Linear Time Algorithm for Parsing RNA Secondary Structure

Accurate prediction of pseudoknotted RNA secondary structure is an important computational challenge. Typical prediction algorithms aim to find a structure with minimum free energy according to some thermodynamic (“sum of loop energies”) model that is implicit in the recurrences of the algorithm. However, a clear definition of what exactly are the loops and stems in pseudoknotted structures, and their associated energies, has been lacking. We present a comprehensive classification of loops in pseudoknotted RNA secondary structures. Building on an algorithm of Bader et al. [2] we obtain a linear time algorithm for parsing a secondary structures into its component loops. We also give a linear time algorithm to calculate the free energy of a pseudoknotted secondary structure. This is useful for heuristic prediction algorithms which are widely used since (pseudoknotted) RNA secondary structure prediction is NP-hard. Finally, we give a linear time algorithm to test whether a secondary structure is in the class handled by Akutsu’s algorithm [1]. Using our tests, we analyze the generality of Akutsu’s algorithm for real biological structures.