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Gibbs/MCMC Sampling for Multiple RNA Interaction with Sub-optimal Solutions

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Algorithms for Computational Biology (AlCoB 2016)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 9702))

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Abstract

The interaction of two RNA molecules involves a complex interplay between folding and binding that warranted the development of RNA-RNA interaction algorithms. However, these algorithms do not handle more than two RNAs. We note our recent successful formulation for the multiple (more than two) RNA interaction problem based on a combinatorial optimization called Pegs and Rubber Bands. Even then, however, the optimal solution obtained does not necessarily correspond to the actual biological structure. Moreover, a structure produced by interacting RNAs may not be unique to start with. Multiple solutions (thus sub-optimal ones) are needed. Here, a sampling approach that extends our previous formulation for multiple RNA interaction is developed. By clustering the sampled solutions, we are able to reveal representatives that correspond to realistic structures. Specifically, our results on the U2-U6 complex and its introns in the spliceosome of yeast, and the CopA-CopT complex in E. Coli are consistent with published biological structures.

S. Mneimneh—Supported by a Research Starter Award in Informatics from the PhRMA Foundation. Partially supported by CoSSMO CUNY.

S.A. Ahmed—Supported by a PSC CUNY Award 68671-00 46.

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Notes

  1. 1.

    We use “first time” because many solutions can represent the same candidate; for instance, a window can split in different ways, but we still refer to it as a window split.

References

  1. Ahmed, S.A., Mneimneh, S.: Multiple RNA interaction with sub-optimal solutions. In: Basu, M., Pan, Y., Wang, J. (eds.) ISBRA 2014. LNCS, vol. 8492, pp. 149–162. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  2. Ahmed, S.A., Mneimneh, S., Greenbaum, N.L.: A combinatorial approach for multiple RNA interaction: formulations, approximations, and heuristics. In: Du, D.-Z., Zhang, G. (eds.) COCOON 2013. LNCS, vol. 7936, pp. 421–433. Springer, Heidelberg (2013)

    Chapter  MATH  Google Scholar 

  3. Alkan, C., Karakoc, E., Nadeau, J.H., Sahinalp, S.C., Zhang, K.: RNA-RNA interaction prediction and antisense RNA target search. J. Comput. Biol. 13(2), 267–282 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Andronescu, M., Zhang, Z.C., Condon, A.: Secondary structure prediction of interacting RNA molecules. J. Mol. Biol. 345(5), 987–1001 (2005)

    Article  Google Scholar 

  5. Cao, S., Chen, S.J.: Free energy landscapes of RNA/RNA complexes: with applications to snRNA complexes in spliceosomes. J. Mol. Biol. 357(1), 292–312 (2006)

    Article  Google Scholar 

  6. Chen, H.L., Condon, A., Jabbari, H.: An \(o(n^5)\) algorithm for MFE prediction of kissing hairpins and 4-chains in nucleic acids. J. Comput. Biol. 16(6), 803–815 (2009)

    Article  MathSciNet  Google Scholar 

  7. Chitsaz, H., Backofen, R., Sahinalp, S.C.: biRNA: fast RNA-RNA binding sites prediction. In: Salzberg, S.L., Warnow, T. (eds.) WABI 2009. LNCS, vol. 5724, pp. 25–36. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  8. Chitsaz, H., Salari, R., Sahinalp, S.C., Backofen, R.: A partition function algorithm for interacting nucleic acid strands. Bioinformatics 25(12), i365–i373 (2009)

    Article  Google Scholar 

  9. Ding, Y., Lawrence, C.E.: A statistical sampling algorithm for RNA secondary structure prediction. Nucleic Acids Res. 31(24), 7280–7301 (2003)

    Article  Google Scholar 

  10. Dirks, R.M., Bois, J.S., Schaeffer, J.M., Winfree, E., Pierce, N.A.: Thermodynamic analysis of interacting nucleic acid strands. SIAM Rev. 49(1), 65–88 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  11. Durbin, R., Eddy, S.R., Krogh, A., Mitchison, G.: Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids. Cambridge University Press, Cambridge (1998). Chap. 11

    Book  MATH  Google Scholar 

  12. Gallager, R.G.: Discrete Stochastic Processes, vol. 321. Springer Science & Business Media, Newyork (2012). Chap. 4

    MATH  Google Scholar 

  13. Geman, S., Geman, D.: Stochastic relaxation, gibbs distributions, and the bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. PAMI 6(6), 721–741 (1984)

    Article  MATH  Google Scholar 

  14. Hastings, W.K.: Monte carlo sampling methods using markov chains and their applications. Biometrika 57(1), 97–109 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  15. Huang, F.W., Qin, J., Reidys, C.M., Stadler, P.F.: Partition function and base pairing probabilities for RNA-RNA interaction prediction. Bioinformatics 25(20), 2646–2654 (2009)

    Article  Google Scholar 

  16. Jaccard, P.: Etude comparative de la distribution florale dans une portion des Alpes et du Jura. Impr. Corbaz (1901)

    Google Scholar 

  17. Kolb, F.A., Engdahl, H.M., Slagter-Jäger, J.G., Ehresmann, B., Ehresmann, C., Westhof, E., Wagner, E.G.H., Romby, P.: Progression of a loop-loop complex to a four-way junction is crucial for the activity of a regulatory antisense RNA. EMBO J. 19(21), 5905–5915 (2000)

    Article  Google Scholar 

  18. Kolb, F.A., Malmgren, C., Westhof, E., Ehresmann, C., Ehresmann, B., Wagner, E., Romby, P.: An unusual structure formed by antisense-target RNA binding involves an extended kissing complex with a four-way junction and a side-by-side helical alignment. RNA 6(3), 311–324 (2000)

    Article  Google Scholar 

  19. Li, A.X., Marz, M., Qin, J., Reidys, C.M.: RNA-RNA interaction prediction based on multiple sequence alignments. Bioinformatics 27(4), 456–463 (2011)

    Article  Google Scholar 

  20. Liu, J.S.: The collapsed gibbs sampler in bayesian computations with applications to a gene regulation problem. J. Am. Stat. Assoc. 89(427), 958–966 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  21. McCaskill, J.S.: The equilibrium partition function and base pair binding probabilities for RNA secondary structure. Biopolymers 29(6–7), 1105–1119 (1990)

    Article  Google Scholar 

  22. Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: Equation of state calculations by fast computing machines. J. Chem. Phys. 21(6), 1087–1092 (1953)

    Article  MATH  Google Scholar 

  23. Metzler, D., Nebel, M.E.: Predicting RNA secondary structures with pseudoknots by MCMC sampling. J. Math. Biol. 56(1–2), 161–181 (2008)

    MathSciNet  MATH  Google Scholar 

  24. Meyer, I.M.: Predicting novel RNA-RNA interactions. Curr. Opin. Struct. Biol. 18(3), 387–393 (2008)

    Article  Google Scholar 

  25. Mneimneh, S.: On the approximation of optimal structures for RNA-RNA interaction. IEEE/ACM Trans. Comput. Biol. Bioinf. (TCBB) 6(4), 682–688 (2009)

    Article  MathSciNet  Google Scholar 

  26. Mneimneh, S., Ahmed, S.A.: Multiple RNA interaction: beyond two. To appear in IEEE Trans. Nanobiosci. (2015)

    Google Scholar 

  27. Mneimneh, S., Ahmed, S.A.: A sampling approach for multiple RNA interaction: finding sub-optimal solutions fast. In: BIOINFORMATICS 2015 - Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms, Rome, Italy, 21–23 February 2015

    Google Scholar 

  28. Mneimneh, S., Ahmed, S.A., Greenbaum, N.L.: Multiple RNA interaction - formulations, approximations, and heuristics. In: BIOINFORMATICS 2013 - Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms, Barcelona, Spain, 11–14 February 2013, pp. 242–249 (2013)

    Google Scholar 

  29. Mückstein, U., Tafer, H., Hackermüller, J., Bernhart, S.H., Stadler, P.F., Hofacker, I.L.: Thermodynamics of RNA-RNA binding. Bioinformatics 22(10), 1177–1182 (2006)

    Article  Google Scholar 

  30. Newby, M.I., Greenbaum, N.L.: A conserved pseudouridine modification in eukaryotic U2 snRNA induces a change in branch-site architecture. RNA 7(6), 833–845 (2001)

    Article  Google Scholar 

  31. Pervouchine, D.D.: IRIS: intermolecular RNA interaction search. Genome Inform. Ser. 15(2), 92 (2004)

    MathSciNet  Google Scholar 

  32. Salari, R., Backofen, R., Sahinalp, S.C.: Fast prediction of RNA-RNA interaction. Algorithms Mol. Biol. 5(5) (2010)

    Google Scholar 

  33. Sashital, D.G., Cornilescu, G., Butcher, S.E.: U2–U6 RNA folding reveals a group II intron-like domain and a four-helix junction. Nat. Struct. Mol. Biol. 11(12), 1237–1242 (2004)

    Article  Google Scholar 

  34. Sun, J.S., Manley, J.L.: A novel U2–U6 snRNA structure is necessary for mammalian mRNA splicing. Genes Dev. 9(7), 843–854 (1995)

    Article  Google Scholar 

  35. Tong, W., Goebel, R., Liu, T., Lin, G.: Approximation algorithms for the maximum multiple RNA interaction problem. In: Widmayer, P., Xu, Y., Zhu, B. (eds.) COCOA 2013. LNCS, vol. 8287, pp. 49–59. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  36. Tong, W., Goebel, R., Liu, T., Lin, G.: Approximating the maximum multiple RNA interaction problem. Theoret. Comput. Sci. 556, 63–70 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  37. Wei, D., Alpert, L.V., Lawrence, C.E.: Rnag: a new gibbs sampler for predicting RNA secondary structure for unaligned sequences. Bioinformatics 27(18), 2486–2493 (2011)

    Article  Google Scholar 

  38. Zhao, C., Bachu, R., Popović, M., Devany, M., Brenowitz, M., Schlatterer, J.C., Greenbaum, N.L.: Conformational heterogeneity of the protein-free human spliceosomal U2–U6 snRNA complex. RNA 19(4), 561–573 (2013)

    Article  Google Scholar 

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Authors and Affiliations

  1. Hunter College and The Graduate Center City University of New York, New York, NY, USA

    Saad Mneimneh & Syed Ali Ahmed

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  1. Saad Mneimneh
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Correspondence to Saad Mneimneh .

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Editors and Affiliations

  1. CETA-Ciemat, Trujillo, Spain

    María Botón-Fernández

  2. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  3. University of Extremadura, Cáceres, Spain

    Sergio Santander-Jiménez

  4. University of Extremadura, Cáceres, Spain

    Miguel A. Vega-Rodríguez

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Mneimneh, S., Ahmed, S.A. (2016). Gibbs/MCMC Sampling for Multiple RNA Interaction with Sub-optimal Solutions. In: Botón-Fernández, M., Martín-Vide, C., Santander-Jiménez, S., Vega-Rodríguez, M.A. (eds) Algorithms for Computational Biology. AlCoB 2016. Lecture Notes in Computer Science(), vol 9702. Springer, Cham. https://doi.org/10.1007/978-3-319-38827-4_7

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  • DOI: https://doi.org/10.1007/978-3-319-38827-4_7

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