Salt-dependent folding energy landscape of RNA three-way junction

Abstract

RNAs are highly negatively charged chain molecules. Metal ions play a crucial role in RNA folding stability and conformational changes. In this work, we employ the recently developed tightly bound ion (TBI) model, which accounts for the correlation between ions and the fluctuation of ion distributions, to investigate the ion-dependent free energy landscape for the three-way RNA junction in a 16S rRNA domain. The predicted electrostatic free energy landscape suggests that 1), ion-mediated electrostatic interactions cause an ensemble of unfolded conformations narrowly populated around the maximally extended structure; and 2), Mg(2+) ion-induced correlation effects help bring the helices to the folded state. Nonelectrostatic interactions, such as noncanonical interactions within the junctions and between junctions and helix stems, might further limit the conformational diversity of the unfolded state, resulting in a more ordered unfolded state than the one predicted from the electrostatic effect. Moreover, the folded state is predominantly stabilized by the coaxial stacking force. The TBI-predicted folding stability agrees well with the experimental measurements for the different Na(+) and Mg(2+) ion concentrations. For Mg(2+) solutions, the TBI model, which accounts for the Mg(2+) ion correlation effect, gives more improved predictions than the Poisson-Boltzmann theory, which tends to underestimate the role of Mg(2+) in stabilizing the folded structure. Detailed control tests indicate that the dominant ion correlation effect comes from the charge-charge Coulombic correlation rather than the size (excluded volume) correlation between the ions. Furthermore, the model gives quantitative predictions for the ion size effect in the folding energy landscape and folding cooperativity.

Figure 1

An illustration for the folding of an RNA three-way junction. (A) The left panel shows the extended Y-state where the angle between any two adjacent stems is 120°; the right panel shows the folded y-state where two stems are coaxially stacked and the angle between the other stem and the coaxial axis is ∼60°. The model is constructed using a grooved primitive (coarse-grained) model (35,36). The values k_f and k_o denote the folding and opening rates, respectively. (B) The secondary structure of a modified 16S ribosomal RNA three-way junction (25).

Figure 2

The free energy landscapes (in k_BT) for the RNA three-way junction at different [Na⁺] (A–C) and [Mg²⁺] (with 0.05 M Na⁺ background, D–F) concentrations. The x axis (θ) is the interaxis angles between 18-bp helix and 15-bp helix. The y axis is the free energy relative to the fully unfolded state at θ = 120°. For the folded state θ = 60°, the nonelectrostatic free energy (for the coaxial-stacking) is included in the total free energy.

Figure 3

Folding free energy (in k_BT) for the three-way junction as a function of (A) Na⁺ concentration and (B) Mg²⁺ concentration (with 0.05M Na⁺ background), respectively. The experimental data are taken from the literature (22,25). In panel B, we use different ion radii for Mg²⁺ (4.5 Å, 3.5 Å, 2 Å, and 1 Å) to test the sensitivity of the PB predictions on the ion size. The dotted line is calculated from TBI without the excluded volume correlation.

Figure 4

Distribution of the tightly bound Mg²⁺ ions for the states with θ = 120°, 90°, and 60° in a mixed solution with 0.001 M Mg²⁺ and 0.05 M Na⁺. The outmost spheres with color changing from dark to light represent phosphates with strong to weak charge neutralization, i.e., more ions are found around the dark color spheres (phosphates) than around the lighter color spheres (phosphates).

Figure 5

The folding free energy ΔG in k_BT for the RNA three-way junction as a function of divalent ion concentration for mixed divalent ion/Na⁺ solutions. Here Na⁺ concentration is fixed at 0.05 M. The results are calculated from TBI. From bottom to top, the divalent ion sizes are: 3.5 Å, 4.5 Å (Mg²⁺), and 5.5 Å. The experimental data are taken from the literature (22,25).

Figure 6

The folding free energy ΔG in k_BT of the RNA three-way junction as a function of (A) Na⁺ concentration and (B) Mg²⁺ concentration (with 0.05 M Na⁺ background) for the different structural parameters d_Y and d_y (see Supporting Material I and Fig. 7A). The two parameters are simultaneously increased or decreased, but we keep the same ratio of the radius of gyration R_g(Y)/R_g(y) between the folded (y) and the unfolded (Y) states.

Figure 7

(A–B) An illustration of the structure parameters. (C–E) The determination of the axis about which we rotate the 18-bp helix stem to transform the unfolded Y-state into the folded y-state. The rotation axis passes through point A and is perpendicular to the three-way junction plane.