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Fast Algorithm for the Minimum Chebyshev Distance in RNA Secondary Structure

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Broadband Communications, Networks, and Systems (Broadnets 2019)

Abstract

Minimum Chebyshev distance computation between base-pair and structures cost most time while comparing RNA secondary structures. We present a fast algorithm for speeding up the minimum Chebyshev distance computation. Based on the properties of RNA dot plots and Chebyshev distance, this algorithm uses binary search to reduce the size of base pairs and compute Chebyshev distances rapidly. Compared with O(n) time complexity of the original algorithm, the new one takes nearly [O(log2n), O(1)] time.

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References

  1. National Natural Science Foundation of China, Chinese Academy of Sciences. Major Scientific Issues in the Study of RNA in China’s Discipline Development Strategy. Science Press, China (2017)

    Google Scholar 

  2. Krieger, E., Sander, B., Vriend, G.: Homology modeling. In: Structural Bioinformatics, vol. 44 (2003)

    Google Scholar 

  3. Thiel, B.C., Flamm, C., Hofacker, I.L.: RNA structure prediction: from 2D to 3D. Emerg. Top. Life Sci. 1(3), 275–285 (2017)

    Article  Google Scholar 

  4. Galvanek, R., Hoksza, D.: Template-based prediction of RNA tertiary structure using its predicted secondary structure. In: 2017 IEEE International Conference on Bioinformatics and Biomedicine (BIBM), pp. 2238–2240. IEEE (2017)

    Google Scholar 

  5. Zhao, Y., Huang, Y., Gong, Z., Wang, Y., Man, J., Xiao, Y.: Automated and fast building of three-dimensional RNA structures. Sci. Rep. 2, 1–6 (2012)

    Article  Google Scholar 

  6. Waterman, M.S., Smith, T.F.: RNA secondary structure: a complete mathematical analysis. Math. Biosci. 42(3–4), 257–266 (1978)

    Article  Google Scholar 

  7. Nussinov, R., Jacobson, A.B.: Fast algorithm for predicting the secondary structure of single-stranded RNA. Proc. Natl. Acad. Sci. U.S.A. 77(11), 6309–6313 (1980)

    Article  Google Scholar 

  8. Waterman, M.S., Smith, T.F.: Rapid dynamic programming algorithms for RNA secondary structure. Adv. Appl. Math. 7(4), 455–464 (1986)

    Article  MathSciNet  Google Scholar 

  9. Akutsu, T.: Dynamic programming algorithms for RNA secondary structure prediction with pseudoknots. Discret. Appl. Math. 104(1–3), 45–62 (2000)

    Article  MathSciNet  Google Scholar 

  10. García, R.: Prediction of RNA pseudoknotted secondary structure using stochastic context free grammars (SCFG). CLEI Electron. J. 9(2) (2006)

    Google Scholar 

  11. Sakakibara, Y., Brown, M., Hughey, R., Mian, I.S., Sjölander, K., Underwood, R.C., Haussler, D.: Stochastic context-free grammars for tRNA modeling. Nucleic Acids Res. 22(23), 5112–5120 (1994)

    Article  Google Scholar 

  12. Anderson, J.W.J., Tataru, P., Staines, J., Hein, J., Lyngsø, R.: Evolving stochastic context-free grammars for RNA secondary structure prediction. BMC Bioinform. 13(1), 78 (2012)

    Article  Google Scholar 

  13. Pal, S.K., Ray, S.S., Ganivada, A.: RNA secondary structure prediction: soft computing perspective. Granular Neural Networks, Pattern Recognition and Bioinformatics. SCI, vol. 712, pp. 195–222. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57115-7_7

    Chapter  Google Scholar 

  14. Batenburg, F.H.V., Gultyaev, A.P., Pleij, C.W.: An APL-programmed genetic algorithm for the prediction of RNA secondary structure. J. Theor. Biol. 174(3), 269–280 (1995)

    Article  Google Scholar 

  15. Shapiro, B.A., Bengali, D., Kasprzak, W., Wu, J.C.: RNA folding pathway functional intermediates: their prediction and analysis. J. Mol. Biol. 312, 27–44 (2001)

    Article  Google Scholar 

  16. Wiese, K.C., Deschenes, A., Glen, E.: Permutation based RNA secondary structure prediction via a genetic algorithm. In: Proceedings of the 2003 Congress on Evolutionary Computation, pp. 335–342 (2003)

    Google Scholar 

  17. Wiese, K.C., Deschênes, A.A., Hendriks, A.G.: RnaPredict - an evolutionary algorithm for RNA secondary structure prediction. IEEE/ACM Trans. Comput. Biol. Bioinf. 5(1), 25–41 (2008)

    Article  Google Scholar 

  18. Schmitz, M., Steger, G.: Description of RNA folding by simulated annealing. J. Mol. Biol. 255(1), 254–266 (1996)

    Article  Google Scholar 

  19. Tsang, H.H., Wiese, K.C.: SARNA-predict: accuracy improvement of RNA secondary structure prediction using permutation based simulated annealing. IEEE/ACM Trans. Comput. Biol. Bioinf. 7(4), 727–740 (2010)

    Article  Google Scholar 

  20. Liu, Q., Ye, X., Zhang, Y.: A Hopfield neural network based algorithm for RNA secondary structure prediction. In: Proceedings of the 1st International Conference on Multi-symposiums on Computer and Computational Sciences, pp. 1–7 (2006)

    Google Scholar 

  21. Haynes, T., Knisley, D., Knisley, J.: Using a neural network to identify secondary RNA structures quantified by graphical invariants. MATCH Commun. Math. Comput. Chem. 60, 277–290 (2008)

    MathSciNet  MATH  Google Scholar 

  22. Zou, Q., Zhao, T., Liu, Y., Guo, M.: Predicting RNA secondary structure based on the class information and Hopfield network. Comput. Biol. Med. 39(3), 206–214 (2009)

    Article  Google Scholar 

  23. Koessler, D.R., Knisley, D.J., Knisley, J., Haynes, T.: A predictive model for secondary RNA structure using graph theory and a neural network. BMC Bioinform. 11, S6–S21 (2010)

    Article  Google Scholar 

  24. Song, D., Deng, Z.: A fuzzy dynamic programming approach to predict RNA secondary structure. In: Bücher, P., Moret, B.M.E. (eds.) WABI 2006. LNCS, vol. 4175, pp. 242–251. Springer, Heidelberg (2006). https://doi.org/10.1007/11851561_23

    Chapter  Google Scholar 

  25. Oluoch, I.K., Akalin, A., Vural, Y., Canbay, Y.: A review on RNA secondary structure prediction algorithms. In: 2018 International Congress on Big Data, Deep Learning and Fighting Cyber Terrorism (IBIGDELFT), Ankara, Turkey, pp. 18–23. IEEE (2018)

    Google Scholar 

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

    Article  Google Scholar 

  27. Markham, N.R., Zuker, M.: UNAFold: software for nucleic acid folding and hybridization. In: Keith, J.M. (ed.) Bioinformatics: Structure, Functions and Applications, vol. 453, pp. 3–31. Humana Press, Totowa (2008)

    Chapter  Google Scholar 

  28. Ding, Y., Chan, C.Y., Lawrence, C.E.: Clustering of RNA secondary structures with application to messenger RNAs. J. Mol. Biol. 359, 554–571 (2006)

    Article  Google Scholar 

  29. Agius, P., Bennett, K.P., Zuker, M.: Comparing RNA secondary structures using a relaxed base-pair score. RNA 16(5), 865–878 (2010)

    Article  Google Scholar 

  30. Schirmer, S., Ponty, Y., Giegerich, R.: Introduction to RNA secondary structure comparison. Methods Mol. Biol. 1097(1097), 247–273 (2014)

    Article  Google Scholar 

  31. Lopez, M.A., Reisner, S.: Hausdorff approximation of convex polygons. Comput. Geom. 2(32), 139–158 (2005)

    Article  MathSciNet  Google Scholar 

  32. Moulton, V., Zuker, M., Steel, M., Pointon, R., Penny, D.: Metrics on RNA secondary structures. J. Comput. Biol.: J. Comput. Mol. Cell Biol. 7(1–2), 277–292 (2000)

    Article  Google Scholar 

  33. Chen, Q., Chen, B., Zhang, C.: Interval based similarity for function classification of RNA pseudoknots. In: Chen, Q., Chen, B., Zhang, C. (eds.) Intelligent Strategies for Pathway Mining. LNCS (LNAI), vol. 8335, pp. 175–192. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-04172-8_8

    Chapter  Google Scholar 

  34. Fu, W., Huang, J., Xu, L.: RNA secondary structure representation and conversion algorithms. Comput. Eng. Appl. (14), 43–45, 85 (2004)

    Google Scholar 

  35. Reuter, J.S., Mathews, D.H.: RNAstructure: software for RNA secondary structure prediction and analysis. BMC Bioinform. 11(1), 129 (2010)

    Article  Google Scholar 

  36. Zhang, Y.: Track exploration under Chebyshev distance. Math. Teach. 8, 19–22 (2015)

    Google Scholar 

  37. Tsang, H.H., Jacob, C.: RNADPCompare: an algorithm for comparing RNA secondary structures based on image processing techniques, pp. 1288–1295. IEEE (2011)

    Google Scholar 

  38. Kang, X., Wei, S.: Identifying tampered regions using singular value decomposition in digital image forensics. In: 2008 International Conference on Computer Science and Software Engineering, Wuhan, Hubei, pp. 926–930 (2008)

    Google Scholar 

  39. Chowdhury, A.S., Chatterjee, R., Ghosh, M., Ray, N.: Cell tracking in video microscopy using bipartite graph matching. In: 2010 20th International Conference on pattern Recognition, Istanbul, pp. 2456–2459 (2010)

    Google Scholar 

  40. Demirci, S., Erer, I., Ersoy, O.: Weighted Chebyshev distance classification method for hyperspectral imaging. In: Proceedings of SPIE 9482, Next-Generation Spectroscopic Technologies VIII, p. 948218 (2015)

    Google Scholar 

  41. Ritter, G.X., Urcid-Serrano, G., Schmalz, M.S.: Lattice associative memories that are robust in the presence of noise. In: Proceedings of SPIE 5916, Mathematical Methods in Pattern and Image Analysis, p. 59160Q (2005)

    Google Scholar 

  42. Ritter, G.X., Urcid, G.: Learning in lattice neural networks that employ dendritic computing. In: Kaburlasos, V.G., Ritter, G.X. (eds.) Computational Intelligence Based on Lattice Theory, vol. 67, pp. 25–44. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72687-6_2

    Chapter  Google Scholar 

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Correspondence to Changwu Wang .

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Ke, T., Wang, C., Liu, W., Liu, J. (2019). Fast Algorithm for the Minimum Chebyshev Distance in RNA Secondary Structure. In: Li, Q., Song, S., Li, R., Xu, Y., Xi, W., Gao, H. (eds) Broadband Communications, Networks, and Systems. Broadnets 2019. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 303. Springer, Cham. https://doi.org/10.1007/978-3-030-36442-7_16

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  • DOI: https://doi.org/10.1007/978-3-030-36442-7_16

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