Dynamic programming algorithms for RNA secondary structure prediction with pseudoknots
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We present three heuristic strategies for folding RNA sequences into secondary structures including kissing hairpin motifs. The new idea is to construct a kissing hairpin motif from an overlay of two simple canonical pseudoknots. The difficulty is that the overlay does not satisfy Bellman's Principle of Optimality, and the kissing hairpin cannot simply be built from optimal pseudoknots. Our strategies have time/space complexities ofO(n4)/O(n2),O(n4)/O(n3), and O(n5)/O(n2). All strategies have been implemented in the program pKiss and were evaluated against known structures. Surprisingly, our simplest strategy performs best. As it has the same complexity as the previous algorithm for simple pseudoknots, the overlay idea opens a way to construct a variety of practically useful algorithms for pseudoknots of higher topological complexity within O(n4) time and O(n2) space.