pulling speed (v) (nm/s) 50 200 400 800

slope of F vs time plot 1.8 7.6 14.7 28.4

± ± ± ±

0.06 0.4 1.0 1.3

using eq 339

number of traces (n)

± ± ± ±

91 154 179 114

1.981 7.925 15.850 31.699

0.039 0.155 0.310 0.620

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RESULTS Higher Loading Rate Shifts the Rupture Force. At first, we investigated the effect of loading rate (r, pN/s) on the mechanical unfolding of the P5ab hairpin. This was accomplished by moving the trap at a CS (v, nm/s). We moved the trap at four speeds, namely, v = 50, 200, 400, and 800 nm/s, which corresponded to loading rates r = 1.8 ± 0.06, 7.6 ± 0.4, 14.7 ± 1.0, and 28.4 ± 1.3 pN/s (mean ± std error, n

where kB is the Boltzmann constant, T is 298 K, x is the extension, P is the persistence length, L is the contour length, and K is the stretch modulus. The fitted parameters are Phandle = 3−6 nm, Lhandle = 0.25 nm/bp, Khandle = 600−800 pN, PRNA = 1 nm, LRNA = 0.59 nm/base, and KRNA = 1600 pN. The fitted parameters agree with the reported values.33,34 In the CF mode, the hairpin was held at a preset force near equilibrium. At equilibrium, the molecule hopped between C


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loading rate. By using least-squares fitting, we extracted the distance to the transition state (Δx‡u) for unfolding (Table 2). The data clearly highlights that the barrier position systematically decreased from 11.7 to 9.45 nm as the two strands were separated under high loading rates.

≥ 90 traces). We employed two different methods to determine the loading rates for different pulling speeds. In the first method, r was calculated directly from the slopes of force versus time traces (Table 1). In the second method, we used the formulation (eq 3) given by Dudko and colleagues39 ⎡ ⎤−1 2βLlp(1 + βFlp) 1 ⎢ ⎥ ̇ + r ≡ F (F ) = v ⎢⎣ κs 3 + 5βFlp + 8(βFlp)5/2 ⎥⎦

Table 2. Transition Distance (Δxu‡), Most Probable Force (Fu*), and Mean Unfolding Force ⟨Fu⟩

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r (pN/s)

where L is the handle contour length (284 nm), lp is the persistence length (1.00 nm), β = 1/kBT = 0.243 pN−1 nm−1, and F = 14.5 pN. The fitted parameters are consistent with the reported values.33,34 The effective stiffness (κs = trap stiffness + molecule stiffness) was calculated to be 0.045 ± 0.001 pN/nm (mean ± std error, n = 27 traces). The uncertainties associated with the loading rates in eq 3 were calculated by error propagation of the standard error for the effective stiffnesses (F )̇ 2 (κs) using relation σ(F )̇ = 2 σ(κs).

1.8 7.6 14.7 28.4

14.79 15.03 15.25 15.58

± ± ± ±

0.01 0.02 0.02 0.03

⟨Fu⟩ (pN) 14.68 14.86 15.10 15.48

± ± ± ±

0.03 0.03 0.03 0.04

Δxu‡ (nm) 11.70 10.99 10.20 9.45

± ± ± ±

0.35 0.5 0.43 0.56

Furthermore, as predicted by Bell, Fu* exhibited a direct correlation with the loading rate (Fu* ∝ ln r), specifically under optimum and higher loading rates (7.6, 14.7, and 28.4 pN/s), as shown in Figure 2a. Nonetheless, for any given r, the average unfolding ⟨Fu⟩ was found to be lower than Fu* (Figure 2b,

v κs

The loading rates obtained from the two methods largely agreed with each other as shown in Table 1, except for the faster pulling, 800 nm/s. The FECs for the P5ab hairpin at different r values are shown in Figure 1c. Using a serial WLC equation (eq 1; see Experimental Section), the expected unfolding distance (Δx) for the 49 nt hairpin is 21.07 nm. The unfolding (blue) and refolding (red) traces in Figure 1c indicated a net extension change, Δxu ≈ 21 nm, at 14 pN that agrees with the theoretical value. The traces exhibited all-or-none phenotype, suggesting a two-state (F ↔ U) transition, which is consistent with the previous single-molecule studies.20,22 However, as r increased to 32 pN/s (or 28.4 pN/s), the mean rupture force ⟨Fu⟩ shifted from 14.68 ± 0.03 pN (91 FECs) to a slightly higher value, 15.48 ± 0.04 pN (114 FECs), as indicated by the arrow in Figure 1d. Similarly, the mean refolding force, ⟨Ff⟩, shifted to a lower value as the pulling rates were increased (Figure 1e), giving rise to hysteresis. The unfolding and refolding traces nearly superposed at slow pulling rates. The ∼21 nm change in distance (Δx) was observed for all traces within the error range, irrespective of the loading rates (Figure 1f). This suggested that the stretching speed did not obstruct in the unfolding or refolding of the hairpin. Distance to the Activation Barrier (Δx‡). To investigate the effect of loading rate on the barrier position (Δxu‡) during helix unzipping (F → U), we used the Bell−Evans model40,41 that relates r with the transition distance (Δxu‡) as a function of the rupture force (Fu), shown by eq 4 below. P(Fu) =

Fu* (pN)

⎛ ⎞⎞ ⎛ F Δx ‡ ⎞ k0 k k T ⎛ ⎛ F Δx ‡ ⎞ exp⎜⎜ u u ⎟⎟ exp⎜⎜− 0 B ‡ ⎜⎜exp⎜⎜ u u ⎟⎟ − 1⎟⎟⎟⎟ r ⎝ kBT ⎠ ⎠⎠ ⎝ r Δx u ⎝ ⎝ kBT ⎠ (4)

where kB is the Boltzmann constant, T is the temperature, and k0 is the rate constant. Briefly, the above relation is composed of two factors: the first term is the off-rate as a function of the load and the second term denotes the survival probability of an unruptured bond as a function of the duration of the pulling experiment, t. The Bell−Evans relationship has been successfully used to identify transition distances in several systems including proteins, for example, T4-lysozyme,51 and more recently in G-quadruplex DNA.52 The fitted curves are shown with solid lines in Figure 1d. The maximum in the fitted curve is defined as the most probable rupture force, Fu*, at the

Figure 2. Rupture force is proportional to the loading rate (Fu* ∝ ln r). (a) Data points corresponding to 7.6, 14.7, and 28.4 pN/s displayed a better fit (adjusted R2 = 0.97), suggesting that Bell’s relationship holds true for the optimum and higher r values. For the complete data range (including the lower value of 1.8 pN/s), the adjusted R2 is 0.91. (b) The variation between the statistical mean force and the most probable rupture force (blue) or refolding (red) along the pulling rate is shown. D


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Noticeably, the tertiary interactions were previously not observed in single-molecule studies.54,55 This underscores that the rate of mechanical loading affects the apparent outcome of the force measurements, particularly in the detection of intermediate states even in complex RNA structures. Height of the Activation Barrier (ΔG‡). To fully characterize the activation barrier along the folding or the unfolding path, it is important that both the barrier position (Δx‡) and barrier height (ΔG‡) are accurately determined. For the unfolding reaction, the barrier height at the most probable force, F*, can be written as

Table 2). This discrepancy can be explained by the nature of the fitted curves. As shown in Figure 1d, the bell-shaped curves for the hairpin rupture are skewed at low forces, wherein the counts are relatively small compared to the number of incidences at the peak. As a result of the asymmetric distribution, Fu* is higher than the statistical mean force, ⟨Fu⟩. To investigate the effect of r on the barrier position during refolding (U → F), we used the following relationship P(Ff ) =

⎛ kkT ⎛ F Δx ‡ ⎞ ⎛ F Δx ‡ ⎞⎞ k0 exp⎜⎜ − f f ⎟⎟ exp⎜⎜ − 0 B ‡ exp⎜⎜ − f f ⎟⎟⎟⎟ r ⎝ kBT ⎠ ⎝ kBT ⎠⎠ ⎝ r Δxf (5)

ΔGu‡(F *) = ΔGu‡(0) − F *Δx u‡

where Δx‡f is the distance to the transition state. The derivation was followed similar to that of the probability distribution of the rupture force described in eq 4 above. Accordingly, the transition distances during refolding (Δx‡f ) are 11.68 ± 0.59 nm at 1.8 pN/s, 10.5 ± 0.35 nm at 7.6 pN/s, 9.23 ± 0.35 at 14.7 pN/s, and 7.8 ± 0.49 nm at 28.4 pN/s (Figure 1e). Here again, we observed that Δx‡f decreased from 11.7 to 7.8 nm under the influence of higher r. We also find that during refolding, Ff* is lower than the average ⟨Ff⟩ (Figure 2b). This can be explained by the fitted bell curves that are skewed in the higher-force region. The number of events at these forces are low to shift Ff* toward the statistical mean. In the above mechanical unfold−refold experiments, the reaction coordinate is one dimensional, defined as the end-toend distance of the hairpin under an externally applied load. Therefore, for a two-state F ↔ U conversion, the transition state can be approached from either the folded or the unfolded state. In other words, under ideal conditions, the barrier position should concur irrespective of the initial state. Alternatively, the transition distances should add up to yield the net extension change, which is 21 nm in case of P5ab. This indeed appears to be the case when the hairpin was subjected to loading rate 7.6 pN/s. Thus, Δx‡u(F→U) = 10.99 ± 0.5 nm and Δx‡f (U→F) = 10.52 ± 0.35 nm overlapped at the barrier, such that Δx‡u + Δx‡f ≈ 21 nm for a two-state conversion (Table 3).

where ΔG‡u(0) is the free energy in the absence of any force and Δx‡u is the transition distance. For a molecule, barrier crossing is the rate-limiting step, which can be mathematically expressed as

(

k = A 0 exp −

1.8 7.6 14.7 28.4

Δxu‡ (nm) 11.70 10.99 10.20 9.45

± ± ± ±

0.35 0.50 0.43 0.56

Δxf‡ (nm) 11.68 10.52 9.23 7.80

± ± ± ±

0.59 0.35 0.35 0.49

Δx (nm)a 23.38 21.51 19.43 17.25

± ± ± ±

ΔGu‡(0) kBT

), where A is the pre-exponential factor. 0

s−1, which agrees with the We determined A0 to be 10 previously reported values (see Experimental Section).17,21 The barrier heights (ΔG‡) at different pulling speeds are indicated in Figure 3. The plot underscores that a faster pulling rate inadvertently shifted the transition barrier (Δx‡u) toward the initial state and reduced the barrier height (ΔG‡u). In fact, for both the unfolding and refolding reactions, the height was reduced by ∼2.5 kBT. The data so far indicated that a controlled application of the force facilitated barrier crossing by reducing the barrier height. Also, how the barrier is approached is crucial, which dictates the free-energy landscape of the molecule. The net effect of the loading rate on the free-energy landscape is illustrated in Figure 4. In the absence of any force, the barrier height is determined at ΔG‡u (F = 0) ∼ 50 kT using the Bell−Evans relationship. Evidently, a small load of 1.8 pN/s (or 2 pN/s) significantly lowered the barrier height to 7.6 ± 0.03 kT. As we further increased the loading rates to 7.6, 14.7, and 28.4 pN/s (or 8, 16, and 32 pN/s, respectively, according to eq 3), the barrier height further reduced, whereas the position shifted by ∼2.5 nm toward the folded state. This implies that under the influence of high loading rate, the hairpin approaches the barrier early. The new barrier was located at the C12−G39 bp. It is plausible that the mismatches at A13A14·G37G38 also contributed in shifting the barrier position. Work Distribution at Different Loading Rates. Next, we examined the effect of loading rate on the work done in the unfolding of the P5ab hairpin. In the CS assay, a finite loading rate is applied to separate the complementary strands of the hairpin. Previously, JE and CFT have been used to test the work fluctuations in the rupture of the P5abc hairpin using single-molecule experiments.42,43 The methods were used to deduce equilibrium free energies from nonequilibrium force measurements. We were interested in comparing the work done in the unzipping and re-zipping of the P5ab helix at different loading rates. Hence, we subjected a certain P5ab molecule to multiple pull−relax cycles at the following loading rates: 1.8, 7.6, and 28.4 pN/s. The plot in Figure 5 shows the CFT analyses (see Experimental Section) and the equilibrium free energy (ΔG). The forward and reverse work became more distributive at higher r values, which was also highlighted by the standard deviations. Additionally, at 28.4 pN/s, the average reverse work (−⟨WR⟩) reduced by 3 kT, which explains the appearance of hysteresis in the refolding trajectories (Figure

Table 3. Unfolding (Δxu‡) and Refolding (Δxf‡) Transition Distances at Different Loading Rates r (pN/s)

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0.69 0.61 0.55 0.74

a Total distance change (Δx) is determined from the sum of transition distances (Δxu‡ + Δxf‡). The expected rupture distance for the 49 nt P5ab hairpin is ≈21 nm.

However, the same cannot be stated for the low (1.8 pN/s) or high (14.7 and 28.4 pN/s) loading rates, for which the net extension (Δx) was either greater or lesser than the expected value of 21 nm, as indicated. Hence, the conclusion is that a pulling speed of 200 nm/s or a loading rate of 7.6 pN/s is the ideal condition for studying force-dependent denaturation and renaturation of RNA secondary structures as in the P5ab helix. Accordingly, the barrier for the P5ab hairpin lies around 10.5− 11.0 nm, which corresponds to the central AA·GG bulge. Recently, by employing r = 7.6 pN/s, we deciphered the key tertiary kissing-loop interactions in the folding of the guanine riboswitch53 in addition to the multiple secondary structures. E

4.3±0.2


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Figure 3. Effect of pulling rate on the barrier properties. (a, b) Double Y-plots indicating the barrier position and height as a function of the pulling rate during (a) unfolding and (b) refolding of the P5ab hairpin.

FECs recorded at the optimal speed, v = 200 nm/s (or r ∼ 7.6 pN/s), revealed interesting features. As shown in Figure 6a, the FECs for P5ab displayed at least three intermediate states, namely, I1, I, and I2. The hairpin unfolded via different routes along F → I1 → I → I2 → U. Out of 321 FECs that exhibited a net extension of Δx ∼ 21 nm, 255 traces displayed a partial melting with extensions of 4.06 ± 0.60 nm (F → I1), 32 traces showed 11.59 ± 0.66 nm (F → I), and 6 traces exhibited 15.71 ± 0.59 nm (F → I2) before transitioning to the linear state. Using the WLC model (eq 1), the extensions were related to the opening of 9.5 ± 1.4, 27.2 ± 1.5, and 37.1 ± 1.4 nts that corresponded to intermediate states I1, I, and I2. Additionally, the probability density distribution in Figure 6b indicated that the frequency of unwinding through the intermediates decreased, with F → U > F → I1 → U > F → I → U > F → I2 → U. The transition distance from the folded conformation to the respective intermediate state was determined by the Bell−Evans model (Figure 6c). The results specify that the barrier positions for the three routes, namely, F → U, F → I → U, and F → I2 → U, fall within 10.0−11.0 nm, which corresponded to the AA·GG bulge. However, for the F → I1 → U path, the helix may have encountered an additional barrier around ∼3.7 nm, which corresponded to the single-base bulge U5. The presence of the intermediate states was further confirmed by CF experiments, wherein a single P5ab molecule was held at a preset force near equilibrium at 14.5 pN (Figure 6d). The hairpin fluctuated with extensions measuring Δx (F → U) = 21.20 ± 0.34 nm, Δx (F → I1) = 4.1 ± 0.4 nm, Δx (F → I) = 12.4 ± 0.6 nm, and Δx (F → I2) = 15.7 ± 0.4 nm (mean ± SD from four independent molecules). Similarly, during refolding, the RNA displayed transitions that measured Δx (U → I2) = 4.71 ± 0.7 nm, Δx (U → I) = 8.73 ± 0.86 nm, and Δx (U → I1) = 16.70 ± 0.63 nm that corresponded to the I2, I, and I1 states. The barrier position and intermediate states (dashed lines) are indicated on the 49 nt P5ab hairpin (Figure 6e). We speculate that the checkpoint at I2 is due to the G21G22· U29U30 wobble base pairs and the GAAA tetraloop. Taken together, our data from CS and CF measurements convincingly show that the P5ab hairpin can unzip and re-zip following a complex route, which may not be necessarily a twostate route. The various folding routes are shown in Figure 7.

Figure 4. Free-energy landscape for the P5ab hairpin at increasing loading rates. The barrier position (Δx‡) shifted toward the left of the plot as r increased from 2 to 32 pN/s. In the absence of any force (F = 0), the barrier height was measured at ∼50 kT (data not shown due to different scales). Data is shown as mean ± std error for both the x and y axes. The errors range from 0.35 to 0.56 (x axis) and 0.03 to 0.06 (y axis).

1c). Nevertheless, the equilibrium free energy (ΔG), identified at the intersection of WF and WR in Figure 5, remained unperturbed irrespective of r, which is consistent with the previous work measurements.42 Interestingly, at r = 7.6 pN/s, the unfolding and refolding free energies calculated by Jarzynski’s equality (Experimental Section) were ΔGu = 77.98 ± 0.15 kT and ΔGf = 78.13 ± 0.32 kT, which are nearly identical to the CFT values. This emphasizes that the optimal pulling speed for investigating force-induced denaturation and renaturation of the P5ab hairpin is 200 nm/s (or r = 7.6 pN/s). In fact, 7.6 pN/s also proved to be an ideal loading rate in determining the folding intermediates of the guanine riboswitch that comprises secondary and tertiary interactions.53 P5ab Unfolds through Multiple Intermediate States. Having investigated the effect of loading rates on the barrier properties and the work done in the unzipping and re-zipping of the helix strands, we set out to further explore if the F ↔ U transition is strictly a two-state transition. A closer look at the F


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Figure 5. Work distributions for hairpin unfolding and refolding by CFT. The unfolding and the refolding work distributions were measured at different loading rates as indicated. The number of traces for each condition is indicated. The equilibrium free energy, ΔG (indicated by circle), was consistent near 78 kT at all loading rates.

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through F → I1 → U, F → I → U, and F → I2 → U. A closer look at the extension versus time trace (Figure 6d) revealed that the helix denaturation and renaturation can occur though any of the three intermediates to achieve the final state, as schematically illustrated in Figure 7. Although mechanical folding experiments are on the rise, the importance of the loading rate (r pN/s) is often unappreciated by users. If pulling experiments are performed under ideal conditions (e.g., stretching speed, loading rate, trap stiffness, handle lengths, ionic concentrations, etc.), the technique can reveal crucial information, which is otherwise undetected. In this article, we compared the barrier properties and the work done during the hairpin denaturation and renaturation as a function of the loading rate, r (1.8, 7.6, 14.7, and 28.4 pN/s). The equilibrium free energy remained constant across the loading rates; however, the folding paths varied. At very low (1.8 pN/s) and high (28.4 pN/s) loading rates, the folding was essentially two-state (F ↔ U). However, at optimum r, 7.6 pN/ s, and to a far lesser extent, 14.7 pN/s, the folding paths were complex and interrupted by multiple intermediate states. The barrier properties including the position and height were also affected under higher loading rates. Thus, the barrier shifted toward the initial folded state, whereas the height decreased significantly from 50 (F = 0) to 5 kT at higher loads (Figures 3 and 4). It is known that base stacking is the main driving force for helix propagation. Hence, any structural defect in the form of mismatches, bulges, and wobble pairs in the formation of duplex helix must be detected, as it can provide crucial information on the intermediate states and folding pathways. Considering that all the detection systems of the tweezers

DISCUSSION Hairpins are considered to fold through a two-state pathway. The 49 nt P5ab hairpin is a classic example, which is known to fold cooperatively. In the past, theoretical and experimental studies have investigated the effect of mechanical manipulations on single-molecule proteins16−18 and DNA hairpins.21,44−47 Limited mechanical studies have been carried out on some RNA hairpins.33,48−50 In this article, we investigated all the dominant and subdominant folding routes, the intermediate states, and the free-energy landscape of the P5ab RNA hairpin under an applied external load using optical tweezers. By applying a well-calibrated force in two different experimental settings, CS (where r ≠ 0) and CF (where r = 0), we followed the transition of a linear RNA to its hairpin conformation and vice versa. Results from both the experiments clearly indicated that the 49 nt hairpin folds by a complex route, involving multiple intermediate states: I1, I, and I2 (Figure 6). The three checkpoints in the P5ab folding path are located near 3.7 nm (I1), between 10.5 and 11.0 nm (I), and 15.5 and 16 nm (I2) that corresponded to the mismatches or the wobble pairs. Of these, only the I state imposed a major barrier in the folding. A recent theoretical study30 has also reported the intermediate state (I) in the P5ab folding, which is consistent with our results. The single-base bulge at U5 (I1) did not impose a major barrier; however, the checkpoint effectively altered the unfolding route. The normalized probability density distribution in Figure 6b highlights that 40% of the traces unfolded through the F → I1 → U pathway. Our studies indicated that unfolding via F → U was the dominant path, as proposed earlier.20,22 Additionally, we provided evidence for unfolding G


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Figure 6. P5ab hairpin displays at least three intermediate states in mechanical assays. (a) The fitted FECs display f ive states F, I1, I, I2, and U at r = 7.6 pN/s. (b) Probability density distributions along various unfolding pathways are shown. (c) The transition distances (Δx‡) from the folded hairpin state indicate a major barrier between 10.0 and 11.0 nm. (d) A typical extension vs time trace measured at 14.5 pN. The states are indicated by dashed lines following eq 1. (e) Intermediate states (dashed gray line) and the barrier position (red arrows) are mapped on the P5ab hairpin sequence from the CS and CF assays.

the slow and fast loading rates, the folding was strictly twostate. In between the two extreme rates of mechanical force applications somewhere lies the optimal loading rate, whereby the hairpin is allowed to sample the mismatches during the breaking or formation of the bonds between the complementary strands. In other words, at the optimal loading rate (7.6 pN/s, in this study), the applied force as a thermodynamic variable is in harmony with the system undergoing the change. As a result, three intermediate states (I1, I, and I2) were readily observed during the unfolding and refolding trajectories in P5ab. This shows that the mechanistic and kinetic landscapes during the folding and unfolding of the A-form helix structure in RNAs could be affected by the pulling force and the loading rate employed in the experiment. We find that the CS assay performed at the optimal loading rate, r = 7.6 pN/s, is comparable to the CF assay (where r = 0) near the transition force, 14.5 pN. It is our understanding that in the CS assay, the optimal loading rate has a narrow range, which depends on the hairpin sequence (GC content) and length; however, 7.6 pN/s may be broadly suitable for investigating the secondary and tertiary interactions in complex RNA structures. Recently, using a similar approach, we identified tertiary kissing-loop interactions in the guanine riboswitch, which are crucial in the formation of the receptor conformation.53 We anticipate more forthcoming studies from our group and others in near future that will decisively help understand the relevance of optimum loading rates in force-induced mechanical studies.

Figure 7. Schematic illustrations of folding and unfolding pathways in the P5ab hairpin. The hairpin (F) or the linear (U) RNA uses various pathways along F ↔ I1 ↔ I ↔ I2 ↔ U to reach the final state.

instrument are in the best condition, the intermediate states in the P5ab hairpin folding were detected only when subjected to an optimum pulling force, 7.6 pN/s. This is because helix denaturation and renaturation under a slow pulling rate (1.8 pN/s) can be compared with the thermodynamic reversible work done along the path, wherein the change occurs in controlled small increments such that the system is in equilibrium throughout the process. Accordingly, a reversible folding−unfolding was observed at 1.8 pN/s (Figure 1c). The mismatches encountered during strand melting and annealing were buffered by the equilibrium due to a slow loading rate, thereby masking the appearances of the intermediate states. On the other hand, the helix denaturation−renaturation under the fast loading rate (28.4 pN/s) can be treated similar to the irreversible thermodynamic system. The transition between the initial and the final state occurred too rapidly, such that the intermediate states along the path were missed. Thus, in both H


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S. Kumar, M. Kong for technical assistance with RNA preparations, and Ahmed Osman for writing codes for tweezers. We thank the National Science Foundation for support through NSF CAREER (CHE-1151815) awarded to M.M. We also thank financial support from the Single-Molecule and RNA Biology Institute.

In conclusion, we have shown that the 49 nt P5ab hairpin folds through a complex route that involves multiple intermediate states and not exclusively through a two-state route. The intermediate states were frequently observed when a controlled tension at an optimal rate, r = 7.6 pN/s, was applied to the tethered hairpin molecule. The results will have a broader implication in designing single-molecule experiments toward the identification of the folding pathways and intermediate states in complex RNA molecules with tertiary and secondary interactions such as riboswitches.

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SIGNIFICANCE STATEMENT Hairpins form the basic structural unit in RNA structures and molecular assemblies, yet the folding pathways in the helix formation are poorly understood. Previously, the folding of a 49 nt P5ab hairpin has been described as two-state (U → F), which occurs rapidly without any intermediates. The contiguous base stacking is the main driving force for chain propagation. The identification and complete understanding of the intermediate states, activation barrier, thermodynamics, and kinetics are some of the key components to solve the RNA folding problem. As it stands currently, the folding problem is not solved. Although single-molecule studies that use forcespectroscopy as the preferred method have increased, it is often challenging to understand the implications of the loading rate in stretching a biomolecule. Although a lot of theoretical work has been performed in this direction, the experimental work is limited. Here, we revisited the helix zipping and unzipping routes in the P5ab hairpin using optical tweezers. Additionally, we investigated the effect of force on the barrier properties in the free-energy landscape. By following the equilibrium (CF) and nonequilibrium (CS) trajectories of a single molecule of the P5ab hairpin, we show that P5ab folds via multiple intermediates and not by a two-state collapse. We anticipate that the results presented in this article will be extended to other RNA molecules to identify short-lived intermediate states en route to their native conformation.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Maumita Mandal: 0000-0001-6012-7909 Present Addresses ○

Single-Molecule and RNA Biology Institute, Pittsburgh, Pennsylvania 15218, United States (M.M.). ∇ Deutsche Electron Synchrotron, 22761 Hamburg, Germany (K.M.). # Indian Institute of Technology Bombay, Mumbai, India (U.M.) (A.M.). ⊥ Stanford University, Stanford, California 94305, United States (B.P.). ^ Salk Institute for Biological Sciences, La Jolla, California 92037, United States (H.X.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We dedicate this work in the memory of late Ignacio Tinoco Jr., who has been a mentor and inspiration in carrying out this work. We thank Dr. Steven Smith for helping us build the highresolution minioptical tweezers. We would like to acknowledge I


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Direct Observation of Folding Energy Landscape of RNA Hairpin at

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