RNAfold

RNAfold web server overview

The RNAfold web server on ProteinIQ runs RNAfold from the ViennaRNA Package 2.7.2 with its default Turner 2004 energy parameters (Lorenz et al., 2011). Paste the 16 nt sequence CGCAGGGAUACCCGCG and it returns the minimum free energy (MFE) structure (((.(((...)))))) with an energy of -5.60 kcal/mol, a PostScript structure plot, and RNAfold's own text output.

One job can hold many FASTA records, and each is folded on its own into one row of a results table. With Compute partition function on, the table adds the ensemble free energy, the frequency of the MFE structure, the ensemble diversity, and the centroid and MEA structures, and the plots gain a base-pair probability dot plot for every sequence.

The prediction is thermodynamic, not evolutionary or learned. RNAfold scores every possible nested pairing with the Turner nearest-neighbor energy parameters (stacking, hairpin, bulge and loop contributions) and finds the global optimum by dynamic programming. In the benchmark of Mathews et al. (1999), free energy minimization with the earlier Turner 1999 parameters recovered on average 73% of known base pairs in RNA domains under 700 nucleotides. Because the model assumes nested base pairs, RNAfold does not predict pseudoknots.

Pricing

An RNAfold job costs at least 6 credits. The quote depends only on the number of sequences: 5 credits plus 0.5 per sequence, rounded to a whole credit. The exact quote appears before submission.

Each cell is a quote from the current calculator for one job with one FASTA record per sequence. Sequence length does not change the quote: ten 100 nt sequences and ten 1,000 nt sequences both cost 10 credits. Temperature, the partition function, circular folding and the other settings do not change it either. Plain text without headers counts one sequence per line.

Inputs

Sequences may contain A, C, G and U, and T is read as U. Letters outside these, such as N, are passed to RNAfold, which folds them as positions that cannot pair. A FASTA record whose sequence is written on the > header line is refused before submission, because RNAfold reads that whole line as the name and would fold an empty sequence.

Give each sequence its own FASTA header, and the results table fills one row per record:

>tRNA_acceptor
GGGCGAAUUCCUUUUU
>hairpin
GGGGAAAACCCC

If your sequences are copied from a text document, the TXT to FASTA converter can create named records. A DNA template can be turned into the transcript with DNA to RNA. Each strand is folded on its own; for two strands that pair with each other, use RNAcofold. Runtime and memory grow steeply with length, since the algorithm is $O(n^3)$ in time.

Settings

Every other RNAfold option keeps its ViennaRNA 2.7.2 default. Folding constraints, SHAPE reactivities, G-quadruplexes, --maxBPspan, --noGU and alternative energy parameter sets are not offered on this page. The ViennaRNA tool runs RNAfold with two more controls, Salt concentration and Parameter file content, for a different energy parameter file.

Lower temperatures stabilize pairing, and results far from 37°C are extrapolations (see Temperature effects below). Disallow lonely pairs removes thermodynamically weak single pairs and usually gives cleaner helices. Leave Dangling ends at the default unless you need to match an analysis run with another mode.

Outputs

Without the partition function, each row reports:

Turning on the partition function adds these columns:

Every value in the table is read from RNAfold's own output. rnafold.txt is everything RNAfold printed, record after record, exactly as the command line shows it. rnafold_plots.zip holds the PostScript plots RNAfold writes for each record, named after its FASTA header: the _ss.ps structure plot and, with the partition function, the _dp.ps base-pair probability dot plot.

RNAfold folds each record on its own, so a batch gives the same values as separate runs. Records that share a name also share one plot file, which keeps the last of them, as it does on the command line. To draw a structure as SVG or another format, use RNAplot.

Understanding results

Reading dot-bracket notation

Dot-bracket notation encodes a secondary structure as a string the same length as the sequence. A . is an unpaired base, and ( with its matching ) are the two partners of a base pair. Pairs nest like balanced parentheses, so the first ( closes with the last ).

In (((.(((...)))))), the outer three pairs and the inner three pairs form a stem interrupted by a single unpaired bulge, capping a loop of three unpaired bases. The notation cannot represent crossing pairs, which is why pseudoknots never appear in RNAfold output. To compute the free energy of a structure you wrote yourself in this notation, use RNAeval.

Reading the energy values

The 72 nt pre-miR-21 precursor in the examples below returns an MFE (kcal/mol) of -34.600 and the 16 nt hairpin returns -5.600, and both sit on the same scale. Each value is the free energy change from the open, fully unpaired strand (defined as 0 kcal/mol) to the reported structure, summed over every stack, loop and dangling end in the Turner model. Negative means more stable than the open chain.

An MFE of 0 with a structure of only dots means no fold beats the open chain. Pre-miR-21 gives exactly that when folded at 90°C.

Because the value is a sum, it grows with length. We folded random sequences with equal A, C, G and U content at 37°C (20 sequences per length) and averaged the results.

Longer RNAs therefore have more negative MFEs almost by default, and the per-nucleotide value levels off near -0.3 kcal/mol. Composition shifts the scale as well. Random 100 nt sequences (30 per setting) averaged -12.6 kcal/mol at 30% G+C, -23.8 at 50% and -41.4 at 70%, because G-C pairs stack more strongly than A-U pairs.

Raw MFE (kcal/mol) values therefore cannot rank sequences of different length or G+C content, as in the batch example below where the 66 nt record scores -5.400 and the 56 nt record -2.400. Dividing by Length (nt) removes the length effect only roughly.

A fairer reference is the same sequence with its nucleotides shuffled, which keeps length and composition. We shuffled pre-miR-21 200 times: the copies averaged -16.7 kcal/mol (standard deviation 3.4), so the real precursor at -34.6 sits 5.2 standard deviations below them. Its stability is more than a composition effect.

To repeat this check, submit the sequence and a few dozen shuffled copies as one multi-record FASTA job and compare the MFE (kcal/mol) rows. A shuffle that preserves only composition is the simplest control; one that preserves dinucleotides is stricter, because stacking energies depend on neighboring bases.

Interpreting the ensemble metrics

The MFE structure is the single best guess, but a thermodynamic prediction is only as trustworthy as the ensemble around it. A high MFE Frequency with a low Ensemble Diversity means the molecule has one dominant fold, and the MFE, centroid and MEA structures usually agree. A low frequency with high diversity means many structures compete within a few kcal/mol, and the centroid or MEA structure, or a sample of suboptimal structures, gives a more honest picture.

The Ensemble Free Energy is always lower than or equal to the MFE because it sums over every structure, not just the best one. The gap between them widens as more structures contribute.

The two energies and MFE Frequency are tied together: $p_{\mathrm{MFE}} = e^{-(E_{\mathrm{MFE}} - G)/RT}$, where $G$ is the ensemble free energy and $RT$ is 0.616 kcal/mol at 37°C. For pre-miR-21 the gap is -34.600 minus -36.070, or 1.47 kcal/mol, and $e^{-1.47/0.616}$ is 0.092, the reported frequency. Every 1.4 kcal/mol of gap lowers the frequency about tenfold at 37°C.

A low MFE Frequency is normal for long RNAs and does not mean a poor prediction. The random sequences in the table above average 0.047 at 100 nt and 0.0046 at 200 nt, while pre-miR-21 sits at 0.092 and still forms a clean hairpin. The frequency counts one exact string, and many near-copies (a frayed end, a pair slipped by one base) each take a share.

What separates a settled molecule from a scattered one is Ensemble Diversity and Centroid Distance. Pre-miR-21 has 3.510 and 2.710 base pairs. A 60 nt random sequence with a lower MFE Frequency of 0.041 has 17.970 and 13.000 (full numbers below). The centroid is the structure closest to the ensemble on average, so its distance is smaller than the diversity in both cases.

Choosing between the MFE, centroid and MEA structures

For pre-miR-21 the three structures differ at one place. U33 and U34 can both pair with A42, with probabilities of 0.46 and 0.49. The MFE structure takes U33-A42. The MEA structure takes U34-A42 at the same -34.600 kcal/mol. The centroid takes neither, because it contains exactly the pairs with a probability above 0.5 (confirmed against the pair probabilities for this sequence; Carvalho and Lawrence, 2008).

That is also why its Centroid Energy of -31.900 is higher than the MFE: it has 31 pairs instead of 32, and no structure lies below the MFE. A higher centroid energy is expected and is not an error.

The table contrasts pre-miR-21 with a random 60 nt sequence we generated (GACAGAUAGUGCACACGACCGGCGUCGGAGAAACUCUAUUUGCCGCCUGACAAGUCAAUG), both at 37°C with the partition function on.

In the second column the centroid is within 0.2 kcal/mol of the MFE yet shares no pair with it. The sequence has at least two unrelated folds of nearly equal stability, and either string alone would mislead. Report the dot plot instead, or sample alternatives with RNAsubopt. RNAdistance reports the base-pair distance (its P representation) between two dot-bracket strings.

Against known structures, Ding et al. (2005) found that centroids made 30.0% fewer prediction errors, measured as positive predictive value, than MFE structures on a set of structural RNAs. Lu et al. (2009) found that structures maximizing expected accuracy with a similar partition function raised the average positive predictive value from 66% to 68% at the same 73% sensitivity. The gains are real but modest.

MEA Score is the expected-accuracy objective at RNAfold's default gamma of 1: twice the probability of each included pair plus the unpaired probability of each unpaired base. It cannot exceed Length (nt), and pre-miR-21 reaches 67.170 of 72.

Reading the base-pair probability dot plot

With Compute partition function on, rnafold_plots.zip holds a _dp.ps file for each sequence, a PostScript dot plot that any PostScript viewer opens. Both axes run along the sequence. Per the RNAfold documentation, the upper right half shows a square for each pair with area proportional to its pairing probability, and the lower left half shows one square for each pair in the MFE structure.

Compare mirrored positions across the diagonal. A pair is well determined when the MFE square below the diagonal has a large square opposite it above. An MFE square with only a faint partner above is a pair the ensemble does not back. A helix appears as a line of squares running perpendicular to the diagonal, and competing helices show up as separate lines in the same rows or columns.

In pre-miR-21, 22 of the 32 MFE pairs have a probability of 0.99 or higher and 27 reach 0.9. The weak ones are the end pair 1:72 (0.54), 36:40 (0.60), 32:43 (0.75) and 33:42 (0.46), with 34:42 (0.49) beside it in the same column as a one-base slip.

Mathews (2004) found that MFE pairs with a probability of 0.99 or more had an average positive predictive value of 91.0% against 65.8% for all MFE pairs, an average over a benchmark set and not a guarantee for one pair.

The results table has no per-pair probabilities, mountain plot or per-position entropy, so the dot plot is the only place to see them. For the local probability that each base is unpaired, use RNAplfold.

Temperature effects

Temperature (°C) rescales the energy parameters, so the same sequence gets different folding energies. We folded pre-miR-21 at several temperatures with the partition function on.

The MFE rises by about 0.8 kcal/mol per degree between 25 and 37°C. The structure keeps 32 pairs over that range while the ensemble spreads, so MFE Frequency and Ensemble Diversity register warming earlier than the MFE structure does.

At 90°C the MFE structure is the open chain, and the 0.004 is the probability of that open chain. McCaskill (1990) noted that the temperature dependence of the partition function carries information about melting behavior. The parameters are rescaled from their 37°C values, so results near 0 or 100°C are extrapolations.

Common misreadings

The MFE structure is a prediction, not the observed fold. Mathews et al. (1999) found that the lowest-free-energy structure contained on average 73% of known base pairs for domains under 700 nt with the parameters of that time, and Lu et al. (2009) report an average positive predictive value of 66% at 73% sensitivity. Accuracy varies by RNA: Mathews et al. (2004) describe sequences predicted with under 40% accuracy by energetics alone.

Only nested pairs are modeled. Pseudoknots, which occur in some ribozymes and viral frameshift signals, are missing or replaced by an alternative nested helix, and G-quadruplexes are not considered. The ProteinIQ form has no input for folding constraints or probing data such as SHAPE, so an experimentally known helix cannot be imposed.

The model sees the sequence at one temperature. It has no proteins, ligands, metal ions or transcription-coupled folding, so a riboswitch or a protein-bound RNA can adopt a fold that differs from its MFE structure.

Several numbers read as better than they are. A more negative MFE (kcal/mol) is not a more accurate prediction. Ensemble Free Energy is lower than the MFE by construction and is not a better score. MFE Frequency is the probability of one exact string, not confidence in the fold.

Letters outside A, C, G and U, such as N, fold as positions that cannot pair: GGGGAAANCCCC returns ((((....)))). A sequence with many such characters folds as if they were loops.

How RNAfold works

The MFE prediction uses the Zuker dynamic programming recursion (Zuker and Stiegler, 1981). Instead of scoring each candidate structure separately, RNAfold builds the optimal structure for every subsequence and combines those optima, which makes the global minimum reachable in $O(n^3)$ time for a sequence of length $n$.

Energies come from the Turner 2004 nearest-neighbor model (Mathews et al., 2004), where the stability of a helix depends on which base-pair steps stack on each other, and loops carry length- and sequence-dependent penalties.

The partition function uses McCaskill's algorithm (McCaskill, 1990) over the same energy model. Rather than the single lowest-energy fold, it computes the Boltzmann-weighted sum over all structures, which yields base-pairing probabilities and the ensemble free energy. From those probabilities RNAfold derives two alternative structures (Lorenz et al., 2011).

The centroid is the structure closest, on average, to every other structure in the ensemble, so it tends to keep only pairs the ensemble strongly agrees on. The MEA structure is assembled to maximize the summed probabilities of the pairs and unpaired positions it includes.

RNAfold examples

Canonical 16 nt hairpin with default MFE settings

This short sequence demonstrates the standard RNAfold run: one linear RNA folded at 37°C with the default energy model and no partition-function calculation.

• Input: CGCAGGGAUACCCGCG as the FASTA record canonical_hairpin

RNAfold returns a six-base-pair hairpin with one unpaired bulge and an MFE of -5.600 kcal/mol. The negative energy means this is the lowest-energy nested secondary structure found under these settings; it does not establish that this is the only structure populated in solution or that the RNA adopts it in vivo.

Human pre-miR-21 ensemble analysis

This example folds the 72 nt human pre-miR-21 precursor from RNAcentral (URS00000AF93C) and enables the partition function to compare the MFE prediction with representative structures from the full thermodynamic ensemble.

• Input: hsa_mir_21_precursor_URS00000AF93C, a 72 nt RNA sequence
• Non-default setting: Compute partition function = enabled to return ensemble, centroid, and MEA metrics

The MFE structure has an energy of -34.600 kcal/mol, while the complete ensemble has a lower free energy of -36.070 kcal/mol. An MFE Frequency of 0.092 means the exact MFE structure accounts for about 9.2% of the Boltzmann ensemble under the model.

The centroid and MEA structures keep the same stem-loop and differ from the MFE structure only at the apex: the centroid lacks one apical pair, and the MEA structure moves it by one position (explained above). That fits the reported Ensemble Diversity of 3.510. These values describe a thermodynamic model, not experimental confirmation of the precursor's cellular structure or processing.

Two-sequence FASTA batch with lonely pairs disallowed

This batch example shows how RNAfold processes two independently named FASTA records in one job and returns one result row per sequence.

• Inputs: viennarna_seq1 (66 nt) and viennarna_seq2 (56 nt)
• Non-default setting: Disallow lonely pairs = enabled to exclude isolated base pairs

The two records are folded independently rather than as an interacting pair. Under the same 37°C settings, viennarna_seq1 returns an MFE of -5.400 kcal/mol and viennarna_seq2 returns -2.400 kcal/mol. The more negative value indicates a lower predicted folding free energy for the first sequence in this job, but energies across different sequence lengths should not be treated as a normalized measure of structural quality or biological function.

ProteinIQ and the ViennaRNA RNAfold WebServer

The reference RNAfold web server is the RNAfold WebServer, part of the ViennaRNA Web Services run by the Institute for Theoretical Chemistry at the University of Vienna (Gruber et al., 2008). ProteinIQ is not affiliated with the ViennaRNA team; it runs the published ViennaRNA 2.7.2 RNAfold program on its own servers.

The Vienna server states limits of 7,500 nt for partition function calculations and 10,000 nt for MFE-only predictions. Its help page says results are deleted after 2 days, that anyone who guesses a results URL can open it, and that the servers are based on ViennaRNA 2.6.3. It can send an email when a job finishes.

The Vienna form offers options this page does not: folding constraints, G-quadruplex prediction, no GU pairs at helix ends, Turner 1999, Andronescu 2007 and DNA energy parameters, salt concentration, energy corrections for modified bases, and SHAPE reactivity data. Its outputs include an interactive SVG structure plot, plots with reliability annotation from the partition function, and a mountain plot.

On ProteinIQ, one job folds a multi-record FASTA file into a results table, with sequences up to about 32,700 nt each; paid plans have no cap on the number of sequences. Every job is saved to the workspace's job history with its inputs, settings and files, and paid plans can submit jobs through the ProteinIQ API. ProteinIQ charges credits for each job, as listed under pricing; the Vienna server is free to use.

Limitations and alternatives

RNAfold folds one full-length strand into its global MFE structure. Several sibling ViennaRNA tools cover cases it is not built for:

For a deep-learning alternative that predicts base pairing without the nested-structure assumption, including some pseudoknots, see SMRTNet. The wider choice of methods is covered under RNA secondary structure prediction.

FAQ

What does RNAfold predict?

RNAfold predicts the minimum free energy secondary structure of an RNA sequence: which bases pair with which, returned as a dot-bracket string and a free energy in kcal/mol. With the partition function enabled it also reports ensemble metrics and the centroid and MEA structures.

Is this the real ViennaRNA RNAfold?

Yes. ProteinIQ runs the RNAfold executable from ViennaRNA 2.7.2 with its default Turner 2004 energy parameters, and every value in the results table is read from RNAfold's own output, so results match the command-line RNAfold at the same settings.

How accurate is RNAfold?

Mathews et al. (1999) found that free energy minimization recovered on average 73% of known base pairs in RNA domains shorter than 700 nucleotides, against 64% for the previous version of the algorithm and parameters. Accuracy varies widely between sequences and falls for long RNAs, pseudoknotted RNAs and structures held by proteins or ions. A high MFE frequency and low ensemble diversity mean one fold dominates.

Which energy parameters does RNAfold use?

ProteinIQ uses the ViennaRNA 2.7.2 default, the Turner 2004 nearest-neighbor parameter set, scaled to the folding temperature you choose (37°C by default). Stacking energies depend on the neighboring base pairs, and hairpin, bulge, interior and multibranch loops carry length- and sequence-dependent penalties.

What is minimum free energy in RNA folding?

The minimum free energy is the lowest folding free energy among all possible secondary structures for a sequence. The structure that achieves it is the MFE structure, the single most thermodynamically stable fold under the chosen temperature and energy model.

Does RNAfold predict pseudoknots?

No. RNAfold only models nested base pairs, so crossing interactions and pseudoknots are excluded by design. For pseudoknot-capable prediction, use a deep-learning model such as SMRTNet.

What is the difference between the MFE, centroid, and MEA structures?

The MFE structure is the single lowest-energy fold. The centroid is the structure closest on average to all structures in the ensemble. The MEA structure maximizes the expected number of correctly assigned pairs and unpaired bases. The centroid and MEA only appear when the partition function is enabled, and they are most useful when the ensemble has several competing structures.

Sources

• Zuker M, Stiegler P. "Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information." Nucleic Acids Research 9, 133-148 (1981). doi:10.1093/nar/9.1.133
• McCaskill JS. "The equilibrium partition function and base pair binding probabilities for RNA secondary structure." Biopolymers 29, 1105-1119 (1990). doi:10.1002/bip.360290621
• Mathews DH, Sabina J, Zuker M, Turner DH. "Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure." Journal of Molecular Biology 288, 911-940 (1999). doi:10.1006/jmbi.1999.2700
• Mathews DH, Disney MD, Childs JL, Schroeder SJ, Zuker M, Turner DH. "Incorporating chemical modification constraints into a dynamic programming algorithm for prediction of RNA secondary structure." Proceedings of the National Academy of Sciences 101, 7287-7292 (2004). doi:10.1073/pnas.0401799101
• Mathews DH. "Using an RNA secondary structure partition function to determine confidence in base pairs predicted by free energy minimization." RNA 10, 1178-1190 (2004). doi:10.1261/rna.7650904
• Ding Y, Chan CY, Lawrence CE. "RNA secondary structure prediction by centroids in a Boltzmann weighted ensemble." RNA 11, 1157-1166 (2005). doi:10.1261/rna.2500605
• Gruber AR, Lorenz R, Bernhart SH, Neuböck R, Hofacker IL. "The Vienna RNA websuite." Nucleic Acids Research 36, W70-W74 (2008). doi:10.1093/nar/gkn188
• Carvalho LE, Lawrence CE. "Centroid estimation in discrete high-dimensional spaces with applications in biology." Proceedings of the National Academy of Sciences 105, 3209-3214 (2008). doi:10.1073/pnas.0712329105
• Lu ZJ, Gloor JW, Mathews DH. "Improved RNA secondary structure prediction by maximizing expected pair accuracy." RNA 15, 1805-1813 (2009). doi:10.1261/rna.1643609
• Lorenz R, et al. "ViennaRNA Package 2.0." Algorithms for Molecular Biology 6, 26 (2011). doi:10.1186/1748-7188-6-26