K-partite RNA secondary structures

• Authors: Minghui Jiang;Pedro J. Tejada;Ramoni O. Lasisi;Shanhong Cheng;D. Scott Fechser
• Venue: WABI'09 Proceedings of the 9th international conference on Algorithms in bioinformatics
• Year: 2009

RNA secondary structure prediction is a fundamental problem in structural bioinformatics. The prediction problem is difficult because RNA secondary structures may contain pseudoknots formed by crossing base pairs. We introduce kpartite secondary structures as a simple classification of RNA secondary structures with pseudoknots. An RNA secondary structure is k-partite if it is the union of k pseudoknot-free sub-structures. Most known RNA secondary structures are either bipartite or tripartite. We show that there exists a constant number k such that any secondary structure can be modified into a k-partite secondary structure with approximately the same free energy. This offers a partial explanation of the prevalence of k-partite secondary structures with small k. We give a complete characterization of the computational complexities of recognizing k-partite secondary structures for all k≥2, and show that this recognition problem is essentially the same as the k-colorability problem on circle graphs. We present two simple heuristics, iterated peeling and first-fit packing, for finding k- partite RNA secondary structures. For maximizing the number of base pair stackings, our iterated peeling heuristic achieves a constant approximation ratio of at most k for 2 ≤ k ≤ 5, and at most 6/1-(1-6/k)k ≤ 6/1-e-6 k ≥ 6. Experiment on sequences from PseudoBase shows that our first-fit packing heuristic outperforms the leading method HotKnots in predicting RNA secondary structures with pseudoknots. Source code, data set, and experimental results are available at http://www.cs.usu.edu/~mjiang/rna/kpartite/.