Docking kinetics and equilibrium of a GAAA tetraloop-receptor motif probed by single-molecule FRET

Abstract

Docking kinetics and equilibrium of fluorescently labeled RNA molecules are studied with single-molecule FRET methods. Time-resolved FRET is used to monitor docking/undocking transitions for RNAs containing a single GAAA tetraloop-receptor tertiary interaction connected by a flexible single-stranded linker. The rate constants for docking and undocking are measured as a function of Mg2+, revealing a complex dependence on metal ion concentration. Despite the simplicity of this model system, conformational heterogeneity similar to that noted in more complex RNA systems is observed; relatively rapid docking/undocking transitions are detected for approximately two-thirds of the RNA molecules, with significant subpopulations exhibiting few or no transitions on the 10- to 30-s time scale for photobleaching. The rate constants are determined from analysis of probability densities, which allows a much wider range of time scales to be analyzed than standard histogram procedures. The data for the GAAA tetraloop receptor are compared with kinetic and equilibrium data for other RNA tertiary interactions.

Fig. 1.

Docking reaction of the model GAAA tetraloop-receptor system. The GAAA tetraloop is shown in bold, and the receptor is in boxed type. The curved arrows illustrate the freedom of motion between the tetraloop and receptor domains allowed by the A₇ single-stranded linker. In the docked configuration, the Cy3–Cy5 distance is ≈35 Å and increases to as much as 70 Å in the undocked state. The 5′-biotin strand allows surface immobilization.

Fig. 2.

Raster-scanned single-molecule fluorescence images demonstrating the effect of Mg²⁺ on docking equilibrium and the conformational heterogeneity of the GAAA tetraloop-receptor system. (a and b) Representative raster-scanned images of the same RNA molecules with no (a) and high (5.0 mM) (b) Mg²⁺ concentrations are shown. Each pixel depicts a false color representation of donor/acceptor emission with intensity proportional to number of donor (green) vs. acceptor (red) fluorescence photons. The size of each image is 12.5 × 12.5 μm; the intensity scale is 0–10 kHz for an incident power of 1.1 μW. (c and d) Corresponding histograms of the average E_FRET of each molecule are shown for no Mg²⁺ (1,841 molecules) (c) and 5.0 mM Mg²⁺ (823 molecules) (d) conditions. The histograms are overlaid with fits to a sum of two or three Gaussian distributions, respectively.

Fig. 3.

Typical time-resolved fluorescence intensity and corresponding FRET efficiency, E_FRET, traces for the GAAA tetraloop-receptor system at ≈0 mM Mg²⁺ (a), 0.50 mM Mg²⁺ (b), and 5.0 mM Mg²⁺ (c). The donor and acceptor signals are plotted in green and red, respectively. At zero Mg²⁺ concentrations, decreased oxygen scavenger efficacy led to very occasional photophysical blinking events (e.g., a), which are readily identified by a threshold in total count rate and eliminated from the docking/undocking analysis. Two E_FRET states are resolved at all Mg²⁺ concentrations. The high E_FRET state (E_FRET = 0.68) is assigned as docked, and the low E_FRET state (E_FRET = 0.22) is assigned as undocked.

Fig. 4.

Normalized probability density plots of the docked (Upper) and undocked (Lower) states for ≈0 mM (black), 0.50 mM (red), and 5.0 mM Mg²⁺ (green). The regions at high probability densities are quite well fit by single exponential functions (solid line) but deviate somewhat from pure exponential behavior at longer times, suggesting possible heterogeneity in the docking kinetics.

Fig. 5.

Mg²⁺ dependence of k_dock (○) and k_undock (▵) of the GAAA tetraloop-receptor interaction. The Mg²⁺ dependence of the docking rate constants is fit to a Hill-type equation of the form derived by Kim et al. (2). In this model, k_dock = {k₁(K_Mg)ⁿ + k₂[Mg²⁺]ⁿ}/{(K_Mg)ⁿ + [Mg²⁺]ⁿ}, where k₁ and k₂ are the rate constants for docking in the absence and presence of Mg²⁺, respectively, n is the Hill coefficient, and K_Mg is the apparent dissociation equilibrium constant for Mg²⁺ binding to undocked RNA. Similarly, k_undock = {k_-1(K_Mg′)ⁿ + k_-2[Mg²⁺]ⁿ}, where k_-1 and k_-2 are the undocking rate constants in the absence and presence of Mg²⁺, respectively, and K_Mg′ is the apparent dissociation equilibrium constant for Mg²⁺ binding to docked RNA. A combined fit to the measured rate constants for k_dock (solid line) and k_undock (dashed line) is shown, with k₁ = 4.1 ± 2.1 s^-1, k₂ = 71 ± 7 s^-1, K_Mg = 1.84 ± 0.46 mM, k_-1 = 10.0 ± 2.1 s^-1, k_-2 = 3.2 ± 2.2 s^-1, K_Mg′ = 0.9 ± 1.2 mM, and a Hill coefficient of n = 1.06 ± 0.19.