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A dynamic programming algorithm for prediction of RNA secondary structure has been revised to accommodate folding constraints determined by chemical modification and to include free energy increments for coaxial stacking of helices when they are either adjacent or separated by a single mismatch. Furthermore, free energy parameters are revised to account for recent experimental results for terminal mismatches and hairpin, bulge, internal, and multibranch loops. To demonstrate the applicability of this method, in vivo modification was performed on 5S rRNA in both Escherichia coli and Candida albicans with 1-cyclohexyl-3-(2-morpholinoethyl) carbodiimide metho-p-toluene sulfonate, dimethyl sulfate, and kethoxal. The percentage of known base pairs in the predicted structure increased from 26.3% to 86.8% for the E. coli sequence by using modification constraints. For C. albicans, the accuracy remained 87.5% both with and without modification data. On average, for these sequences and a set of 14 sequences with known secondary structure and chemical modification data taken from the literature, accuracy improves from 67% to 76%. This enhancement primarily reflects improvement for three sequences that are predicted with <40% accuracy on the basis of energetics alone. For these sequences, inclusion of chemical modification constraints improves the average accuracy from 28% to 78%. For the 11 sequences with <6% pseudoknotted base pairs, structures predicted with constraints from chemical modification contain on average 84% of known canonical base pairs. R ecent discoveries have shown that RNA plays a larger role in biology than previously realized, e.g., in posttranscriptional regulation (1), development (2, 3), immunity (4, 5), and peptide bond formation (6, 7). It is necessary to determine the native structures of RNAs to understand their mechanisms of action, and determining secondary structure is a crucial step in this process.RNA secondary structure can be predicted by free energy minimization with nearest neighbor parameters to evaluate stability (8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18). Previous studies demonstrated that nuclease cleavage data can be used to refine structure prediction and improve accuracy (8, 11). A predicted secondary structure can guide further experiments or comparative sequence analysis (19) and also aid in the design of RNA molecules (20,21).Chemical modification is a technique that reveals solvent accessible nucleotides (22). The nucleotides accessible to 1-cyclohexyl-3-(2-morpholinoethyl) carbodiimide metho-ptoluene sulfonate, dimethyl sulfate, and kethoxal are unpaired, in A-U or G-C pairs at helix ends, in G-U pairs anywhere, or adjacent to G-U pairs. This limited specificity differs from that observed with nucleases, and an algorithm allowing constraints from such chemical modification has not been reported. Chemical modification is used extensively to test hypothesized RNA secondary structures (19,(23)(24)(25)(26)(27)(28). Chemical modification can also be used to deduce possible tertia...

Improved thermodynamic parameters for prediction of RNA duplex formation are derived from optical melting studies of 90 oligoribonucleotide duplexes containing only Watson-Crick base pairs. To test end or base composition effects, new sets of duplexes are included that have identical nearest neighbors, but different base compositions and therefore different ends. Duplexes with terminal GC pairs are more stable than duplexes with the same nearest neighbors but terminal AU pairs. Penalizing terminal AU base pairs by 0.45 kcal/mol relative to terminal GC base pairs significantly improves predictions of ∆G°3 7 from a nearest-neighbor model. A physical model is suggested in which the differential treatment of AU and GC ends accounts for the dependence of the total number of Watson-Crick hydrogen bonds on the base composition of a duplex. On average, the new parameters predict ∆G°3 7 , ∆H°, ∆S°, and T M within 3.2%, 6.0%, 6.8%, and 1.3°C, respectively. These predictions are within the limit of the model, based on experimental results for duplexes predicted to have identical thermodynamic parameters.The thermodynamics of secondary structure formation are important for unraveling structure-function relationships for RNA. For example, these thermodynamics provide a foundation for predicting secondary structure and stability, both of which can correlate with function. Moreover, predicting secondary structure is a crucial intermediate step toward predicting three-dimensional structure (1, 2). In addition, differences between the thermodynamics of secondary structure formation and of overall folding can provide insight into the thermodynamics of tertiary structure formation (3-7).Watson-Crick base pairs are one of the most important motifs in RNA secondary structures. The thermodynamics of Watson-Crick base pair formation have been studied in short RNA duplexes (8, 9). The results are well-represented by a nearest-neighbor model in which the thermodynamic stability of a base pair is dependent on the identity of the adjacent base pairs. This model has been termed an individual nearest-neighbor (INN) model (10, 11). The pioneering implementation by Borer et al. (8) employed 6 nearest-neighbor parameters and separate initiation parameters for duplexes with and without a GC base pair. Due to advances in oligoribonucleotide synthesis (12), Freier et al. (9) were able to determine all 10 nearest-neighbor parameters in the INN model and the initiation parameter for duplexes with at least one GC base pair. The initiation parameter for duplexes with only AU base pairs was not determined.It has been suggested that a nearest-neighbor model that treats terminal base pairs differently from internal base pairs (8) or treats terminal GC base pairs differently from terminal AU base pairs (10, 11, 13) may improve modeling of duplex stability. The model proposed by Gray (10) has been termed an independent short sequence (ISS) model because the 14 sequence-dependent parameters of the model must be combined into 12 "short sequence" p...

Thermodynamic parameters for prediction of RNA duplex stability are reported. One parameter for duplex initiation and 10 parameters for helix propagation are derived from enthalpy and free-energy changes for helix formation by 45 RNA oligonucleotide duplexes. The oligomer sequences were chosen to maximize reliability of secondary structure predictions. Each of the 10 nearest-neighbor sequences is wellrepresented among the 45 oligonucleotides, and the sequences were chosen to minimize experimental errors in AGI at 37°C. These parameters predict melting temperatures of most oligonucleotide duplexes within 5°C. This is about as good as can be expected from the nearest-neighbor model. Free-energy changes for helix propagation at dangling ends, terminal mismatches, and internal G-U mismatches, and free-energy changes for helix initiation at hairpin loops, internal loops, or internal bulges are also tabulated.Stabilities of RNA duplexes and secondary structures of RNAs are often predicted by using free-energy parameters from a nearest-neighbor model (1-5). Sometimes, however, predictions are inconsistent with experimental data (6-10). One factor hindering successful predictions is that the reliability of parameters was limited by the availability of model oligonucleotides (2). Recent breakthroughs in synthesis of RNA oligoribonucleotides (11-16) permit design of oligonucleotides to provide improved parameters. This paper presents thermodynamic parameters derived from data on 45 complementary RNA duplexes. The parameters are able to predict the stabilities of RNA duplexes within the limits ofthe nearest-neighbor model. MATERIALS AND METHODSChoice of Sequences. Sequences were selected to minimize errors in the free-energy change for duplex formation at 37°C, AG97 (17,18). Thus, as much as possible, melting temperatures at 0.1 mM are near 37°C to minimize extrapolation. The oligomers were also chosen to independently represent all 10 nearest-neighbor sequences comprising Watson-Crick base pairs.Oligonucleotide Synthesis. Oligonucleotides not reported elsewhere were synthesized on solid support using phosphoramidite procedures and purified as described (11,19). Purities were confirmed by high-performance liquid chromatography for all oligomers.Thermodynamic Parameters. Absorbance vs. temperature melting curves were measured in 1 M NaCl/0.005 M Na2HPO4/0.5 mM EDTA (disodium salt), pH 7, as described (11). Concentrations were determined from the high-temperature absorbance using extinction coefficients calculated as described (20). In units of 0.1 mM-1 cm-1, calculated hightemperature extinction coefficients at 280 nm not reported elsewhere are as follows: GUGCAC, 2.77; GUCUAGAC, 3.66; GAUAUAUC, 3.05; GUAUAUAC, 3.00. Thermodynamic parameters of helix formation were obtained by two methods. (t) Individual melting curves were fit to a two-state model with sloping baselines and the enthalpy and entropy changes derived from the fits were averaged (21), and (ii) reciprocal melting temperature, tm-1, vs. log (CT) was plot...

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The Nearest Neighbor Database (NNDB, http://rna.urmc.rochester.edu/NNDB) is a web-based resource for disseminating parameter sets for predicting nucleic acid secondary structure stabilities. For each set of parameters, the database includes the set of rules with descriptive text, sequence-dependent parameters in plain text and html, literature references to experiments and usage tutorials. The initial release covers parameters for predicting RNA folding free energy and enthalpy changes.

The accuracy of computer predictions of RNA secondary structure from sequence data and free energy parameters has been increased to roughly 70%. Performance is judged by comparison with structures known from phylogenetic analysis. The algorithm also generates suboptimal structures. On average, the best structure within 10% of the lowest free energy contains roughly 90% of phylogenetically known helixes. The algorithm does not include tertiary interactions or pseudoknots and employs a crude model for singlestranded regions. The only favorable interactions are base pairing and stacking of terminal unpaired nucleotides at the ends of helixes. The excellent performance is consistent with these interactions being the primary interactions determining RNA secondary structure.RNA is important for functions such as catalysis, RNA splicing, regulation of transcription and translation, and transport of proteins across membranes (1). Many RNA sequences are known. Determination of secondary structures, however, is difficult. Thermodynamics has been applied to predict RNA secondary structure from sequence (2, 3), but with modest success. Predictions of suboptimal structures make the method more useful (4). We report combining several recent advances to improve predictions of RNA secondary structures. Three advances are incorporated in this work. (i) New methods for synthesizing RNA make it possible to obtain model systems with a large variety of sequence (5, 6). This technique has led to measurements of improved parameters and the realization that non-base-paired nucleotides contribute sequence-dependent interactions that stabilize secondary structure (7, 8). (ii) A computer algorithm has been developed that allows incorporation of non-base-paired interactions in the prediction of optimal and suboptimal secondary structures (9). (iii) Several RNA secondary structures have been determined by phylogeny (10-15). Comparison of predicted and known structures allows optimization of parameters that have not been measured. Resultant predictions appear sufficiently reliable to aid planning and interpretation of experiments on RNA. MATERIALS AND METHODSThermodynamic Parameters. When possible, free energy increments at 370C, AG037, were taken from experiments in 1 M NaCl. For fully base-paired regions, experiments on dGCATGC indicate that 1 M NaCl mimics solutions containing 1-100 mM Mg2+ in the presence of 0.15-1 M NaCl (16).Relatively few experiments are available for loop structures, and, therefore, little is known about interactions determining loop stability. This situation forced approximations. (i) Jacobson-Stockmayer theory (17) was used to extrapolate the length dependence of AG37 for bulge, hairpin, and internal loops: AG0(n) = AG(nmax) + 1.75 RTln (n/nmax).For this equation n is the number of unpaired nucleotides in the loop, nma is the maximum-length loop for which experimental data is available, R is the gas constant (1.987 cal mol'lK-l; 1 cal = 4.184 J), and T is the temperature in K (310.15 K for 370C). (ii) When...