Surprising Sequence Effects on GU Closure of Symmetric 2×2 Nucleotide RNA Internal Loops

Abstract

GU base pairs are important RNA structural motifs and often close loops. Accurate prediction of RNA structures relies upon understanding the interactions determining structure. The thermodynamics of some two-by-two nucleotide internal loops closed by GU pairs are not well understood. Here, several self-complementary oligonucleotide sequences expected to form duplexes with two-by-two nucleotide internal loops closed by GU pairs were investigated. Surprisingly, NMR revealed that many of the sequences exist in equilibrium between hairpin and duplex conformations. This equilibrium is not observed with loops closed by Watson-Crick pairs. To measure the thermodynamics of some two-by-two nucleotide internal loops closed by GU pairs, non-self-complementary sequences were designed that preclude formation of hairpins. The measured thermodynamics indicate that some internal loops closed by GU pairs are unusually unstable. This instability accounts for the observed equilibria between duplex and hairpin conformations. Moreover, it suggests that future three dimensional structures of loops closed by GU pairs may reveal interactions that unexpectedly destabilize folding.

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INTRODUCTION

Much of biology is encoded in DNA sequences. The library of genomic and transcriptomic DNA and RNA sequences is expanding at a phenomenal rate.^1-4 Translation of coded information into biological insight would be greatly accelerated if secondary and 3D structures of RNA could be accurately predicted from sequence. Most known RNA secondary structures have been defined by sequence comparison and/or chemical mapping, often combined with basic knowledge of RNA thermodynamics.^5-15

Three dimensional structures of RNA have been determined by X-ray crystallography, cryoelectron microscopy and NMR and are thus harder to determine than secondary structures.^16-23 Accurate modeling of the intermolecular interactions important for RNA folding would hasten determination of both secondary and 3D structure, but such modeling is still challenging.^24-28 RNAPuzzles, a blind competition to predict RNA 3D structure, demonstrated the importance of accurate RNA secondary structure prediction for 3D prediction and the need for improvements, especially in modeling of noncanonical motifs.^{25, 28} Thus, detailed structural analysis of RNA loops with idiosyncratic stabilities can provide insight into structure-energetics relationships in RNA and contribute to development of de novo prediction rules.

RNA loops are important for function^29-31 and for binding potential therapeutics.^32-35 Approximating loop stability and probability from sequence is a key to accurate prediction of secondary structure.^{6, 36, 37} Moreover, small loops provide benchmarks for testing computational approaches for predicting RNA thermodynamic stability and 3D structure.^{7, 38-42} Many previous experimental and computational studies have focused on 2×2 nucleotide (nt) internal loops with GA pairs, which typically have two base-base hydrogen bonds.^43-50 This paper reports thermodynamics and NMR spectra for a series of RNA 2×2 nt loops that contain noncanonical pairs unlikely to have two hydrogen bonds and that are closed by GU pairs.

GU pairs often close loops.⁵¹ For example, 24% of 2×2 nt internal loops in one secondary structure database have at least one GU closing pair.⁵² The thermodynamics and structures of internal loops potentially closed by GU pairs are particularly idiosyncratic.^{43-45, 53, 54} For example, the 5′GAGU/3′UGAG loop in (5′GACGAGUGUCA)₂ has a major and minor structure.⁴³ The major structure is novel, with two GG pairs, extruded U’s, and an AA stack^{40, 43, 44} and is thus unexpectedly a 4×4 nt loop. The minor structure is also unusual in that the GU and AG pairs have rare hydrogen bonding patterns.⁵⁵ This contrasts with duplexes having internal loops, 5′UAGG/3′GGAU, 5′UAGA/3′AGAU, 5′AAGU/3′UGAA, 5′CAGG/3′GGAC and 5′GAGC/3′CGAG, which each have a single structure with two imino (cis WC/WC) AG pairs flanked by either wobble UG or Watson-Crick pairs.⁴³ Thus, the eight nucleotides of these internal loops have at least eight base-base hydrogen bonds compared to the four in the major structure of 5′GAGU/3′UGAG.

Thermodynamic measurements on the above loops closed by Watson-Crick pairs^{53, 56-58} indicate that on average the extra hydrogen bond in a GC as compared to an AU pair stabilizes by 1.4 kcal/mol at 37°C, similar to previous estimates.^{59, 60} The stability of the 5′GAGU/3′UGAG loop, however, is not markedly weaker than that of 5′UAGG/3′GGAU, 5′UAGA/3′AGAU, and 5′AAGU/3′UGAA. Evidently, stabilities and structures of internal loops depend on more than number of hydrogen bonds.

Accurate prediction of 3D structures and dynamics for RNA depends on force fields that realistically balance hydrogen bonding with base stacking, along with other interactions.^{26, 42, 61, 62} The structure of the 5′GAGU/3′UGAG internal loop⁴⁴ suggests that 2×2 nt internal loops closed by GU pairs can provide additional benchmarks for testing that balance.⁴⁰ Optical melting experiments and 1D imino proton NMR spectra of the GU closed loops studied here reveal unexpected equilibria and structures that will challenge computations. The results also update thermodynamic parameters for symmetric 2×2 nt loops closed by GU because revised thermodynamic parameters for nearest neighbor canonical pairs containing at least one GU have been used in the calculations.⁶³

MATERIALS AND METHODS

Sequence design

Non-self-complementary duplexes (AB) were designed to minimize the prevalence of hairpin conformation. The “tic-tac-toe” method⁶⁴ was used to minimize base pairing in hairpins (strands A and B) and in self-complementary duplexes (AA and BB).

RNA Preparation

Oligonucleotides were purchased from Dharmacon. RNA was dissolved in either melting buffer (1.0 M NaCl, 20 mM sodium cacodylate, 0.5 mM Na₂EDTA, at pH=7.0) or NMR buffer (90:10 (v/v) H₂O/D₂O, 80 mM NaCl, 20 mM NaH₂PO₄ (self-complementary duplexes) or 50 mM NaH₂PO₄ (non-self-complementary duplexes), 0.05 mM Na₂EDTA, at pH 6.1-6.3). RNA was incubated at 80 °C for 3 min and then slow cooled to room temperature to anneal the duplexes.

UV Melting

Melting curves for duplexes and for each single strand used for non-self-complementary duplexes were measured at 280 nm with a Beckman Coulter DU 640 spectrophotometer. Oligonucleotide concentrations ranged between 1 μM and 200 μM as calculated from absorbance at 80 °C and using extinction coefficients from Borer⁶⁵ and Richards.⁶⁶ Data collection began at 12 °C and was ramped to about 80 °C at a rate of 1 °C/min.

Melting Analysis

Thermodynamic parameters (ΔH° and ΔS°) were extracted from melting curves by curve fitting. Melting curves were fit to a two-state model using MeltWin as previously described.⁶⁷ In addition, thermodynamic parameters were determined by measuring the concentration dependence of melting temperature, T_M, and plotting 1/T_M versus ln(C_T/a):

$$1/{\mathrm{T}}_{\mathrm{M}}=(\mathrm{R}/\mathrm{\Delta }\mathrm{H}°)\text{ln}\left({\mathrm{C}}_{\mathrm{T}}/\mathrm{a}\right)+\mathrm{\Delta }\mathrm{S}°/\mathrm{\Delta }\mathrm{H}°$$ (1)

Here, a is 1 or 4, respectively, for self-complementary and non-self-complementary duplexes. Melting was deemed to be two-state if the ΔH° obtained by the concentration dependence of T_M and by curve fitting agreed within 15%.

With the exception of 5′GCGUGCCUUGCG/3′CGCAUCCGACGC, the single strands either had no cooperative melting or an apparent T_M lower than the heteroduplexes (Figures S1-S6). The two strands for 5′GCGUGCCUUGCG/3′CGCAUCCGACGC yielded melting curves with clear cooperative transitions and similar T_M values (Figure S4). In this case, 1D NMR imino proton spectra and 2D NOESY spectra at 10 and 25 °C and 0.1 M Na⁺ revealed that the expected heterodimer was more than 90% of the sample. The remainder was in self-complementary duplexes composed of each individual strand. The melting curves at 1 M Na⁺ for the mixture of 5′CGCAGCCUACGC/3′GCGUUCCGUGCG were treated as a simple two state transition. Agreement by better than 15% for ΔH° values derived from eq 1 and by curve fitting suggest the self-complementary duplexes had little effect on the measured thermodynamics.

Calculation of internal loop thermodynamics

Previously, two different methods have been used to calculate thermodynamic increments for internal loops. When thermodynamics for a duplex with the same Watson-Crick/GU pairs but no internal loop were available, then those values were subtracted from measured values for the duplex and then adjusted for the Watson-Crick or GU nearest neighbor missing from the duplex with the internal loop.^{68, 69} If a relevant all Watson-Crick/GU duplex was not available, then published nearest neighbor parameters^{36, 70} were subtracted from the measured values of the duplex, ΔG°_duplex, containing the internal loop. For duplexes with terminal GC pairs, the equation is:

$$\mathrm{\Delta }\mathrm{G}{°}_{\text{loop}}=\mathrm{\Delta }\mathrm{G}{°}_{\text{duplex}}-\sum \mathrm{\Delta }\mathrm{G}{°}_{\text{NN}}-\mathrm{\Delta }\mathrm{G}{°}_{\text{init}}-\mathrm{\Delta }\mathrm{G}{°}_{\text{sym}}$$ (2)

Here, Σ ΔG°_NN is the sum of the nearest neighbor parameters for Watson-Crick and GU pairs, ΔG°_init is the free energy increment for duplex initiation, and ΔG°_sym = –TΔS°_sym accounts for the symmetry difference between self-complementary (ΔS°_sym = –1.4 cal/K mol) and non-self-complementary duplexes (ΔS°_sym = 0 cal/K mol).⁷¹ For consistency here, eq 2 has been used for all 2×2 nt internal loops, including those previously measured. Additionally, updated values for nearest neighbor GU pairs have been used.⁶³ Thus, some loop ΔH°, ΔS°, and ΔG° values differ from those reported in previous publications.

As an example of the calculations, the ΔG° increment at 37 °C (eq 2) for formation of the loop, 5′GCAU/3′UACG, in the duplex, (CGGGCAUCCG)₂, was calculated as:

$$\mathrm{\Delta }\mathrm{G}{°}_{37}(5\prime \mathrm{G}\underset{\_}{\text{CA}}\mathrm{U}/3\prime \mathrm{U}\underset{\_}{\text{AC}}\mathrm{G})=-6.74-2(-2.36)-2(-3.26)-2(-1.80)-4.09-0.43=3.58\text{kcal/mol at}37°\mathrm{C}.$$ (3)

Here, –6.74 kcal/mol is the measured ΔG°₃₇ of duplex formation. The other numbers are nearest neighbor parameters taken from Xia et al. and J. Chen et al.^{63, 70} The calculated value of 3.58 kcal/mol for loop formation is more stable than the 6.00 kcal/mol previously reported.⁷² The difference is that the previous calculation subtracted the measured ΔG°₃₇ of −11.2 kcal/mol for (5′CGGGUCCG)₂⁷³ and added the best value of 1.29 kcal/mol for the (5′GU/3′UG) middle nearest neighbor available at that time.³⁶ Use of the measured value for (5′CGGGUCCG)₂, however, neglects the fact that the 5′GGUC/3′CUGG quartet is unusually stable^{63, 73} but absent in (5′CGGGCAUCCG)₂.

For sequences that formed only hairpins, the loop was treated as a hairpin loop of four nucleotides because we are unaware of a GXYU loop with the GU pair in a wobble conformation.^74-77 This is consistent with previous calculations of hairpin thermodynamics.^{78, 79}

NMR

NMR spectra were measured with either a 500 MHz or 600 MHz Varian Inova spectrometer. RNA concentrations for NMR were ~1 mM unless otherwise noted. One-dimensional imino proton spectra were obtained using a 1-1-spin-echo pulse⁸⁰ with excitation maximum adjusted to the imino region. Two-dimensional NOESY spectra were obtained using WATERGATE water suppression.^{81, 82}

RESULTS

Studies started with self-complementary sequences⁷² designed to form symmetric duplexes with a central 2×2 nt internal loop. As discussed below, however, there were conditions in which NMR showed that the sequences can also form a hairpin, thus revealing an unexpected conformational pliability for GU pairs.

Self-Complementary Oligonucleotides

5′CGGGCAUCCG forms a duplex between 0.13 and 1 mM oligonucleotide

A plot of 1/T_M vs ln C_T for 5′CGGGCAUCCG at 1 M Na⁺ was linear with a positive slope between oligonucleotide concentrations of 12.5 and 140 μM, but turned over at lower concentrations (Figure 1). A fit of the linear portion of the 1/T_M vs log C_T plot in Figure 1 to eq 1 provided the thermodynamic parameters listed in Table 1 for formation of the duplex, (5′CGGGCAUCCG)₂. The thermodynamic values are within experimental error of those previously reported (Figure 1 caption and Table 2).⁷²

Figure 1.

Plot of 1/T_M vs log C_T for 5′CGGGCAUCCG at 1 M Na⁺. Error bars are ±1 °C. The linear fit (shown with the line) to oligonucleotide concentrations between 12.5 and 140 μM gave values for ΔH°, ΔS°, and ΔG°₃₇ of –38.0 kcal/mol, –100.9 eu, and –6.74 kcal/mol, respectively. Values are similar to those reported previously: –39.5 kcal/mol, –106.3 eu, and –6.49 kcal/mol, respectively.⁷²

Table 1.

Thermodynamic Parameters for Duplex Formation in 1 M NaCl.

	TM−1 vs ln (CT/n) plots				Average of melt curve fits
Sequences	−ΔH° (kcal/mol)	−ΔS° (eu)	−ΔG°37 (kcal/mol)	Tm (°C)b	−ΔH° (kcal/mol)	−ΔS° (eu)	−ΔG°37 (kcal/mol)	Tm (°C)b
(5′CGGGCAUCCG)2	38.0±4.6	100.9±14.5	6.74±0.23	45.9	40.6±6.1	108.8±19.3	6.83±0.13	46.1
5′GCGUGACUAGCGCGCAUCAGUCGC5′	80.0±8.4	229.0±26.4	8.95±0.31	46.7	77.6±11.7	221.2±36.8	8.96±0.31	47.0
5′GCUGACUACGAACGAUCAGUGC5′	77.2±3.5	225.0±11.3	7.40±0.04	40.6	88.2±6.5	260.4±20.7	7.45±0.13	40.3
5′GCGUGAAUAGCGCGCAUAAGUCGC5′	46.2±5.4	125.7±17	7.19±0.24	41.5	46.3±12.0	125.9±38.7	7.28±0.20	42.1
5′GCGUGCUUUGCGCGCAUUCGACGC5′	51.0±5.0	141.4±16.1	7.18±0.15	41.0	50.1±8.5	138.2±27.9	7.26±0.15	41.6
5′GCGUGUCUUGCGCGCAUCUGACGC5′	64.1±7.7	179.6±21.4	8.43±0.25	46.2	73.3±15.3	208.3±48.5	8.71±0.33	46.4
5′GCGUGCCUUGCGCGCAUCCGACGC5′	44.1±4.6	118.3±14.8	7.42±0.23	43.4	51.5±7.4	142.0±23.5	7.49±0.33	42.8
5′GCGUUUCGUGCGCGCAGCUUACGC5′	77.7±4.6	221.7±14.3	8.93±0.14	46.9	84.5±9.3	243.2±29.0	9.11±0.34	46.8
(5′CGGACAUCCG)2	70.7±6.9	203.5±21.7	7.60±0.18	45.7	64.9±11.9	184.8±33.3	7.57±0.40	46.3
(5′GGACAUCC)2a	37.1	106.7	4.03	23.8	55.4	167.0	3.92	27.4

^aWu et al. 1995.⁸³ Error limits are omitted because of difficulty fitting data with low melting temperatures.

^bMelting temperatures are at 0.1 mM total oligonucleotide.

Table 2.

Thermodynamic Parameters for Internal Loops.

Sequence	ΔG°37 (kcal/mol)	ΔH° (kcal/mol)	ΔS° (eu)
(5′CGGGCAUCCG)2	3.58 3.83a	20.5 19.0a	54.5 48.9a
5′GCGUGACUAGCGCGCAUCAGUCGC5′	3.62	−8.8	−39.9
5′GCUGACUACGAACGAUCAGUGC5′	2.19	−15.1	−55.7
5′GCGUGAAUAGCGCGCAUAAGUCGC5′	5.38	25.1	63.4
5′GCGUGCUUUGCGCGCAUUCGACGC5′	5.37	23.2	57.4
5′GCGUGUCUUGCGCGCAUCUGACGC5′	4.13	10.06	19.1
5′GCGUGCCUUGCGCGCAUCCGACGC5′	5.14	30.1	80.5
5′GCGUUUCGUGCGCGCAGCUUACGC5′	4.30	9.35	16.3
(5′CGGACAUCCG)2	3.82	−1.40	−16.8
(5′GGACAUCC)2b	2.67	10.95	26.7

^aChristiansen & Znosko (2008).⁷² Loop parameters were calculated with Watson-Crick nearest neighbor parameters from Xia et al.⁷⁰ and J. Chen et al.⁶³

^bWu et al. 1995.⁸³ Loop parameters were calculated with Watson-Crick nearest neighbor parameters from Xia et al.⁷⁰ and J. Chen.⁶³

One-dimensional NMR at 0.1 and 1 M Na⁺ revealed the presence of one conformation at 1 mM and 100 μM oligonucleotide, respectively, but more than one conformation at 20 μM oligonucleotide and 0.1 M Na⁺ (Figure 2 and Figure S7). Presence of a hairpin conformation at low RNA concentration could explain the non-linear portion of the 1/T_M vs ln C_T plot in Figure 1. The 1D NMR spectrum at 100 μM oligonucleotide and 1 M Na⁺ (Figure S7) had imino proton resonances equivalent to those seen at 1 mM oligonucleotide and 0.1 M Na⁺. Thermodynamic experiments are typically done at 1 M Na⁺ where duplex formation is favored relative to hairpin.

Figure 2.

Imino proton NMR spectra of 1 mM and 0.02 mM 5′CGGGCAUCCG in 0.1 M Na⁺ at 5 °C. The additional peaks in the low concentration spectrum are likely due to a small amount of hairpin.

5′CGGGCUUCCG forms a hairpin at 1 mM oligonucleotide

Surprisingly, replacing the central A of 5′CGGGCAUCCG with a U resulted in a 1/T_M vs ln C_T plot with melting temperature essentially independent of oligonucleotide concentration at 1 M Na⁺ (Figure 3). This is consistent with a hairpin to random coil transition. Imino proton NMR spectra at 50 μM and 1 mM of 5′CGGGCUUCCG at 0 °C and 0.1 M Na⁺ each have six clear resonances (Figure 4a). A 2D NOESY spectrum (150 ms mixing time) confirmed three CG pairs. G4H1 was confirmed by a strong imino (11.04 ppm) to amino cross-peak. A positive ROESY (10 ms mixing time) cross-peak between 11.04 and 13.49 ppm for G4H1 indicated slow conformational exchange. This chemical shift difference is consistent with a hairpin loop having two conformations. One possible minor conformation is a “kissing hairpin” with two GC pairs^{22, 84, 85} and a stabilizing 3′ dangling end U (Figure S8).^{71, 86-88}

Figure 3.

Plots of 1/T_M vs log C_T at 1 M Na⁺ for 5′CGGGCUUCCG (blue), 5′GGCGAAUGCC (green), 5′GCGUGCUUUGCG/3′CGCAUUCGACGC (orange), and 5′GCUGAAUACG/3′CGAUAAGUGC (black). Error bars are ±1 °C.

Figure 4.

Imino proton NMR spectra in 0.1 M Na⁺ for: (a) 5′CGGGCUUCCG; a 2D spectrum contains an exchange peak for G4 at 11.04/13.49 ppm, revealing two conformations in slow exchange, (b) 5′GGCGAAUGCC, (c) 5′CCUGUCUAGG; two resonances are overlapped at 13.3 ppm, (d) 5′GUCGCCUGAC. A 2D spectrum for sequence d reveals that the peak around 12.3 ppm contains two resonances for G8. In general, red and blue resonance assignments refer to hairpins and duplexes, respectively, as determined from 2D spectra.

Fitting of the optical melting curves for 5′CGGGCUUCCG to a unimolecular transition from hairpin to random coil provided the thermodynamic parameters in Table 3. The thermodynamics of hairpin formation have been studied for sequences with related loops, 5′GGACGCUUGUCC, 5′GGACUUCGGUCC, and 5′GGCUUCGGCC.^{78, 79} The first sequence has a CG instead of GC pair closing the loop and the last two sequences have the loop sequence including closing pair in reverse compared to 5′CGGGCUUCCG. These hairpin results are also listed in Table 3, with the loop parameters updated with current nearest neighbor parameters for the Watson-Crick paired stems.⁷⁰

Table 3.

Thermodynamic Parameters for Hairpins in 1 M NaCl.^a

		Experiment			Loop Formationb
sequence	TM a	ΔG°37	ΔH°	ΔS°	ΔG°37	ΔH°	ΔS°
	(°C)	kcal/mol	kcal/mol	eu	kcal/mol	kcal/mol	eu
5′GGCGAAUGCC	64.9	–2.47	–29.86	–88.31	4.21	–1.59	–18.71
5′CGGGCUUCCG	49.6	–0.86	–21.99	–68.14	4.76	2.04	–8.74
5′GGACGCUUGUCCa	70.9	–4.478	–45.078	–130.878	3.4	–7.77	–36.1
5′GGACUUCGGUCCa	76.4	–6.378	–55.978	–159.978	1.6	–18.67	–65.2
GGCUUCGGCC	72.2	–4.179	–40.179	–116.179	2.6	–11.8	–46.5

^aT_M is calculated from ΔH° and ΔS°.

^bLoop parameters for Antao and Tinoco⁷⁸ were recalculated with Watson-Crick nearest neighbor parameters of Xia et al.⁷⁰

5′GGCGAAUGCC forms a hairpin at 1 mM oligonucleotide

Replacing the central C of 5′CGGGCAUCCG with an A while maintaining a stem of three GC pairs resulted in a concentration independent melting temperature for 5′GGCGAAUGCC at 1 M Na⁺ (Figure 3). This is consistent with a hairpin to random coil transition. NMR spectra at 10 °C, 0.1 M Na⁺ and 50 μM or 1 mM oligonucleotide have four clear resonances, consistent with a single major conformation having three CG pairs and a G or U resonance at 10.6 ppm (Figure 4b). The concentration independent NMR is also consistent with a hairpin conformation. Fitting of the optical melting curves to a unimolecular transition from hairpin to random coil provided the thermodynamic parameters in Table 3.

5′CCUGUCUAGG, 5′GGCGACUGCC, 5′CCAUUCGUGGA, and 5′GUCGCCUGAC each form an equilibrium mixture of duplex and hairpin

For ~1 mM RNA samples of 5′CCUGUCUAGG, 5′GGCGACUGCC, 5′CCAUUCGUGGA, and 5′GUCGCCUGAC, 1D imino proton NMR spectra at 0.1 M Na⁺ have more resonances than expected for a single conformation (Figures 4c,d, S9, S10). Moreover, the relative areas of resonances change with oligonucleotide concentration (Figure 4c,d, S9, S10). Increasing Na⁺ to 1 M for 5′CCUGUCUAGG and 5′CCAUUCGUGGA also changed relative intensities of resonances (Figures S11 and S12). For 5′CCAUUCGUGGA, the chemical shifts of 10.3, 11.3, and 11.95 ppm for the imino resonances retained at 50 μM RNA (Figure S10) are in a similar pattern as those reported for the UUCG tetraloop in 5′GGCACUUCGGUGCC.⁷⁷ Evidently, 5′CCUGUCUAGG, 5′GGCGACUGCC, 5′CCAUUCGUGGA, and 5′GUCGCCUGAC, exist in equilibria between duplex and hairpin.

5′CGGACAUCCG, 5′GAGACUUCUC and 5′GCAUCUGC form duplexes at 0.1 mM oligonucleotide and 1 M NaCl

To check for possible duplex/hairpin equilibria in loops with AU closure, imino proton spectra at 1 M Na⁺ were measured for 5′CGGACAUCCG, 5′GAGACUUCUC, and 5′GCAUCUGC (Figure 5). No extra imino proton resonances were detected, consistent with only duplex formation. Moreover, for 5′CGGACAUCCG and 5′GAGACUUCUC, respectively, one and two resonances with chemical shifts above 13.6 ppm were detected, consistent with the number of expected types of Watson-Crick AU pairs in the duplexes. For 5′GCAUCUGC, a 2D spectrum in water revealed a single resonance representative of the expected Watson-Crick AU pairs as identified by a UH3/AH2 NOE. The chemical shift of the UH3 was 13.6 ppm as expected for the proposed duplex. To our knowledge, a hairpin loop of the form 5′AXYU, with the AU forming a Watson-Crick pair and XY being any combination of A, C, G, and U, has never been deposited in the PDB.⁸⁹ Previously, no extra resonances were observed for 5′GCAAAUGC, 5′GGAACUCC, and 5′GGACAUCC.⁸³ Evidently, the duplex/hairpin type equilibria or pure hairpin observed for some loops closed by GU pairs are unlikely to occur with AU closure.

Figure 5.

Imino proton NMR spectra for 0.1 mM RNA in 1 M NaCl at 5 °C for duplexes with AU flanked 2×2 nt loops. (a) (5′CGGACAUCCG)₂, (b) (5′GAGACUUCUC)₂, and (c) (5′GCAUCUGC)₂.

The thermodynamics of duplex formation for (5′GAGACUUCUC)₂ and (5′GCAUCUGC)₂ have been reported.⁷² Thermodynamics for (5′CGGACAUCCG)₂ were measured (Table 1 and Figure S13) to provide values for the 5′ACAU/3′UACA loop. The loop ΔG°₃₇ of 3.82 kcal/mol is less favorable than the 2.67 kcal/mol derived from the thermodynamics of duplex formation for (5′GGACAUCC)₂, which had melting temperatures lower by about 20 °C (Tables 1 and 2).⁸³ Low melting temperatures make it difficult to fit lower baselines of melting curves.

Non-Self-Complementary Oligonucleotides that form Duplexes

To avoid equilibria between duplex and hairpin, non-self-complementary oligonucleotides were used to measure thermodynamics for several internal loops closed by GU pairs. Sequences and 1D NMR spectra are shown in Figures 6 and S14. Thermodynamic results are listed in Tables 1 and 2.

Figure 6.

Imino proton NMR spectra at 0.1 M Na⁺ and ~ 1 mM duplex for:

(a) 5′GCGUGCUUUGCG/3′CGCAUUCGACGC,

(b) 5′GCGUGUCUUGCG/3′CGCAUCUGACGC,

(c) 5′GCGUGAAUAGCG/3′CGCAUAAGUCGC,

(d) 5′GCGUGACUAGCG/3′CGCAUCAGUCGC,

(e) 5′GCGUUUCGUGCG/3′CGCAGCUUACGC, and

f) 5′GCGUGCCUUGCG/3′CGCAUCCGACGC.

DISCUSSION

Insights into intermolecular interactions important for RNA folding can facilitate interpretation of the sequences in RNA transcriptomes. Small model systems provide benchmarks able to bridge experimental results with computations. Here, thermodynamic results are presented for seven 2×2 nt internal loops closed by GU pairs and two hairpin loops.

GU pairs are common in RNA secondary structure and often close internal loops.^{51, 52} Thus, the thermodynamics for closure of loops by GU pairs is important for prediction of secondary structure from sequence by a variety of methods, including sequence comparison,^{5, 9, 10, 15} single sequence with or without chemical modification restraints^{8, 13, 36, 90} and/or NMR constraints.⁹¹

The ΔG°₃₇ values for the internal loops studied here in duplexes without 3′ dangling A’s range from 3.6 to 5.4 kcal/mol (Table 2). This range is noteworthy because every difference of 1.4 kcal/mol changes an equilibrium constant by 10-fold at 37 °C. Thus, the thermodynamic results reported here can provide benchmarks for computational methods⁴² that predict the thermodynamics of RNA loops on the basis of fundamental interactions.

The range of ΔG°₃₇ values reported here for internal loops is smaller than the range of 0.4 to 6.0 kcal/mol previously reported.⁷² This difference is largely due to extracting loop parameters using only nearest neighbor parameters,^{63, 70} and elimination of the unexpected equilibria between internal loops and hairpin loops as revealed by NMR.

The (5′GACU)₂ loop was studied in two duplexes. One had terminal CG pairs and the other differed by having them replaced with 3′ dangling end A’s (Tables 1 and 2 and Figure S14). The respective values for ΔG°₃₇ of the loops are 3.6 and 2.2 kcal/mol. Evidently, the nature of termini can affect the contribution of an internal loop to duplex stability. A related non-nearest neighbor effect has previously been observed for bulged loops measured in the presence or absence of 3′ dangling end A’s.⁹² Clearly, the nearest neighbor model is sometimes a rough approximation when loops are involved. In contrast, it is an excellent model when only canonical base pairs are present^{63, 70} and even in some other cases with 2×2 internal loops (Table S1). Future structural and computational studies may provide insight into fundamental principles determining the applicability of nearest neighbor approximations.

Table 2 summarizes thermodynamics for the internal loops studied here. All the loops fall into category 1, defined as 2×2 nt loops “unlikely to have a mismatch with two hydrogen bonds between bases”.⁹³ For this type of loop closed by GU or AU pairs, parameters determined by Christiansen and Znosko⁵² from a dataset of 97 internal loops with 2×2 nts predict a loop ΔG°₃₇ of 3.0±0.2 kcal/mol. For the loops in Table 2, the ΔG°₃₇ values for (5′GAAU)₂, (5′GCUU)₂, (5′GCCU)₂, (5′GUCU)₂, and (5′UUCG)₂ may differ from 3.0 kcal/mol by more than experimental error and may reflect non-nearest neighbor effects. Thus, their 3D structures may provide insight into key interactions determining stability.

One surprise for the self-complementary sequences studied here was that under conditions tested, the sequences with GU pairs exist in hairpin/duplex equilibria or were only hairpins. For sequences with hairpin/duplex equilibria, melting curves used to measure thermodynamics do not represent a two-state transition from duplex to single strand. Thus, six non-self-complementary duplexes with GU closed self-complementary internal loops were studied to provide revised internal loop thermodynamics (Tables 1 and 2). Table 4 provides a summary of available values of ΔG°₃₇, ΔH° and ΔS° for all symmetric 2×2 nt internal loops as calculated with eq. 1.

Table 4.

Nearest Neighbor Thermodynamics for 2×2 Symmetric Internal Loops at 37 °C in 1 M NaCl^a

ΔG°	(kcal/mol at 37°C)
	GA	AG	UU	GG	CA	CU	UC	CC	AC	AA
GC	−2.5b	−1.4b	−0.6c	−0.8d	1.2c	1.3c	1.3d	1.4d	0.8c	1.4c
CG	−1.0e	−0.7e,f	−0.1g	0.6g	1.4g	1.6g	1.7g	1.9g	1.9g	1.5g,e
UA	0.6b	1.4h	1.0c	2.2i	2.3c	2.6c	3.3c	4.9d	3.5d	2.7c
AU	0.6b	2.1h	0.9c	2.1i	3.3c,j	3.0d	3.1d	3.8d	2.8c	3.0c
UG	−0.8b	2.7h	1.9c	1.0d	2.5d	3.5d	4.3j	1.6d	2.0d	1.1c
GU	0.2b	(1.0)h,k	1.6d	1.7d	3.7d,j	5.4j	4.1j	5.1j	3.6j	5.4j
ΔH°	(kcal/mol)
	GA	AG	UU	GG	CA	CU	UC	CC	AC	AA
GC	−27.5b	−19.2b	−18.1c	−20.5d	−5.1c	−19.4c	−10.9d	10.8d	−12.3c	−5.0c
CG	−11.6e	−17.0e,f	−13.9g	−24.1g	−7.2g	3.0g	0.8g	1.8g	−5.9g	−1.4g,e
UA	−17.8b	−20.6h	−11.0c	−1.6i	7.9c	2.1c	8.3c	10.0d	18.5d	10.4c
AU	−15.5b	−7.1h	−18.1c	−6.9i	4.8c,j	1.9d	11.8d	12.5d	11.3c	7.5c
UG	−20.1b	−21.8h	−0.3c	15.3d	−9.7d	29.4d	9.4j	10.8d	7.1d	−3.1c
GU	−14.2b	(−10.4)h,k	10.5d	4.9d	19.8d,j	23.2j	10.1j	30.1j	−8.8j	25.1j
ΔS°	(cal/(K*mol))
	GA	AG	UU	GG	CA	CU	UC	CC	AC	AA
GC	−80.6b	−57.4b	−56.3c	−63.6d	−20.2c	−66.9c	−39.4d	30.1d	−42.2c	−20.5c
CG	−34.0e	−52.7e,f	−44.3g	−79.7g	−27.5g	4.6g	−2.7g	−0.3g	−24.9g	−9.3g,e
UA	−59.2b	−70.9h	−38.6c	−12.3i	17.8c	−1.8c	16.1c	16.4d	48.2d	25.0c
AU	−52.0b	−29.4h	−61.3c	−29.0i	4.9c,j	−3.6d	28.0d	28.0d	27.2c	14.5c
UG	−62.1b	−78.8h	−7.1c	46.1d	−39.3d	83.5d	16.3j	29.6d	16.7d	−13.6c
GU	−46.4b	(−36.8)h,k	28.5d	10.1d	51.7d,j	57.4j	19.1j	80.5j	−39.9j	63.4j

^aLeft most column lists base pairs closing loop and top row lists non-canonical pairs in loop. For example, bottom loop in right most column is 5′GAAU/3′UAAG (ΔG°₃₇=5.4 kcal/mol). Bold values are averages from measurements on more than one duplex.

^bWalter et al. (1994).⁵⁶

^cWu et al. (1995).⁸³

^dChristiansen & Znosko (2008).⁷²

^eSantaLucia et al. (1990).⁵⁷

^fXia et al. (1997).⁵⁸

^gSantaLucia et al. (1991).⁶⁹

^hSchroeder & Turner (2001).⁵³

ⁱBurkard et al. (2001).⁹⁴

^jThis work.

^kUnpublished NMR shows that the sequence melted⁵³ forms a duplex rather than a hairpin. Although there may be multiple conformations for the loop,^{43, 44, 55} the values given assume a single conformation closed by wobble GU pairs.

The self-complementary sequence, 5′CGGGCUUCCG, formed only a hairpin (Figures 3 and 4a). The ΔG°₃₇ (Table 3) calculated for the hairpin loop, GGCUUC, is +4.8 kcal/mol whereas that calculated for a related loop, CGCUUG, is +3.4 kcal/mol using published experimental data⁷⁸ for 5′GGACGCUUGUCC and nearest neighbor parameters for Watson-Crick pairs.⁷⁰ The average of the two values, 4.1 kcal/mol, is the same as that predicted from parameters of Mathews et al.⁶ when the GU pair in the loop is approximated as an AC pair. As known previously,^{6, 78, 79} the CUUCGG hairpin loop is unusually stable. As expected, the reverse loop sequence, GGCUUC, is less stable (Table 3).

Thermodynamic parameters for the (5′GCUU)₂, (5′GUCU)₂, and (5′GCCU)₂ internal loops were obtained from non-self-complementary duplexes (Table 2). The loop ΔG°₃₇ values are very unfavorable at 5.4, 4.1, and 5.1 kcal/mol, respectively. This may reflect unfavorable stacking interactions, backbone distortion, and/or competition with water that leads to reduced hydrogen bonding between G and U as compared to other internal loops. In contrast, the self-complementary sequence, 5′CGGGCUUCCG, forms a hairpin that may be stabilized by non-nearest neighbor interactions previously detected for hairpins closed by a GU pair with the 5′G directly preceded by two G residues.^{36, 95}

The non-self-complementary duplex, 5′GAGUAAUGAC/3′CUCGAAGCUG, has a measured ΔG°₃₇ of −5.2 kcal/mol.⁵³ With the nearest neighbor parameters used here,^{63, 70} the ΔG°₃₇ increment for the non-self-complementary internal loop, 5′UAAU/3′GAAG, is 3.13 kcal/mol. This is close to the average of 3.25 kcal/mol for the values of 1.1 and 5.4 kcal/mol in Table 4 for the (UAAG)₂ and (GAAU)₂ loops. This suggests that the difference between 1.1 and 5.4 kcal/mol may be due to differences of interactions in the 5′UA/3′GA and 5′GA/3′UA nearest neighbors rather than differences in the 5′AA/3′AA stacks.

The duplex, (5′GACGAGUGUCA)₂, unexpectedly exhibits an equilibrium between two 3D conformations,⁴³ and both are novel.^{44, 55} In contrast, replacing the potential GU pairs with AU to give (GACAAGUGUCA)₂ results in a single conformation with two imino AG pairs, as also seen for sequences with the 5′AG/3′GA loop closed by UA, GC, or CG Watson-Crick pairs.^{43, 46} Evidently, small motifs expected to have GU pairs can have structures useful as benchmarks for predicting 3D structure.⁴⁰

The structural heterogeneity of potential GU pairs closing loops presumably reflects the properties of the individual bases. G has the highest dipole moment,⁹⁶ the most atoms capable of hydrogen bonding, and a large surface area, which favors stacking. In contrast, U has the least propensity to stack^97-102 and a dipole moment roughly half that of G. These properties allow many different patterns of hydrogen bonding for GU pairs.¹⁰³ Moreover, the range (1.1 to 5.4 kcal/mol) in ΔG°₃₇ values for 2×2 nt loops closed by GU or UG and with noncanonical pairs having less than two base-base hydrogen bonds is larger than the range (2.3 to 4.9 kcal/mol) for those closed by AU or UA pairs or by GC or CG pairs (0.8 to 1.9 kcal/mol) (Table 4).

In general, the unexpected presence of hairpins in solutions of the self-complementary sequences studied here may be partially a consequence of unfavorably constrained stacking forced by duplex formation. The results reported here suggest that experimental structures and thermodynamics of loops closed by GU pairs can provide stringent benchmarks for testing the accuracy of RNA force fields in balancing hydrogen bonding, stacking, and backbone interactions. In particular, loops with unusual thermodynamics may also have unusual structures. The experiments reported here were conducted between pH 6 and 7, the pH range most important physiologically. Results at different pHs and/or in the presence of Mg²⁺ could provide additional challenges for computations.