title: RNAdualPF: software to compute the dual partition function with sample applications in molecular evolution theory.
abstract: BACKGROUND
  RNA inverse folding is the problem of finding one or more sequences that fold into a user-specified target structure s0, i.e. whose minimum free energy secondary structure is identical to the target s0. Here we consider the ensemble of all RNA sequences that have low free energy with respect to a given target s0.
  
  
  RESULTS
  We introduce the program RNAdualPF, which computes the dual partition function Z∗, defined as the sum of Boltzmann factors exp(-E(a,s0)/RT) of all RNA nucleotide sequences a compatible with target structure s0. Using RNAdualPF, we efficiently sample RNA sequences that approximately fold into s0, where additionally the user can specify IUPAC sequence constraints at certain positions, and whether to include dangles (energy terms for stacked, single-stranded nucleotides). Moreover, since we also compute the dual partition function Z∗(k) over all sequences having GC-content k, the user can require that all sampled sequences have a precise, specified GC-content. Using Z∗, we compute the dual expected energy 〈E∗〉, and use it to show that natural RNAs from the Rfam 12.0 database have higher minimum free energy than expected, thus suggesting that functional RNAs are under evolutionary pressure to be only marginally thermodynamically stable. We show that C. elegans precursor microRNA (pre-miRNA) is significantly non-robust with respect to mutations, by comparing the robustness of each wild type pre-miRNA sequence with 2000 [resp. 500] sequences of the same GC-content generated by RNAdualPF, which approximately [resp. exactly] fold into the wild type target structure. We confirm and strengthen earlier findings that precursor microRNAs and bacterial small noncoding RNAs display plasticity, a measure of structural diversity.
  
  
  CONCLUSIONS
  We describe RNAdualPF, which rapidly computes the dual partition function Z∗and samples sequences having low energy with respect to a target structure, allowing sequence constraints and specified GC-content. Using different inverse folding software, another group had earlier shown that pre-miRNA is mutationally robust, even controlling for compositional bias. Our opposite conclusion suggests a cautionary note that computationally based insights into molecular evolution may heavily depend on the software used. C/C++-software for RNAdualPF is available at http://bioinformatics.bc.edu/clotelab/RNAdualPF .
authors.affiliation: Biology Department, Boston College, 140 Commonwealth Avenue, Chestnut Hill, 02467, MA, USA.|Present Address: Systems Biology Program Centro Nacional de Biotecnología Consejo Superior de Investigaciones Científicas (CSIC) C/ Darwin 3, Madrid, 28049, Spain.
authors.forename: Juan Antonio
authors.initials: JA
authors.lastname: Garcia-Martin
authors.affiliation: Biology Department, Boston College, 140 Commonwealth Avenue, Chestnut Hill, 02467, MA, USA.
authors.forename: Amir H
authors.initials: AH
authors.lastname: Bayegan
authors.affiliation: Research Programme on Biomedical Informatics (GRIB), Department of Experimental and Health Sciences, Universitat Pompeu Fabra, IMIM (Hospital del Mar Medical Research Institute), Dr. Aiguader, 88, Barcelona, Spain.
authors.forename: Ivan
authors.initials: I
authors.lastname: Dotu
authors.affiliation: Biology Department, Boston College, 140 Commonwealth Avenue, Chestnut Hill, 02467, MA, USA. clote@bc.edu.
authors.forename: Peter
authors.initials: P
authors.lastname: Clote
mesh_terms: D000465:Algorithms; D000818:Animals; D017173:Caenorhabditis elegans / Q000235:genetics*; D019295:Computational Biology / Q000379:methods*; D016208:Databases, Factual; D004926:Escherichia coli / Q000235:genetics*; D019143:Evolution, Molecular; D035683:MicroRNAs / Q000235:genetics*; D012313:RNA / Q000737:chemistry; D059370:RNA Folding; D012342:RNA, Small Nuclear / Q000235:genetics*; D017423:Sequence Analysis, RNA / Q000379:methods; D012984:Software
chemical_list: D035683:MicroRNAs; D012342:RNA, Small Nuclear; D012313:RNA
keywords: Boltzmann ensemble; Partition function; RNA secondary structure; Robustness