Mg2+-RNA interaction free energies and their relationship to the folding of RNA tertiary structures

Abstract

Mg2+ ions are very effective at stabilizing tertiary structures in RNAs. In most cases, folding of an RNA is so strongly coupled to its interactions with Mg2+ that it is difficult to separate free energies of Mg2+-RNA interactions from the intrinsic free energy of RNA folding. To devise quantitative models accounting for this phenomenon of Mg2+-induced RNA folding, it is necessary to independently determine Mg2+-RNA interaction free energies for folded and unfolded RNA forms. In this work, the energetics of Mg2+-RNA interactions are derived from an assay that measures the effective concentration of Mg2+ in the presence of RNA. These measurements are used with other measures of RNA stability to develop an overall picture of the energetics of Mg2+-induced RNA folding. Two different RNAs are discussed, a pseudoknot and an rRNA fragment. Both RNAs interact strongly with Mg2+ when partially unfolded, but the two folded RNAs differ dramatically in their inherent stability in the absence of Mg2+ and in the free energy of their interactions with Mg2+. From these results, it appears that any comprehensive framework for understanding Mg2+-induced stabilization of RNA will have to (i) take into account the interactions of ions with the partially unfolded RNAs and (ii) identify factors responsible for the widely different strengths with which folded tertiary structures interact with Mg2+.

Fig. 1.

Thermodynamic cycle for Mg²⁺-induced RNA folding. The cycle separates the folding reaction (vertical arrows) from Mg²⁺ association (sloping horizontal arrows), where I is a partially folded state of the RNA and N represents the native structure. Experimental free energies for BWYV RNA are associated with each reaction arrow. The I and N states have been positioned in the vertical dimension approximately to scale according to the chemical potential (relative free energy) of the particular state. Free energies refer to buffers containing 54 mM Na⁺, 10 mM Mops (pH 7.0), and Cl⁻ anion at 25°C.

Fig. 2.

Representative titration of an indicator dye, HQS, with MgCl₂ in the presence (open circles) or absence (closed circles) of 4.18 mM A1088U RNA nucleotides in otherwise identical buffers (60 mM K⁺/10 mM Mops, pH 7.0/Cl⁻ anion). The two data sets have been normalized to the same extrapolated maximum fluorescence intensity. The ordinate is the total molarity of added Mg²⁺. The solid line has been fit to the HQS alone titration with a single-site-binding isotherm, K = 337 M⁻¹. The horizontal arrow shows the relationship between the bulk Mg²⁺ concentration (C_Mg²⁺,ref) and the value ΔC_Mg²⁺ = C_{Mg²⁺,sample} − C_Mg²⁺,ref (see text).

Fig. 3.

Energetics of BWYV RNA folding in 54 mM Na+ (pH 7.0) at 25°C. (A) Unfolding pathway of BWYV pseudoknot RNA. Bold nucleotides connected by thin lines are Watson–Crick pairs; lines with arrowheads indicate 5′–3′ connectivity of nucleotides; thick bars represent tertiary hydrogen bonds as deduced from a crystal structure (19). Thermal denaturation causes a first loss of tertiary hydrogen bonding followed by denaturation of the shorter Watson–Crick helix, as deduced from thermodynamic studies of variant sequences (21). 3′ nucleotides (boxed in the hairpin structure) have been changed to U in the variant termed U-tail. (B) ΔCMg2+nt curves for BWYV (gray circles) and U-tail (black circles) RNAs at 54 mM Na+. Error bars are derived from the average of three independent titrations. The solid lines are polynomials fit to the data as described in Materials and Methods. The difference between the two polynomials, ΔCMg2+BWYV − ΔCMg2+Utail, is also plotted (right ordinate, expressed in ions per RNA). (C) Free energy changes upon addition of MgCl2 to BWYV RNA (ΔGN-Mg2+, gray curve) or U-tail RNA (ΔGI-Mg2+, black curve), as calculated from titration data in B; the difference between these two curves is plotted as the dashed curve, ΔΔGMg2+. Circles are values of ΔΔGMg2+ calculated from unfolding free energies derived from melting experiments (see Materials and Methods).

Fig. 4.

Energetics of folding a 58-mer rRNA fragment in 60 mM K+ (pH 6.8) at 15°C. (A) Nucleotides 1051–1108 of the E. coli 23S rRNA showing secondary structure (thin lines) and base–base tertiary interactions (thick bars) found in a crystal structure (22). The positions of two variants of the E. coli sequence are shown in outline, one stabilizing (U1061A) and the other destabilizing (A1088U). The I-state form of this RNA presumably retains most of the shown secondary structure interactions but almost certainly differs in detail. (B) Mg2+-induced 58-mer RNA folding as monitored by (left ordinate) UV absorbance at 295 (gray circles) or 260 (black circles) nm, after subtraction of baselines and normalization (see Materials and Methods). The solid line is a plot of the Hill equation in which the midpoint of the transition is at 0.103 mM and the exponent is 3.99. The right ordinate indicates the difference between ΔCMg2+RNA measured for U1061A and A1088U RNAs, taken from C and reported per RNA molecule (open circles). The dashed line (right ordinate) is an extrapolation of ΔΓ2+ from ΔCMg2+RNA data between 0.4 and 1.0 mM C2+ (see Materials and Methods). (C) ΔCMg2+nt measured for U1061A (gray curve) and A1088U (black curve) RNAs. Averaged data points and error bars are calculated from six independent titrations.

Fig. 5.

Thermodynamic cycle and energy level diagram for Mg²⁺-induced folding of a 58-mer rRNA fragment. Labeling of RNA states and their positioning in the vertical dimension according to their relative free energies is as in Fig. 1. Three of the free energies are derived from experiment; the one in parentheses is calculated from the other three. Free energies refer to buffers containing 60 mM K⁺, 10 mM Mops (pH 6.8), and Cl⁻ anion at 15°C.