MD-jeep: An Implementation of a Branch and Prune Algorithm for Distance Geometry Problems

  • Antonio Mucherino
  • Leo Liberti
  • Carlile Lavor
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6327)


We present MD-jeep, an implementation of a Branch & Prune (BP) algorithm, which we employ for the solution of distance geometry problems related to molecular conformations. We consider the problem of finding the conformation of a molecule from the distances between some pairs of its atoms, which can be estimated by experimental techniques. We reformulate this problem as a combinatorial optimization problem, and describe a branch and prune solution strategy. We discuss its software implementation, and its complexity in terms of floating-point operations and memory requirements. MD-jeep has been developed in the C programming language. The sources of the presented software are available on the Internet under the GNU General Public License (v.2).


Protein Data Bank Penalty Function Binary Tree Atomic Position Molecular Conformation 
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.
    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 Acids Research 28, 235–242 (2000)CrossRefGoogle Scholar
  2. 2.
    Coope, I.D.: Reliable Computation of the Points of Intersection of n Spheres in n-space. ANZIAM Journal 42, 461–477 (2000)MathSciNetGoogle Scholar
  3. 3.
    Biswas, P., Toh, K.-C., Ye, Y.: A Distributed SDP Approach for Large-Scale Noisy Anchor-Free Graph Realization with Applications to Molecular Conformation. SIAM Journal on Scientific Computing 30, 1251–1277 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Crippen, G.M., Havel, T.F.: Distance Geometry and Molecular Conformation. John Wiley & Sons, New York (1988)zbMATHGoogle Scholar
  5. 5.
    Havel, T.F.: Distance Geometry. In: Grant, D.M., Harris, R.K. (eds.) Encyclopedia of Nuclear Magnetic Resonance, pp. 1701–1710. Wiley, New York (1995)Google Scholar
  6. 6.
    Hodsdon, M.E., Ponder, J.W., Cistola, D.P.: The NMR Solution Structure of Intestinal Fatty Acid-binding Protein Complexed with Palmitate: Application of a Novel Distance Geometry Algorithm. Journal of Molecular Biology 264, 585–602 (1996)CrossRefGoogle Scholar
  7. 7.
    Lavor, C., Liberti, L., Maculan, N.: Discretizable Molecular Distance Geometry Problem, Tech. Rep. q-bio.BM/0608012, arXiv (2006)Google Scholar
  8. 8.
    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
  9. 9.
    Lavor, C., Mucherino, A., Liberti, L., Maculan, N.: Discrete Approaches for Solving Molecular Distance Geometry Problems using NMR Data. International Journal of Computational Biosciences (to appear 2010)Google Scholar
  10. 10.
    Lavor, C., Mucherino, A., Liberti, L., Maculan, N.: Computing Artificial Backbones of Hydrogen Atoms in order to Discover Protein Backbones. In: IEEE Conference Proceedings, International Multiconference on Computer Science and Information Technology (IMCSIT 2009), Workshop on Computational Optimization (WCO 2009), Mragowo, Poland, pp. 751–756 (2009)Google Scholar
  11. 11.
    Lavor, C., Mucherino, A., Liberti, L., Maculan, N.: An Artificial Backbone of Hydrogens for Finding the Conformation of Protein Molecules. In: Proceedings of the Computational Structural Bioinformatics Workshop (CSBW 2009), Washington DC, USA, pp. 152–155 (2009)Google Scholar
  12. 12.
    Liberti, L., Lavor, C., Maculan, N.: A Branch-and-Prune Algorithm for the Molecular Distance Geometry Problem. International Transactions in Operational Research 15(1), 1–17 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Liberti, L., Lavor, C., Mucherino, A., Maculan, N.: Molecular Distance Geometry Methods: from Continuous to Discrete. International Transactions in Operational Research (to appear 2010)Google Scholar
  14. 14.
    Moré, J.J., Wu, Z.: Distance Geometry Optimization for Protein Structures. Journal of Global Optimization 15, 219–223 (1999)zbMATHCrossRefGoogle Scholar
  15. 15.
    Mucherino, A., Lavor, C.: The Branch and Prune Algorithm for the Molecular Distance Geometry Problem with Inexact Distances. In: Proceedings of World Academy of Science, Engineering and Technology (WASET), International Conference on Bioinformatics and Biomedicine (ICBB 2009), Venice, Italy, pp. 349–353 (2009)Google Scholar
  16. 16.
    Mucherino, A., Lavor, C., Liberti, L.: The Discretizable Distance Geometry Problem. Optimization Letters (in revision)Google Scholar
  17. 17.
    Mucherino, A., Liberti, L., Lavor, C., Maculan, N.: Comparisons between an Exact and a MetaHeuristic Algorithm for the Molecular Distance Geometry Problem. In: ACM Conference Proceedings, Genetic and Evolutionary Computation Conference (GECCO 2009), Montréal, Canada, pp. 333–340 (2009)Google Scholar
  18. 18.
    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, Monticello, IL, pp. 480–489 (1979)Google Scholar
  19. 19.
    Schwieters, C.D., Kuszewski, J.J., Clore, G.M.: Using Xplor-NIH for NMR Molecular Structure Determination. Progress in Nuclear Magnetic Resonance Spectroscopy 48, 47–62 (2006)CrossRefGoogle Scholar
  20. 20.
    Wu, D., Wu, Z.: An Updated Geometric Build-Up Algorithm for Solving the Molecular Distance Geometry Problem with Sparse Distance Data. Journal of Global Optimization 37, 661–673 (2007)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Antonio Mucherino
    • 1
  • Leo Liberti
    • 2
  • Carlile Lavor
    • 3
  1. 1.INRIA Lille Nord Europe, Villeneuve d’AscqFrance
  2. 2.LIXÉcole PolytechniquePalaiseauFrance
  3. 3.Dept. of Applied MathematicsState University of CampinasCampinas-SPBrazil

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