RNA structure prediction including pseudoknots through direct enumeration of states

Abstract

The accurate prediction of RNA secondary structure from primary sequence has had enormous impact on research from the past forty years. While many algorithms are available to make these predictions, the inclusion of non-nested loops, termed pseudoknots, still poses challenges. Here, we describe a new method to compute the entire free energy landscape of secondary structures of RNA resulting from a primary RNA sequence, by combining a polymer physics model for the entropy of pseudoknots with exhaustive enumeration of the set of possible structures. Our polymer physics model can address arbitrarily complex pseudoknots and has only two free loop entropy parameters that correspond to concrete physical quantities, over an order of magnitude fewer than even the sparsest state-of-the-art algorithms. Our model outperforms previously published methods in predicting pseudoknots, while performing on par with current methods in the prediction of nonpseudoknotted structures. For RNA sequences of ∼ 45 nucleotides, or ∼ 90 with minimal heuristics, the complete enumeration of possible secondary structures can be accomplished quickly despite the NP-complete nature of the problem. * Electronic address: okimchi@g.harvard.edu † Electronic address: ljc37@cam.ac.uk 1 More generally, we can define a probability q( R) of a nucleotide at the origin being base paired with a nucleotide a vector R away. Then, vs is defined as vs = d R q( R) and rs is the value of | R| for which q( R) is non-negligible.