Probing the mechanical folding kinetics of TAR RNA by hopping, force-jump, and force-ramp methods

Abstract

Mechanical unfolding and refolding of single RNA molecules have previously been observed in optical traps as sudden changes in molecular extension. Two methods have been traditionally used: "force-ramp", with the applied force continuously changing, and "hopping". In hopping experiments the force is held constant and the molecule jumps spontaneously between two different states. Unfolding/refolding rates are measured directly, but only over a very narrow range of forces. We have now developed a force-jump method to measure the unfolding and refolding rates independently over a wider range of forces. In this method, the applied force is rapidly stepped to a new value and either the unfolding or refolding event is monitored through changes in the molecular extension. The force-jump technique is compared to the force-ramp and hopping methods by using a 52-nucleotide RNA hairpin with a three-nucleotide bulge, i.e., the transactivation response region RNA from the human immunodeficiency virus. We find the unfolding kinetics and Gibbs free energies obtained from all three methods to be in good agreement. The transactivation response region RNA hairpin unfolds in an all-or-none two-state reaction at any loading rate with the force-ramp method. The unfolding reaction is reversible at small loading rates, but shows hysteresis at higher loading rates. Although the RNA unfolds and refolds without detectable intermediates in constant-force conditions (hopping and force-jump), it shows partially folded intermediates in force-ramp experiments at higher unloading rates. Thus, we find that folding of RNA hairpins can be more complex than a simple single-step reaction, and that application of several methods can improve understanding of reaction mechanisms.

FIGURE 1

The 52-basepair region of the TAR RNA hairpin is flanked by two ∼500-basepair DNA/RNA handles shown with the RNA in black and the DNA in gray. The 3′ terminus of the DNA handle A and the 5′ end of the DNA handle B (gray lines) are labeled with biotin and digoxigenin, respectively. The entire molecule is attached to two microspheres coated with either streptavidin or anti-digoxigenin antibody. The drawing is not to scale. The arrows indicate the direction of the applied force (F_y). The forces in the other two directions (F_x and F_z) are approximately zero during the experiments.

FIGURE 2

Hopping experiment. (A) A time trace of force (F_y) under feedback control. The force was set to 12.7 pN. The white line shows the smoothed value with a 30-point sliding boxcar average. (B) Distribution of force in the y direction under feedback control. (C) A time trace of the extension of TAR RNA at 12.4 pN. The two states of the extension were ∼18 nm apart. (D) Plots of the logarithm of the rates versus force for unfolding (▪) and refolding (○). Data were fitted to Eq. 4 (solid lines). We obtained ln A of −24 ± 16 and of 7 ± 5 nm for unfolding and ln A of 21 ± 8 and of 8 ± 3 nm for refolding. A is given in units of s⁻¹.

FIGURE 3

Force-jump experiment. (A) Two cycles of the force-jump experiments. Time traces of the force and extension of the molecule are plotted in the top and bottom panels, respectively. (B) Plots of the probability of the folded hairpin as a function of the time at 12.7 pN (+, 322 observations) and at 14.2 pN (×, 144 observations). Dashed curves represent the fit of data to a single exponential (Eq. 3). (C) Plots of the logarithm of the rate constants versus force for unfolding (▪) and refolding (○). A fit of the unfolding rates versus force to Eq. 4 (solid line) yields ln A of −28 ± 2 and of 8.2 ± 0.5 nm. For refolding, we derived ln A of 22 ± 3 and of 8 ± 1 nm.

FIGURE 4

Force-ramp experiment. (A) Typical force-extension curves of TAR RNA collected at loading rates of 0.4 and 1.7 pN/s. Unfolding trajectories are shown in gray and refolding in black. (B) Distribution of the unfolding (gray) and refolding (black) force at two loading rates. The unfolding force is defined as the force at which the molecule starts to rip; the refolding force is the force at which the zipping starts. (C) Distribution of the number of nucleotides in the zipping transition at two unloading rates. Measured ΔX in nm was converted to the number of single-stranded nucleotides with equivalent length at the refolding force using Eq. 1. The persistence length and the contour length of the RNA were assumed to be 1 nm and 0.59 nm, respectively. (D) Plots of the ln[r ln[1/N]] and ln[−r ln[1/U]] versus force. N and U are the folded and unfolded fractions, respectively. Solid boxes and crosses represent unfolding data collected at 0.4 and 1.7 pN/s, respectively. Open circles and asterisks represent refolding data collected at 0.4 and 1.7 pN/s, respectively. Data collected at 0.4 pN/s were fit to Eqs. 8 and 9 (solid lines). For unfolding, ln A and are −28.8 ± 0.9 and 8.4 ± 0.8 nm, respectively. For refolding, ln A is 28.8 ± 0.9 and is 10.9 ± 0.9 nm. Fitting for data collected at 1.7 pN/s were not shown.

FIGURE 5

Force-ramp experiment at intermediate loading rate. (A) Force-extension curves of TAR RNA collected at a loading rate of 1.0 pN/s. (B) A time trace of force in the same force-ramp cycle. (C and D) Noise of the force (σ_F) in 0.2 pN bins as a function of force. Neither unfolding nor refolding transitions are included. Open circles and asterisks represent the noise due to single-strand and hairpin RNA, respectively. The overlap force region between the forms of the RNA reflects the distribution of the transition forces.

FIGURE 6

Comparison of rates measured from different methods. The logarithm of the rates from force-ramp (▴), hopping (▪), and force-jump (•) are plotted as a function of the force. (A) Unfolding. Rates from all experiments are pooled together and fitted to Eq. 4. We obtained of 8.3 ± 0.1 nm and ln A of −28.3 ± 0.4. (B) Refolding. Data collected by each method were fitted to Eq. 4 independently: solid line, force-ramp; dotted line, hopping; and dashed line, force-jump.