Efficient sampling of RNA secondary structures from the Boltzmann ensemble of low-energy

We adapt here a surprising technique, the boustrophedon method, to speed up the sampling of RNA secondary structures from the Boltzmann low-energy ensemble. This technique is simple and its implementation straight-forward, as it only requires a permutation in the order of some operations already performed in the stochastic traceback stage of these algorithms. It nevertheless greatly improves their worst-case complexity from $${\mathcal{O}}({n^2})$$ to $${\mathcal{O}}({n\log(n)})$$ , for n the size of the original sequence. Moreover the average-case complexity of the generation is shown to be improved from $${\mathcal{O}}({n\sqrt{n}})$$ to $${\mathcal{O}}({n\log(n)})$$ in an Boltzmann-weighted homopolymer model based on the Nussinov–Jacobson free-energy model. These results are extended to the more realistic Turner free-energy model through experiments performed on both structured (Drosophilia melanogaster mRNA 5S) and hybrid (Staphylococcus aureus RNAIII) RNA sequences, using a boustrophedon modified version of the popular software UnaFold. This improvement allows for the sampling of greater and more significant sets of structures in a given time.

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