Abstract
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 k-partite 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 \(\frac6{1-(1-6/k)^k} \le \frac6{1-e^{-6}} < 6.01491\) for 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/.
Supported in part by NSF grant DBI-0743670.
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References
Ageev, A.A.: A triangle-free circle graph with chromatic number 5. Discrete Mathematics 152, 295–298 (1996)
Akutsu, T.: Dynamic programming algorithms for RNA secondary structure prediction with pseudoknots. Discrete Applied Mathematics 104, 45–62 (2000)
Aspvall, B., Plass, M.F., Tarjan, R.E.: A linear-time algorithm for testing the truth of certain quantified boolean formulas. Information Processing Letters 8, 121–123 (1979)
van Batenburg, F.H.D., Gultyaev, A.P., Pleij, C.W.A.: An APL-programmed genetic algorithm for the prediction of RNA secondary structure. Journal of Theoretical Biology 174, 269–280 (1995)
van Batenburg, F.H.D., Gultyaev, A.P., Pleij, C.W.A., Ng, J., Oliehoek, J.: Pseudobase: a database with RNA pseudoknots. Nucleic Acids Research 28, 201–204 (2000)
Condon, A., Davy, B., Rastegari, B., Zhao, S., Tarrant, F.: Classifying RNA pseudoknotted structures. Theoretical Computer Science 320, 35–50 (2004)
Cong, J., Hossain, M., Sherwani, N.A.: A provably good multilayer topological planar routing algorithms in IC layout designs. IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems 12, 70–78 (1993)
Dirks, R.M., Pierce, N.A.: A partition function algorithm for nucleic acid secondary structure including pseudoknots. Journal of Computational Chemistry 24, 1664–1677 (2003)
Eppstein, D.: Testing bipartiteness of geometric intersection graphs. In: Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2004), pp. 860–868 (2004)
Garey, M.R., Johnson, D.S., Miller, G.L., Papadimitriou, C.H.: The complexity of coloring circular arcs and chords. SIAM Journal on Algebraic & Discrete Methods 1, 216–227 (1980)
Haslinger, C., Stadler, P.F.: RNA structures with pseudo-knots: graph theoretical, combinatorial, and statistical properties. Bulletin of Mathematical Biology 61, 437–467 (1999)
Hofacker, I.L.: Vienna RNA secondary structure server. Nucleic Acids Research 31, 3429–3431 (2003)
Huang, F.W.D., Peng, W.W.J., Reidys, C.M.: Folding 3-noncrossing RNA pseudoknot structures (2008), http://arxiv.org/abs/0809.4840v1
Ieong, S., Kao, M.-Y., Lam, T.-W., Sung, W.-K., Yiu, S.-M.: Predicting RNA secondary structure with arbitrary pseudoknots by maximizing the number of stacking pairs. Journal of Computational Biology 10, 981–995 (2003)
Jabbari, H., Condon, A., Zhao, S.: Novel and efficient RNA secondary structure prediction using hierarchical folding. Journal of Computational Biology 15, 139–163 (2008)
Jiang, M.: Approximation algorithms for predicting RNA secondary structures with arbitrary pseudoknots. ACM/IEEE Transactions on Computational Biology and Bioinformatics (to appear), http://dx.doi.org/10.1109/TCBB.2008.109
Kleinberg, J., Tardos, E.: Algorithm Design. Addison-Wesley, Reading (2005)
Lyngsø, R.B.: Complexity of pseudoknot prediction in simple models. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 919–931. Springer, Heidelberg (2004)
Lyngsø, R.B., Pedersen, C.N.S.: RNA pseudoknot prediction in energy-based models. Journal of Computational Biology 7, 409–427 (2000)
Nussinov, R., Pieczenik, G., Griggs, J.R., Kleitman, D.J.: Algorithms for loop matching. SIAM Journal on Applied Mathematics 35, 68–82 (1978)
Rastegari, B., Condon, A.: Parsing nucleic acid pseudoknotted secondary structure: algorithm and applications. Journal of Computational Biology 14, 16–32 (2007)
Reeder, J., Giegerich, R.: Design, implementation and evaluation of a practical pseudoknot folding algorithm based on thermodynamics. BMC Bioinformatics 5, 104 (2004)
Ren, J., Rastegari, B., Condon, A., Hoos, H.H.: HotKnots: Heuristic prediction of RNA secondary structures including pseudoknots. RNA 11, 1494–1504 (2005)
Rivas, E., Eddy, S.R.: A dynamic programming algorithm for RNA structure prediction including pseudoknots. Journal of Molecular Biology 285, 2053–2068 (1999)
Rødland, E.A.: Pseudoknots in RNA secondary structures: representation, enumeration, and prevalence. Journal of Computational Biology 13, 1197–1213 (2006)
Ruan, J., Stormo, G.D., Zhang, W.: An iterated loop matching approach to the prediction of RNA secondary structure with pseudoknots. Bioinformatics 20, 58–66 (2004)
Uemura, Y., Hasegawa, A., Kobayashi, S., Yokomori, T.: Tree adjoining grammars for RNA structure prediction. Theoretical Computer Science 210, 277–303 (1999)
Unger, W.: On the k-colouring of circle-graphs. In: Cori, R., Wirsing, M. (eds.) STACS 1988. LNCS, vol. 294, pp. 61–72. Springer, Heidelberg (1988)
Unger, W.: The complexity of colouring circle graphs. In: Finkel, A., Jantzen, M. (eds.) STACS 1992. LNCS, vol. 577, pp. 389–400. Springer, Heidelberg (1992)
Witwer, C., Hofacker, I.L., Stadler, P.F.: Prediction of consensus RNA secondary structures including pseudoknots. IEEE/ACM Transactions on Computational Biology and Bioinformatics 1, 66–77 (2004)
Zuker, M.: Mfold web server for nucleic acid folding and hybridization prediction. Nucleic Acids Research 31, 3406–3415 (2003)
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Jiang, M., Tejada, P.J., Lasisi, R.O., Cheng, S., Fechser, D.S. (2009). K-Partite RNA Secondary Structures. In: Salzberg, S.L., Warnow, T. (eds) Algorithms in Bioinformatics. WABI 2009. Lecture Notes in Computer Science(), vol 5724. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04241-6_14
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DOI: https://doi.org/10.1007/978-3-642-04241-6_14
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