RNA Secondary Structure Prediction Using Hierarchical Folding

Algorithms for prediction of RNA secondary structure— the set of base pairsthat form when an RNA molecule folds— are valuable to biologists who aim tounderstand RNA structure and function. Improving the accuracy and efficiencyof prediction methods is an ongoing challenge, particularly for pseudoknottedsecondary structures, in which base pairs overlap. This challenge is biologicallyimportant, since pseudoknotted structures play essential roles in functions ofmany RNA molecules, such as splicing and ribosomal frameshifting. State-of-the-art methods, which are based on free energy minimization, have high run-time complexity (typically Θ(n) or worse), and can handle (minimize over)only limited types of pseudoknotted structures.We analyze a new approach for prediction of pseudoknotted structures, mo-tivated by the hypothesis that RNA structures fold hierarchically, with pseudo-knot free (non-overlapping) base pairs forming first, and pseudoknots forminglater so as to minimize energy relative to the folded pseudoknot free structure.Our HFold algorithm, based on work of S. Zhao, uses two-phase energy min-imization to predict hierarchically-formed secondary structures in O(n) time,matching the complexity of the best algorithms for pseudoknot free secondarystructure prediction via energy minimization. Our algorithm can handle a widerange of biological structures, including kissing hairpins and nested kissing hair-pins, which have previously required Θ(n) time.We also report on the experimental evaluations of HFold and present thor-ough analyses of the results. We show that if the input structure to the algo-rithm is correct, running the algorithm results in 16% accuracy improvementon average over the accuracy of the true pseudoknot free structures. However ifthe input structure is not correct, the accuracy improvement is not significant.If the first 10 suboptimal foldings are given as input to our algorithm insteadof just the minimum free energy structure (MFE), the prediction accuracy im-proves significantly over the accuracy of the MFE structures. This improvementis even more when the number of suboptimal foldings as input to our algorithmincreases. The comparison of the energy of the structures predicted by HFoldon the true pseudoknot free structures with the energy of the true structurescalculated using a different method with the same energy model shows that theenergy model may be the cause for the cases for which HFold predicts struc-tures far from the true structures. Our experimental result provides some waysin which the hierarchical folding hypothesis might need to be refined.