RNAiFold: a web server for RNA inverse folding and molecular design.

Synthetic biology and nanotechnology are poised to make revolutionary contributions to the 21st century. In this article, we describe a new web server to support in silico RNA molecular design. Given an input target RNA secondary structure, together with optional constraints, such as requiring GC-content to lie within a certain range, requiring the number of strong (GC), weak (AU) and wobble (GU) base pairs to lie in a certain range, the RNAiFold web server determines one or more RNA sequences, whose minimum free-energy secondary structure is the target structure. RNAiFold provides access to two servers: RNA-CPdesign, which applies constraint programming, and RNA-LNSdesign, which applies the large neighborhood search heuristic; hence, it is suitable for larger input structures. Both servers can also solve the RNA inverse hybridization problem, i.e. given a representation of the desired hybridization structure, RNAiFold returns two sequences, whose minimum free-energy hybridization is the input target structure. The web server is publicly accessible at http://bioinformatics.bc.edu/clotelab/RNAiFold, which provides access to two specialized servers: RNA-CPdesign and RNA-LNSdesign. Source code for the underlying algorithms, implemented in COMET and supported on linux, can be downloaded at the server website.

INTRODUCTION

Given a target RNA secondary structure, the RNA inverse folding problem consists of determining one or more sequences, whose minimum free-energy (MFE) structure, with respect to the Turner energy model (1), is the target structure. RNAiFold is a web server that provides access to two new algorithms, CPdesign and LNSdesign, that solve the RNA inverse folding problem. These algorithms are described in Garcia-Martin et al. (2), where applications are given, along with benchmarking studies against other methods.

Although there are other approaches for solving RNA inverse folding problem previously described (3–8), all of these algorithms can be classified as heuristic methods, which start with an initial sequence that is iteratively modified until it either folds into the target structure or some stopping criterion is reached. In contrast, CPdesign uses constraint programming (CP) to provide the first complete solution of inverse folding, capable of generating all solutions, as well as of determining that there are no solutions to a given inverse folding problem. LNSdesign uses CP to solve sub-problems, but uses the large neighborhood search (LNS) heuristic to tackle larger inverse folding problems; however, by using a heuristic, LNSdesign can no longer generate all solutions, or determine that there is no solution to a given inverse folding problem. RNAiFold represents a step forward in RNA design, as both CPdesign and LNSdesign allow the user to specify a wide range of design constraints (both nucleotide and base pairing constraints) in solving inverse folding. Both CPdesign and LNSdesign allow the user flexibility in specifying design constraints, such as sequence template for stipulating the occurrence of certain nucleotides at certain positions, GC-content, upper and lower bounds for base pairs of certain types (strong-GC, weak-AU and wobble-GU), the maximum number of consecutive nucleotides (e.g. disallowing runs of five or more occurrences of ‘A’), as well as requiring the returned sequence to be compatible (or not to be compatible) with certain base pairs located at certain positions. Additionally, the user can stipulate folding temperature and treatment of stacked single-stranded nucleotides (also known as dangles). Both CPdesign and LNSdesign allow for inverse co-folding for a target hybridization structure for two RNAs, i.e. determining two RNA sequences, whose minimum free-energy hybridization structure is the given target structure. The Supplementary Data includes:

Figure of the web server input page with file upload selected.

Figure of input page with paste input expanded.

Figure of input page with verbose input expanded.

Definitions of all structural measures.

WEB SERVER

RNAiFold is a web server that provides access to two tools: RNA-CPdesign, which applies CP, and RNA-LNSdesign, which applies LNS. The web server currently allows jobs to run for at most 30 min. For design problems requiring more computation time, the user is urged to download and locally run our software. As explained, RNA-CPdesign and RNA-LNSdesign provide somewhat different functionality; however, the input and output format is identical for both, hence, will be treated together. Throughout the article, when we mention the input and output format of LNSdesign, the reader should realize that the same is true of CPdesign.

Input

Although not required, it is best for the user to enter an email address. For jobs that require long computation time, the results will automatically be sent to the user, if the email address is present; in any case, the browser window will be provided a link to open later when the computation has terminated.

Supplementary Figure S1 depicts the input form for both web servers CPdesign and LNSdesign. The user may upload a file, paste the input (Supplementary Figure S2), or choose to fill in text fields in a more verbose manner (Supplementary Figure S3).

Later in the text, we discuss in detail the input format for file uploads and for pasting in the large text field. After this discussion, it will be clear how to fill in fields for the more verbose manner of entering a query. RNAiFold solves the RNA inverse folding problem; hence, the mandatory minimal query is a desired target secondary structure. The target structure may be pasted into the text field, or a file containing the target structure may be uploaded, or entered into the verbose form. Optional FASTA comment and optional sequence constraints may be included. The input must be in the following form:

> FASTA comment (optional)

Sequence constraints (optional)

Target structure in dot bracket notation (required)

The server does not require sequence constraints to appear before the target structure, and any permutation of the aforementioned three lines is acceptable. Note that if sequence constraints are given, then the input sequence length must be the same as that of the structure. An example is given later in the text.

Example: the target structure is that of a transfer RNA along with FASTA comment and sequence constraints, as follows:

Note the presence of ‘GAGCUUG’ in positions 1–7, ‘ACG’ in positions 35–37 and ‘CUGGCUCG’ in positions 67–74. The sequence constraints ensure that any sequence returned by LNSdesign has the stipulated nucleotides at the indicated positions (‘N’ mean any nucleotide). Allowable sequence constraints are all one-character IUPAC codes.

In this example, the desired target structure is the cloverleaf structure of a transfer RNA, and the sequence constraints ensure an ‘ACG’ anticodon, corresponding to the CGU codon for arginine. As well, the first seven ‘GAGCUUG’ and last eight nucleotides ‘CUGGCUCG’, together comprise the acceptor stem, known to be critical for proper binding of aminoacyl synthetase. The sequence constraints and structure come from the sequence and consensus structure the Rfam database http://rfam.sanger.ac.uk/ for Chlamydomonas reinhardtii chloroplast transfer RNA, with EMBL accession code L13782.1/442-515. This example is interesting, as the Rfam consensus secondary structure of L13782.1/442-515 is different from its minimum free-energy structure, which is not a cloverleaf structure. The output of LNSdesign is discussed later in the text, in the ‘Output’ section and is depicted in Figure 1.

Figure 1.

(Left) Results page for sequence determined by LNSdesign in 22 s, whose MFE is the input target structure. The output sequence meets the user-defined constraints of ‘GAGCUUG’ in positions 1–7, ‘ACG’ in positions 35–37 and ‘CUGGCUCG’ in positions 67–74. These constraints ensure that the acceptor stem and anticodon are identical to those of C. reinhardtii chloroplast transfer RNA, with EMBL accession code L13782.1/442-515. (Right) Results page of a target hybridization structure of an unknown sequence of 20 nt with another unknown sequence of 10 nt, given in dot bracket notation (with ampersand), by (((….))).(((((((((&))))))))). Note that VarRNA cannot display hybridization structures, and thus, a concatenated structure is presented.

RNA-LNSdesign allows the user to give additional constraints on all returned sequences. The constraints are the following:

Limit canonical base pairs: minimum and maximum number of base pairs in the MFE structure of any returned sequence. Values can be stipulated for strong (GC), weak (AU) and wobble (GU) pairs. Default values are 0 for the minimum and − (no limit) for the maximum.

Limit consecutive nucleotides: minimum and maximum number of consecutive nucleotides of each type (A, C, G and U) in all returned sequences. Note that the value 0 (zero) indicates that the MFE structure (target structure) of any returned sequence cannot contain any base pair of the specified type. Default − (no limit) for the maximum.

Limit GC content: minimum and maximum per cent of GC-content (number of either G or C nucleotides divided by sequence length). Default is 0% for minimum and 100% for maximum.

Compatible base pairs: RNA-LNSdesign allows the user to specify those positions in the returned sequence(s) that can form a base pair, even if these base pairs are not part of the target structure. In this fashion, one could design an RNA whose MFE structure is the given target structure, but which is compatible with another structure. To specify these positions, the input (pasted in the text field, or uploaded in a file, or specified in the verbose form) should include the desired ‘compatible’ structure, given in dot bracket notation, preceded by the ‘at’ symbol (‘@’).

Incompatible base pairs: RNA-LNSdesign allows the user to specify positions in the returned sequence(s) that cannot form a base pair. To specify these positions, the input (pasted in the text field, or uploaded in file, or specified in the verbose form) should include the disallowed base pairs, given in dot bracket notation, preceded by the ‘pound’ symbol (‘#’). Note that if disallowed base pairs appear in the target structure, then LNSdesign will return no solutions.

Verbose form

An alternate input format is given in the verbose form, depicted in Supplementary Figure S3. Here, the user may enter the formerly described target structure, sequence constraints and constraints for compatible and incompatible base pairs. Note that no leading symbol ‘@’ or ‘#’ is required, respectively, for compatible and incompatible base pairs, and that any field may be left blank, with the exception of the field for the target structure.

In addition, the user can stipulate the temperature at which folding occurs (default is 37°C), and treatment of dangles. As LNSdesign uses a COMET plugin for Vienna RNA Package, the treatment of dangles (stacked single-stranded nucleotides) follows that of the Vienna Package—the user is referred to Vienna Package website for further explanation. Default dangle treatment for LNSdesign is 1, which is the default for Vienna Package RNAfold. However, the user can choose dangle treatment 0 (no dangle), 1 (default for Vienna Package minimum free-energy structure computation), 2 (default for Vienna Package partition function computation) and 3 (Vienna Package treatment of dangles and coaxial stacking).

Inverse co-folding

RNA-LNSdesign allows for co-folding: given a hybridization structure, together with optional constraints, LNSdesign returns two sequences, whose MFE hybridization is the input, target structure. Note that hybridization may involve inter-molecular base pairs, as well as intra-molecular base pairs, provided that there are no pseudoknots.

The input format for the RNA inverse co-folding problem consists of the following form:

> FASTA comment (optional)

Target hybridization structure, with ampersand (‘&’) (required)

Sequence constraints with ampersand (‘&’) (optional)

The target hybridization structure is represented in dot bracket notation, following the convention of Vienna RNA Package RNAcofold. Namely, an ampersand (‘&’) separates the two single-molecule portions of the hybridization structure. Sequence constraints are represented by the concatenation of two sequences, separated by ampersand, where as before, the user may indicate that certain positions in all returned sequences must have specific nucleotides in indicated positions. The sequence constraint is optional, but if provided, it must have the same length as the input hybridization structure, including the ampersand.

To represent the hybridization of an unknown sequence of 20 nt with another unknown sequence of 10 nt, where there is a stem–loop structure from positions 1–10 for the unknown sequence of 20 nt, whereas positions 11–20 of the first sequence hybridize with positions 1–10 of the second sequence, we give the dot bracket notation (with ampersand): (((….))).(((((((((&))))))))).

Output

If the user gives an email address, then after submitting the job, an email will be sent as soon as the results are available. Three possible types of results can be returned:

Solution found: a file of results will be attached, with the following information:

Input target structure

A listing of the sequence(s) found.

The numbers of base pairs of each type (strong, weak and wobble).

Computation time

Structural measures

No solution found: time is limited to 30 min; hence, a solution may not be found within this limit.

No possible solution: if the target structure (with specified constraints) has no solution and the time limit has not been reached, then LNSdesign will state this in the results file.

On the earlier-explained example of a target transfer RNA structure with the sequence constraints of ‘GAGCUUG’ in positions 1–7, anticodon ‘ACG’ in positions 35–37, ‘CUGGCUCG’ in positions 67–74, LNSdesign returns an RNA sequence, whose MFE structure is the target structure, an image of the sequence and structure, such as depicted in the Figure 1 (right):

Here, the objective structure and sequence pattern constitute the user-defined target structure and sequence constraints (if any). The solution sequence is then given, followed by its minimum free-energy (MFE) structure, which must be the target structure. The number of strong (GC), weak (AU) and wobble (GU) pairs are given, followed by CPU computation time in seconds. Free energy of the MFE structure is given in kcal/mol, followed by the expected base pair distance from the target structure, the ensemble defect, which is another measure of distance between low-energy structures in the Boltzmann ensemble and the target structure, the average pointwise entropy and two measures of structural diversity. All of these values provide information on the extent to which the Boltzmann ensemble of low-energy structures for the output RNA sequence resembles the target structure. These measures are explained in Garcia-Martin et al. (2) and in Supplementary Data S4.

Cluster and software specs

The web server http://bioinformatics.bc.edu/clotelab/RNAiFold runs on a Linux cluster with head and file server nodes, and 25 compute nodes, including 6 Dell Power Edge 1850, 2× Intel Xeon P4 (2.80 GHz), 2 GB random access memory (RAM), 11 Dell Power Edge 1750, 2× Intel Xeon P4 (2.80 GHz), 4 GB RAM and 8 Dell Power Edge 1950, 2× Intel Xeon E5430 Quad core (2.80 GHz), 16 GB RAM. The CPdesign and LNSdesign software is written in version 2.1.1 of COMET, an optimization programming language available at http://dynadec.com/support/downloads/. CPdesign and LNSdesign use a plugin to version 1.8.5 of Vienna RNA Package, which uses the Turner 99 energy model. In the future, it is likely that RNAiFold later migrates to version 2.* of Vienna RNA Package, which uses the Turner 2004 energy model.

Comparison with other software and web servers

Table 1 compares current inverse folding software and web servers. To the best of our ability, we attempt to compare various aspects of existent RNA inverse folding software and web servers. This comparison table is intended only to provide an overview of how RNAiFold differs from existent software.

Table 1.

Comparison table for RNA inverse folding software and web servers

Software	WS	PK	H	T	D	SeqC	StrC	O	Num
RNAiFold	✓		✓	✓	0,1,2,3	✓	✓	mfe	50
RNAinverse	✓			✓	0,1,2,3	IUPAC		mfe, prob	100
RNA-SSD	✓			✓	3?	IUPAC		mfe	10
INFO-RNA	✓				3?	IUPAC		mfe,prob	50
NUPACK	✓		✓*	✓	0,1,2	✓		ens def	10
MODENA		✓			?			mfe,prob	?
Inv		✓			?			mfe	?
Frnakenstein				✓	3?		✓	various	?

Soft, Software; WS, web server; PK, pseudoknots; H, hybridization; T, temperature; D, dangle; SeqC, sequence constraints; StrC, structural constraints; O, optimization strategy; Num, maximum number of sequences returned.

Note that NUPACK optimization strategy uses ensemble defect (ens def) (9), and there is an asterisk after ‘✓’, to indicate that by an algorithmic tour de force, hybridization of more than two structures is supported. Note also that IUPAC refers to a limited subset of IUPAC (and non-IUPAC) symbols as explained in the text describing each software earlier in the text.

Our CP algorithm, RNAiFold (2), whose source code is publicly available, can output millions of solution sequences; nevertheless, the RNAiFold web server is restricted to output up to 50 solution sequences. RNAiFold supports IUPAC sequence constraints, allows the user to stipulate GC-content, the number of GC, AU and GU base pairs, as well as the maximum number of successive nucleotides, such as the size upper bound of poly-A regions. RNAiFold additionally supports compatibility and incompatibility structural constraints, as described in the text, and can solve inverse folding for the hybridization of two structures.

Historically, RNAInverse (10,11) is the first method described in the literature. It is available as part of the Vienna RNA Package web server http://rna.tbi.univie.ac.at/cgi-bin/RNAinverse.cgi. RNAinverse relies on a simple greedy strategy called adaptive walk, allows only limited sequence constraints restricted to A, U, C, G, T, X, K and I, as well as prohibiting GU wobble pairs, but does not allow structural constraints. The RNAinverse algorithm may strive to determine a sequence, whose MFE structure is the target structure (objective is mfe), or alternatively, strive to determine a sequence, which takes on the target structure with probability greater than a user-defined parameter, with default 0.5 (objective is prob).

RNA-SSD (4), which is available through the web server RNA Designer at

http://www.rnasoft.ca/cgi-bin/RNAsoft/RNAdesigner/rnadesign.pl, uses a sophisticated initialization procedure to choose an initial RNA sequence, and applies stochastic local search in place of an adaptive walk. Sequence constraints are limited to A, C, G, U, R, Y, N and X; no structural constraints are supported. In addition, GC-content for base paired regions and (independently) for loop regions can be stipulated. No choice of dangle treatment is allowed; however, as RNA-SSD relies on RNAfold from the Vienna RNA Package, it seems likely the dangle treatment is that of -d3, which includes coaxial stacking.

The program, INFO-RNA (5), uses a novel initialization step, which uses a dynamic programming algorithm to choose a sequence having the lowest free energy among all sequences compatible with the target structure. INFO-RNA (5) is available via web server at http://rna.informatik.uni-freiburg.de:8080/INFORNA/Input.jsp. The web server supports sequence constraints in the form of IUPAC symbols and allows the user to stipulate an upper bound on the number of constraint violations.

The program, NUPACK Design (7), uses a similar approach to that of RNA-SSD, but, in this case, instead of finding sequences whose MFE structure is the given target structure, NUPACK-DESIGN attempts to find sequences having minimal ensemble defect (12). Most remarkably, NUPACK solves inverse folding for the hybridization of two or more structures. IUPAC sequence constraints are supported, as well as control of GC-, AU- and GU-content, and the prohibition of occurrence of certain user-specified subsequences. It would appear that NUPACK supports treatment of dangles in a similar fashion to −d 0,1,2 option in the Vienna RNA Package. Moreover, inverse folding for both DNA and RNA is supported, where in the case of DNA, the user can stipulate Na+ and Mg++ concentrations. The NUPACK web server is available at http://www.nupack.org/design/new.

The program, Inv (8), uses a stochastic local search routine to determine a sequence whose minimum free-energy pseudoknotted structure is a given target 3-non-crossing RNA structure. Inv uses a dynamic programming method that, nevertheless, requires time, which is exponential in sequence length. There is no web server available.

The program, MODENA (6), uses a genetic algorithm to maximize proximity to the target structure and to minimize the free energy of a solution. Source code can be downloaded from http://rna.eit.hirosaki-u.ac.jp/modena/, but there is no web server available.

Finally, Frnakenstein (13) is a recent Python program that calls Vienna RNA Package RNAfold and RNAeval within a genetic algorithm to evolve collection of RNA sequences to have low energy structures with respect to one or more target structures (as solution sequences are compatible with than one target structure, structural compatibility constraints are supported). Source code can be downloaded from http://www.stats.ox.ac.uk/anderson/Code/frnakenstein.html; however, there is no web server. Frnakenstein (13) allows the user to stipulate population size for its genetic algorithm, which thus determines the number of output sequences. A realistic upper bound on population size depends on run time, which is slow, as Python is an interpreted language.

CONCLUSION

RNAiFold is a website that provides public access to the CPdesign and LNSdesign algorithms for solving the RNA inverse folding problem. RNAiFold supports a number of user-defined constraints concerning the nucleotide and base pairing constitution of the sequences returned. The website includes links to download source code, as well as sequences, structures and benchmarking results from extensive testing of the software. Our group has confirmed the use of RNAiFold in RNA molecular design by experimentally validating a novel construct described in a forthcoming publication.

SUPPLEMENTARY DATA

Supplementary Data are available at NAR Online: Supplementary Figures 1–3.

FUNDING

National Science Foundation [DMS-1016618]. Funding for open access charge: Waived by Oxford University Press.

Conflict of interest statement. None declared.