A Polymer Physics Framework for the Entropy of Arbitrary Pseudoknots

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 arising from two main factors: (1) no physical model exists to estimate the loop entropies of complex intramolecular pseudoknots; and (2) their NP-complete enumeration has impeded their study. Here, we address both challenges. First, we develop a polymer physics model which can address arbitrarily complex pseudoknots using only two parameters corresponding to concrete physical quantities – over an order of magnitude fewer than the sparsest state-of-the-art phenomenological methods. Second, by coupling this model to exhaustive enumeration of the set of possible structures, we compute the entire free energy landscape of secondary structures resulting from a primary RNA sequence. We demonstrate that for RNA structures of _ 80 nucleotides, with minimal heuristics, the complete enumeration of possible secondary structures can be accomplished quickly despite the NP-complete nature of the problem. We further show that despite our loop entropy model’s parametric sparsity, it performs better than or on par with previously published methods in predicting both pseudoknotted and non-pseudoknotted structures on a benchmark dataset of RNA structures of _ 80 nucleotides. We suggest ways in which the accuracy of the model can be further improved.