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Nucleic Acids Research Advance Access originally published online on June 16, 2009
Nucleic Acids Research 2009 37(Web Server issue):W281-W286; doi:10.1093/nar/gkp477
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Nucleic Acids Research, 2009, Vol. 37, No. suppl_2 W281-W286
© 2009 The Author(s)
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/2.0/uk/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Articles

RNAmutants: a web server to explore the mutational landscape of RNA secondary structures

Jerome Waldispühl1,2, Srinivas Devadas2,3, Bonnie Berger1,2,* and Peter Clote4,*

1Department of Mathematics, 2Computer Science and Artificial Intelligence Laboratory, MIT, Cambridge, MA 02139, 3Electrical Engineering and Computer Science, MIT, Cambridge and 4Department of Biology, Boston College, Chestnut Hill, MA 02467, USA

*To whom correspondence should be addressed. Tel: +1 617 552 1332; Fax: +1 617 552 2011; Email: clote{at}bc.edu Correspondence may also be addressed to Bonnie Berger. Tel: +1 617 253 1827; Fax: +1 617 258 5429; Email: bab{at}mit.edu

Received February 26, 2009. Revised May 6, 2009. Accepted May 17, 2009.


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 DEFINITIONS AND METHODS
 WEB SERVER
 CONCLUSION
 SUPPLEMENTARY DATA
 FUNDING
 REFERENCES
 
The history and mechanism of molecular evolution in DNA have been greatly elucidated by contributions from genetics, probability theory and bioinformatics—indeed, mathematical developments such as Kimura's neutral theory, Kingman's coalescent theory and efficient software such as BLAST, ClustalW, Phylip, etc., provide the foundation for modern population genetics. In contrast to DNA, the function of most noncoding RNA depends on tertiary structure, experimentally known to be largely determined by secondary structure, for which dynamic programming can efficiently compute the minimum free energy secondary structure. For this reason, understanding the effect of pointwise mutations in RNA secondary structure could reveal fundamental properties of structural RNA molecules and improve our understanding of molecular evolution of RNA. The web server RNAmutants provides several efficient tools to compute the ensemble of low-energy secondary structures for all k-mutants of a given RNA sequence, where k is bounded by a user-specified upper bound. As we have previously shown, these tools can be used to predict putative deleterious mutations and to analyze regulatory sequences from the hepatitis C and human immunodeficiency genomes. Web server is available at http://bioinformatics.bc.edu/clotelab/RNAmutants/, and downloadable binaries at http://rnamutants.csail.mit.edu/.


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
DEFINITIONS AND METHODS
 WEB SERVER
 CONCLUSION
 SUPPLEMENTARY DATA
 FUNDING
 REFERENCES
 
Understanding the molecular evolution of DNA has proven essential to modern biology. One of the main fields that has contributed to our understanding of molecular evolution is population genetics, in its modern form founded by Fisher (1) and Wright (2) in the early part of the last century, when they posed and partially solved the question of expected time (number of generations) for gene allele fixation or extinction, known subsequently as the (discrete) Fisher–Wright problem. This difficult problem of probability theory was solved using various techniques, including the Fokker–Planck single-variable diffusion equation (1–4), the coalescent (5,6), and a direct analysis of Markov chains (7). The Fisher–Wright model forms the foundation of Kimura's widely accepted neutral theory of molecular evolution, now a cornerstone of modern genetics (8).

A mutation in a protein coding gene may be deleterious depending on whether it causes a change of the coded amino acid. A measure of selective pressure on protein coding genes is the term Ka/Ks (also known as dN/dS), which is the ratio of the rate of nonsynonymous substitutions (Ka) to synonymous substitutions in a protein coding region (CDS). In contrast, a mutation in a nonprotein coding RNA gene may be deleterious if the underlying functional structure is changed. At present, there is no widely adopted measure of selective pressure in noncoding RNA genes; however, as explained in Waldispühl et al. (9), RNAmutants can be used to quantify the deleterious nature of pointwise mutations in noncoding RNA genes. The rationale for the consideration of mutational effects on RNA secondary structure is explained in the next paragraph.

The function of structural noncoding RNA [ribozymes (10), riboswitches (11), precursor microRNA (12), selenocysteine insertion sequence (SECIS) elements (13), transfer RNA, etc.] depends on tertiary structure, which Banerjee et al. (14) have shown experimentally to largely depend on secondary structure. Secondary structure can be predicted using dynamic programming energy minimization (15); indeed, Mathews et al. (16) have shown that the minimum free energy (MFE) structure, as determined in mfold (17) or RNAfold (18), includes 73% of the base pairs in the native as inferred from the X-ray structure or by comparative sequence analysis secondary structure, on average, when tested on RNA sequences of length 700 nt.

Computational tools like mfold of Zuker (17), Vienna RNA Package of Hofacker et al. (18), RNAStructure of Mathews and Turner (19), Sfold of Ding et al. (20,21), RNAbor of Freyhult et al. (22,23) and RNAsat of Waldispühl and Clote (24) probe the landscape of secondary structures of a given RNA sequence. RNA sequence/structure alignment tools like Dynalign by Mathews and Turner (25), FOLDALIGN by Havgaard et al. (26), MSARI of Coventry et al. (27), RNAz of Washietl et al. (28), etc., can be considered to be the RNA analog of BLAST and ClustalW, whereby conservation of secondary structure base pairing is taken into account.

Understanding the effect of pointwise mutations on RNA secondary structure reveals fundamental properties of structurally important RNA and may suggest potentially deleterious mutations in RNA viral pathogens. Designed explicitly for this purpose, the algorithm RNAmutants (9) allows users to analyze the low energy ensemble of mutant RNA sequences and structures. Given an RNA sequence s of length n, an upper bound K for the number of mutations allowed, a desired number N of secondary structures samples to be generated, and a temperature 0 ≤ T ≤ 100 in degrees Celsius, RNAmutants computes the following for all k ≤ K simultaneously: (i) the MFE structure MFEFormulaFormula, its free energy and the Boltzmann partition function ZFormulaFormula, over all secondary structures of all k-point mutants; (ii) a plot of the ensemble free energy –RT ln ZFormulaFormula, as a function of k; and (iii) a collection of N RNA mutant sequences and their secondary structures, as sampled using the partition function. By comparing low-energy structures from mutant RNA with the consensus structures from the Rfam database (29), one can infer putative deleterious mutations, as performed in (9).


   DEFINITIONS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 DEFINITIONS AND METHODS
WEB SERVER
 CONCLUSION
 SUPPLEMENTARY DATA
 FUNDING
 REFERENCES
 
Definitions
Given RNA sequence s = s1, ..., sn, for all 0 ≤ k ≤ n, let ZFormulaFormula denote the Boltzmann partition function at absolute temperature T for the collection of all secondary structures on all k-point mutants; i.e.

Formula 1 (1)
where the first sum is taken over all k-point mutants s' = s'1, ..., s'n of s = s1, ..., sn, and the second sum is taken over all secondary structures S of the (fixed) k-point mutant. Similarly, let mfeFormulaFormula denote the k-point mutant s' = s'1, ..., s'n of s whose secondary structure has least free energy over all k-point mutants of s, and let MFEFormulaFormula denote its secondary structure. In the sequel, mfeFormulaFormula is called the k-superoptimal mutant and MFEFormulaFormula is called the k-superoptimal secondary structure. Finally, we let Zk, mfek, MFEk denote the corresponding values at default temperature T = 37°C.

Partition function and superoptimal structures
In (30), we introduced a novel algorithm to compute the partition function ZFormulaFormula for all k-point mutants of a given RNA sequence at absolute temperature T, with respect to the Nussinov energy model (31). In contrast to the Nussinov energy model, where each base pair contributes energy term of –1, the widely accepted Turner energy model (32) includes negative, stabilizing free energy terms for stacked base pairs as well as positive, destabilizing free energy terms for hairpins, bulges, internal loops and multiloops. With the exception of multiloops, for which an affine approximation is applied, these free energy parameters were obtained from UV absorption (optical melting) experiments first pioneered by Tinoco's Lab (33) and systematically carried out by Turner's Lab (32,34). For instance, at 37°C, Turner's rules assign stacking free energy of –2.24 kcal/mol to

Formula

Waldispühl et al. (35) developed a general algorithm AMSAG, applicable both to RNA and transmembrane protein structure prediction. Subsequently, Clote et al. (30) designed an algorithm to compute the partition function ZFormulaFormula with respect to the Nussinov energy model (31), and applied AMSAG to determine the k-superoptimal secondary structures with respect to an energy model intermediate between the Nussinov and Turner models. Recently, Waldispühl et al. (9) created a unified framework for simultaneously computing k-superoptimal secondary structures MFEFormulaFormula as well as the partition functions ZFormulaFormula with respect to the full Turner energy model. The resulting program, RNAmutants, was then applied to the analysis of regulatory portions of the hepatitis C and human immunodeficiency viral genomes. Of particular interest is the determination of putative deleterious mutations, many of which were validated in prior experimental work.

Using dynamic programming, RNAmutants computes mfeFormulaFormula, MFEFormulaFormula and ZFormulaFormula for all values of 0 ≤ k ≤ K in worst-case time O(n3K2) and space O(n2K). From statistical mechanics, it is known that the expected internal energy <Ek> of all k-point mutants and their secondary structures is equal to RT2 times the partial derivative of ln ZFormulaFormula, and hence can be approximated using the difference ZFormula-ZFormulaFormula (30). Ensemble free energy -RT ln ZFormulaFormula can be computed as well and plotted as a function of k. Similarly, other thermodynamic parameters (heat capacity, etc.) can be obtained from the partition function.


   WEB SERVER
TOP
 ABSTRACT
 INTRODUCTION
 DEFINITIONS AND METHODS
 WEB SERVER
CONCLUSION
 SUPPLEMENTARY DATA
 FUNDING
 REFERENCES
 
Input
The web server (http://bioinformatics.bc.edu/clotelab/RNAmutants) runs on a Linux cluster with head and file server nodes, and 25 compute nodes, including 6 Dell Power Edge 1750, 2x Intel Xeon P4 (2.80 GHz), 2 GB RAM, 11 Dell Power Edge 1750, 2x Intel Xeon P4 (2.80 GHz), 4 GB RAM, and 8 Dell Power Edge 1950, 2x Intel Xeon E5430 Quad core (2.80 GHz), 16 GB RAM.

The input form for RNAmutants is shown in Figure 1. The user must submit an RNA sequence, either by pasting in the space provided, or by uploading a file. As well, the user must enter a valid email address (This email may be bogus; however, for long jobs that cannot be done interactively, the results will be sent to the email address provided), an upper bound for the number of pointwise mutations, the desired number of sampled structures, and optionally the temperature in degrees Celsius. Input for each job is saved under a unique anonymized job ID, sent to the user's email address, thus allowing the user to retrieve information from the old runs. As long as the user's browser is open, updates to the results page will be made; however, for long runs, the user will receive an email with job ID and link to the completed results page.


Figure 1
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  		Figure 1. Input form for RNAmutants.

 
Output
If K denotes the user-specified upper bound for the number of mutations, then RNAmutants computes for each k ≤ K the k-superoptimal sequence mfek, secondary structure MFEk and free energy Ek, where we recall that the superoptimal secondary structure MFEk is that which has lowest free energy over all secondary structures of all k-point mutants of the input RNA sequence. Additionally, RNAmutants computes the Boltzmann partition function Zk = {sum}S e–E(S)/RT for each k ≤ K, and using this computes a sample of structures from the low energy ensemble, following a technique similar to (but distinct from) that of Ding and Lawrence (20). RNAmutants, output of mfek, MFEk and Ek is depicted in Figure 2, while sampled sequence/structure pairs are given in Figure 3.


Figure 2
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  		Figure 2. Initial portion of one output file from RNAmutants for 51-nt portion of the 3'-untranslated region from murine β-galactoside binding protein mRNA, with NCBI accession code MUSGBPA. Web server displays all 51 superoptimal secondary structures, their free energy and mutation locations. Mutated nucleotides are shown in lower case. Each line contains the partition functin value Z(K), the sampled mutated sequence, its minimum free energy structure and the free energy of that structure.

 

Figure 3
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  		Figure 3. Initial portion of output file of 100 mutant sequence/structure pairs from RNAmutants for the 51-nt portion of the 3'-untranslated region from murine β-galactoside binding protein mRNA, with NCBI accession code MUSGBPA. Mutated nucleotides are shown in lower case.

 
By writing scripts to postprocess the output, a number of interesting results can be obtained, as exemplified in Figures 4–6. Figure 4 was generated using RNAplot and RNAfold from the Vienna RNA Package (18), using the 51 nt portion of the 3'-untranslated region from murine β-galactoside binding protein mRNA, with NCBI accession code MUSGBPA (29). This figure shows the Rfam consensus structure (29), the MFE structure and the 20-superoptimal structure. The upper triangular portion of Figure 5A shows the base pairing frequencies over all sampled structures for the 88-nt hepatitis delta virus ribozyme with EMBL accession code X85253.1 [GenBank] /682-769, while the lower triangular portion shows the base pairs in the MFE structure. (We follow the dot plot conventions of Vienna RNA Package.) Figure 5B shows superoptimal and ensemble free energy (y-axis), plotted as a function of number of pointwise mutations (x-axis). Figure 6 displays the mutational profile of the 48-nt HAR1 region, an important region of the novel RNA gene HAR1F (36), expressed in Cajal–Retzius neurons in the developing human neocortex, a gene believed to show significant evolutionary acceleration. The RNAmutants Web server provides a tool to display the mutational profile determined for nc RNA genes.


Figure 4
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  		Figure 4. Rfam consensus structure (left), MFE structure (middle) and 20-superoptimal structure (right) for hepatitis delta virus ribozyme with EMBL accession number X85253.1 [GenBank] /682-769. Free energies Rfam data from (29); structure images produced with RNAplot (18).

 

Figure 5
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  		Figure 5. (A) Base pair frequencies for sampled sequence/structure pairs for hepatitis delta virus ribozyme with EMBL accession number X85253.1/682-769. The upper triangular portion of (A) represents the base pair frequencies over all 20 000 sampled structures (1000 samples for each k-point mutant, for 1 ≤ k ≤ 20), while the lower triangular portion represents the MFE structure of the wild-type sequence. (B) Plot of k-superoptimal and k-ensemble free energies, where the latter is defined by –RT ln(Zk), where Zk is the partition function over all k-point mutants.

 

Figure 6
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  		Figure 6. Mutability profile of 48-nt HAR1 region, where the number of mutations ranges from 1 to 40. HAR1 is part of the novel RNA gene HAR1F (39), expressed in Cajal–Retzius neurons in the developing human neocortex, a gene believed to show significant evolutionary acceleration. As in traffic lights, red regions are not mutated, while green regions are mutated from wild-type nucleotide. The x-axis represents nucleotide position, as suggested by the logo plot below; the y-axis represents position-specific mutability. Mutability value of 0 corresponds to finding no mutations at that position among all samples, depicted by RGB color triple (255, 0, 0), while mutability value of 1 corresponds to finding every sample mutated at that position, depicted by RGB color triple (0, 255, 0), while fractional ratios of mutant positions are depicted by the triple ({alpha}, β, 0), where {alpha} + β = 255. Python scripts that produced this PPM figure can be downloaded at the web server.

 

   CONCLUSION
TOP
 ABSTRACT
 INTRODUCTION
 DEFINITIONS AND METHODS
 WEB SERVER
 CONCLUSION
SUPPLEMENTARY DATA
 FUNDING
 REFERENCES
 
RNAmutants is a novel application which computes, for each k ≤ K; (i) the MFE structure MFEFormulaFormula, free energy EFormulaFormula and the Boltzmann partition function ZFormulaFormula, over all secondary structures of all k-point mutants; (ii) a plot of the ensemble free energy -RT ln ZFormulaFormula, as a function of k; and (iii) a collection of RNA mutant sequences and their secondary structures, as sampled using the partition function. Since RNAmutants runs in worst-case O(n3K2) time, where n is the length of input RNA sequence, and K is an upper bound for the number of mutations, the web server cannot provide computational resources for large values of n and K. In such cases, the user should download executable code, which can be retrieved from the web server. RNAmutants allows the user to estimate the impact of mutations on the structure of functional RNA, and better understand the evolutionary process of RNA molecules.


   SUPPLEMENTARY DATA
TOP
 ABSTRACT
 INTRODUCTION
 DEFINITIONS AND METHODS
 WEB SERVER
 CONCLUSION
 SUPPLEMENTARY DATA
FUNDING
 REFERENCES
 
Supplementary Data are available at NAR Online.


   FUNDING
TOP
 ABSTRACT
 INTRODUCTION
 DEFINITIONS AND METHODS
 WEB SERVER
 CONCLUSION
 SUPPLEMENTARY DATA
 FUNDING
REFERENCES
 
Deutscher Akademischer Austauschdienst for a visit to Max Planck Institute of Molecular Genetics (to P.C.); foundation Digiteo - Triangle de la Physique (to P.C.); National Science Foundation (DBI-0543506 and DMS-0817971 to P.C.). Funding for open access charge: National Science Foundation (DBI-0543506).

Conflict of interest statement. None declared.


   ACKNOWLEDGEMENTS
 
RNAmutants software was written by J. Waldispühl, who designed the web site http://rnamutants.csail.mit.edu/. The web server and downloadable scripts at bioinformatics.bc.edu/clotelab/RNAmutants were developed by P. Clote, using a general framework created by Jason Piersampieri and Yann Ponty. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.


   Footnotes
 
The authors wish it to be known that, in their opinion, the first and the last, author should be regarded as joint First Authors.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 DEFINITIONS AND METHODS
 WEB SERVER
 CONCLUSION
 SUPPLEMENTARY DATA
 FUNDING
 REFERENCES
 

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