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Background  The general problem of RNA secondary structure prediction under the widely used thermodynamic model is known to be NP-complete when the structures considered include arbitrary pseudoknots. For restricted classes of pseudoknots, several polynomial time algorithms have been designed, where the  O ( n  6 )time and  O ( n  4 ) space algorithm by Rivas and Eddy is currently the best available program.    Results  We introduce the class of canonical simple recursive pseudoknots and present an algorithm that requires  O ( n  4 ) time and  O ( n  2 ) space to predict the energetically optimal structure of an RNA sequence, possible containing such pseudoknots. Evaluation against a large collection of known pseudoknotted structures shows the adequacy of the canonization approach and our algorithm.    Conclusions  RNA pseudoknots of medium size can now be predicted reliably as well as efficiently by the new algorithm.

Design, implementation and evaluation of a practical pseudoknot folding algorithm based on thermodynamics.