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Improved Approximation Algorithms for Predicting RNA Secondary Structures with Arbitrary Pseudoknots

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Algorithmic Aspects in Information and Management (AAIM 2007)

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Abstract

We study three closely related problems motivated by the prediction of RNA secondary structures with arbitrary pseudoknots: the Maximum Base Pair Stackings problem proposed by Ieong et al. [19] , the Maximum Stacking Base Pairs problem proposed by Lyngsø [22], and the 2-Interval Pattern problem proposed by Vialette [36] . For Maximum Base Pair Stackings and Maximum Stacking Base Pairs, we present improved approximation algorithms that can incorporate covariance information from comparative analysis as explicit input of candidate base pairs. For 2-Interval Pattern, we present improved approximation algorithms on unitary and near-unitary input, and propose a new variant called Length-Weighted Balanced 2-Interval Pattern, which is natural in the nearest-neighbor energy model that emphasizes base pair stacking.

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References

  1. Abrahams, J.P., van den Berg, M., van Batenburg, E., Pleij, C.: Prediction of RNA secondary structure, including pseudoknotting, by computer simulation. Nucleic Acids Research 18(10), 3035–3044 (1990)

    Article  Google Scholar 

  2. Akutsu, T.: Dynamic programming algorithms for RNA secondary structure prediction with pseudoknots. Discrete Applied Mathematics 104(1-3), 45–62 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bafna, V., Narayanan, B., Ravi, R.: Nonoverlapping local alignments (weighted independent sets of axis-parallel rectangles). Discrete Applied Mathematics 71, 41–53 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bar-Yehuda, R., Halldórsson, M.M., Naor, J(S.), Shachnai, H., Shapira, I.: Scheduling split intervals. SIAM Journal on Computing 36(1), 1–15 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. 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(3), 269–280 (1995)

    Article  Google Scholar 

  6. 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(1), 201–204 (2000)

    Article  Google Scholar 

  7. Berman, P.: A d/2 approximation for maximum weight independent set in d-claw free graphs. Nordic Journal of Computing 7, 178–184 (2000)

    MathSciNet  MATH  Google Scholar 

  8. Berman, P., DasGupta, B., Muthukrishnan, S.: Simple approximation algorithm for nonoverlapping local alignments. In: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’02), pp. 677–678 (2002)

    Google Scholar 

  9. Blin, G., Fertin, G., Vialette, S.: New results for the 2-interval pattern problem. In: Sahinalp, S.C., Muthukrishnan, S.M., Dogrusoz, U. (eds.) CPM 2004. LNCS, vol. 3109, pp. 311–322. Springer, Heidelberg (2004)

    Google Scholar 

  10. Cary, R.B., Stormo, G.D.: Graph-theoretic approach to RNA modeling using comparative data. In: Proceedings of the 3rd International Conference on Intelligent Systems for Molecular Biology (ISMB’95), pp. 75–80 (1995)

    Google Scholar 

  11. Chen, E., Yang, L., Yuan, H.: Improved algorithms for largest cardinality 2-interval pattern problem. Journal of Combinatorial Optimization, Special Issue on Bioinformatics (to appear)

    Google Scholar 

  12. Crochemore, M., Hermelin, D., Landau, G.M., Vialette, S.: Approximating the 2-interval pattern problem. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 426–437. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  13. Crochemore, M., Hermelin, D., Landau, G.M., Rawitz, D., Vialette, S.: Approximating the 2-interval pattern problem. Theoretical Computer Science (to appear)

    Google Scholar 

  14. Gultyaev, A.P., van Batenburg, F.H.D., Pleij, C.W.A.: The computer simulation of RNA folding pathways using a genetic algorithm. Journal of Molecular Biology 250(1), 37–51 (1995)

    Article  Google Scholar 

  15. Halldórsson, M.M.: Approximating discrete collections via local improvements. In: Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’95), pp. 160–169 (1995)

    Google Scholar 

  16. Hofacker, I.L.: Vienna RNA secondary structure server. Nucleic Acids Research 31(13), 3429–3431 (2003)

    Article  Google Scholar 

  17. Hofacker, I.L., Fontana, W., Stadler, P.F., Bonhoeffer, S., Tacker, M., Schuster, P.: Fast folding and comparison of RNA secondary structures. Monatshefte für Chemie 125(2), 167–188 (1994)

    Article  Google Scholar 

  18. Hurkens, C.A.J., Schrijver, A.: On the size of systems of sets every t of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems. SIAM Journal on Discrete Mathematics 2(1), 68–72 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  19. 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(6), 981–995 (2003)

    Article  Google Scholar 

  20. Jiang, M.: A 2-approximation for the preceding-and-crossing structured 2-interval pattern problem. Journal of Combinatorial Optimization, Special Issue on Bioinformatics (to appear)

    Google Scholar 

  21. Jiang, M.-h., Mayne, M., Gillespie, J.: Delta: A toolset for the structural analysis of biological sequences on a 3D triangular lattice. In: Măndoiu, I.I., Zelikovsky, A. (eds.) ISBRA 2007. LNCS (LNBI), vol. 4463, pp. 518–529. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  22. 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)

    Google Scholar 

  23. Lyngsø, R.B., Pedersen, C.N.S.: RNA pseudoknot prediction in energy-based models. Journal of Computational Biology 7(3/4), 409–427 (2000)

    Article  Google Scholar 

  24. Lyngsø, R.B., Zuker, M., Pedersen, C.N.S.: Fast evaluation of interval loops in RNA secondary structure prediction. Bioinformatics 15(6), 440–445 (1999)

    Article  Google Scholar 

  25. Mathews, D.H., Sabina, J., Zuker, M., Turner, D.H.: Expanded sequence dependence of thermodynamic parameters improves prediction of RNA secondary structure. Journal of Molecular Biology 288(5), 911–940 (1999)

    Article  Google Scholar 

  26. Micali, S., Vazirani, V.V.: An \(O(\sqrt{|V|} |E|)\) algorithm for finding maximum matching in general graphs. In: Proceedings of the 21st Annual Symposium on Foundations of Computer Science (FOCS’80), pp. 17–27 (1980)

    Google Scholar 

  27. Nussinov, R., Pieczenik, G., Griggs, J.R., Kleitman, D.J.: Algorithms for loop matching. SIAM Journal on Applied Mathematics 35(1), 68–82 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  28. Pace, N.R., Thomas, B.C., Woese, C.R.: Probing RNA structure, function, and history by comparative analysis. In: The RNA World, 2nd edn., pp. 113–141. Cold Spring Harbor Laboratory Press, Cold Spring Harbor (1999)

    Google Scholar 

  29. Rivas, E., Eddy, S.R.: A dynamic programming algorithm for RNA structure prediction including pseudoknots. Journal of Molecular Biology 285, 2053–2068 (1999)

    Article  Google Scholar 

  30. Ruan, J., Stormo, G.D., Zhang, W.: An iterated loop matching approach to the prediction of RNA secondary structure with pseudoknots. Bioinformatics 20(1), 58–66 (2004)

    Article  Google Scholar 

  31. Sankoff, D.: Simultaneous solution of the RNA folding, alignment and protosequence problems. SIAM Journal on Applied Mathematics 45(5), 810–825 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  32. Shapiro, B.A., Wu, J.C.: Predicting RNA H-type pseudoknots with the massively parallel genetic algorithm. Computer Applications in the Biosciences 13(4), 459–471 (1997)

    Google Scholar 

  33. Tabaska, J.E., Cary, R.B., Gabow, H.N., Stormo, G.D.: An RNA folding method capable of identifying pseudoknots and base triples. Bioinformatics 14(8), 691–699 (1998)

    Article  Google Scholar 

  34. Tinoco, I., Borer, P.N., Dengler, B., Levine, M.D., Uhlenbeck, O.C., Crothers, D.M., Gralla, J.: Improved estimation of secondary structure in ribonucleic acids. Nature New Biology 246, 40–42 (1973)

    Google Scholar 

  35. Uemura, Y., Hasegawa, A., Kobayashi, S., Yokomori, T.: Tree adjoining grammars for RNA structure prediction. Theoretical Computer Science 210(2), 277–303 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  36. Vialette, S.: On the computational complexity of 2-interval pattern matching problems. Theoretical Computer Science 312, 223–249 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  37. Zuker, M.: Mfold web server for nucleic acid folding and hybridization prediction. Nucleic Acids Research 31(13), 3406–3415 (2003)

    Article  Google Scholar 

  38. Zuker, M., Sankoff, D.: RNA secondary structures and their prediction. Bulletin of Mathematical Biology 46, 591–621 (1984)

    MATH  Google Scholar 

  39. Zuker, M., Stiegler, P.: Optimal computer folding of large RNA sequences using thermodynamics and auxiliary information. Nucleic Acids Research 9(1), 133–148 (1981)

    Article  Google Scholar 

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Ming-Yang Kao Xiang-Yang Li

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Jiang, M. (2007). Improved Approximation Algorithms for Predicting RNA Secondary Structures with Arbitrary Pseudoknots. In: Kao, MY., Li, XY. (eds) Algorithmic Aspects in Information and Management. AAIM 2007. Lecture Notes in Computer Science, vol 4508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72870-2_38

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  • DOI: https://doi.org/10.1007/978-3-540-72870-2_38

  • Publisher Name: Springer, Berlin, Heidelberg

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