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The Discretizable Molecular Distance Geometry Problem seems Easier on Proteins

  • Leo Liberti
  • Carlile Lavor
  • Antonio Mucherino
Chapter

Abstract

Distance geometry methods are used to turn a set of interatomic distances given by Nuclear Magnetic Resonance (NMR) experiments into a consistent molecular conformation. In a set of papers (see the survey [8]) we proposed a Branch-and-Prune (BP) algorithm for computing the set X of all incongruent embeddings of a given protein backbone. Although BP has a worst-case exponential running time in general, we always noticed a linear-like behaviour in computational experiments. In this chapter we provide a theoretical explanation to our observations. We show that the BP is fixed-parameter tractable on protein-like graphs and empirically show that the parameter is constant on a set of proteins from the Protein Data Bank.

Keywords

Branch-and-Prune Symmetry Distance geometry Fixed-parameter tractable Protein conformation 

Notes

Acknowledgements

The authors wish to thank the Brazilian research agencies FAPESP and CNPq and the French research agency CNRS and École Polytechnique for financial support.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.LIX, École PolytechniquePalaiseauFrance
  2. 2.Department of Applied MathsUniversity of CampinasCampinas-SPBrazil
  3. 3.IRISAUniversity of Rennes 1RennesFrance

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