Reduced model captures Mg(2+)-RNA interaction free energy of riboswitches

Abstract

The stability of RNA tertiary structures depends heavily on Mg(2+). The Mg(2+)-RNA interaction free energy that stabilizes an RNA structure can be computed experimentally through fluorescence-based assays that measure Γ2+, the number of excess Mg(2+) associated with an RNA molecule. Previous explicit-solvent simulations predict that the majority of excess Mg(2+) ions interact closely and strongly with the RNA, unlike monovalent ions such as K(+), suggesting that an explicit treatment of Mg(2+) is important for capturing RNA dynamics. Here we present a reduced model that accurately reproduces the thermodynamics of Mg(2+)-RNA interactions. This model is able to characterize long-timescale RNA dynamics coupled to Mg(2+) through the explicit representation of Mg(2+) ions. KCl is described by Debye-Hückel screening and a Manning condensation parameter, which represents condensed K(+) and models its competition with condensed Mg(2+). The model contains one fitted parameter, the number of condensed K(+) ions in the absence of Mg(2+). Values of Γ2+ computed from molecular dynamics simulations using the model show excellent agreement with both experimental data on the adenine riboswitch and previous explicit-solvent simulations of the SAM-I riboswitch. This agreement confirms the thermodynamic accuracy of the model via the direct relation of Γ2+ to the Mg(2+)-RNA interaction free energy, and provides further support for the predictions from explicit-solvent calculations. This reduced model will be useful for future studies of the interplay between Mg(2+) and RNA dynamics.

Figure 1

Secondary and tertiary structures of the two riboswitches used in this study. Mg²⁺ further stabilizes tertiary interactions induced by the metabolites. Metabolites are shown in magenta, and binding pockets are shaded. (A and B) Secondary (A) and tertiary (B) structures of the adenine riboswitch aptamer. The adenine metabolite stabilizes the tertiary interaction between the P2 and P3 helices. (C and D) Secondary (C) and tertiary (D) structures of the SAM-I riboswitch aptamer. The SAM metabolite stabilizes the tertiary interaction between the P3 helix and the nonlocal P1 helix, stabilizing the P1 helix and preventing strand invasion by the competing antiterminator helix in the expression platform. To see this figure in color, go online.

Figure 2

Comparison of the Mg²⁺ distribution about the SAM-I riboswitch in SBM and explicit-solvent Amber simulations. Distances to the closest RNA heavy atom were computed and binned. SBM captures well the general shape of the distribution, but misses the more subtle hydration features. The chelated ion at 2 Å could have been included in the SBM, but was omitted for simplicity. These curves were used to calibrate the excluded volume between Mg²⁺ and RNA atoms. The position of the maximum of the peak as well as the weighted average position between 3 and 5 Å both suggest that σ_MgRNA = 3.4 Å. To see this figure in color, go online.

Figure 3

NLPB calculations of Manning condensation for the adenine riboswitch. (A) The Manning condensed ions obtained from NLPB in the absence of Mg²⁺ over a wide range of KCl concentrations. The Manning condensed fraction is not constant with concentration, as predicted by Manning theory for an infinite line of charge. (B) The Manning condensed ions partitioned into the three ionic species. The Debye length is held constant at the value for 50 mM KCl, whereas the Mg²⁺ level is increased. θ₂₊ increases with increasing Mg²⁺ concentration. (C) Competition between condensed Mg²⁺ and condensed K⁺. Manning condensed ions from NLPB calculations are plotted along with fits to Eq. 13. Cl⁻ is a nonnegligible portion of the condensed fraction. The fit to Eq. 13 is better if Cl⁻ is ignored (green), but subtracting it from θ₊ (black) is more appropriate, so that the effect of condensed Cl⁻ will be included in the effective electrostatic potential. A schematic of the A = 0 assumption (Eq. 14) is plotted as a dashed line. To see this figure in color, go online.

Figure 4

Comparison of preferential interaction coefficients of the adenine riboswitch at 50 mM KCl obtained for several choices of θ₀ to experimental data. Although NLPB estimates suggest that θ₀ = 28.4 ions, θ₀ = 20 ions provides a closer fit to the experimental data. Manning condensed K⁺ cannot be neglected, as seen by the data for θ₀ = 0. To see this figure in color, go online.

Figure 5

Excess Mg²⁺ (Γ₂₊) and Mg²⁺-RNA interaction free energy (ΔG_Mg²⁺) in the hybrid SBM with explicit Mg²⁺ agree with previous experimental and computational findings. Uncertainties from bootstrap analysis are plotted as error bars, but are too small to see in most cases. (A) Comparison between Γ₂₊ for the adenine riboswitch obtained in this study with SBM and a previous experimental fluorescence study (39). The 71 base RNA has a net charge of −70. KCl is present at 50 mM. Even at comparatively low concentrations, Mg²⁺ is able to effectively compete with K⁺ and Cl⁻. (B) The Mg²⁺ interaction free energy (ΔG_Mg²⁺) obtained from Eq. 1 by integrating Γ₂₊. Agreement between the two curves suggests that SBMs with explicit Mg²⁺ are capable of capturing the energetic stabilization due to Mg²⁺. (C) Comparison between Γ₂₊ for the SAM-I riboswitch obtained in this study with SBM and a previous Amber 99 molecular dynamics study (21). The 94 base RNA has a net charge of −92. KCl is present at 100 mM. Since θ₀ is 18 ions, all values of Γ₂₊ above 9 ions are unaffected by K⁺ condensation. (D) Predicted ΔG_Mg²⁺ obtained by integrating Γ₂₊ of SAM-I. No data exist for comparison. To see this figure in color, go online.