RNA Folding Including Pseudoknots: A New Parameterized Algorithm and Improved Upper Bound

Abstract

Predicting the secondary structure of an RNA sequence is an important problem in structural bioinformatics. The general RNA folding problem, where the sequence to be folded may contain pseudoknots, is computationally intractable when no prior knowledge on the pseudoknot structures the sequence contains is available. In this paper, we consider stable stems in an RNA sequence and provide a new characterization for its stem graph, a graph theoretic model that has been used to describe the overlapping relationships for stable stems. Based on this characterization, we identify a new structure parameter for a stem graph. We call this structure parameter crossing width. We show that given a sequence with crossing width c for its stem graph, the general RNA folding problem can be solved in time O(2^c k ³ n ²), where n is the length of the sequence, k is the maximum length of stable stems. Moreover, this characterization leads to an $O(2^{(1+2k^2)n}n^{2}k^{3})$ time algorithm for the general RNA folding problem where the lengths of stems in the sequence are at most k, this result improves the upper bound of the problem to 2^O(n) n ² when the maximum stem length is bounded by a constant.