Predicting the secondary structure of RNA is an intermediate in predicting RNA three-dimensional structure. Commonly, determining RNA secondary structure from sequence uses free energy minimization and nearest neighbor parameters. Current algorithms utilize a sequence-independent model to predict free energy contributions of dinucleotide bulges. To determine if a sequence-dependent model would be more accurate, short RNA duplexes containing dinucleotide bulges with different sequences and nearest neighbor combinations were optically melted to derive thermodynamic parameters. These data suggested energy contributions of dinucleotide bulges were sequence-dependent, and a sequence-dependent model was derived. This model assigns free energy penalties based on the identity of nucleotides in the bulge (3.06 kcal/mol for two purines, 2.93 kcal/mol for two pyrimidines, 2.71 kcal/mol for 5′-purine-pyrimidine-3′, and 2.41 kcal/mol for 5′-pyrimidine-purine-3′). The predictive model also includes a 0.45 kcal/mol penalty for an A-U pair adjacent to the bulge and a −0.28 kcal/mol bonus for a G-U pair adjacent to the bulge. The new sequence-dependent model results in predicted values within, on average, 0.17 kcal/mol of experimental values, a significant improvement over the sequence-independent model. This model and new experimental values can be incorporated into algorithms that predict RNA stability and secondary structure from sequence.

Trinucleotide bulges in RNA commonly occur in nature. Yet, little data exists concerning the thermodynamic parameters of this motif. Algorithms that predict RNA secondary structure from sequence currently attribute a constant free energy value of 3.2 kcal/mol to all trinucleotide bulges, regardless of bulge sequence. To test the accuracy of this model, RNA duplexes that contain frequent naturally occurring trinucleotide bulges were optically melted, and their thermodynamic parameters—enthalpy, entropy, free energy, and melting temperature—were determined. The thermodynamic data were used to derive a new model to predict the free energy contribution of trinucleotide bulges to RNA duplex stability: ΔG°37, trint bulge = ΔG°37, bulge + ΔG°37, AU + ΔG°37, GU. The parameter ΔG°37, bulge is variable depending upon the purine and pyrimidine composition of the bulge, ΔG°37, AU is a 0.49 kcal/mol penalty for an A-U closing pair, and ΔG° 37, GU is a −0.56 kcal/mol bonus for a G-U closing pair. With both closing pair and bulge sequence taken into account, this new model predicts free energy values within 0.30 kcal/mol of the experimental value. The new model can be used by algorithms that predict RNA free energies as well as algorithms that use free energy minimization to predict RNA secondary structure from sequence.

The standard sodium concentration for RNA optical melting experiments is 1.021 M. Algorithms that predict Tm, ΔG°37, and secondary structure from sequence generally rely on parameters derived from optical melting experiments performed in 1.021 M sodium. Physiological monovalent cation concentrations are much lower than 1.021 M. In fact, many molecular biology techniques require buffers containing monovalent cation concentrations other than 1.021 M. Predictions based on the 1.021 M Na+ parameters may not be accurate when the monovalent cation concentration is not 1.021 M. Here, we report thermodynamic data from optical melting experiments for a set of 18 RNA duplexes, each melted over a wide range of sodium ion concentrations (71, 121, 221, and 621 mM). Using these data and previously published data for the same sequences melted in 1.021 M Na+, we report Tm and ΔG°37 correction factors to scale the standard 1.021 M Na+ RNA parameters to other sodium ion concentrations. The recommended Tm correction factor predicts the melting temperature within 0.7 °C, and the recommended ΔG°37 correction factor predicts the free energy within 0.14 kcal/mol. These correction factors can be incorporated into prediction algorithms that predict RNA secondary structure from sequence and provide Tm and ΔG°37 values for RNA duplexes.

Currently, several models for predicting the secondary structure of RNA exist, one of which is free energy minimization using the Nearest Neighbor Model. This model predicts the lowest-free energy secondary structure from a primary sequence by summing the free energy contributions of the Watson–Crick nearest neighbor base pair combinations and any noncanonical secondary structure motif. The Nearest Neighbor Model also assumes that the free energy of the secondary structure motif is dependent solely on the identities of the nucleotides within the motif and the motif’s nearest neighbors. To test the current assumption of the Nearest Neighbor Model that the non-nearest neighbors do not affect the stability of the motif, we optically melted different stem–loop oligonucleotides to experimentally determine their thermodynamic parameters. In each of these oligonucleotides, the hairpin loop sequence and the adjacent base pairs were held constant, while the first or second non-nearest neighbors were varied. The experimental results show that the thermodynamic contributions of the hairpin loop were dependent upon the identity of the first non-nearest neighbor, while the second non-nearest neighbor had a less obvious effect. These results were then used to create an updated model for predicting the thermodynamic contributions of a hairpin loop to the overall stability of the stem–loop structure.

To better elucidate RNA structure–function relationships and to improve the design of pharmaceutical agents that target specific RNA motifs, an understanding of RNA primary, secondary, and tertiary structure is necessary. The prediction of RNA secondary structure from sequence is an intermediate step in predicting RNA three-dimensional structure. RNA secondary structure is typically predicted using a nearest neighbor model based on free energy parameters. The current free energy parameters for 2 × 3 nucleotide loops are based on a 23-member data set of 2 × 3 loops and internal loops of other sizes. A database of representative RNA secondary structures was searched to identify 2 × 3 nucleotide loops that occur in nature. Seventeen of the most frequent 2 × 3 nucleotide loops in this database were studied by optical melting experiments. Fifteen of these loops melted in a two-state manner, and the associated experimental ΔG°37,2×3 values are, on average, 0.6 and 0.7 kcal/mol different from the values predicted for these internal loops using the predictive models proposed by Lu, Turner, and Mathews [Lu, Z. J., Turner, D. H., and Mathews, D. H. (2006) Nucleic Acids Res. 34, 4912–4924] and Chen and Turner [Chen, G., and Turner, D. H. (2006) Biochemistry 45, 4025–4043], respectively. These new ΔG°37,2×3 values can be used to update the current algorithms that predict secondary structure from sequence. To improve free energy calculations for duplexes containing 2 × 3 nucleotide loops that still do not have experimentally determined free energy contributions, an updated predictive model was derived. This new model resulted from a linear regression analysis of the data reported here combined with 31 previously studied 2 × 3 nucleotide internal loops. Most of the values for the parameters in this new predictive model are within experimental error of those of the previous models, suggesting that approximations and assumptions associated with the derivation of the previous nearest neighbor parameters were valid. The updated predictive model predicts free energies of 2 × 3 nucleotide internal loops within 0.4 kcal/mol, on average, of the experimental free energy values. Both the experimental values and the updated predictive model can be used to improve secondary structure prediction from sequence.

Hydrogen-bonding, intrastrand base-stacking, and interstrand base-stacking energies were calculated for RNA and DNA dimers at the MP2(full)/6-311G** level of theory. Standard A-form RNA and B-form DNA geometries from average fiber diffraction data were employed for all base monomer and dimer geometries, and all dimer binding energies were obtained via single-point calculations. The effects of water solvation were considered using the PCM model. The resulting dimer binding energies were used to calculate the 10 unique RNA and 10 unique DNA computational nearest-neighbor energies, and the ranking of these computational nearest neighbor energies are in excellent agreement with the ranking of the experimental nearest-neighbor free energies. These results dispel the notion that average fiber diffraction geometries are insufficient for calculating RNA and DNA stacking energies.

Many naturally occurring RNA structures contain single mismatches, many of which occur near the ends of helices. However, previous thermodynamic studies have focused their efforts on thermodynamically characterizing centrally placed single mismatches. Additionally, algorithms currently used to predict secondary structure from sequence are based on two assumptions for predicting the stability of RNA duplexes containing this motif. It has been assumed that the thermodynamic contribution of small RNA motifs is independent of both its position in the duplex and the identity of the non-nearest neighbors. Thermodynamically characterizing single mismatches three nucleotides from both the 3′ and 5′ ends (i.e., off-center) of an RNA duplex and comparing these results to those of the same single mismatch−nearest neighbor combination centrally located have allowed for the investigation of these effects. The thermodynamic contributions of 13 single mismatch−nearest neighbor combinations are reported, but only nine combinations are studied at all three duplex positions and are used to determine trends and patterns. In general, the 5′- and 3′-shifted single mismatches are relatively similar, on average, and more favorable in free energy than centrally placed single mismatches. However, close examination and comparison shows there are several associated idiosyncrasies with these identified general trends. These peculiarities may be due, in part, to the identities of the single mismatch, the nearest neighbors, and the non-nearest neighbors, along with the effects of the single mismatch position in the duplex. The prediction algorithm recently proposed by Davis and Znosko [Davis, A. R., and Znosko, B. M. (2008) Biochemistry 47, 10178−10187] is used to predict the thermodynamic parameters of single mismatch contribution, and those values are compared to the measured values presented here. This comparison suggests the proposed model is a good approximation but could be improved by the addition of parameters that account for positional and/or non-nearest neighbor effects. However, more data are required to improve our understanding of these effects and to accurately account for them.

Relatively few thermodynamic parameters are available for RNA triloops. Therefore, 24 stem−loop sequences containing naturally occurring triloops were optically melted, and the thermodynamic parameters ΔH°, ΔS°, ΔG°37, and TM for each stem−loop were determined. These new experimental values, on average, are 0.5 kcal/mol different from the values predicted for these triloops using the model proposed by Mathews et al. [Mathews, D. H., Disney, M. D., Childs, J. L., Schroeder, S. J., Zuker, M., and Turner, D. H. (2004) Proc. Natl. Acad. Sci. U.S.A. 101, 7287−7292]. The data for the 24 triloops reported here were then combined with the data for five triloops that were published previously. A new model was derived to predict the free energy contribution of previously unmeasured triloops. The average absolute difference between the measured values and the values predicted using this proposed model is 0.3 kcal/mol. These new experimental data and updated predictive model allow for more accurate calculations of the free energy of RNA stem−loops containing triloops and, furthermore, should allow for improved prediction of secondary structure from sequence.

Because of the availability of an abundance of RNA sequence information, the ability to rapidly and accurately predict the secondary structure of RNA from sequence is becoming increasingly important. A common method for predicting RNA secondary structure from sequence is free energy minimization. Therefore, accurate free energy contributions for every RNA secondary structure motif are necessary for accurate secondary structure predictions. Tandem mismatches are prevalent in naturally occurring sequences and are biologically important. A common method for predicting the stability of a sequence asymmetric tandem mismatch relies on the stabilities of the two corresponding sequence symmetric tandem mismatches [Mathews, D. H., Sabina, J., Zuker, M., and Turner, D. H. (1999) J. Mol. Biol. 288, 911–940]. To improve the prediction of sequence asymmetric tandem mismatches, the experimental thermodynamic parameters for the 22 previously unmeasured sequence symmetric tandem mismatches are reported. These new data, however, do not improve prediction of the free energy contributions of sequence asymmetric tandem mismatches. Therefore, a new model, independent of sequence symmetric tandem mismatch free energies, is proposed. This model consists of two penalties to account for destabilizing tandem mismatches, two bonuses to account for stabilizing tandem mismatches, and two penalties to account for A-U and G-U adjacent base pairs. This model improves the prediction of asymmetric tandem mismatch free energy contributions and is likely to improve the prediction of RNA secondary structure from sequence.

Due to their prevalence and roles in biological systems, single mismatches adjacent to G-U pairs are important RNA structural elements. Since there are only limited experimental values for the stability of single mismatches adjacent to G-U pairs, current algorithms using free energy minimization to predict RNA secondary structure from sequence assign predicted thermodynamic values to these types of single mismatches. Here, thermodynamic data are reported for frequently occurring single mismatches adjacent to at least one G-U pair. This experimental data can be used in place of predicted thermodynamic values in algorithms that predict secondary structure from sequence using free energy minimization. When predicting the thermodynamic contributions of previously unmeasured single mismatches, most algorithms apply the same thermodynamic penalty for an A-U pair adjacent to a single mismatch and a G-U pair adjacent to a single mismatch. A recent study, however, suggests that the penalty for a G-U pair adjacent to a tandem mismatch should be 1.2 ± 0.1 kcal/mol, and the penalty for an A-U pair adjacent to a tandem mismatch should be 0.5 ± 0.2 kcal/mol [Christiansen, M. E. and Znosko, B. M. (2008) Biochemistry 47, 4329−4336]. Therefore, the data reported here are combined with the existing thermodynamic dataset of single mismatches, and nearest neighbor parameters are derived for an A-U pair adjacent to a single mismatch (1.1 ± 0.1 kcal/mol) and a G-U pair adjacent to a single mismatch (1.4 ± 0.1 kcal/mol).