Single-molecule transition-state analysis of RNA folding

Abstract

How RNA molecules fold into functional structures is a problem of great significance given the expanding list of essential cellular RNA enzymes and the increasing number of applications of RNA in biotechnology and medicine. A critical step toward solving the RNA folding problem is the characterization of the associated transition states. This is a challenging task in part because the rugged energy landscape of RNA often leads to the coexistence of multiple distinct structural transitions. Here, we exploit single-molecule fluorescence spectroscopy to follow in real time the equilibrium transitions between conformational states of a model RNA enzyme, the hairpin ribozyme. We clearly distinguish structural transitions between effectively noninterchanging sets of unfolded and folded states and characterize key factors defining the transition state of an elementary folding reaction where the hairpin ribozyme's two helical domains dock to make several tertiary contacts. Our single-molecule experiments in conjunction with site-specific mutations and metal ion titrations show that the two RNA domains are in a contact or close-to-contact configuration in the transition state even though the native tertiary contacts are at most partially formed. Such a compact transition state without well formed tertiary contacts may be a general property of elementary RNA folding reactions.

Fig. 1.

Folding of the hairpin ribozyme. (a) The WT AC₅ hairpin ribozyme used in this study. Watson–Crick and noncanonical base pairs of the docked conformer are indicated by solid and dashed lines, respectively. Tertiary interactions are represented as follows: pink, g+1:C25 Watson–Crick base pair; gray, ribose zipper; purple, U42 binding pocket (34). Biotin, Cy3, and Cy5 were attached as indicated (18). (b) Schematic of the docking and undocking transitions of the hairpin ribozyme with an experimental time trajectory showing the corresponding FRET changes at 37°C.

Fig. 2.

Effect of mutations on the rate constants for docking and undocking. (a Left) k_dock and k_undock,₁ of the WT and mutant ribozymes at 12 mM Mg²⁺ and 37°C. (a Right) k_dock and k_undock,₁ of WT and mutant ribozymes at 12 mM Mg²⁺ and 25°C. (b) Dependence of the Φ-values on Mg²⁺ concentration. Values for the dG11 and dC12 mutations were obtained at 37°C, and those for the a+1/U25 mutant were obtained at 25°C. The error bars for the φ-values of dG11 are smaller than the symbols.

Fig. 3.

Effect of metal ion concentration on the rate constant for docking and undocking. (a) Dependence of k_dock (•) and k_undock (○) of the WT ribozyme on [Mg²⁺] at 37°C. k_dock values are fit to the Hill equation (solid line), k_dock ≅ k_max [Mg²⁺]ⁿ/([Mg²⁺]ⁿ + (Mg_1/2)ⁿ). Mg_1/2 = 830 mM is the magnesium half-saturation point; n = 0.6 is the Hill constant, which approximates the average slope ∂log(k_dock)/∂log[Mg²⁺]. (Inset) [Mg²⁺] dependence of all four undocking rate constants observed at 25°C. At this temperature, k_dock increases continuously with [Mg²⁺] in a similar fashion to the k_dock values at 37°C (data not shown). (b) The [Na⁺] dependence of k_dock and k_undock,₁ (triangles) in the absence of Mg²⁺ and the [Mg²⁺] dependence of k_dock and k_undock,₁ in the presence of 500 mM Na⁺ (circles). k_dock values are fit to the Hill equation (solid line), yielding Mg_1/2 = 60 mM, n = 0.8 and Na_1/2 = 2.1 M, n = 3, respectively.

Fig. 4.

A theoretical model describing the electrostatic interactions of the hairpin ribozyme with metal ions. Domains A and B of the ribozyme were modeled as two connected cylinders (blue) with their relative orientations depicted in gray. The nonlinear Poisson–Boltzmann equation was used to determine the divalent metal ion distribution around the RNA in solvent containing 25 mM monovalent and 10 mM divalent salt. The 3D isoconcentration contour (red) at 3.0 M shows the accumulation of divalent metal ions at the domain interface in the docked state and the contact model of the transition state. On titration with Mg²⁺ alone, the most probable transition state is represented by the contact model, where domains A and B are in contact as shown. However, at <1 mM Mg²⁺ in the absence of Na⁺, on titration with Na⁺ alone, or on Mg²⁺ titration in a background of 500 mM Na⁺, the more appropriate transition state is a noncontact model where the two domains are only slightly separated (see text). In all cases, docking likely occurs via an ensemble of transitions states that all satisfy these restrictions. The figure was rendered by using the program grasp (50).

Fig. 5.

Effect of urea concentration on the rate constants for docking (•) and undocking (○).

Fig. 6.

Free energy diagram of the docking and undocking transitions in dependence of either a mutation that disrupts a tertiary interaction or an increase in Mg²⁺ concentration, as concluded from our single-molecule studies. The symbols are defined as and .