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A Pseudo de Bruijn Graph Representation for Discretization Orders for Distance Geometry

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Bioinformatics and Biomedical Engineering (IWBBIO 2015)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 9043))

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Abstract

Instances of the distance geometry can be represented by a simple weighted undirected graph G. Vertex orders on such graphs are discretization orders if they allow for the discretization of the K-dimensional search space of the distance geometry. A pseudo de Bruijn graph B associated to G is proposed in this paper, where vertices correspond to (K + 1)-cliques of G, and there is an arc from one vertex to another if, and only if, they admit an overlap, consisting of K vertices of G. This pseudo de Bruijn graph B can be exploited for constructing discretization orders for G for which the consecutivity assumption is satisfied. A new atomic order for protein backbones is presented, which is optimal in terms of length.

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References

  1. Almeida, F.C.L., Moraes, A.H., Gomes-Neto, F.: An Overview on Protein Structure Determination by NMR. Historical and Future Perspectives of the Use of Distance Geometry Methods. In: [19], pp. 377–412 (2013)

    Google Scholar 

  2. de Bruijn, N.G.: A Combinatorial Problem, Koninklijke Nederlandse Akademie v. Wetenschappen 49, 758–764 (1946)

    Google Scholar 

  3. Canutescu, A.A., Shelenkov, A.A., Dunbrack Jr., R.L.: A Graph-Theory Algorithm for Rapid Protein Side-Chain Prediction. Protein Science 12, 2001–2014 (2003)

    Google Scholar 

  4. Cassioli, A., Günlük, O., Lavor, C., Liberti, L.: Discretization Vertex Orders in Distance Geometry. To appear in Discrete Applied Mathematics (2015)

    Google Scholar 

  5. Chikhi, R., Rizk, G.: Space-Efficient and Exact de Bruijn Graph Representation based on a Bloom Filter. Algorithms for Molecular Biology 8(22), 9 (2013)

    Google Scholar 

  6. Compeau, P.E.C., Pevzner, P.A., Tesler, G.: How to Apply de Bruijn Graphs to Genome Assembly. Nature Biotechnology 29, 987–991 (2011)

    Google Scholar 

  7. Costa, V., Mucherino, A., Lavor, C., Cassioli, A., Carvalho, L.M., Maculan, N.: Discretization Orders for Protein Side Chains. Journal of Global Optimization 60(2), 333–349 (2014)

    Google Scholar 

  8. Drezen, E., Rizk, G., Chikhi, R., Deltel, C., Lemaitre, C., Peterlongo, P., Lavenier, D.: GATB: Genome Assembly & Analysis Tool Box. To appear in Bioinformatics. Oxford Press (2014)

    Google Scholar 

  9. Ellis, T., Adie, T., Baldwin, G.S.: DNA Assembly for Synthetic Biology: from Parts to Pathways and Beyond. Integrative Biology 3, 109–118 (2011)

    Article  Google Scholar 

  10. Kim, D.-S., Ryu, J.: Side-chain Prediction and Computational Protein Design Problems. Biodesign 2(1), 26–38 (2014)

    MathSciNet  Google Scholar 

  11. Lavor, C., Lee, J., Lee-St. John, A., Liberti, L., Mucherino, A., Sviridenko, M.: Discretization Orders for Distance Geometry Problems. Optimization Letters 6(4), 783–796 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  12. Lavor, C., Liberti, L., Maculan, N., Mucherino, A.: The Discretizable Molecular Distance Geometry Problem. Computational Optimization and Applications 52, 115–146 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  13. Lavor, C., Liberti, L., Mucherino, A.: The interval,Branch-and-Prune Algorithm for the Discretizable Molecular Distance Geometry Problem with Inexact Distances. Journal of Global Optimization 56(3), 855–871 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  14. Liberti, L., Lavor, C., Maculan, N.: A Branch-and-Prune Algorithm for the Molecular Distance Geometry Problem. International Transactions in Operational Research 15, 1–17 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  15. Liberti, L., Lavor, C., Maculan, N., Mucherino, A.: Euclidean Distance Geometry and Applications. SIAM Review 56(1), 3–69 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  16. Liberti, L., Lavor, C., Mucherino, A., Maculan, N.: Molecular Distance Geometry Methods: from Continuous to Discrete. International Transactions in Operational Research 18(1), 33–51 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  17. Malliavin, T.E., Mucherino, A., Nilges, M.: Distance Geometry in Structural Biology: New Perspectives. In: [19], pp. 329–350 (2013)

    Google Scholar 

  18. Mucherino, A.: On the Identification of Discretization Orders for Distance Geometry with Intervals. In: Nielsen, F., Barbaresco, F. (eds.) GSI 2013. LNCS, vol. 8085, pp. 231–238. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  19. Mucherino, A., Lavor, C., Liberti, L., Maculan, N. (eds.): Distance Geometry: Theory, Methods and Applications, 410 pages. Springer (2013)

    Google Scholar 

  20. Mucherino, A., Lavor, C., Malliavin, T., Liberti, L., Nilges, M., Maculan, N.: Influence of Pruning Devices on the Solution of Molecular Distance Geometry Problems. In: Pardalos, P.M., Rebennack, S. (eds.) SEA 2011. LNCS, vol. 6630, pp. 206–217. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  21. Saxe, J.: Embeddability of Weighted Graphs in k-Space is Strongly NP-hard. In: Proceedings of 17th Allerton Conference in Communications, Control and Computing, pp. 480–489 (1979)

    Google Scholar 

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Author information

Authors and Affiliations

  1. IRISA, University of Rennes 1, Rennes, France

    Antonio Mucherino

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  1. Antonio Mucherino
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Editors and Affiliations

  1. Dpto. de Arquitectura y Tecnología de Computadores (ATC)., E.T.S. de Ingenierías en Informática y Telecomunicación. CITIC-UGR, Universidad de Granada, c/ Periodista Daniel Saucedo Aranda s/n, 18071, Granada, Spain

    Francisco Ortuño

  2. E.T.S. Ingenierías Informática y de Telecomunicación , , Dpto. Arquitectura y Tecnología de Computadores, CITIC-UGR, Universidad de Granada, C Periodista Rafael Gómez Montero, 18071, Granada, Spain

    Ignacio Rojas

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Mucherino, A. (2015). A Pseudo de Bruijn Graph Representation for Discretization Orders for Distance Geometry. In: Ortuño, F., Rojas, I. (eds) Bioinformatics and Biomedical Engineering. IWBBIO 2015. Lecture Notes in Computer Science(), vol 9043. Springer, Cham. https://doi.org/10.1007/978-3-319-16483-0_50

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  • DOI: https://doi.org/10.1007/978-3-319-16483-0_50

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-16482-3

  • Online ISBN: 978-3-319-16483-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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