Consecutive GA Pairs Stabilize Medium Size RNA Internal Loops

Abstract

Internal loops in RNA are important for folding and function. Consecutive non-canonical pairs can form in internal loops having at least two nucleotides on each side. Thermodynamic and structural insights for such internal loops should improve approximations for their stabilities and predictions of secondary and three-dimensional structures. Most natural internal loops are purine rich. A series of oligoribonucleotides that form purine rich internal loops of 5 – 10 nucleotides, including kink-turn loops, were studied by UV melting, exchangeable proton and phosphorus NMR. Three consecutive GA pairs with the motif of $\begin{array}{c}\hfill 5^{\prime }\mathrm{Y}\underset{¯}{\mathrm{GGA}}\hfill \\ \hfill 3^{\prime }\mathrm{R}\mathrm{AAG}\hfill \end{array}$ or $\begin{array}{c}\hfill \underset{¯}{\mathrm{GGA}}\mathrm{R}{3}^{\prime }\hfill \\ \hfill \mathrm{AAG}\mathrm{Y}{5}^{\prime }\hfill \end{array}$ (i.e. $\begin{array}{c}\hfill 5^{\prime }\underset{¯}{\mathrm{GGA}}{3}^{\prime }\hfill \\ \hfill 3^{\prime }\mathrm{AAG}{5}^{\prime }\hfill \end{array}$ closed on at least one side with a CG, UA, or UG pair with Y representing C or U and R representing A or G) stabilize internal loops having six to ten nucleotides. Certain motifs with two consecutive GA pairs are also stabilizing. In internal loops with three or more nucleotides on each side, the motif $\begin{array}{c}\hfill 5^{\prime }\mathrm{U}\underset{¯}{\mathrm{G}}\hfill \\ \hfill 3^{\prime }\mathrm{G}\mathrm{A}\hfill \end{array}$ has stability similar to $\begin{array}{c}\hfill 5^{\prime }\mathrm{C}\underset{¯}{\mathrm{G}}\hfill \\ \hfill 3^{\prime }\mathrm{G}\mathrm{A}\hfill \end{array}$. A revised model for predicting stabilities of internal loops with 6 – 10 nucleotides is derived by multiple linear regression. Loops with 2 × 3 nucleotides are predicted well by a previous thermodynamic model.

Sequence dependent secondary structure interactions in RNA usually dominate energetically over tertiary interactions (1-5). Thus free energy parameters derived from studies of short oligonucleotides (5-9) allow prediction of RNA secondary structures with about 73% accuracy on average without consideration of tertiary structure when the RNA is shorter than about 500 nucleotides (8, 9). This accuracy could be improved with more knowledge of the sequence dependence of stabilities for loops in RNA. This work provides insight into the sequence dependence of stability for internal loops. Internal loops are important elements of tertiary structure (10-17) and are binding sites for proteins and therapeutics (17-25).

Thermodynamics and structures of internal loops in oligoribonucleotides have been studied by UV melting and NMR, respectively (5, 6, 26-40). Current free energy parameters derived for internal loops (9) are largely based on knowledge of 2 × 2¹ and 2 × 3 internal loops, where “n1 × n2” represents an internal loop with n1 and n2 nucleotides on each side, respectively. Currently, only the thermodynamic effect of the first non-canonical pair on each side of an internal loop is considered in structure prediction algorithms.

Stabilities of size symmetric (i.e. n1 = n2) internal loops are more sequence dependent than size asymmetric (i.e. n1 ≠ n2) loops (27). Presumably this is because asymmetric loops are more flexible. This flexibility is also reflected in the observation that asymmetric loops are typically relatively unstructured in solution (21, 24, 26, 30, 41-44). Structured consecutive non-canonical pairs have been observed, however, in large internal loops and hairpins (31-33, 45-49).

The motif of three consecutive sheared GA pairs $\begin{array}{c}\hfill 5^{\prime }\underset{¯}{\mathrm{GGA}}{3}^{\prime }\hfill \\ \hfill 3^{\prime }\mathrm{AAG}{5}^{\prime }\hfill \end{array}$ is the most stable among 3 × 3 internal loops (33, 34). Two consecutive GA pairs $\begin{array}{c}\hfill 5^{\prime }\underset{¯}{\mathrm{GA}}{3}^{\prime }\hfill \\ \hfill 3^{\prime }\mathrm{AG}{5}^{\prime }\hfill \end{array}$ are also the most stable among 2 × 2 internal loops. (Throughout the paper, each top strand is written from 5′ to 3′ as going from left to right.) Formation of consecutive sheared GA pairs is well conserved in some size asymmetric loops, including certain types of kink-turn motifs (17-23, 50). This suggests that thermodynamic stabilization due to consecutive GA pairs may not be restricted to 2 × 2 and 3 × 3 internal loops. Biophysical and biochemical studies of a kink-turn suggest formation of three consecutive GA pairs within the 3 × 6 internal loop $\begin{array}{c}\hfill \mathrm{G}\underset{¯}{\mathrm{GGA}}\mathrm{G}\hfill \\ \hfill \mathrm{C}\mathrm{AAGAAG}\mathrm{C}\hfill \end{array}$ even in the absence of Mg²⁺(aq) and protein (51). Consecutive two or three GA pairs are also found in internal loops in signal recognition particle (SRP) RNA (33, 52); in the substrate loop of VS ribozyme (53, 54); in multibranch loops such as the P5abc domain of the Tetrahymena thermophila group I intron (14, 55, 56); in the putative catalytic site of hammerhead ribozymes (57); and in a variety of structural elements in ribosomal RNA (33, 37, 58-60).

Here, the thermodynamics of internal loops with 5 – 10 nucleotides are presented. Multiple linear regression is used to develop a revised thermodynamic model for loops larger than 2 × 3. Three consecutive GA pairs with the motif of $\begin{array}{c}\hfill \mathrm{Y}\underset{¯}{\mathrm{GGA}}\hfill \\ \hfill \mathrm{R}\mathrm{AAG}\hfill \end{array}$ or $\begin{array}{c}\hfill \underset{¯}{\mathrm{GGA}}\mathrm{R}\hfill \\ \hfill \mathrm{AAG}\mathrm{Y}\hfill \end{array}$ (i.e.$\frac{\mathrm{GGA}}{\mathrm{AAG}}$ closed on at least one side with a CG, UA, or UG pair with Y representing C or U and R representing A or G) can stabilize X₃ × W_3-6 and X₄ × W_4-6 internal loops. The motifs of $\begin{array}{c}\hfill \mathrm{R}\underset{¯}{\mathrm{GGA}}\hfill \\ \hfill \mathrm{Y}\mathrm{AAG}\hfill \end{array}$ and $\begin{array}{c}\hfill \underset{¯}{\mathrm{GGA}}\mathrm{Y}\hfill \\ \hfill \mathrm{AAG}\mathrm{R}\hfill \end{array}$ (i.e. $\frac{\mathrm{GGA}}{\mathrm{AAG}}$ motif not closed with at least one YR canonical pair) are also stabilizing but less than those with the closing canonical pair reversed. Two consecutive GA pairs with the motif $\begin{array}{c}\hfill \mathrm{Y}\underset{¯}{\mathrm{GA}}\hfill \\ \hfill \mathrm{R}\mathrm{AG}\hfill \end{array}$, $\begin{array}{c}\hfill \mathrm{R}\underset{¯}{\mathrm{GA}}\hfill \\ \hfill \mathrm{Y}\mathrm{AG}\hfill \end{array}$, $\begin{array}{c}\hfill \mathrm{Y}\underset{¯}{\mathrm{GG}}\hfill \\ \hfill \mathrm{R}\mathrm{AA}\hfill \end{array}$ or $\begin{array}{c}\hfill \mathrm{R}\underset{¯}{\mathrm{GG}}\hfill \\ \hfill \mathrm{Y}\mathrm{AA}\hfill \end{array}$ stabilize 3 × 3, 3 × 4, 4 × 4, and 4 × 5 nucleotide internal loops (i.e. loops with the closing base pair 3′ to the A of a GA pair and with asymmetry n2 − n1 < 2). In 3 × 3 and larger loops, the motif $\begin{array}{c}\hfill \mathrm{U}\underset{¯}{\mathrm{G}}\hfill \\ \hfill \mathrm{G}\mathrm{A}\hfill \end{array}$ has stability similar to $\begin{array}{c}\hfill \mathrm{C}\underset{¯}{\mathrm{G}}\hfill \\ \hfill \mathrm{G}\mathrm{A}\hfill \end{array}$ even though UG pairs are usually less stable than CG pairs.

The thermodynamic model developed here will help improve RNA secondary structure prediction, particularly prediction of medium size internal loops, including those that form kink-turns. Internal loops are also often involved in formation of tertiary structure (10-17) and tertiary structure can perturb secondary structure (55, 61, 62). Thus the results presented here should also facilitate 3D structure modeling of RNAs and consideration of tertiary interactions in predicting secondary structure.

MATERIALS AND METHODS

Oligoribonucleotide Synthesis and Purification

Oligoribonucleotides were synthesized using the phosphoramidite method (63, 64) and purified as described before (33, 34). CPG supports and phosphoramidites were acquired from Proligo, Glen Research, or ChemGenes. Purities were checked by reverse phase HPLC or analytical TLC on a Baker Si500F silica gel plate (250 μm thick) and all were greater than 95% pure.

UV Melting Experiments and Thermodynamics

Concentrations of single-stranded oligonucleotides were calculated from the absorbance at 280 nm at 80 °C and extinction coefficients predicted from those of dinucleotide monophosphates and nucleosides (65, 66) with the RNAcalc program (67). Purine riboside (P) was assumed to be the same as adenosine for approximation of extinction coefficients. Small mixing errors for non-self-complementary duplexes do not affect thermodynamic measurements appreciably (68).

Oligonucleotides were lyophilized and redissolved in 1.0 M NaCl, 20 mM sodium cacodylate, and 0.5 mM disodium EDTA at pH 7. Curves of absorbance at 280 nm versus temperature were acquired using a heating rate of 1 °C/min with a Beckman Coulter DU640C spectrophotometer having a Peltier temperature controller cooled with flowing water.

Melting curves were fit to a two-state model with the MeltWin program (http://www.meltwin.com), assuming linear sloping baselines and temperature-independent ΔH° and ΔS° (7, 67, 69). Additionally, the temperature at which half the strands are in duplex, T_M, at total strand concentration, C_T, was used to calculate thermodynamic parameters for non-self-complementary duplexes according to (70):

$${{\mathrm{T}}_{\mathrm{M}}}^{-1}=(\mathrm{R}∕\Delta {\mathrm{H}}^{°})\ln ({\mathrm{C}}_{\mathrm{T}}∕4)+(\Delta ∕{\mathrm{S}}^{°}∕\Delta {\mathrm{H}}^{°})$$ (1)

Here R is the gas constant, 1.987 cal/mol·K. The ΔH° values from T_M⁻¹ plots and from the average of the fits of melting curves to two-state transitions agree within 15% (Table 1), suggesting that the two-state model is a good approximation for these transitions. The equation ΔG°₃₇ = ΔH° − (310.15)ΔS° was used to calculate the free energy change at 37 °C (310.15 K).

Table 1.

Measured thermodynamic Parameters for Duplex Formation in 1 M NaCl, pH7.

	TM−1 vs ln(CT/4) plots (eq 1)				Average of melt curve fits
Sequences	−ΔH° (kcal/mol)	−ΔS° (eu)	−ΔG°37 (kcal/mol)	Tma (°C)	−ΔH° (kcal/mol)	−ΔS° (eu)	−ΔG°37 (kcal/mol)	Tma (°C)
2 × 3 internal loops
GGCGA GGCU PCCGAAGCCG	84.7±4.3	234.6±12.9	11.92±0.26	58.1	80.1±5.7	220.8±17.1	11.65±0.40	58.2
GGCGAAGGCU PCCGAG CCG	82.7±1.7	228.7±5.3	11.72±0.10	57.8	74.0±2.3	202.2±7.1	11.23±0.12	58.1
GGCGGAGGCU PCCGAG CCG	82.6±4.7	228.6±14.5	11.71±0.27	57.7	76.6±4.3	210.3±13.4	11.40±0.17	58.1
GGUGAAGGCU PCCGAG CCG	83.9±1.7	236.1±5.3	10.70±0.07	53.2	86.4±1.8	243.8±5.4	10.80±0.11	53.1
GGUGGAGGCU PCCGAG CCG	87.2 ±1.9	247.3±5.8	10.53±0.08	51.9	77.8±3.9	218.2±12.0	10.11±0.21	52.0
GGUGA GGCU PCCGAAGCCG	82.9±2.0	233.5±6.3	10.43±0.08	52.3	7 8.5±3.3	220.2±10.1	10.25±0.14	52.4
GGUGA GGCU PCCAAAGCCG	79.7 ±1.9	224.9±5.8	9.96±0.07	51.0	76.2±2.0	214.0±6.2	9.83±0.07	51.0
GGUGAAGGCU PCCGAG UCG	74.9 ±2.6	213.8±8.0	8.57±0.06	45.7	71.2±5.4	202.4±17.1	8.45±0.13	45.6
GGUGA GGCU PCCGAAGUCG	67.8 ±2.8	192.5±8.8	8.13±0.04	44.5	62.5±2.2	175.3±7.0	8.08±0.07	44.9
GGUAGAGGCU PCCGAG CCG	75.5±2.0	213.4±6.1	9.27±0.06	48.7	72.2±3.3	203.4±10.4	9.15±0.13	48.7
3 × 3 internal loops
GGUGUAGGCU PCCGAAGCCG	85.2±3.1	237.8±9.5	11.41±0.17	55.8	8 8.5±4.6	247.8±13.8	11.61±0.28	55.9
GGUGAAGGCU PCCGAUGCCG	88.4±2.2	249.5±6.8	11.07±0.10	53.8	82.9±3.4	232.3±10.5	10.81±0.14	53.9
GGUAGAGGCU PCCGAAGCCG	86.2±2.9	242.9±8.9	10.90±0.13	53.5	8 9.9±2.5	254.1±7.9	11.06±0.13	53.5
GGCGAAGGCU PCCGAUGCCG	78.2±2.0	214.6±6.2	11.66±0.12	58.8	75.1±5.0	205.1±15.3	11.52±0.30	59.1
2 × 4 internal loops
GGUGA GGCU PCCGAAGGCCG	75.7±4.7	213.9±14.6	9.36±0.14	49.0	70.5±6.9	197.6±21.3	9.16±0.32	49.0
GGUGGAAGGCU PCCGAG CCG	75.6±1.8	213.6±5.8	9.32±0.06	48.9	72.3±4.8	203.5±15.0	9.19±0.18	48.8
GGCGAAAGGCU PCCGAG CCG	68.2±3.1	188.3±9.5	9.82±0.14	52.7	62.0±6.6	168.9±20.7	9.62±0.22	53.3
3 × 4 internal loops
GGUGGAAGGCUb PCCGAAG CCG	91.9±1.4	2 58.1±4.3	11.82±0.07	56.0	89.4±3.7	250.5±11.3	11.71±0.19	56.1
GGCGGA GGCU PCCGAAGGCCG	89.0±1.2	246.5±3.5	12.55±0.07	59.5	83.2±3.2	228.9±9.8	12.22±0.15	59.8
GGUGGA GGCUb PCCGAAGGCCG	91.4±3.0	257.4±9.1	11.56±0.15	55.0	85.4±3.9	238.9±11.9	11.26±0.22	55.2
GGC GAAGGCU PCCGAAGGCCG	86.2±2.6	2 3 8.5±7.8	12.22±0.16	58.9	79.5±3.5	218.2±10.8	11.84±0.18	59.2
GGU GAAGGCU PCCGAAGGCCG	89.9±1.6	253.8±4.8	11.16±0.07	53.9	82.0±2.5	229.4±7.7	10.81±0.16	54.1
GAGCGGA CGAC CUCGAAGAGCUG	93.3±3.7	266.5±11.5	10.61±0.15	51.2	92.8±3.6	265.1±11.3	10.60±0.16	51.2
GGC AAAGGCU PCCGAAGGCCG	77.2±2.1	213.5±6.4	10.96±0.11	55.9	74.8±3.8	206.1±11.6	10.85±0.21	56.0
GAGC AGACGAC CUCGAAAGGCUG	88.7±6.4	254.3±20.1	9.80±0.24	48.9	88.7±8.7	254.4±27.0	9.82±0.37	48.9
GGCGAAAGGCU PCCGAAG CCG	70.4±3.5	193.1±10.9	10.45±0.18	55.3	69.9±7.0	191.4±21.5	10.50±0.34	55.7
GAGCAAGACGAC CUCG AAGGCUG	78.3±4.0	222.0±12.5	9.44±0.13	49.0	82.7±3.6	235.9±11.0	9.59±0.20	48.9
GAGCAGGACGAC CUCG AAGGCUG	81.6±3.3	232.7±10.5	9.42±0.10	48.4	78.9±5.7	224.2±17.9	9.34±0.20	48.5
GGUAGA GGCU PCCGAAGGCCG	72.7±2.8	205.4±8.7	9.01±0.09	48.0	64.4±8.7	179.6±26.9	8.68±0.36	47.7
GAGCAGGACGAC CUCGAUG GCUG	78.2±2.0	223.3±6.3	8.96±0.05	46.9	88.5±4.5	255.7±14.5	9.18±0.11	46.6
GAGCAGAGCGAC CUCGAGA GCUG	52.8±2.9	144.7±9.1	7.94±0.07	45.5	47.0±10.0	126.2±31.5	7.83±0.33	45.8
2 × 5 internal loops
GGUGA GGCU PCCGAAGGACCG	79.3±6.1	229.4±19.4	8.14±0.15	43.4	6 8.7±5.9	196.0±18.2	7.95±0.26	43.5
GGCGA GGCUc PCCGAGUAACCG	54.4±2.5	147.7±7.8	8.55±0.09	49.0	53.1±5.2	143.6±16.3	8.52±0.14	49.1
4 × 4 internal loops
GGUGGAAGGCUb PCCGAAGGCCG	108.1±4.1	300.6±12.4	14.91±0.30	63.0	108.5±3.1	301.8±9.4	14.93±0.25	63.0
GGCGGAUGGCUb PCCGAAGUCCG	105.4±1.7	289.3±5.1	15.71±0.14	66.6	108.6±2.6	298.6±7.5	15.97±0.23	66.5
GGCGAAAGGCU PCCGAAGGCCG	89.6±2.4	248.8±7.3	12.45±0.15	58.9	86.0±6.4	237.8±19.4	12.29±0.36	59.3
GAGCAGGACGAC CUCGAAAGGCUG	94.9±2.7	271.6±8.5	10.65±0.10	51.1	92.1±2.8	262.9±8.6	10.56±0.11	51.2
GAGCAAGACGAC CUCGAAAGGCUG	91.0±4.0	261.7±12.5	9.83±0.13	48.7	87.9±5.9	251.9±18.3	9.72±0.27	48.7
CGCGAAAGGC GCGAAAGCCG	54.7±2.5	152.0±7.9	7.56±0.05	42.9	47.1±8.9	127.2±29.2	7.62±0.12	44.3
GAGCAGAGCGAC CUCGAAGAGCUG	81.7±2.8	235.5±8.8	8.61±0.05	45.1	79.8±4.3	229.8±13.6	8.57±0.08	45.1
CGCAAAAGGC GCGAAAACCG	38.3±1.8	103.3±7.0	6.29±0.05	35.0	37.3±7.3	99.5±20.1	6.47±0.01	36.5
GAGCAAAGCGAC CUCGAAGAGCUG	73.9±2.6	212.9±8.3	7.80±0.04	42.4	69.8±5.2	199.9±16.5	7.75±0.09	42.5
CGGAAAACGC GCCAAAAGCG	31.6±1.8	87.4±6.2	4.48±0.15	18.1	30.8±9.9	83.8±34.7	4.78±0.81	20.3
3 × 5 internal loops
GGCGGA GGCU PCCGAAGGACCG	83.2±3.0	233.6±9.1	10.75±0.14	53.6	72.5±5.0	200.6±15.7	10.28±0.16	53.9
GGUGGA GGCU PCCGAAGGACCG	81.2±1.7	230.8±5.2	9.57±0.05	49.1	77.2±5.7	218.5±17.6	9.42±0.27	49.1
GGCGAA GGCU PCCGAAGGACCG	71.0±2.2	197.4±6.8	9.79±0.09	51.9	6 5.5±5.4	180.2±17.1	9.63±0.17	52.4
GGUGAA GGCU PCCGAAGGACCG	78.6±2.8	224.7±8.7	8.86±0.06	46.5	74.2±4.6	211.2±14.5	8.74±0.11	46.5
GGCAAA GGCU PCCGAAGGACCG	66.8±2.4	185.9±7.6	9.10±0.08	49.4	65.8±3.4	183.1±10.8	9.06±0.14	49.4
GGUAGA GGCU PCCGAAGGACCG	76.0±5.7	219.4±18.3	7.96±0.11	43.0	68.0±6.9	193.9±21.7	7.87±0.21	43.2
GGCGA GGCU PCCGAAAAAACCG	68.4±5.9	191.2±18.5	9.12±0.24	49.2	64.0±6.1	177.4±19.2	8.95±0.24	49.2
4 × 5 internal loops
GGUGGAA GGCUd PCCGAAGGACCG	91.5±3.5	259.7±10.8	10.93±0.15	52.7	88.1±2.9	249.2±9.1	10.78±0.16	52.7
GGCGAAA GGCU PCCGAAGGACCG	69.0±2.7	190.6±8.4	9.89±0.12	52.9	68.7±4.6	189.5±14.2	9.93±0.19	53.1
3 × 6 internal loops
GGUGGA GGCUb,e PCCGAAGUUUCCG	85.3±6.7	239.7±20.5	10.97±0.32	54.0	89.6±3.2	253.0±10.0	11.16±0.21	53.9
GGCGGA GGCUb PCCGAAGUUUCCG	86.9±3.5	242.1±10.6	11.77±0.18	56.9	81.3±8.2	225.1±25.2	11.54±0.43	57.4
GGUGGA GGCUb PCCGAAGAAACCG	90.8±1.9	259.1±6.0	10.47±0.07	51.1	84.5±4.2	239.4±13.0	10.25±0.19	51.3
GGCGGA GGCUb PCCGAAGAAACCG	72.9±4.0	202.5±12.3	10.09±0.16	52.9	66.0±5.8	181.1±18.2	9.84±0.20	53.4
GGCGAA GGCU PCCGAAGAAACCG	66.6±2.3	185.5±7.2	9.06±0.07	49.3	58.5±7.2	159.9±22.9	8.88±0.16	50.0
GGCGGA GGCU PCCGAAAAAACCG	56.0±3.7	152.4±11.6	8.76±0.14	49.9	53.6±6.9	144.5±21.7	8.78±0.17	50.6
GGCGAA GGCU PCCGAAAAAACCG	59.9±3.0	165.2±9.3	8.71±0.10	48.7	53.8±5.4	145.9±17.0	8.58±0.18	49.3
GGCGGA GGCU PCCGAGAAAACCG	57.8±5.6	158.9±17.4	8.56±0.24	48.3	50.1±6.3	134.4±19.7	8.41±0.26	49.1
GGCAAA GGCU PCCGAAAAAACCG	58.2±2.5	160.4±7.9	8.47±0.07	47.7	6 0.5±7.0	167.6±22.3	8.51±0.20	47.5
GGUGUA GGCU PCCGAAAAAACCG	61.2±5.8	173.6±18.5	7.39±0.17	41.4	56.0±3.5	156.9±11.5	7.37±0.16	41.7
4 × 6 internal loops
GGUGGAA GGCUb PCCGAAGAAACCG	90.3±2.2	259.3±6.9	9.88±0.07	48.9	82.4±3.9	234.6±12.1	9.64±0.15	49.2
GGUGGAA GGCU PCCGAAAAAACCG	77.9±2.4	223.9±7.6	8.46±0.04	44.9	72.0±6.2	205.3±19.3	8.32±0.22	44.9
GGCGAAA GGCU PCCGAAAAAACCG	59.5±3.8	163.7±12.0	8.72±0.14	48.8	54.9±7.4	149.0±23.1	8.64±0.25	49.4
GGCGAAA GGCU PCCGAGAAAACCG	53.5±5.5	145.1±17.3	8.49±0.24	48.8	48.8±7.8	130.4±24.5	8.41±0.22	49.4

^aAt C_T = 0.1 mM.

^bImino proton spectra (Figure 2) are consistent with secondary structure shown.

^ckink-turn in U4 snRNA (17, 22).

^dKt-58 (17).

^ePredicted to be kink-turn in helix 78 of E. Coli 23S rRNA (17, 50).

Self-structure (hairpin and/or duplex) of individual single strands may compete with designed non-self-complementary duplexes. Melting data for individual single strands are listed in Supporting Information Table S1. The rough standard of sequence design was that the T_ms of duplexes are 5 °C higher than those of individual single strands and the ΔG°_{37 (duplex with loop)} values are at least 1.4 kcal/mol more favorable than those of duplex formation by individual single strands. It is possible, however, to measure reasonable thermodynamic parameters even when the T_m of a competing homoduplex is a few degrees higher than that of the heteroduplex (71).

NMR Spectroscopy

All exchangeable proton spectra were acquired on a Varian Inova 500 MHz (¹H) spectrometer. One-dimensional imino proton spectra were acquired with an S pulse sequence and temperatures ranging from 0 to 55 °C. SNOESY (72) spectra were recorded with a 150 ms mixing time at 5 or 10 °C. The Felix (2000) software package (Molecular Simulations Inc.) was used to process 2D spectra. Proton spectra were referenced to H₂O or HDO at a known temperature dependent chemical shift relative to 3-(trimethylsilyl) tetradeutero sodium propionate (TSP). The 1D ¹H-decoupled ³¹P spectra (referenced to external standard of 85% H₃PO₄ at 0 ppm) were acquired on a Bruker Avance 500 MHz (¹H) spectrometer at 30 °C. Sample buffer conditions were 80 mM NaCl, 10 mM sodium phosphate, 0.5 mM Na₂EDTA. Total volumes were 300 μL with 90:10 (v:v) H₂O:D₂O or 100% D₂O.

RESULTS

Thermodynamics

Measured thermodynamic parameters for duplexes at 1 M NaCl are listed in Table 1. Thermodynamic parameters for formation of the internal loops (Table 2) were calculated from measured parameters of duplexes according to the following equation (73):

$$\Delta {{\mathrm{G}}^{°}}_{37,\text{loop}}=\Delta {{\mathrm{G}}^{°}}_{37\left(\text{duplex with loop}\right)}-\Delta {{\mathrm{G}}^{°}}_{37\left(\text{duplex without loop}\right)}+\Delta {{\mathrm{G}}^{°}}_{37\left(\text{interrupted base stack}\right)}$$ (2a)

For example,

$$\Delta {{\mathrm{G}}^{°}}_{37}\begin{array}{ccc}\hfill \mathrm{U}\hfill & \underset{¯}{\mathrm{GGAA}}\hfill & \hfill \mathrm{G}\hfill \\ \hfill \mathrm{G}\hfill & \mathrm{AAG}\hfill & \hfill \mathrm{C}\hfill \end{array}=\Delta {{\mathrm{G}}^{°}}_{37}\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \underset{¯}{\mathrm{GGAA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAG}\hfill & \mathrm{CCG}\hfill \end{array}-\Delta {{\mathrm{G}}^{°}}_{37}\begin{array}{c}\hfill \mathrm{GGUGGCU}\hfill \\ \hfill \mathrm{PCCGCCG}\hfill \end{array}+\Delta {{\mathrm{G}}^{°}}_{37}\begin{array}{c}\hfill \mathrm{UG}\hfill \\ \hfill \mathrm{GC}\hfill \end{array}$$ (2b)

Here, ΔG°₃₇ $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \hfill \underset{¯}{\mathrm{GGAA}}\hfill & \hfill \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAG}\hfill & \hfill \mathrm{CCG}\hfill \end{array}$ is the measured value of the duplex containing the internal loop, ΔG°₃₇ $\begin{array}{c}\hfill \mathrm{GGUGGCU}\hfill \\ \hfill \mathrm{PCCGCCG}\hfill \end{array}$ is the measured value of the duplex without the loop (33), and ΔG°₃₇ $\begin{array}{c}\hfill \mathrm{UG}\hfill \\ \hfill \mathrm{GC}\hfill \end{array}$ is the free energy increment for the nearest neighbor interaction interrupted by the internal loop (7, 8). Nearest-neighbor parameters (7, 8) are used to estimate the difference of one or two base pairs compared with $\begin{array}{c}\hfill \mathrm{GGUGGCU}\hfill \\ \hfill \mathrm{PCCGCCG}\hfill \end{array}$ (33). Identical calculations can be done for measured values for ΔH°_loop and ΔS°_loop. All the measured thermodynamic parameters used in this calculation are derived from T_M⁻¹ versus ln(C_T/4) plots (eq 1). In Tables 1 and 2, sequences are ordered from smallest to largest according to internal loop size, and from the most stable to least stable according to measured loop stability at 37 °C, ΔG°_{37, loop}. The ΔG°_{37, loop} value is also often put in parentheses following each duplex or internal loop in the Results and Discussion sections.

Table 2.

Measured and predicted thermodynamic Parameters for Internal Loop Formation in 1 M NaCl, pH7^a

Sequence	ΔG°37, loop (kcal/mol)	ΔH°loop (kcal/mol)	ΔS° loop (eu)
2 × 3 internal loops
GGCGA GGCU PCCGAAGCCG	−0.37±0.66 (−0.23)	−12.4±10.6	−38.7±32.3
GGCGAAGGCU PCCGAG CCG	−0.17±0.62 (−0.23)	−10.4±9.8	−32.8±30.1
GGCGGAGGCU PCCGAG CCG	−0.16±0.67 (−0.23)	−10.3±10.8	−32.7±33.0
GGUGAAGGCU PCCGAG CCG	−0.06±0.53 (0.50)	−13.9±9.4	−44.6±28.9
GGUGGAGGCU PCCGAG CCG	0.11±0.54 (0.50)	−17.2±9.5	−55.8±29.0
GGUGA GGCU PCCGAAGCCG	0.21±0.54 (0.50)	−12.9±9.5	−42.0±29.1
GGUGA GGCU PCCAAAGCCG	0.41±0.52 (0.50)	−10.9±7.9	−36.4±24.2
GGUGAAGGCU PCCGAG UCG	0.92±0.60 (1.23)	−6.2±10.0	−22.8±30.5
GGUGA GGCU PCCGAAGUCG	1.36±0.60 (1.23)	0.9±10.1	−1.5±30.7
GGUAGAGGCU PCCGAG CCG	1.37±0.53 (1.91)	−5.5±9.4	−21.9±29.0
3 × 3 internal loops
GGUGGAGGCUb,f PCCGAAGCCG	−2.62±0.78 (−2.39)	−24.3±12.4	−69.7±37.5
GGUGGAGGCUb,f PCCAAAGCCG	−2.27±0.59 (−1.44)	−23.9±9.7	−69.5±29.5
GGCGGAGGCUb,f PCCGAAGUCG	−2.00±0.77 (−2.39)	−18.9±11.8	−54.5±35.9
GGUGUAGGCU PCCGAAGCCG	−0.77±0.56 (−0.03)	−15.2±9.7	−46.3±29.9
GGUGAAGGCUb,f PCCGAAGCCG	−0.48±0.57 (−0.03)	−14.2±11.1	−44.2±34.0
GGUGAAGGCU PCCGAUGCCG	−0.43±0.54 (−0.03)	−18.4±9.5	−58.0±29.2
GGCGAAGGCUb,f PCCGAAGCCG	−0.37±0.76 (0.18)	−8.9±11.9	−27.5±36.4
GGUAGAGGCU PCCGAAGCCG	−0.26±0.54 (0.65)	−16.2±9.6	−51.4±29.7
GGCGAAGGCU PCCGAUGCCG	−0.11±0.62 (0.18)	−5.9±9.9	−18.7±30.3
2 × 4 internal loops
GGUGA GGCU PCCGAAGGCCG	1.28±0.55 (0.87)	−5.7±10.4	−22.4±31.9
GGUGGAAGGCU PCCGAG CCG	1.32±0.53 (0.87)	−5.6±9.4	−22.1±28.9
GGCGAAA GGCU PCCGAG CCG	1.73±0.62 (1.08)	4.1±10.1	7.6±31.1
3 × 4 internal loops
GGUGGAAGGCUf PCCGAAG CCG	−1.18±0.53 (−0.78)	−21.9±9.4	−66.6±28.7
GGCGGA GGCU PCCGAAGGCCG	−1.00±0.61 (−0.57)	−16.7±9.8	−50.6±29.9
GGUGGA GGCUf PCCGAAGGCCG	−0.92±0.55 (−0.78)	−21.4±9.7	−65.9±29.8
GGC GAAGGCU PCCGAAGGCCG	−0.67±0.63 (−0.57)	−13.9 ± 10 . 0	−42.6 ± 30 . 7
GGU GAAGGCU PCCGAAGGCCG	−0.52±0.53 (0.17)	−19.9±9.4	−62.3±28.8
GAGCGGA CGAC CUCGAAGAGCUG	0.07±0.59 (−0.57)	−26.6±10.4	−85.2±31.3
GGC AAAGGCU PCCGAAGGCCG	0.59±0.61 (0.61)	−4.9±9.9	−17.6±30.3
GAGC AGACGAC CUCGAAAGGCUG	0.88±0.61 (0.61)	−22.0±11.5	−73.0±35.4
GGCGAAAGGCU PCCGAAG CCG	1.10±0.63 (0.88)	1.9±10.3	2.8±31.6
GAGCAAGACGAC CUCG AAGGCUG	1.24±0.58 (0.61)	−11.6±10.4	−40.7±31.7
GAGCAGGACGAC CUCG AAGGCUG	1.26±0.58 (0.61)	−14.9±10.2	−51.4±31.0
GGUAGA GGCU PCCGAAGGCCG	1.63±0.54 (2.53)	−2.7±9.7	−13.9±29.7
GAGCAGGACGAC CUCGAUG GCUG	1.72±0.57 (1.79)	−11.5±9.9	−42.0±29.8
GAGCAGAGCGAC CUCG AGAGCUG	2.74±0.57 (2.70)	13.9±10.1	36.6±30.5
2 × 5 internal loops
GGUGA GGCU PCCGAAGGACCG	2.50±0.55 (2.48)	−9.3±11.1	−37.9±34.4
GGCGA GGCUc PCCGAGUAACCG	3.00±0.62 (2.69)	17.9±10.0	48.2±30.7
4 × 4 internal loops
GGUGGAAGGCUf PCCGAAGGCCG	−4.27±0.61 (−3.31)	−38.1±10.1	−109.1±31.0
GGCGGAUGGCUf PCCGAAGUCCG	−4.16±0.62 (−1.52)	−33.1±9.8	−93.4±30.1
GGCGAAAGGCU PCCGAAGGCCG	−0.90±0.63 (−0.74)	−17.3±10.0	−52.9±30.5
GAGCAGGACGAC CUCGAAAGGCUG	0.03±0.57 (0.17)	−28.2±10.0	−90.3±30.3
GAGCAAGACGAC CUCGAAAGGCUG	0.85±0.58 (0.17)	−24.3±10.4	−80.4±31.7
CGCGAAAGGC GCGAAAGCCG	0.96±0.07 (0.44)	−5.6±1.9	−21.3±7.3
GAGCAGAGCGAC CUCGAAGAGCUG	2.07±0.33 (2.26)	−15.0±10.1	−54.2±30.4
CGCAAAAGGC GCGAAAACCG	2.23±0.07 (2.26)	10.8±1.9	27.4±7.3
GAGCAAAGCGAC CUCGAAGAGCUG	2.88±0.57 (2.26)	−7.2±10.0	−31.6±30.3
CGGAAAACGC GCCAAAAGCG	3.01±0.17 (2.26)	11.4±2.2	27.1±7.2
3 × 5 internal loops
GGCGGA GGCU PCCGAAGGACCG	0.80±0.62 (−0.11)	−10.9±10.1	−37.7±31.0
GGUGGA GGCU PCCGAAGGACCG	1.07±0.53 (−0.32)	−11.2±9.4	−39.3±28.8
GGCGAA GGCU PCCGAAGGACCG	1.76±0.61 (2.25)	1.3±9.9	−1.5±30.4
GGUGAA GGCU PCCGAAGGACCG	1.78±0.53 (2.04)	−8.6±9.7	−33.2±29.7
GGCAAA GGCU PCCGAAGGACCG	2.45±0.61 (3.16)	5.5±10.0	10.0±30.6
GGUAGA GGCU PCCGAAGGACCG	2.68±0.54 (3.90)	−6.0±10.8	−27.9±33.7
2 × 6 internal loops
GGCGA GGCU PCCGAAAAAACCG	2.43±0.65 (3.15)	3.9±11.3	4.7±35.0
4 × 5 internal loops
GGUGGAA GGCUd PCCGAAGGACCG	−0.29±0.55 (−0.70)	−21.5±9.9	−68.2±30.4
GGCGAAA GGCU PCCGAAGGACCG	1.66±0.62 (1.87)	3.3±10.1	5.3±30.8
3 × 6 internal loops
GGUGGA GGCUe,f PCCGAAGUUUCCG	−0.33±0.62 (0.20)	−15.3±11.4	−48.2±35.0
GGCGGA GGCUf PCCGAAGUUUCCG	−0.22±0.63 (0.41)	−14.6±10.3	−46.2±31.5
GGUGGA GGCUf PCCGAAGAAACCG	0.17±0.54 (0.20)	−20.8±9.4	−67.6±29.0
GGCGGA GGCUf PCCGAAGAAACCG	1.46±0.62 (0.41)	−0.6±10.4	−6.6±32.1
GGCGAA GGCU PCCGAAGAAACCG	2.49±0.60 (2.77)	5.7±9.9	10.4±30.5
GGCGGA GGCU PCCGAAAAAACCG	2.79±0.62 (2.77)	16.3±10.4	43.5±31.8
GGCGAA GGCU PCCGAAAAAACCG	2.84±0.62 (2.77)	12.4±10.1	30.7±31.1
GGCGGA GGCU PCCGAGAAAACCG	2.99±0.64 (2.77)	14.5±11.1	37.0±34.4
GGCAAA GGCU PCCGAAAAAACCG	3.08±0.61 (3.68)	14.1±10.0	35.5±30.7
GGUGUA GGCU PCCGAAAAAACCG	3.25±0.56 (2.56)	8.8±10.8	17.9±33.9
4 × 6 internal loops
GGUGGAA GGCUf PCCGAAGAAACCG	0.76±0.54 (0.32)	−20.3±9.5	−67.8±29.2
GGUGGAA GGCU PCCGAAAAAACCG	2.18±0.53 (2.68)	−7.9±9.6	−32.4±29.4
GGCGAAA GGCU PCCGAAAAAACCG	2.83±0.62 (2.89)	12.8±10.4	32.2±32.0
GGCGAAA GGCU PCCGAGAAAACCG	3.06±0.64 (2.89)	18.8±11.0	50.8±34.4

^aCalculated from eq 2a and data in Table 1 unless otherwise noted. Experimental error for ΔG°37, ΔH°, and ΔS° for the canonical stems are estimated as 4%, 12%, and 13.5%, respectively, according to reference (7) . Values in parentheses are ΔG°_predicted, predicted according to eq 3a for 2 × 3 loops and eq 4 for other loops.

^bData from reference (33).

^cKink-turn in U4 snRNA (17, 22).

^dKt-58 (17).

^ePredicted to be kink-turn in helix 78 of E. Coli 23S rRNA (17, 50).

^fImino proton spectra (Figure 2) are consistent with secondary structure shown.

Models for Predicting Thermodynamic Stabilities of Medium Size RNA Internal Loops

Measured thermodynamic results reported here and previous data on 2 × 3, 2 × 4, and 3 × 3 internal loops (28-30, 33, 34, 68) can be compared to predictions from the model in the current RNAstructure 4.0 algorithm (9), which is also similar to that used in MFOLD (8):

$$\Delta {{\mathrm{G}}^{°}}_{\text{predicted}}=\Delta {{\mathrm{G}}^{°}}_{\text{loop initiation}}\left(\mathrm{n}\right)+\mathrm{m}1\Delta {{\mathrm{G}}^{°}}_{\mathrm{AU}∕\mathrm{GU}\text{penalty}}+\mid \mathrm{n}1-\mathrm{n}2\mid \Delta {{\mathrm{G}}^{°}}_{\mathrm{asym}}+\mathrm{m}2\Delta {{\mathrm{G}}^{°}}_{\mathrm{UU}\text{bonus}}+\mathrm{m}3\Delta {{\mathrm{G}}^{°}}_{5^{\prime }\mathrm{YA}∕3^{\prime }\mathrm{RG}\text{bonus}}+\mathrm{m}4\Delta {{\mathrm{G}}^{°}}_{\mathrm{GG}\text{bonus}}+\mathrm{m}5\Delta {{\mathrm{G}}^{°}}_{5^{\prime }\mathrm{YG}∕3^{\prime }\mathrm{RA}\text{bonus}}+\mathrm{m}{5}^{\prime }\Delta {{\mathrm{G}}^{°}}_{5^{\prime }\mathrm{RG}∕3^{\prime }\mathrm{YA}\text{bonus}}.$$ (3a)

or

$$\Delta {{\mathrm{G}}^{°}}_{\text{predicted}}=\Delta {{\mathrm{G}}^{°}}_{\text{loop initiation}}\left(\mathrm{n}\right)+\mathrm{m}1\Delta {{\mathrm{G}}^{°}}_{\mathrm{AU}∕\mathrm{GU}\text{penalty}}+\mid \mathrm{n}1-\mathrm{n}2\mid \Delta {{\mathrm{G}}^{°}}_{\mathrm{asym}}+\mathrm{m}2\Delta {{\mathrm{G}}^{°}}_{\mathrm{UU}\text{bonus}}+\mathrm{m}3\Delta {{\mathrm{G}}^{°}}_{\mathrm{AG}\text{bonus}}+\mathrm{m}4\Delta {{\mathrm{G}}^{°}}_{\mathrm{GG}\text{bonus}}+\mathrm{m}5\Delta {{\mathrm{G}}^{°}}_{\mathrm{GA}\text{bonus}}$$ (3b)

Here eq 3a and 3b are for 2 × 3 and larger loops, respectively (9). ΔG°_{loop initiation}(n) is the free energy for initiating an internal loop with n nucleotides that is closed by two GC/CG pairs, ΔG°_{AU/GU penalty} is the penalty for replacing a closing GC/CG pair with an AU/UA or GU/UG pair, m1 to m5′ are 1 or 2, n1 and n2 are the number of nucleotides on each side of the loop (n = n1 + n2, n1 ≤ n2), and ΔG°_{XW bonus} terms are increments applied for particular first non-canonical pairs with X on the 3′ side and W on the 5′ side of the adjacent canonical helix. ΔG°_{5′YX/3′RW bonus} is applied for an XW first non-canonical pair adjacent to a YR canonical pair (defined as UG, UA or CG with the pyrimidine on the 5′ side of the XW non-canonical pair).

The data in Table 2 and previously published (28-30, 33, 34, 68) (Supporting Information Table S2) was fit to eq 3a and 3b. Comparison with measured values in Table 2 and those previously published gives R² = 0.92 and standard deviation of 0.36 kcal/mol for 2 × 3 loops and R² = 0.47 and standard deviation of 1.11 kcal/mol for larger loops. The good fit for 2 × 3 loops suggests that eq 3a is a good model, so the new data was only used to slightly revise the previous parameters (Table 3). In contrast, the poor fit for loops larger than 2 × 3 (Figure 1) suggests that eq 3b can be improved for such loops.

Table 3.

Free Energy Parameters at 37 °C (kcal/mol) for Medium Size Internal Loops^a

Free energy parameters	2 × 3 loops	n1 + n2 > 5 loops
ΔG° loop initiation(5)	2.15 ± 0.14j
ΔG° loop initiation(6)		2.00 ± 0.11
ΔG° loop initiation(7)		2.25 ± 0.20
ΔG° loop initiation(8)		2.26 ± 0.18
ΔG° loop initiation(9)		2.33 ± 0.28
ΔG° loop initiation(10)		2.90 ± 0.34
ΔG°AU/GU penalty	0.73 ± 0.07	0.74 ± 0.11
ΔG° asym	0.45 ± 0.08k	0.45 ± 0.08
ΔG°UU bonusb	−0.34 ± 0.15	−0.51 ± 0.12
ΔG°5′YA/3′RG bonus b,c	−0.39 ± 0.22	-0.65 ± 0.29
ΔG°GG bonusb	−0.74 ± 0.28
ΔG°5′YG/3′RA bonusb	−1.41 ± 0.08
ΔG°5′RG/3′YA bonusb	−1.06 ± 0.17
ΔG°GA bonusb		−0.91 ± 0.08
ΔG°middle GA bonus (3 × 3 loop)d		−1.07 ± 0.23
ΔG°5′GU/3′AN penalty (3 × 3 loop)e		0.96 ± 0.25
ΔG°2×(5′GA/3′CG) bonus (3 × 3 loop) b,f		−0.96 ± 0.42
ΔG°2GA bonusg		−1.18 ± 0.16
ΔG°3GA bonush		−2.36 ± 0.15
ΔG°5′UG/3′GA bonusb,i		−0.95 ± 0.16

^aThese parameters are used to predict the free energy of 2 × 3 (left) and larger (right) internal loops having more than one nucleotides on each side in 1 M NaCl according to eq 3a and 4, respectively.

^bApplied for first non-canonical pair.

^cApplied for an AG first non-canonical pair adjacent to a YR canonical pair (defined as UG, UA or CG with the pyrimidine on the 5′ side of AG pair).

^dApplied for 3 × 3 loops with a middle pair of GA and at least one non-pyrimidine-pyrimidine first non-canonical pair unless a ΔG°_{2GA bonus} or ΔG°_{3GA bonus} has been used.

^eApplied for 3 × 3 loops with a single first non-canonical GA pair that has a U 3× to the G of the GA pair.

^fApplied for loops with two motifs of 5′GA/3′CG in 3 × 3 loops. Note that this parameter is only applied once to a loop.

^gApplied to loops with the motif 5′YGA/3′RAG, 5′RGA/3′YAG, 5′YGG/3′RAA, or 5′RGG/3′YAA in 3 × 3, 3 × 4, 4 × 4, and 4 × 5 loops (i.e. loops with the closing base pair 3′ to the A of a GA pair) unless the motif has been represented by a 3GA bonus. Note that this parameter is applied for 5′RGGA/3′YAAG or 5′GGAY/3′AAGR (i.e. $\frac{\mathrm{GGA}}{\mathrm{AAG}}$ not closed with at least one YR canonical pair), which are not represented by a 3GA bonus. This parameter is also applied for an unusually stable 4×4 loop, $\begin{array}{ccc}\hfill \mathrm{U}\hfill & \hfill \underset{¯}{\mathrm{GGAA}}\hfill & \mathrm{G}\hfill \\ \hfill \mathrm{G}\hfill & \hfill \mathrm{AAGG}\hfill & \mathrm{C}\hfill \end{array}$ (see text).

^hApplied for loops with the motif of 5′YGGA/3′RAAG or 5′GGAR/3′AAGY (i.e. $\frac{\mathrm{GGA}}{\mathrm{AAG}}$ closed on at least one side with a YR canonical pair).

ⁱApplied for 3 × 3 and larger loops with the motif of 5′UG/3′GA.

^jCalculated from the fitted value (2.59 ± 0.11 kcal/mol ) of AG°_{loop initiation}(5) + AG°_asym in 2 × 3 loops minus the fitted value (0.45 ± 0.08) of AG°_asym in loops larger than 2 × 3.

^kValue fit in loops larger than 2 × 3.

Figure 1.

Comparisons between predicted and measured free energies for 3 × 3 and larger loops for model of eq 3b as used in current RNAstructure 4.0 program (9) (R² = 0.47, standard deviation = 1.11 kcal/mol) and model of eq 4 (R² = 0.86, standard deviation = 0.57 kcal/mol).

A previous study of 3 × 3 internal loops concluded that additional terms should be added to eq 3b: ΔG°_{middle bonus} for 3 × 3 loops with a middle pair of GA and at least one non-pyrimidine-pyrimidine first non-canonical pair and ΔG°_{5′GU/3′AN penalty} for 3 × 3 loops with a single first non-canonical GA pair that has a U 3′ to the G of the GA pair (34). With the exception of the loop in $\begin{array}{ccc}\hfill \mathrm{GGC}\hfill & \hfill \underset{¯}{\mathrm{GGAU}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAGU}\hfill & \mathrm{CCG}\hfill \end{array}$ which was omitted, the data for loops larger than 2 × 3 in Table 2 and in previously published sequences (29, 33, 34, 68) (Supporting Information Table S2) are fit well if four additional bonus parameters are added to give eq 4:

$$\Delta {{\mathrm{G}}^{°}}_{\text{predicted}}=\Delta {{\mathrm{G}}^{°}}_{\text{loop initiation}}\left(\mathrm{n}\right)+\mathrm{m}1\Delta {{\mathrm{G}}^{°}}_{\mathrm{AU}∕\mathrm{GU}\text{penalty}}+\mid \mathrm{n}1-\mathrm{n}2\mid \Delta {{\mathrm{G}}^{°}}_{\mathrm{asym}}+\mathrm{m}2\Delta {{\mathrm{G}}^{°}}_{\mathrm{UU}\text{bonus}}+\mathrm{m}3\Delta {{\mathrm{G}}^{°}}_{5^{\prime }\mathrm{YA}∕3^{\prime }\mathrm{RG}\text{bonus}}+\mathrm{m}5\Delta {{\mathrm{G}}^{°}}_{\mathrm{GA}\text{bonus}}+\Delta {{\mathrm{G}}^{°}}_{\text{middle}\mathrm{GA}\text{bonus}(3\times 3\text{loop})}+\Delta {{\mathrm{G}}^{°}}_{5^{\prime }\mathrm{GU}∕3^{\prime }\mathrm{AN}\text{penalty}(3\times 3\text{loop})}+\Delta {{\mathrm{G}}^{°}}_{2\times (5^{\prime }\mathrm{GA}∕3^{\prime }\mathrm{CG})\text{bonus}(3\times 3\text{loop})}+\Delta {{\mathrm{G}}^{°}}_{2\mathrm{GA}\text{bonus}}+\Delta {{\mathrm{G}}^{°}}_{3\mathrm{GA}\text{bonus}}+\mathrm{m}6\Delta {{\mathrm{G}}^{°}}_{5^{\prime }\mathrm{UG}∕3^{\prime }\mathrm{GA}\text{bonus}}$$ (4)

Only the first six parameters are currently included in structure prediction programs such as MFOLD (8) and RNAstructure (9). Here, ΔG°_{2×(5′GA/3′CG) bonus (3 × 3 loop)} is applied for loops with two motifs of $\begin{array}{c}\hfill \mathrm{G}\underset{¯}{\mathrm{A}}\hfill \\ \hfill \mathrm{C}\mathrm{G}\hfill \end{array}$ in 3 × 3 loops, e.g. $\begin{array}{ccc}\mathrm{CGC}\hfill & \underset{¯}{\mathrm{AAG}}\hfill & \mathrm{CGC}\hfill \\ \mathrm{GCC}\hfill & \mathrm{GUA}\hfill & \mathrm{GCG}\hfill \end{array}$ (1.21 kcal/mol) and $\begin{array}{ccc}\mathrm{CGC}\hfill & \underset{¯}{\mathrm{AAG}}\hfill & \mathrm{CGC}\hfill \\ \mathrm{GCC}\hfill & \mathrm{GAA}\hfill & \mathrm{GCG}\hfill \end{array}$ (0.87 kcal/mol) (Supporting Information Table S2) (34). Note that this parameter is only applied once to a loop. Unless the motifs have been represented by a 3GA bonus, the ΔG°_{2GA bonus} is applied for X₃ × W_3-4 and X₄ × W_4-5 loops with the motifs $\begin{array}{c}\hfill \mathrm{Y}\underset{¯}{\mathrm{GA}}\hfill \\ \hfill \mathrm{R}\mathrm{AG}\hfill \end{array}$, $\begin{array}{c}\hfill \mathrm{R}\underset{¯}{\mathrm{GA}}\hfill \\ \hfill \mathrm{Y}\mathrm{AG}\hfill \end{array}$, $\begin{array}{c}\hfill \mathrm{Y}\underset{¯}{\mathrm{GG}}\hfill \\ \hfill \mathrm{R}\mathrm{AA}\hfill \end{array}$ or $\begin{array}{c}\hfill \mathrm{R}\underset{¯}{\mathrm{GG}}\hfill \\ \hfill \mathrm{Y}\mathrm{AA}\hfill \end{array}$ (i.e. loops with the closing base pair 3′ to the A of a GA pair); and for X₃ × W_3-6 and X₄ × W_4-6 loops with the motifs of $\begin{array}{c}\hfill \mathrm{R}\underset{¯}{\mathrm{GGA}}\hfill \\ \hfill \mathrm{Y}\mathrm{AAG}\hfill \end{array}$ and $\begin{array}{c}\hfill \underset{¯}{\mathrm{GAA}}\mathrm{Y}\hfill \\ \hfill \mathrm{AAG}\mathrm{R}\hfill \end{array}$ (i.e. $\frac{\mathrm{GGA}}{\mathrm{AAG}}$ motif not closed with at least one YR canonical pair). The ΔG°_{3GA bonus} is applied for loops larger than 2 × 3 with the motifs $\begin{array}{c}\hfill \mathrm{Y}\underset{¯}{\mathrm{GGA}}\hfill \\ \hfill \mathrm{R}\mathrm{AAG}\hfill \end{array}$ or $\begin{array}{c}\hfill \underset{¯}{\mathrm{GGA}}\mathrm{R}\hfill \\ \hfill \mathrm{AAG}\mathrm{Y}\hfill \end{array}$ (i.e. $\frac{\mathrm{GGA}}{\mathrm{AAG}}$ closed on at least one side with a YR canonical pair). If a ΔG°_{2GA bonus} or ΔG°_{3GA bonus} has been used, then the ΔG°_{middle GA bonus (3 × 3 loop)} is not applied. The ΔG°_{5′UG/3′GA bonus} is applied for each $\begin{array}{c}\hfill \mathrm{U}\underset{¯}{\mathrm{G}}\hfill \\ \hfill \mathrm{GA}\hfill \end{array}$ motif at a loop terminus in loops larger than 2 × 3, so m6 is 1 or 2. Table 3 lists the values of these fitted parameters. Attempts were made to fit the data with fewer parameters, but that always resulted in certain classes of sequences being predicted poorly. For example, at least three consecutive GA pairs are required to provide extra stability to loops with n2 − n1 > 1, so the stabilizing effect of only two consecutive GA pairs is restricted to internal loops with n2 − n1 < 2. This is apparently a non-nearest neighbor effect. The detailed multiple linear regression analysis is given in Supporting Information Table S3.

A ΔG°_{GG bonus} is not used in eq 4 because only the loop in $\begin{array}{ccc}\mathrm{GAGC}\hfill & \underset{¯}{\mathrm{GAG}}\hfill & \mathrm{CGAC}\hfill \\ \mathrm{CUCG}\hfill & \mathrm{AAG}\hfill & \mathrm{GCUG}\hfill \end{array}$ has a GG first non-canonical pair and its stability is predicted well without including a GG bonus. A GG bonus has been found for 2 × 2 loops (74). The result for the 3 × 3 loop studied here suggests that any GG bonus is context dependent.

Listed in parentheses in Table 2 are the free energy increments at 37 °C for internal loops larger than 2 × 3 as predicted by eq 4 with the parameters from Table 3. The correlation with measured values gives R² = 0.86 and standard deviation of 0.57 kcal/mol (Figure 1). The average absolute difference per nucleotide between measured and predicted values is 0.05 kcal/mol. Evidently, the new parameters in eq 4 are justified. The revised values for parameters that appear in both eq 3 and eq 4 are within experimental error of those determined previously (9).

Exchangeable Proton and Phosphorus-31 NMR Spectra

For several loops with interesting stabilities and/or sequences expected to give interesting structures, 1D imino proton NMR spectra confirm that the expected canonical base pairs are present (Figure 2 left panel). Some preliminary assignments are based on NMR melting and comparison with similar duplexes having 3 × 3 internal loops (33). The 2D SNOESY spectra (Figure S1) were also used to confirm assignments and secondary structure. The 1D ¹H-decoupled ³¹P NMR spectra (Figure 2 right panel) were used to probe backbone structural features of the duplexes. Several unusual downfield ³¹P resonances are likely due to the phosphorus residues at 5′GpA3′ nearest neighbors in 5′GA/3′AG motifs. Tandem GA pairs often have a trans ζ phosphate configuration that gives a downfield phosphorus resonance (53, 75, 76). These resonances are not observed for all loops with this motif, however, suggesting that the backbone structure and dynamics depend on context.

Figure 2.

NMR spectra of (a) $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \hfill \underset{¯}{\mathrm{GGA}}\hfill & \hfill \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAG}\hfill & \hfill \mathrm{CCG}\hfill \end{array}$ (0 °C (33)), (b $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \hfill \underset{¯}{\mathrm{GGA}}\hfill & \hfill \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCA}\hfill & \hfill \mathrm{AAG}\hfill & \hfill \mathrm{CCG}\hfill \end{array}$, (c) $\begin{array}{ccc}\hfill \mathrm{GGC}\hfill & \hfill \underset{¯}{\mathrm{GGA}}\hfill & \hfill \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAG}\hfill & \hfill \mathrm{UCG}\hfill \end{array}$, (d) $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \hfill \underset{¯}{\mathrm{GAA}}\hfill & \hfill \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAG}\hfill & \hfill \mathrm{CCG}\hfill \end{array}$, (e) $\begin{array}{ccc}\hfill \mathrm{GGC}\hfill & \hfill \underset{¯}{\mathrm{GAA}}\hfill & \hfill \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAG}\hfill & \hfill \mathrm{CCG}\hfill \end{array}$, f $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \hfill \underset{¯}{\mathrm{GGAA}}\hfill & \hfill \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAG}\hfill & \hfill \mathrm{CCG}\hfill \end{array}$, (g) $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \hfill \underset{¯}{\mathrm{GGA}}\hfill & \hfill \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAGG}\hfill & \hfill \mathrm{CCG}\hfill \end{array}$, (h) $\begin{array}{ccc}\hfill \mathrm{GGC}\hfill & \hfill \underset{¯}{\mathrm{GGAA}}\hfill & \hfill \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAGG}\hfill & \hfill \mathrm{CCG}\hfill \end{array}$, (i) $\begin{array}{ccc}\hfill \mathrm{GGC}\hfill & \hfill \underset{¯}{\mathrm{GGAU}}\hfill & \hfill \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAGU}\hfill & \hfill \mathrm{CCG}\hfill \end{array}$ (10 °C), (j) $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \hfill \underset{¯}{\mathrm{GGA}}\hfill & \hfill \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAGUUU}\hfill & \hfill \mathrm{CCG}\hfill \end{array}$, (k) $\begin{array}{ccc}\hfill \mathrm{GGC}\hfill & \hfill \underset{¯}{\mathrm{GGA}}\hfill & \hfill \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAGUUU}\hfill & \hfill \mathrm{CCG}\hfill \end{array}$, (l) $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \hfill \underset{¯}{\mathrm{GGA}}\hfill & \hfill \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAGAAA}\hfill & \hfill \mathrm{CCG}\hfill \end{array}$, (m) $\begin{array}{ccc}\hfill \mathrm{GGC}\hfill & \hfill \underset{¯}{\mathrm{GGA}}\hfill & \hfill \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAGAAA}\hfill & \hfill \mathrm{CCG}\hfill \end{array}$, and (n) $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \hfill \underset{¯}{\mathrm{GGAA}}\hfill & \hfill \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAGAAA}\hfill & \hfill \mathrm{CCG}\hfill \end{array}$, in 80 mM NaCl, 10 mM sodium phosphate, 0.5 mM Na₂EDTA. Left panel: One-dimensional imino proton spectra in 90:10 (v:v) H₂O:D₂O at 5 °C unless noted otherwise. The sample pHs are given in the right panel, except for spectra (a) pH 5.9 (b) pH 5.4, (d) pH 5.1, and (e) pH 6.7. Numbers on spectra correspond to assignments with numbering starting at left most (5′) nucleotide of top strand and ending at left most (3′) nucleotide of bottom strand. Right panel: The 1D ¹H-decoupled ³¹P spectra at 30 °C in 90:10 (v:v) H₂O:D₂O or 100% D₂O. The spectra were referenced to external standard at 30 °C of 85% H₃PO₄ at 0 ppm. Note that the chemical shift of the phosphate resonance (the highest peak except for (d)) depends on pH or pD. The downfield resonances are labeled with arrows. Values adjacent to sequences are ΔG°_{37, loop} (kcal/mol) from Table 2.

DISCUSSION

Thermodynamic models and parameters for internal loops are important for the prediction of RNA secondary structure (8, 9, 77-82). In turn, RNA secondary structure is the first step for modeling of three-dimensional structure (10-12, 21, 83, 84) and facilitates interpretation of experimental studies, such as folding (13, 15, 23, 51, 55, 56, 61) and ribozyme kinetics (85-87). It may also allow prediction of sites suitable for rational design of therapeutics.

Loops of 2 × 3 nucleotides. Loops with 2 × 3 nucleotides are predicted well by the previous thermodynamic model of eq 3a (9, 28, 29). Linear regression of measured free energy increments on 2 × 3 nucleotide loops reported here (Table 2) and previously (28-30) gives parameters within experimental error of those previously published.

An NMR structure of the 2 × 3 internal loop $\begin{array}{ccc}\mathrm{C}\hfill & \underset{¯}{\mathrm{GA}}\hfill & \mathrm{G}\hfill \\ \mathrm{G}\hfill & \mathrm{AAG}\hfill & \mathrm{C}\hfill \end{array}$ revealed a unique structure with a “shared sheared GA” motif having Hoogsteen edges of two A’s forming base pairs with one G (88). In contrast, flexibility was observed for the loop $\begin{array}{ccc}\mathrm{U}\hfill & \underset{¯}{\mathrm{GA}}\hfill & \mathrm{U}\hfill \\ \mathrm{G}\hfill & \mathrm{AAG}\hfill & \mathrm{G}\hfill \end{array}$ by NMR, possibly due to the destabilizing effect of an $\begin{array}{c}\hfill \underset{¯}{\mathrm{A}}\mathrm{U}\hfill \\ \hfill \mathrm{G}\mathrm{G}\hfill \end{array}$ motif as discussed below (30). Interestingly, the stabilities of $\begin{array}{ccc}\mathrm{G}\hfill & \underset{¯}{\mathrm{GA}}\hfill & \mathrm{G}\hfill \\ \mathrm{G}\hfill & \mathrm{AAG}\hfill & \mathrm{C}\hfill \end{array}$ (averaging −0.10 kcal/mol) and $\begin{array}{ccc}\mathrm{U}\hfill & \underset{¯}{\mathrm{GA}}\hfill & \mathrm{U}\hfill \\ \mathrm{G}\hfill & \mathrm{AAG}\hfill & \mathrm{G}\hfill \end{array}$ (1.90 kcal/mol) (Table 2, Supporting Information Table S2) (29, 30) are predicted well by eq 3a with parameters from Table 3 which give values of −0.23 and 1.58 kcal/mol, respectively. Thus even though the three-dimensional structures are more complex, a simple thermodynamic model works well.

Loops larger than 2 × 3 nucleotides

The motif of three consecutive sheared GA pairs $\frac{\mathrm{GGA}}{\mathrm{AAG}}$ is the most stable among 3 × 3 internal loops (33, 34). To explore the effect of consecutive GA pairs on stability of larger internal loops including kink-turns, sequences were studied with two and three potentially consecutive GA pairs. From the comparison of measured and predicted free energy increments for internal loops larger than 2 × 3 (Table 2 and Figure 1), the model of eq 4 is sufficient for purine rich internal loops, with the exception of $\begin{array}{ccc}\hfill \mathrm{GGC}\hfill & \hfill \underset{¯}{\mathrm{GGAU}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAGU}\hfill & \mathrm{CCG}\hfill \end{array}$ (−4.16 kcal/mol). The terms in eq 4 are discussed below. A sample calculation is shown in Figure 3 for predicting the free energy for formation of a 3 × 3 internal loop. More sample calculations are shown in Supporting Information Figure S2 and in parentheses in Table 2 are predicted free energies for all the loops studied.

Figure 3.

A sample calculation for predicting the free energy at 37 °C for formation of an internal loop. Additional sample calculations are shown in Supporting Information.

Bonus for Three Consecutive GA Pairs in X_3-4 × W_3-6 Internal Loops

All of the internal loops studied here with a $\begin{array}{c}\hfill \mathrm{Y}\underset{¯}{\mathrm{GGA}}\hfill \\ \hfill \mathrm{R}\mathrm{AAG}\hfill \end{array}$ or $\begin{array}{c}\hfill \underset{¯}{\mathrm{GGA}}\mathrm{R}\hfill \\ \hfill \mathrm{AAG}\mathrm{Y}\hfill \end{array}$ motif are more stable than expected from the model in the current MFOLD and RNAstructure 4.0 programs (eq 3b). Thus, a bonus parameter for the $\frac{\mathrm{GGA}}{\mathrm{AAG}}$ motif is included in eq 4. The bonus value of −2.36 kcal/mol is approximately twice that for first non-canonical GA pairs, ΔG°_{GA bonus} (−0.91 kcal/mol) and for two consecutive GA pairs, ΔG°_{2GA bonus} (−1.18 kcal/mol), presumably reflecting interactions of two nearest neighbors in $\frac{\mathrm{GGA}}{\mathrm{AAG}}$. Note that 3 × 3 loops with potentially three consecutive GA pairs are given a ΔG°_{3GA bonus} and two ΔG°_{GA bonus}, but no ΔG°_{middle GA bonus}. The ΔG°_{3GA bonus} accounts for the stacking between GA pairs in $\frac{\mathrm{GGA}}{\mathrm{AAG}}$ and the two ΔG°_{GA bonus} increments account for stacking between each first non-canonical GA pair and adjacent closing base pair.

Note that besides the ΔG°_{3GA bonus}, only one bonus parameter of a first non-canonical GA pair, ΔG°_{GA bonus,} is applied for 3 × 4 loops, $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \underset{¯}{\mathrm{GGAA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAG}\hfill & \mathrm{CCG}\hfill \end{array}$ (−1.18 kcal/mol), $\begin{array}{ccc}\hfill \mathrm{GGC}\hfill & \underset{¯}{\mathrm{GGA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAGG}\hfill & \mathrm{CCG}\hfill \end{array}$ (−1.00 kcal/mol), $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \underset{¯}{\mathrm{GGA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAGG}\hfill & \mathrm{CCG}\hfill \end{array}$ (−0.92 kcal/mol), $\begin{array}{ccc}\hfill \mathrm{GGC}\hfill & \hfill \underset{¯}{\mathrm{GAA}}& \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAGG}& \mathrm{CCG}\hfill \end{array}$ (−0.67 kcal/mol), and $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \hfill \underset{¯}{\mathrm{GAA}}& \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAGG}& \mathrm{CCG}\hfill \end{array}$ (−0.52 kcal/mol) because the 3GA bonus is more favorable than a second first non-canonical GA bonus coupled with a 2GA bonus, and formation of three consecutive GA pairs would preclude formation of a second first non-canonical GA pair. Similarly, ΔG°_{5′UG/3′GA bonus} was not applied for the loop in $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \hfill \underset{¯}{\mathrm{GAA}}& \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAGG}& \mathrm{CCG}\hfill \end{array}$ (−0.52 kcal/mol) because the $\frac{\mathrm{GGA}}{\mathrm{AAG}}$ motif was assumed to be adjacent to the closing CG pair. The imino proton resonances of G8 in $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \underset{¯}{\mathrm{GGAA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAG}\hfill & \mathrm{CCG}\hfill \end{array}$ (−1.18 kcal/mol) (Figure 2f) and G7 in $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \underset{¯}{\mathrm{GGA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAGG}\hfill & \mathrm{CCG}\hfill \end{array}$ (−0.92 kcal/mol) (Figure 2g) are relatively broader than G7 in $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \underset{¯}{\mathrm{GGA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAG}\hfill & \mathrm{CCG}\hfill \end{array}$ (−2.62 kcal/mol) (Figure 2a) (33) and $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \underset{¯}{\mathrm{GGA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCA}\hfill & \mathrm{AAG}\hfill & \mathrm{CCG}\hfill \end{array}$ (−2.27 kcal/mol) (Figure 2b) and G8 in $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \underset{¯}{\mathrm{GGAA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAGG}\hfill & \mathrm{CCG}\hfill \end{array}$ (−4.27 kcal/mol) (Figure 2h). This is consistent with the stacking assumed in the thermodynamic model.

The 4 × 4 loop in $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \underset{¯}{\mathrm{GGAA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAGG}\hfill & \mathrm{CCG}\hfill \end{array}$ (−4.27 kcal/mol) is exceptionally stable, but is predicted reasonably well (−3.31 kcal/mol) by applying ΔG°_{3GA bonus}, ΔG°_{2GA bonus}, 2ΔG°_{GA bonus} and ΔG°_{5′UG/3′GA bonus}. Applying all these bonuses is consistent with the total of five nearest neighbor interactions observed in the crystal structure of a similar loop $\begin{array}{ccc}\mathrm{C}\hfill & \underset{¯}{\mathrm{GGAA}}\hfill & \mathrm{G}\hfill \\ \mathrm{G}\hfill & \mathrm{AAGG}\hfill & \mathrm{C}\hfill \end{array}$ (89). The free energy difference between measurement and prediction may be due to highly coupled base stacking and hydrogen-bonding interactions in this loop as indicated by sharp imino proton resonances (Figure 2h). No ΔG°_{2GA bonus} is added to ΔG°_{3GA bonus} for the 4 × 5 loop in $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \underset{¯}{\mathrm{GGAA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAGGA}\hfill & \mathrm{CCG}\hfill \end{array}$ (−0.29 kcal/mol, kt-58 (17)), however, presumably due to its asymmetry.

The exceptionally stable 4 × 4 loop $\begin{array}{ccc}\hfill \mathrm{GGC}\hfill & \underset{¯}{\mathrm{GGAU}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAAG}\hfill & \mathrm{CCG}\hfill \end{array}$ (−4.16 kcal/mol) was not included in the linear regression analysis. The ³¹P spectrum for this duplex (Figure 2i) shows large dispersion, similar to that observed for the duplex $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \underset{¯}{\mathrm{GGAA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAGG}\hfill & \mathrm{CCG}\hfill \end{array}$ (Figure 2h), which also has an exceptionally stable 4 × 4 loop (−4.27 kcal/mol). This suggests that the terminal UU pair also supports a favorable, rigid structure. The 1D imino (Figure 2i) and 2D SNOESY (Figure S1) spectra indicate formation of a UU pair (with two U imino protons hydrogen bonded to carbonyl groups) (cis Watson-Crick/Watson-Crick UU) besides 3 GA pairs. This is also observed in conserved loops $\begin{array}{ccc}\mathrm{C}\hfill & \underset{¯}{\mathrm{GGAU}}\hfill & \mathrm{U}\hfill \\ \mathrm{G}\hfill & \mathrm{AAGU}\hfill & \mathrm{A}\hfill \end{array}$ in helix 42 of small subunit rRNA (90), $\begin{array}{ccc}\mathrm{G}\hfill & \underset{¯}{\mathrm{UGGAU}}\hfill & \mathrm{U}\hfill \\ \mathrm{U}\hfill & \mathrm{AAAGU}\hfill & \mathrm{A}\hfill \end{array}$ in helix 2 of large subunit rRNA (91), and a kink-turn loop $\begin{array}{ccc}\mathrm{C}\hfill & \underset{¯}{\mathrm{UGA}}\hfill & \mathrm{C}\hfill \\ \mathrm{G}\hfill & \mathrm{UAGUGC}\hfill & \mathrm{G}\hfill \end{array}$ (20). In the UU pairs of these structures, the U′s 3′ and 5′ of the adjacent closing base pair are shifted to the major and minor groove, respectively, which is favorable for base stacking with the adjacent sheared GA pair. Note that an $\frac{\mathrm{AU}}{\mathrm{GU}}$ nearest neighbor is not thermodynamically favorable in 2 × 2 loops (39), probably because there is geometric incompatibility when a UU pair is adjacent to an imino AG pair (cis Watson-Crick/Watson-Crick AG). An imino AG pair forms when the A of an AG pair is 3′ of the closing Watson-Crick pair, as is the case in an $\frac{\mathrm{AU}}{\mathrm{GU}}$ 2 × 2 loop.

On the basis of NMR spectra, three consecutive sheared GA pairs form in two 3 × 6 internal loops, $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \underset{¯}{\mathrm{GGA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAGUUU}\hfill & \mathrm{CCG}\hfill \end{array}$ (predicted to be a kink-turn in helix 78 of E. coli 23 rRNA (17, 50)) and $\begin{array}{ccc}\hfill \mathrm{GGC}\hfill & \underset{¯}{\mathrm{GGA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAGUUU}\hfill & \mathrm{CCG}\hfill \end{array}$, instead of two GU and one AU pair $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \hfill \underset{¯}{\mathrm{GGA}}& \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAGUUU}& \mathrm{CCG}\hfill \end{array}$ and $\begin{array}{ccc}\hfill \mathrm{GGC}\hfill & \hfill \underset{¯}{\mathrm{GGA}}& \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAGUUU}& \mathrm{CCG}\hfill \end{array}$. There are no imino proton resonances indicating the formation of $\frac{\mathrm{GGA}}{\mathrm{UUU}}$ in the 1D proton (Figure 2j and k) and 2D SNOSY spectra (Supporting Information Figure S1j and k). This is further confirmed by the relatively small changes in 1D imino proton spectra when the UUU triplets are replaced by AAA (compare $\begin{array}{ccc}\hfill \mathrm{GGC}\hfill & \underset{¯}{\mathrm{GGA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAGAAA}\hfill & \mathrm{CCG}\hfill \end{array}$ (1.46 kcal/mol, Figure 2m) and $\begin{array}{ccc}\hfill \mathrm{GGC}\hfill & \underset{¯}{\mathrm{GGA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAGUUU}\hfill & \mathrm{CCG}\hfill \end{array}$ (−0.22 kcal/mol, Figure 2k); $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \underset{¯}{\mathrm{GGA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAGAAA}\hfill & \mathrm{CCG}\hfill \end{array}$ (0.17 kcal/mol, Figure 2l) and $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \underset{¯}{\mathrm{GGA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAGUUU}\hfill & \mathrm{CCG}\hfill \end{array}$ (−0.33 kcal/mol, Figure 2j)). Several weak downfield peaks are probably due to minor conformations (Figure 2j and 2k, Supporting Information Figure S1j and k). This structural preference is predicted by the thermodynamic model: $\begin{array}{ccc}\hfill \mathrm{C}\hfill & \underset{¯}{\mathrm{GGA}}\hfill & \hfill \mathrm{G}\hfill \\ \hfill \mathrm{G}\hfill & \mathrm{AAGUUU}\hfill & \hfill \mathrm{C}\hfill \end{array}$ (0.41 kcal/mol predicted) and $\begin{array}{ccc}\hfill \mathrm{U}\hfill & \underset{¯}{\mathrm{GGA}}\hfill & \hfill \mathrm{G}\hfill \\ \hfill \mathrm{G}\hfill & \mathrm{AAGUUU}\hfill & \hfill \mathrm{C}\hfill \end{array}$ (0.20 kcal/mol predicted) vs. (1.02 kcal/mol predicted) and (1.72 kcal/mol predicted). Thus, including a stabilization effect for consecutive GA pairs can help predict multiple GA motifs, including kink-turns (17, 50).

Bonus for Two Consecutive GA Pairs in 3 × 3, 3 × 4, 4 × 4, and 4 × 5 Internal Loops

Two consecutive GA pairs with the motifs $\begin{array}{c}\hfill \mathrm{Y}\underset{¯}{\mathrm{GA}}\hfill \\ \hfill \mathrm{R}\mathrm{AG}\hfill \end{array}$, $\begin{array}{c}\hfill \mathrm{R}\underset{¯}{\mathrm{GA}}\hfill \\ \hfill \mathrm{Y}\mathrm{AG}\hfill \end{array}$, $\begin{array}{c}\hfill \mathrm{Y}\underset{¯}{\mathrm{GG}}\hfill \\ \hfill \mathrm{R}\mathrm{AA}\hfill \end{array}$, or $\begin{array}{c}\hfill \mathrm{R}\underset{¯}{\mathrm{GG}}\hfill \\ \hfill \mathrm{Y}\mathrm{AA}\hfill \end{array}$ (i.e. $\frac{\mathrm{GA}}{\mathrm{AG}}$ or $\frac{\mathrm{GG}}{\mathrm{AA}}$ closed on at least one side with a canonical pair that is 5′ to the G of a GA pair) only stabilize certain types of internal loops, including 3 × 3, 3 × 4, 4 × 4, and 4 × 5 loops. For 3 × 3 loops such as $\begin{array}{ccc}\hfill \mathrm{GAGU}\hfill & \hfill \underset{¯}{\mathrm{GAA}}\hfill & \hfill \mathrm{UGAC}\hfill \\ \hfill \mathrm{CUCA}\hfill & \hfill \mathrm{AGA}\hfill & \hfill \mathrm{ACUG}\hfill \end{array}$ (2.30 kcal/mol), $\begin{array}{ccc}\hfill \mathrm{GAGC}\hfill & \hfill \underset{¯}{\mathrm{GAG}}\hfill & \hfill \mathrm{CGAC}\hfill \\ \hfill \mathrm{CUCG}\hfill & \hfill \mathrm{AGA}\hfill & \hfill \mathrm{GCUG}\hfill \end{array}$ (0.54 kcal/mol), $\begin{array}{ccc}\hfill \mathrm{GAGC}\hfill & \hfill \underset{¯}{\mathrm{GAA}}\hfill & \hfill \mathrm{CGAC}\hfill \\ \hfill \mathrm{CUCG}\hfill & \hfill \mathrm{AGA}\hfill & \hfill \mathrm{GCUG}\hfill \end{array}$ (0.16 kcal/mol), $\begin{array}{ccc}\hfill \mathrm{GAGC}\hfill & \hfill \underset{¯}{\mathrm{AGA}}\hfill & \hfill \mathrm{CGAC}\hfill \\ \hfill \mathrm{CUCG}\hfill & \hfill \mathrm{AAG}\hfill & \hfill \mathrm{GCUG}\hfill \end{array}$ (−0.24 kcal/mol), $\begin{array}{ccc}\hfill \mathrm{GAGC}\hfill & \hfill \underset{¯}{\mathrm{CGA}}\hfill & \hfill \mathrm{CGAC}\hfill \\ \hfill \mathrm{CUCG}\hfill & \hfill \mathrm{AAG}\hfill & \hfill \mathrm{GCUG}\hfill \end{array}$ (−0.36 kcal/mol), $\begin{array}{ccc}\hfill \mathrm{CGC}\hfill & \hfill \underset{¯}{\mathrm{AGA}}\hfill & \hfill \mathrm{GGC}\hfill \\ \hfill \mathrm{GCG}\hfill & \hfill \mathrm{AAG}\hfill & \hfill \mathrm{CCG}\hfill \end{array}$ (−0.45 kcal/mol), $\begin{array}{ccc}\hfill \mathrm{CGAC}\hfill & \hfill \underset{¯}{\mathrm{CGA}}\hfill & \hfill \mathrm{GCAG}\hfill \\ \hfill \mathrm{GCUG}\hfill & \hfill \mathrm{AAG}\hfill & \hfill \mathrm{CGUC}\hfill \end{array}$ (−0.60 kcal/mol), and $\begin{array}{ccc}\hfill \mathrm{GAGC}\hfill & \hfill \underset{¯}{\mathrm{GGA}}\hfill & \hfill \mathrm{CGAC}\hfill \\ \hfill \mathrm{CUCG}\hfill & \hfill \mathrm{AAA}\hfill & \hfill \mathrm{GCUG}\hfill \end{array}$ (−0.65 kcal/mol), the ΔG°_{2GA bonus} and ΔG°_{GA bonus} are applied without adding a ΔG° _{middle GA bonus}.

No extra stabilization was observed for two consecutive GA pairs within 2 × 4, 2 × 5, 2 × 6, 3 × 5, 3 × 6, and 4 × 6 loops. Evidently, this term is restricted to internal loops with asymmetry less than 2 nucleotides. This is in agreement with previous experimental and theoretical modeling studies showing that two consecutive sheared GA pairs in a 2 × 5 internal loop bound to a protein are not present in the free RNA without protein (18, 21). The different contexts exhibiting stabilization for three and two consecutive GA pairs might explain the intolerance of mutation in the $\frac{\mathrm{GGA}}{\mathrm{AAG}}$ motif in the kink-turn (kt-7) $\begin{array}{ccc}\hfill \mathrm{G}\hfill & \underset{¯}{\mathrm{GGA}}\hfill & \hfill \mathrm{G}\hfill \\ \hfill \mathrm{C}\hfill & \mathrm{AAGAAG}\hfill & \hfill \mathrm{C}\hfill \end{array}$ (17, 51).

Structurally, there is a possibility that 2 × 4 internal loops could form consecutive GA pairs or two independent first non-canonical GA pairs. At this stage, two bonus parameters of first non-canonical GA pairs, ΔG°_{GA bonus}, are applied for $\begin{array}{ccc}\hfill \mathrm{GGC}\hfill & \underset{¯}{\mathrm{GAAA}}\hfill & \hfill \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{A}\mathrm{G}\hfill & \hfill \mathrm{CCG}\hfill \end{array}$ because the asymmetry is two. This might not reflect the structure, however.

Thermodynamically stable consecutive GA pairs are an important secondary structure motif, providing preorganized functional groups for tertiary interactions such as the A-minor motif (15-17, 90), and binding of ligands such as protein (17-21, 23) and Mg²⁺ (aq) (88, 92, 93). Similar stabilizing effects are likely in large hairpin loops as well as multibranch loops. Binding of Mg²⁺ (aq) is not expected to significantly stabilize this motif, however, because the thermodynamics of $\begin{array}{ccc}\hfill \mathrm{GGU}\hfill & \underset{¯}{\mathrm{GGA}}\hfill & \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \mathrm{AAG}\hfill & \mathrm{CCG}\hfill \end{array}$ was essentially identical in 1 M NaCl and in 150 mM KCl with 10 mM MgCl₂ (33). Binding of protein might stabilize two consecutive GA pairs within size asymmetric internal loops, however (18, 21, 23).

Sequence Dependent Stabilizing Effect of Consecutive GA Pairs

Closing canonical base pairs are important for stabilizing sheared GA pairs. The ΔG°_{3GA bonus} is applied only for loops closed by at least one YR canonical pair (i.e. UG, UA, or CG with the U or C on the 5′ side of the G of a first non-canonical GA pair), which is favorable for the formation of sheared GA pairs as observed in 2 × 2 loops (36). For loops with three potentially consecutive GA pairs but not closed with at least one YR canonical pair, e.g. $\begin{array}{ccc}\hfill \mathrm{GAGC}\hfill & \hfill \underset{¯}{\mathrm{AGGA}}\hfill & \mathrm{CGAC}\hfill \\ \hfill \mathrm{CUCG}\hfill & \hfill \mathrm{AAG}\hfill & \mathrm{GCUG}\hfill \end{array}$ (1.26 kcal/mol) and $\begin{array}{ccc}\hfill \mathrm{GAGC}\hfill & \hfill \underset{¯}{\mathrm{AGGA}}\hfill & \mathrm{CGAC}\hfill \\ \hfill \mathrm{CUCG}\hfill & \hfill \mathrm{AAAG}\hfill & \mathrm{GCUG}\hfill \end{array}$ (0.03 kcal/mol), the ΔG°_{2GA bonus} is applied. Presumably this is due to the destabilizing effect in changing a CG to a GC closing pair adjacent to a sheared GA pair. Destabilization of 1.27 kcal/mol was observed previously for changing the tetraloop hairpin CGAAAG to GGAAAC (94) even though both sequences have sheared GA pairs (14, 44, 93, 95, 96). Formation of the kink-turn (kt-7) $\begin{array}{ccc}\hfill \mathrm{G}\hfill & \underset{¯}{\mathrm{GGA}}\hfill & \mathrm{G}\hfill \\ \hfill \mathrm{C}\hfill & \mathrm{AAGAAG}\hfill & \mathrm{C}\hfill \end{array}$ instead of $\begin{array}{ccc}\hfill \mathrm{G}\hfill & \hfill \underset{¯}{\mathrm{GGA}}& \mathrm{G}\hfill \\ \hfill \mathrm{C}\hfill & \hfill \mathrm{AAGAAG}& \mathrm{C}\hfill \end{array}$ might be due to binding of protein and/or tertiary interactions (17), even though a sheared GA pair is thermodynamically more favorable with a CG closing base pair. Alternatively, the $\frac{\mathrm{GGA}}{\mathrm{AAG}}$ motif is thermodynamically more favorable closed on the 5′GG3′ side (i.e. $\begin{array}{c}\hfill \mathrm{Y}\underset{¯}{\mathrm{GGA}}\hfill \\ \hfill \mathrm{R}\mathrm{AAG}\hfill \end{array}$ or $\begin{array}{c}\hfill \mathrm{R}\underset{¯}{\mathrm{GGA}}\hfill \\ \hfill \mathrm{Y}\mathrm{AAG}\hfill \end{array}$) than on the 5′GA3′ side (i.e. $\begin{array}{c}\hfill \underset{¯}{\mathrm{GGA}}\mathrm{R}\hfill \\ \hfill \mathrm{AAG}\mathrm{Y}\hfill \end{array}$ or $\begin{array}{c}\hfill \underset{¯}{\mathrm{GGA}}\mathrm{Y}\hfill \\ \hfill \mathrm{AAG}\mathrm{R}\hfill \end{array}$).

Sequence Dependent Stabilizing Effect of AG pairs

No bonus parameter for an AG first non-canonical pair is applied for loops with a single $\begin{array}{c}\hfill \mathrm{R}\underset{¯}{\mathrm{A}}\hfill \\ \hfill \mathrm{Y}\mathrm{G}\hfill \end{array}$ motif (RY is canonical pair AU, GU or GC) such as $\begin{array}{ccc}\hfill \mathrm{GAGC}\hfill & \hfill \underset{¯}{\mathrm{GAG}}\hfill & \hfill \mathrm{CGAC}\hfill \\ \hfill \mathrm{CUCG}\hfill & \hfill \mathrm{AUA}\hfill & \hfill \mathrm{GCUG}\hfill \end{array}$ (1.28 kcal/mol) and $\begin{array}{ccc}\hfill \mathrm{GAGC}\hfill & \hfill \underset{¯}{\mathrm{GAG}}\hfill & \hfill \mathrm{CGAC}\hfill \\ \hfill \mathrm{CUCG}\hfill & \hfill \mathrm{AAA}\hfill & \hfill \mathrm{GCUG}\hfill \end{array}$ (1.08 kcal/mol). In addition, no bonus parameter is applied for loops even with potentially consecutive AG pairs: $\begin{array}{ccc}\hfill \mathrm{GAGC}\hfill & \hfill \underset{¯}{\mathrm{AGAG}}\hfill & \hfill \mathrm{CGAC}\hfill \\ \hfill \mathrm{CUCG}\hfill & \hfill \mathrm{AGA}\hfill & \hfill \mathrm{GCUG}\hfill \end{array}$ (2.74 kcal/mol) $\begin{array}{ccc}\hfill \mathrm{GAGC}\hfill & \hfill \underset{¯}{\mathrm{AGAG}}\hfill & \hfill \mathrm{CGAC}\hfill \\ \hfill \mathrm{CUCG}\hfill & \hfill \mathrm{AAGA}\hfill & \hfill \mathrm{GCUG}\hfill \end{array}$(2.07 kcal/mol), and $\begin{array}{ccc}\hfill \mathrm{GAGC}\hfill & \hfill \underset{¯}{\mathrm{AAAG}}\hfill & \hfill \mathrm{CGAC}\hfill \\ \hfill \mathrm{CUCG}\hfill & \hfill \mathrm{AAGA}\hfill & \hfill \mathrm{GCUG}\hfill \end{array}$ (2.88 kcal/mol). This is consistent with the fact that no stabilization effect is found for the $\begin{array}{c}\hfill \mathrm{R}\underset{¯}{\mathrm{A}}\hfill \\ \hfill \mathrm{Y}\mathrm{G}\hfill \end{array}$ motif in 2 × 3 loops (Table 3, Supporting Information Table S2) (9, 28, 29). The ΔG°_{3GA bonus} is not applied for a 3 × 3 loop $\begin{array}{ccc}\hfill \mathrm{GAGC}\hfill & \hfill \underset{¯}{\mathrm{GAG}}\hfill & \mathrm{CGAC}\hfill \\ \hfill \mathrm{CUCG}\hfill & \hfill \mathrm{AGA}\hfill & \mathrm{GCUG}\hfill \end{array}$ (0.54 kcal/mol) with one AG first noncanonical pair, because backbone narrowing prohibits formation of a Watson-Crick pair 5′ of the A in a sheared GA pair (38, 60, 92). Thus, only bonus parameters of ΔG°_{2GA bonus} and ΔG°_{GA bonus} are applied for the loop in $\begin{array}{ccc}\hfill \mathrm{GAGC}\hfill & \hfill \underset{¯}{\mathrm{GAG}}\hfill & \mathrm{CGAC}\hfill \\ \hfill \mathrm{CUCG}\hfill & \hfill \mathrm{AGA}\hfill & \mathrm{GCUG}\hfill \end{array}$. Nevertheless, bonus parameters are applied for 3 × 3 loops with two $\frac{\mathrm{GA}}{\mathrm{CG}}$ motifs: $\begin{array}{ccc}\hfill \mathrm{CGC}\hfill & \hfill \underset{¯}{\mathrm{AAG}}\hfill & \mathrm{CGC}\hfill \\ \hfill \mathrm{GCC}\hfill & \hfill \mathrm{GUA}\hfill & \mathrm{GCG}\hfill \end{array}$ (1.21 kcal/mol) and $\begin{array}{ccc}\hfill \mathrm{CGG}\hfill & \hfill \underset{¯}{\mathrm{AAG}}\hfill & \mathrm{CGC}\hfill \\ \hfill \mathrm{GCC}\hfill & \hfill \mathrm{GAA}\hfill & \mathrm{GCG}\hfill \end{array}$ (0.87 kcal/mol), presumably due to geometric compatibility of consecutive face-to-face pairs as observed in 2 × 2 loops (38, 92).

Bonus for $\begin{array}{c}\hfill \mathrm{U}\underset{¯}{\mathrm{G}}\hfill \\ \hfill \mathrm{G}\mathrm{A}\hfill \end{array}$ Motif

The thermodynamic parameters in folding algorithms typically assume that UG/GU pairs closing internal loops are equivalent to UA/AU pairs (8, 9). As shown in Table 2, loops with $\begin{array}{c}\hfill \mathrm{U}\underset{¯}{\mathrm{G}}\hfill \\ \hfill \mathrm{G}\mathrm{A}\hfill \end{array}$ and $\begin{array}{c}\hfill \mathrm{C}\underset{¯}{\mathrm{G}}\hfill \\ \hfill \mathrm{G}\mathrm{A}\hfill \end{array}$ motifs have similar stabilities. A stabilization effect of the $\begin{array}{c}\hfill \mathrm{U}\underset{¯}{\mathrm{G}}\hfill \\ \hfill \mathrm{G}\mathrm{A}\hfill \end{array}$ motif was also found in 3 × 3 loops (33, 34). The motif of $\begin{array}{c}\hfill \mathrm{U}\underset{¯}{\mathrm{G}}\hfill \\ \hfill \mathrm{G}\mathrm{A}\hfill \end{array}$ is thermodynamically relatively stable in 2 × 2 loops when compared with the motif of $\begin{array}{c}\hfill \mathrm{U}\underset{¯}{\mathrm{G}}\hfill \\ \hfill \mathrm{A}\mathrm{A}\hfill \end{array}$ but not when compared with $\begin{array}{c}\hfill \mathrm{C}\underset{¯}{\mathrm{G}}\hfill \\ \hfill \mathrm{G}\mathrm{A}\hfill \end{array}$ (29) suggesting that 2 × 2 loops have less flexibility than 3 × 3 loops. The parameter ΔG°_{5′UG/3′GA bonus} of −0.95 kcal/mol compensates for the penalty term of 0.7 kcal/mol for UG closure in current folding algorithms. This correlates with more extensive stacking of $\begin{array}{c}\hfill \mathrm{U}\underset{¯}{\mathrm{G}}\hfill \\ \hfill \mathrm{G}\mathrm{A}\hfill \end{array}$ than $\begin{array}{c}\hfill \mathrm{C}\underset{¯}{\mathrm{G}}\hfill \\ \hfill \mathrm{G}\mathrm{A}\hfill \end{array}$ and a hydrogen bond between the G amino group from a wobble UG pair and GO4′ of the sheared GA pair as shown in an NMR structure with the loop $\begin{array}{c}\hfill \mathrm{U}\underset{¯}{\mathrm{GGA}}\mathrm{G}\hfill \\ \hfill \mathrm{G}\mathrm{AAG}\mathrm{C}\hfill \end{array}$ which contains both a $\begin{array}{c}\hfill \mathrm{C}\underset{¯}{\mathrm{G}}\hfill \\ \hfill \mathrm{G}\mathrm{A}\hfill \end{array}$ motif and a G A motif (33). Formation of UG wobble pairs is consistent with the relatively sharp resonances of the imino protons of G and U from UG pairs (Figures 2 and S1). Note that the U3 imino proton from a UA pair adjacent to a GA pair is relatively broad and shifted upfield (Figure 2b) relative to the usual range of 13 to 15 ppm for a Watson-Crick UA pair. A similar upfield shift was observed previously in the 2 × 2 loop $\begin{array}{c}\hfill \mathrm{U}\underset{¯}{\mathrm{GA}}\mathrm{A}\hfill \\ \hfill \mathrm{A}\mathrm{AG}\mathrm{U}\hfill \end{array}$ (75). Several 3 × 3 loops with $\begin{array}{c}\hfill \mathrm{G}\underset{¯}{\mathrm{G}}\hfill \\ \hfill \mathrm{U}\mathrm{A}\hfill \end{array}$ and $\begin{array}{c}\hfill \mathrm{G}\underset{¯}{\mathrm{A}}\hfill \\ \hfill \mathrm{U}\mathrm{A}\hfill \end{array}$ motifs are typically less stable than predicted by eq 4, which is consistent with previous thermodynamic and NMR studies in 2 × 2 and 2 × 3 loops (29, 30, 40) and a joint X-ray and NMR studies of a kink-turn loop, $\begin{array}{ccc}\hfill \mathrm{CG}\hfill & \underset{¯}{\mathrm{GA}}\hfill & \hfill \mathrm{G}\hfill \\ \hfill \mathrm{GU}\hfill & \mathrm{AGAGA}\hfill & \hfill \mathrm{C}\hfill \end{array}$ with protein binding (18). Thus, depending on the orientation, GU/UG closing base pairs can either destabilize or stabilize internal loops as compared with AU/UA closing pairs.

Comparisons with other loops

It is likely that additional elements of stability remain to be discovered. For example, the loop in $\begin{array}{ccc}\hfill \mathrm{GGC}\hfill & \hfill \underset{¯}{\mathrm{GGAU}}\hfill & \hfill \mathrm{GGCU}\hfill \\ \hfill \mathrm{PCCG}\hfill & \hfill \mathrm{AAGU}\hfill & \hfill \mathrm{CCG}\hfill \end{array}$ (−4.16 kcal/mol), which was not included in the regression analysis, is 2.64 kcal/mol more stable than predicted by eq 4. Further studies are needed for the stable $\frac{\mathrm{AU}}{\mathrm{GU}}$ nearest neighbor. Moreover, NMR studies have revealed structured internal loops with consecutive UU and UC pairs (32, 34, 49, 97) although no thermodynamically significant bonus stabilizing effect has been found yet for consecutive UU and UC pairs (32, 34).

When eq 2a is applied to previous data (98) on the size asymmetric loop E motif, $\begin{array}{ccc}\hfill \mathrm{C}\hfill & \hfill \underset{¯}{\mathrm{GA}A}\hfill & \hfill \mathrm{C}\hfill \\ \hfill \mathrm{G}\hfill & \hfill \mathrm{AUGA}\hfill & \hfill \mathrm{G}\hfill \end{array}$, the ΔG°_{37, loop} is calculated to be 0.37 kcal/mol in 1 M NaCl, which is 1.42 kcal/mol more stable than predicted by eq 4. This size asymmetric loop E motif (G bulge motif) forms in the absence of Mg²⁺ (aq) or Ca²⁺ (aq) as shown by NMR studies (31, 45, 46).

There are unstable 3 × 3 loops with a single first non-canonical GA pair that has a U 3′ to the G of the GA pair, e.g. $\begin{array}{ccc}\hfill \mathrm{GAGC}\hfill & \hfill \underset{¯}{\mathrm{AAA}}\hfill & \hfill \mathrm{CGAC}\hfill \\ \hfill \mathrm{CUCG}\hfill & \hfill \mathrm{AUG}\hfill & \hfill \mathrm{GCUG}\hfill \end{array}$ (1.57 kcal/mol) and $\begin{array}{ccc}\hfill \mathrm{CGC}\hfill & \hfill \underset{¯}{\mathrm{AAA}}\hfill & \hfill \mathrm{GGC}\hfill \\ \hfill \mathrm{GCG}\hfill & \hfill \mathrm{AUG}\hfill & \hfill \mathrm{CCG}\hfill \end{array}$ (1.98 kcal/mol), which give rise to the ΔG°_{5′GU/3′AN penalty} (Supporting Information Table S2) (34). These loops are found in crystal structures. In the conserved 3 × 3 loop $\begin{array}{ccc}\hfill \mathrm{C}\hfill & \hfill \underset{¯}{\mathrm{AAA}}\hfill & \hfill \mathrm{C}\hfill \\ \hfill \mathrm{G}\hfill & \hfill \mathrm{AUG}\hfill & \hfill \mathrm{G}\hfill \end{array}$ in helix 24 of 16S rRNA, three non-canonical pairs form (trans Hoogsteen/sugar edge AA, AG first non-canonical pairs, and trans Watson-Crick/Hoogsteen UA middle pair), but with very little base overlap (90). In the other case, the first non-canonical G in $\begin{array}{ccc}\hfill \mathrm{C}\hfill & \hfill \underset{¯}{\mathrm{AAA}}\hfill & \hfill \mathrm{G}\hfill \\ \hfill \mathrm{G}\hfill & \hfill \mathrm{AUG}\hfill & \hfill \mathrm{C}\hfill \end{array}$ (in helix 38 of 23S rRNA) forms a pair with U to make a base triple (16). The results show that the thermodynamic penalty of ΔG°_{5′GU/3′AN penalty} works well even when the crystal structures are different.

The size symmetric 7 × 7 loop E motif, $\begin{array}{ccc}\hfill \mathrm{C}\hfill & \hfill \underset{¯}{\mathrm{GAUGGUA}}\hfill & \hfill \mathrm{G}\hfill \\ \hfill \mathrm{G}\hfill & \hfill \mathrm{AUGAGAG}\hfill & \hfill \mathrm{C}\hfill \end{array}$, with calculated loop free energy of 0.57 kcal/mol at 37 °C in 1 M NaCl on the basis of published data (98) is predicted well (0.99 kcal/mol) by eq 4 with the loop initiation penalty of 2.81 kcal/mol extrapolated with the equation ΔG°_{loop initiation}(n) = ΔG°_{loop initiation}(9) + 1.75 × RT × ln(14/9) from a loop initiation penalty of 2.33 kcal/mol for internal loops with 9 nucleotides. The value was extrapolated from ΔG°loop initiation(9) because that was the largest loop size represented by at least 10 sequences.

Melting Transition Cooperativity and Enthalpy Changes

As shown in Table 2, asymmetric internal loops typically have less favorable enthalpy changes than symmetric internal loops. This is consistent with previous UV melting studies of bulges and asymmetric internal loops (71, 99, 100) and indicates less cooperativity in duplex melting when the loop is asymmetric.

CONCLUSION

The stabilizing effect of consecutive sheared GA pairs within internal loops larger than five nucleotides is sequence and size dependent. Consecutive sheared GA pairs can form in motifs other than internal loops. Including this thermodynamic effect quantitatively or semiquantitatively should help model RNA secondary and tertiary structures.