RNAdualPF: software to compute the dual partition function with sample applications in molecular evolution theory

Background: RNA inverse folding is the problem of finding one or more sequences that fold into a user-specified target structure s(0), i.e. whose minimum free energy secondary structure is identical to the target s(0). Here we consider the ensemble of all RNA sequences that have low free energy with respect to a given target s(0). Results: We introduce the program RNAdualPF, which computes the dual partition function Z*, defined as the sum of Boltzmann factors exp(-E(a, s(0))/RT) of all RNA nucleotide sequences a compatible with target structure s(0). Using RNAdualPF, we efficiently sample RNA sequences that approximately fold into s(0), 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. Conclusion: 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.