Consecutive GA pairs stabilize medium-size RNA internal loops

Internal loops in RNA are important for folding and function. Consecutive noncanonical pairs can form in internal loops having at least two nucleotides on each side. Thermodynamic and structural insights into 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 5' Y GGA/3' R AAG or GGA R 3'/AAG Y 5' (i.e., 5' GGA 3'/3' AAG 5' 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 6-10 nucleotides. Certain motifs with two consecutive GA pairs are also stabilizing. In internal loops with three or more nucleotides on each side, the motif 5' U G/3' G A has stability similar to 5' C G/3' G A. A revised model for predicting stabilities of internal loops with 6-10 nucleotides is derived by multiple linear regression. Loops with 2 x 3 nucleotides are predicted well by a previous thermodynamic model.     

Factors affecting thermodynamic stabilities of RNA 3 x 3 internal loops

Internal loops in RNA are important for folding and function. The 3 x 3 nucleotide internal loops are the smallest size symmetric loops with a potential noncanonical base pair (middle pair) flanked on both sides by a noncanonical base pair (loop-terminal pair). Thermodynamic and structural insights acquired for 3 x 3 loops should improve approximations for stabilities of 3 x 3 and larger internal loops. Most natural 3 x 3 internal loops are purine rich, which is also true of other internal loops. A series of oligoribonucleotides containing different 3 x 3 internal loops were studied by UV melting and imino proton NMR. Both loop-terminal and middle pairs contribute to the thermodynamic stabilities of 3 x 3 loops. Extra stabilization of -1.2 kcal/mol was found for a GA middle pair when flanked by at least one non-pyrimidine-pyrimidine loop-terminal pair. A penalty of approximately 1 kcal/mol was found for loops with a single loop-terminal GA pair that has a U 3' to the G of the GA pair. A revised model for predicting stabilities of 3 x 3 loops is derived by multiple linear regression.     

Consecutive terminal GU pairs stabilize RNA helices

Consecutive GU pairs at the ends of RNA helices provide significant thermodynamic stability between -1.0 and -3.8 kcal/mol at 37 °C, which is equivalent to approximately 2 orders of magnitude in the value of a binding constant. The thermodynamic stabilities of GU pairs depend on the sequence, stacking orientation, and position in the helix. In contrast to GU pairs in the middle of a helix that may be destabilizing, all consecutive terminal GU pairs contribute favorable thermodynamic stability. This work presents measured thermodynamic stabilities for 30 duplexes containing two, three, or four consecutive GU pairs at the ends of RNA helices and a model to predict the thermodynamic stabilities of terminal GU pairs. Imino proton NMR spectra show that the terminal GU nucleotides form hydrogen-bonded pairs. Different orientations of terminal GU pairs can have different conformations with equivalent thermodynamic stabilities. These new data and prediction model will help improve RNA secondary structure prediction, identification of miRNA target sequences with GU pairs, and efforts to understand the fundamental physical forces directing RNA structure and energetics.     

Thermodynamic characterization of RNA duplexes containing naturally occurring 1 x 2 nucleotide internal loops

Thermodynamic data for RNA 1 x 2 nucleotide internal loops are lacking. Thermodynamic data that are available for 1 x 2 loops, however, are for loops that rarely occur in nature. In order to identify the most frequently occurring 1 x 2 nucleotide internal loops, a database of 955 RNA secondary structures was compiled and searched. Twenty-four RNA duplexes containing the most common 1 x 2 nucleotide loops were optically melted, and the thermodynamic parameters DeltaH degrees , DeltaS degrees , DeltaG degrees 37, and TM for each duplex were determined. This data set more than doubles the number of 1 x 2 nucleotide loops previously studied. A table of experimental free energy contributions for frequently occurring 1 x 2 nucleotide loops (as opposed to a predictive model) is likely to result in better prediction of RNA secondary structure from sequence. In order to improve free energy calculations for duplexes containing 1 x 2 nucleotide loops that do not have experimental free energy contributions, the data collected here were combined with data from 21 previously studied 1 x 2 loops. Using linear regression, the entire dataset was used to derive nearest neighbor parameters that can be used to predict the thermodynamics of previously unmeasured 1 x 2 nucleotide loops. The DeltaG degrees 37,loop and DeltaH degrees loop nearest neighbor parameters derived here were compared to values that were published previously for 1 x 2 nucleotide loops but were derived from either a significantly smaller dataset of 1 x 2 nucleotide loops or from internal loops of various sizes [Lu, Z. J., Turner, D. H., and Mathews, D. H. (2006) Nucleic Acids Res. 34, 4912-4924]. Most of these values were found to be within experimental error, suggesting that previous approximations and assumptions associated with the derivation of those nearest neighbor parameters were valid. DeltaS degrees loop nearest neighbor parameters are also reported for 1 x 2 nucleotide loops. Both the experimental thermodynamics and the nearest neighbor parameters reported here can be used to improve secondary structure prediction from sequence.     

The energetics of small internal loops in RNA

The energetics of small internal loops are important for prediction of RNA secondary and tertiary structure, selection of drug target sites, and understanding RNA structure-function relationships. Hydrogen bonding, base stacking, electrostatic interactions, backbone distortion, and base-pair size compatibility all contribute to the energetics of small internal loops. Thus, the sequence dependence of these energetics are idiosyncratic. Current approximations for predicting the free energies of internal loops consider size, asymmetry, closing base pairs, and the potential to form GA, GG, or UU pairs. The database of known three-dimensional structures allows for comparison with the models used for predicting stability from sequence.     

Thermodynamic study of internal loops in oligoribonucleotides: symmetric loops are more stable than asymmetric loops.

Thermodynamic parameters for internal loops of unpaired adenosines in oligoribonucleotides have been measured by optical melting studies. Comparisons are made between helices containing symmetric and asymmetric loops. Asymmetric loops destabilize a helix more than symmetric loops. The differences in free energy between symmetric and asymmetric loops are roughly half the magnitude suggested from a study of parameters required to give accurate predictions of RNA secondary structure [Papanicolaou, C., Gouy, M., & Ninio, J. (1984) Nucleic Acids Res. 12, 31-44]. Circular dichroism spectra indicate no major structural difference between helices containing symmetric and asymmetric loops. The measured sequence dependence of internal loop stability is not consistent with approximations used in current algorithms for predicting RNA secondary structure.     

Stability of RNA hairpin loops closed by AU base pairs

Thermodynamic parameters are reported for hairpin formation in 1 M NaCl by RNA sequence of the type GCAXUAAUYUGC, where XY is the set of 10 possible mismatch base pairs. A nearest-neighbor analysis of the data indicates that the free energy of loop formation at 37 degrees C varies from 3.2 to 5.0 kcal/mol. These results combined with the model previously developed [Dale et al. (2000) RNA 6, 608] allow improvements in the model to predict the stability of RNA hairpin loops: DeltaG degrees (37L(n) = DeltaG degrees (37i(n)) + DeltaG degrees (37MM) - 0.8 (if first mismatch is GA or UU) - 0.8 (if first mismatch is GG and loop is closed on 5' side by a purine). Here, DeltaG degrees (37i(n) is the free energy for initiating a loop of n nucleotides, and DeltaG degrees (37MM) is the free energy for the interaction of the first mismatch with the closing base pair. Hairpins with GG first mismatches were found to vary in stability depending upon the orientation of the closing base pair (5' or 3' purine relative to the loop). The model gives good agreement when tested against four naturally occurring hairpin sequences.     

Fast evaluation of internal loops in RNA secondary structure prediction.

MOTIVATION: Though not as abundant in known biological processes as proteins, RNA molecules serve as more than mere intermediaries between DNA and proteins. Research in the last 15 years demonstrates that RNA molecules serve in many roles, including catalysis. Furthermore, RNA secondary structure prediction based on free energy rules for stacking and loop formation remains one of the few major breakthroughs in the field of structure prediction, as minimum free energy structures and related quantities can be computed with full mathematical rigor. However, with the current energy parameters, the algorithms used hitherto suffer the disadvantage of either employing heuristics that risk (though highly unlikely) missing the optimal structure or becoming prohibitively time consuming for moderate to large sequences. RESULTS: We present a new method to evaluate internal loops utilizing currently used energy rules. This method reduces the time complexity of this part of the structure prediction from O(n4) to O(n3), thus reducing the overall complexity to O(n3). Even when the size of evaluated internal loops is bounded by k (a commonly used heuristic), the method presented has a competitive edge by reducing the time complexity of internal loop evaluation from O(k2n2) to O(kn2). The method also applies to the calculation of the equilibrium partition function. AVAILABILITY: Source code for an RNA secondary structure prediction program implementing this method is available at ftp://www.ibc.wustl.edu/pub/zuker/zuker .tar.Z     

Factors affecting the thermodynamic stability of small asymmetric internal loops in RNA

Optical melting experiments were used to determine the thermodynamic parameters for oligoribonucleotides containing small asymmetric internal loops. The results show a broad range of thermodynamic stabilities, which depend on loop size, asymmetry, sequence, closing base pairs, and length of helix stems. Imino proton NMR experiments provide evidence for possible hydrogen bonding in GA and UU mismatches in some asymmetric loops. The stabilizing effects of GA, GG, and UU mismatches on the thermodynamic stability of internal loops vary depending on the size and asymmetry of the loop. The dependence of loop stability on Watson-Crick closing base pairs may be explained by an account of hydrogen bonds. Models are presented for approximating the free energy increments of 2 x 3 and 1 x 3 internal loops.     

Solution structure of an RNA internal loop with three consecutive sheared GA pairs

Internal loops in RNA are important for folding and function. Many folding motifs are internal loops containing GA base pairs, which are usually thermodynamically stabilizing, i.e., contribute favorable free energy to folding. Understanding the sequence dependence of folding stability and structure in terms of molecular interactions, such as hydrogen bonding and base stacking, will provide a foundation for predicting stability and structure. Here, we report the NMR structure of the oligonucleotide duplex, 5'GGUGGAGGCU3'/3'PCCGAAGCCG5' (P = purine), containing an unusually stable and relatively abundant internal loop, 5'GGA3'/3'AAG5'. This loop contains three consecutive sheared GA pairs (trans Hoogsteen/Sugar edge AG) with separate stacks of three G's and three A's in a row. The thermodynamic consequences of various nucleotide substitutions are also reported. Significant destabilization of approximately 2 kcal/mol at 37 degrees C is found for substitution of the middle GA with AA to form 5'GAA3'/3'AAG5'. This destabilization correlates with a unique base stacking and hydrogen-bonding network within the 5'GGA3'/3'AAG5' loop. Interestingly, the motifs, 5'UG3'/3'GA5' and 5'UG3'/3'AA5', have stability similar to 5'CG3'/3'GA5' even though UG and UA pairs are usually less stable than CG pairs. Consecutive sheared GA pairs in the 5'GGA3'/3'AAG5' loop are preorganized for potential tertiary interactions and ligand binding.     

Thermodynamics of RNA internal loops with a guanosine-guanosine pair adjacent to another noncanonical pair

Thermodynamic parameters measured by optical melting are reported for formation of RNA duplexes containing tandem noncanonical pairs with at least one guanosine-guanosine (GG) pair. For selected sequences, imino proton NMR provides evidence that the desired duplex forms and that the structure of a GG pair adjacent to a noncanonical pair depends on context. A GG pair next to a different noncanonical pair is more stable than expected from measurements of adjacent GG pairs. This is likely due to an unfavorable stacking interaction between adjacent GG pairs, where areas of high negative charge probably overlap. The results suggest a model where tandem noncanonical pairs closed by two GC pairs are assigned the following free energy increments at 37 degrees C: 0.8 kcal/mol for adjacent GG pairs, 1.0 kcal/mol for GG next to UU, and -0.3 kcal/mol for all others. These values are adjusted by 0.65 kcal/mol for each closing AU pair.     

Analysis of internal loops within the RNA secondary structure in almost quadratic time

MOTIVATION: Evaluating all possible internal loops is one of the key steps in predicting the optimal secondary structure of an RNA molecule. The best algorithm available runs in time O(L(3)), L is the length of the RNA. RESULTS: We propose a new algorithm for evaluating internal loops, its run-time is O(M(*)log(2)L), M < L(2) is a number of possible nucleotide pairings. We created a software tool Afold which predicts the optimal secondary structure of RNA molecules of lengths up to 28 000 nt, using a computer with 2 Gb RAM. We also propose algorithms constructing sets of conditionally optimal multi-branch loop free (MLF) structures, e.g. the set that for every possible pairing (x, y) contains an optimal MLF structure in which nucleotides x and y form a pair. All the algorithms have run-time O(M(*)log(2)L).     

Energetics of internal GU mismatches in ribooligonucleotide helixes

Thermodynamic parameters of helix formation were measured spectroscopically for 16 oligoribonucleotides containing either internal GU mismatches or the corresponding AU pairs. Internal GU mismatches stabilize each helix, but not as much as the corresponding AU pairs. The differences in the enthalpy and entropy changes of helix formation associated with replacing AU pairs with GU mismatches are less than previously realized. At both 25 and 37 degrees C, the decrease in helix stability associated with replacing an AU with a GU is also less than thought previously. Approximations are suggested for predicting the effects of GU mismatches on helix stability.     

Fluctuations in ion pairs and their stabilities in proteins

This report investigates the effect of systemic protein conformational flexibility on the contribution of ion pairs to protein stability. Toward this goal, we use all NMR conformer ensembles in the Protein Data Bank (1) that contain at least 40 conformers, (2) whose functional form is monomeric, (3) that are nonredundant, and (4) that are large enough. We find 11 proteins adhering to these criteria. Within these proteins, we identify 22 ion pairs that are close enough to be classified as salt bridges. These are identified in the high-resolution crystal structures of the respective proteins or in the minimized average structures (if the crystal structures are unavailable) or, if both are unavailable, in the "most representative" conformer of each of the ensembles. We next calculate the electrostatic contribution of each such ion pair in each of the conformers in the ensembles. This results in a comprehensive study of 1,201 ion pairs, which allows us to look for consistent trends in their electrostatic contributions to protein stability in large sets of conformers. We find that the contributions of ion pairs vary considerably among the conformers of each protein. The vast majority of the ion pairs interconvert between being stabilizing and destabilizing to the structure at least once in the ensembles. These fluctuations reflect the variabilities in the location of the ion pairing residues and in the geometric orientation of these residues, both with respect to each other, and with respect to other charged groups in the remainder of the protein. The higher crystallographic B-factors for the respective side-chains are consistent with these fluctuations. The major conclusion from this study is that salt bridges observed in crystal structure may break, and new salt bridges may be formed. Hence, the overall stabilizing (or, destabilizing) contribution of an ion pair is conformer population dependent.     

Thermodynamic examination of 1- to 5-nt purine bulge loops in RNA and DNA constructs

Bulge loops are common features of RNA structures that are involved in the formation of RNA tertiary structures and are often sites for interactions with proteins and ions. Minimal thermodynamic data currently exist on the bulge size and sequence effects. Using thermal denaturation methods, thermodynamic properties of 1- to 5-nt adenine and guanine bulge loop constructs were examined in 10 mM MgCl₂ or 1 M KCl. The ΔG37∘ loop parameters for 1- to 5-nt purine bulge loops in RNA constructs were between 3.07 and 5.31 kcal/mol in 1 M KCl buffer. In 10 mM magnesium ions, the ΔΔG° values relative to 1 M KCl were 0.47–2.06 kcal/mol more favorable for the RNA bulge loops. The ΔG37∘ loop parameters for 1- to 5-nt purine bulge loops in DNA constructs were between 4.54 and 5.89 kcal/mol. Only 4- and 5-nt guanine constructs showed significant change in stability for the DNA constructs in magnesium ions. A linear correlation is seen between the size of the bulge loop and its stability. New prediction models are proposed for 1- to 5-nt purine bulge loops in RNA and DNA in 1 M KCl. We show that a significant stabilization is seen for small bulge loops in RNA in the presence of magnesium ions. A prediction model is also proposed for 1- to 5-nt purine bulge loop RNA constructs in 10 mM magnesium chloride.     

Effects of GA mismatches on the structure and thermodynamics of RNA internal loops

UV melting, CD and NMR studies indicate rGCGAGCG and rGCAGGCG from unusually stable duplexes of type a and b. The observed delta G degree 37's in 1 M NaCl are -6.7 and -6.3 kcal/mol, respectively. For the related duplex, c, delta G degree 37 is -4.2 kcal/mol. The predicted delta G degree 37 from nearest-neighbor parameters (formula; see text) for all three duplexes is -4.7 kcal/mol (Freier, S.M., Kierzek, R., Jaeger, J.A., Sugimoto, N., Caruthers, M.H., Neilson, T., & Turner, D.H. (1986) Proc. Natl. Acad. Sci. U.S.A. 83, 9373-9377). The results suggest a special interaction in the duplexes containing GA mismatches. Presumably, this is hydrogen bonding between G and A. While the thermodynamics for (rGCGAGCG)2 and (rGCAGGCG)2 are similar, CD and the imino region of the proton NMR spectra indicate their structures are different. In particular, (rGCAGGCG)2 exhibits a CD spectrum typical of A-form geometry with a weak negative band at 280 nm. In contrast, the CD spectrum for (rGCGAGCG)2 has an intense positive band at 285 nm. The NMR spectrum of (rGCAGGCG)2 has a resonance corresponding to a hydrogen-bonded GA mismatch, while for (rGCGAGCG)2 no hydrogen-bonded imino proton is observed for the mismatch. The glycosidic torsion angles of the bases in the GA mismatches of (rGCAGGCG)2 and (rCGCAGGCG)2 are anti. Duplexes of type d, where X is A, G, or U, are more stable than e, and the stability differences are similar to those (formula; see text) observed for f versus g. Thus, 3'-dangling ends in this system make contributions to duplex stability that are similar to contributions observed with fully paired duplexes.     

Thermodynamic and spectroscopic study of bulge loops in oligoribonucleotides

Thermodynamic parameters for bulge loops of one to three nucleotides in oligoribonucleotide duplexes have been measured by optical melting. The results indicate bulges Bn of An and Un have similar stabilities in the duplexes, GCGBmGCG + CGCCGC. The stability increment for a bulge depends on more than its adjacent base pairs. For example, the stability increment for a bulge is affected more than 1 kcal/mol by changing two nonadjacent base pairs or by adding terminal unpaired nucleotides (dangling ends) three base pairs away. Thus a nearest-neighbor approximation for helixes with bulges is oversimplified. Many of the non-self-complementary strands used in this study were observed to form homoduplexes. Such duplexes with GA mismatches were particularly stable.     

Statistical potentials for hairpin and internal loops improve the accuracy of the predicted RNA structure

RNA is directly associated with a growing number of functions within the cell. The accurate prediction of different RNA higher-order structures from their nucleic acid sequences will provide insight into their functions and molecular mechanics. We have been determining statistical potentials for a collection of structural elements that is larger than the number of structural elements determined with experimentally determined energy values. The experimentally derived free energies and the statistical potentials for canonical base-pair stacks are analogous, demonstrating that statistical potentials derived from comparative data can be used as an alternative energetic parameter. A new computational infrastructure—RNA Comparative Analysis Database (rCAD)—that utilizes a relational database was developed to manipulate and analyze very large sequence alignments and secondary-structure data sets. Using rCAD, we determined a richer set of energetic parameters for RNA fundamental structural elements including hairpin and internal loops. A new version of RNAfold was developed to utilize these statistical potentials. Overall, these new statistical potentials for hairpin and internal loops integrated into the new version of RNAfold demonstrated significant improvements in the prediction accuracy of RNA secondary structure.     

Thermodynamics of three-way multibranch loops in RNA

RNA multibranch loops (junctions) are loops from which three or more helices exit. They are nearly ubiquitous in RNA secondary structures determined by comparative sequence analysis. In this study, systems in which two strands combine to form three-way junctions were used to measure the stabilities of RNA multibranch loops by UV optical melting and isothermal titration calorimetry (ITC). These data were used to calculate the free energy increment for initiation of a three-way junction on the basis of a nearest neighbor model for secondary structure stability. Imino proton NMR spectra were also measured for two systems and are consistent with the hypothesized helical structures. Incorporation of the experimental data into the mfold and RNA structure computer programs has contributed to an improvement in prediction of RNA secondary structure from sequence.     

Hydration of RNA base pairs

The hydration patterns around the RNA Watson-Crick and non-Watson-Crick base pairs in crystals are analyzed and described. The results indicate that (i) the base pair hydration is mostly "in-plane"; (ii) eight hydration sites surround the Watson-Crick G-C and A-U base pairs, with five in the deep and three in the shallow groove, an observation which extends the characteristic isostericity of Watson-Crick pairs; (iii) while the hydration around G-C base pairs is well defined, the hydration around A-U base pairs is more diffuse; (iv) the hydration sites close to the phosphate groups are the best defined and the most recurrent ones; (v) a string of water molecules links the two shallow groove 2'-hydroxyl groups, and (vi) the water molecules fit into notches, the size and accessibility of which are almost as important as the number and strength of the hydrophilic groups lining the cavity. Residence times of water molecules at specific hydration sites, inferred from molecular dynamics simulations, are discussed in the light of present data.