Influence of Pruning Devices on the Solution of Molecular Distance Geometry Problems

  • Antonio Mucherino
  • Carlile Lavor
  • Therese Malliavin
  • Leo Liberti
  • Michael Nilges
  • Nelson Maculan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6630)


The Molecular Distance Geometry Problem (MDGP) is the problem of finding the conformation of a molecule from inter-atomic distances. In some recent work, we proposed the interval Branch & Prune (iBP) algorithm for solving instances of the MDGP related to protein backbones. This algorithm is based on an artificial ordering given to the atoms of the protein backbones which allows the discretization of the problem, and hence the applicability of the iBP algorithm. This algorithm explores a discrete search domain having the structure of a tree and prunes its infeasible branches by employing suitable pruning devices. In this work, we use information derived from Nuclear Magnetic Resonance (NMR) to conceive and add new pruning devices to the iBP algorithm, and we study their influence on the performances of the algorithm.


Nuclear Magnetic Resonance Torsion Angle Nuclear Magnetic Resonance Data Protein Backbone Nuclear Magnetic Resonance Experiment 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Berg, J.M., Tymoczko, J.L., Stryer, L.: Biochemistry, 6th edn. W.H. Freeman publications, New York (2006)Google Scholar
  2. 2.
    Berman, H.M., Westbrook, J., Feng, Z., Gilliland, G., Bhat, T.N., Weissig, H., Shindyalov, I.N., Bourne, P.E.: The protein data bank. Nucleic Acid Research 28, 235–242 (2000)CrossRefGoogle Scholar
  3. 3.
    Lavor, C., Liberti, L., Maculan, N.: The discretizable molecular distance geometry problem. Technical Report q-bio/0608012, arXiv (2006)Google Scholar
  4. 4.
    Lavor, C., Liberti, L., Maculan, N.: Molecular distance geometry problem. In: Floudas, C., Pardalos, P. (eds.) Encyclopedia of Optimization, 2nd edn., pp. 2305–2311. Springer, New York (2009)Google Scholar
  5. 5.
    Lavor, C., Liberti, L., Mucherino, A.: On the solution of molecular distance geometry problems with interval data. In: IEEE Conference Proceedings, International Workshop on Computational Proteomics, International Conference on Bioinformatics & Biomedicine (BIBM 2010), Hong Kong, pp. 77–82 (2010)Google Scholar
  6. 6.
    Lavor, C., Liberti, L., Mucherino, A.: The iBP algorithm for the discretizable molecular distance geometry problem with interval data (submitted) (Available on Optimization Online)Google Scholar
  7. 7.
    Lavor, C., Mucherino, A., Liberti, L., Maculan, N.: On the computation of protein backbones by using artificial backbones of hydrogens. To appear in Journal of Global Optimization (2011); Available online from July 24, 2010Google Scholar
  8. 8.
    Lavor, C., Mucherino, A., Liberti, L., Maculan, N.: Discrete approaches for solving molecular distance geometry problems using NMR data. International Journal of Computational Biosciences 1(1), 88–94 (2010)Google Scholar
  9. 9.
    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)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    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 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Mielke, S.P., Krishnan, V.V.: An evaluation of chemical shift index-based secondary structure determination in proteins: influence of random coil chemical shifts. Journal of Biomolecular NMR 30(2), 143–196 (2004)CrossRefGoogle Scholar
  12. 12.
    Mucherino, A., Lavor, C.: The branch and prune algorithm for the molecular distance geometry problem with inexact distances. In: Proceedings of the International Conference on Computational Biology, vol. 58, pp. 349–353. World Academy of Science, Engineering and Technology (2009)Google Scholar
  13. 13.
    Mucherino, A., Lavor, C., Liberti, L.: The Discretizable Distance Geometry Problem (submitted)Google Scholar
  14. 14.
    Mucherino, A., Liberti, L., Lavor, C., Maculan, N.: Comparisons between an exact and a metaheuristic algorithm for the molecular distance geometry problem. In: Rothlauf, F. (ed.) Proceedings of the Genetic and Evolutionary Computation Conference, Montreal, pp. 333–340. ACM, New York (2009)Google Scholar
  15. 15.
    Nilges, M., Gronenborn, A.M., Brunger, A.T., Clore, G.M.: Determination of three-dimensional structures of proteins by simulated annealing with interproton distance restraints. application to crambin, potato carboxypeptidase inhibitor and barley serine proteinase inhibitor 2. Protein Engineering 2, 27–38 (1988)CrossRefGoogle Scholar
  16. 16.
    Saxe, J.B.: 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
  17. 17.
    Shen, Y., Delaglio, F., Cornilescu, G., Bax, A.: TALOS+: a hybrid method for predicting protein backbone torsion angles from NMR chemical shifts. Journal of Biomolecular NMR 44(4), 213–236 (2009)CrossRefGoogle Scholar
  18. 18.
    Wishart, D.S., Sykes, B.D., Richards, F.M.: The chemical shift index: a fast and simple method for the assignment of protein secondary structure through NMR spectroscopy. Biochemistry 31(6), 1647–1698 (1992)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Antonio Mucherino
    • 1
  • Carlile Lavor
    • 2
  • Therese Malliavin
    • 3
  • Leo Liberti
    • 4
  • Michael Nilges
    • 3
  • Nelson Maculan
    • 5
  1. 1.CERFACSToulouseFrance
  2. 2.IMECCUNICAMPCampinasBrazil
  3. 3.Institut PasteurParisFrance
  4. 4.LIXÉcole PolytechniquePalaiseauFrance
  5. 5.COPPEFederal University of Rio de JaneiroRio de JaneiroBrazil

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