Journal of Global Optimization

, Volume 60, Issue 2, pp 333–349 | Cite as

Discretization orders for protein side chains

  • Virginia Costa
  • Antonio Mucherino
  • Carlile Lavor
  • Andrea Cassioli
  • Luiz M. Carvalho
  • Nelson Maculan


Proteins are important molecules that are widely studied in biology. Since their three-dimensional conformations can give clues about their function, an optimal methodology for the identification of such conformations has been researched for many years. Experiments of Nuclear Magnetic Resonance (NMR) are able to estimate distances between some pairs of atoms forming the protein, and the problem of identifying the possible conformations satisfying the available distance constraints is known in the scientific literature as the Molecular Distance Geometry Problem (MDGP). When some particular assumptions are satisfied, MDGP instances can be discretized, and solved by employing an ad-hoc algorithm, named the interval Branch & Prune. When dealing with molecules such as proteins, whose chemical structure is known, a priori information can be exploited for generating atomic orderings that allow for the discretization. In previous publications, we presented a handcrafted order for the protein backbones. In this work, we propose 20 new orders for the 20 side chains that can be present in proteins. Computational experiments on artificial and real instances from NMR show the usefulness of the proposed orders.


Discretization orders Distance geometry Branch-and-prune Combinatorial Optimization Proteins 



We are thankful to Thérèse Malliavin and Douglas Gonçalves for the fruitful comments on this paper, as well as to the anonymous referees. We also wish to thank CAPES, that funded a 4-month visit to Rennes for Virginia Costa: part of this work was performed during such a visit. We are also thankful to the French Embassy in São Paulo and UNICAMP (which funded a 2-month chaire in UNICAMP for Antonio Mucherino), to the Brazilian research agencies FAPESP and CNPq, and to the French National Research Agency (ANR).


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Virginia Costa
    • 1
  • Antonio Mucherino
    • 2
  • Carlile Lavor
    • 3
  • Andrea Cassioli
    • 4
  • Luiz M. Carvalho
    • 5
  • Nelson Maculan
    • 1
  1. 1.COPPEFederal University of Rio de JaneiroRio de JaneiroBrazil
  2. 2.IRISAUniversity of Rennes 1RennesFrance
  3. 3.IMECC-UNICAMPUniversity of CampinasCampinasBrazil
  4. 4.LIX, École PolytechniquePalaiseauFrance
  5. 5.IMEState University of Rio de JaneiroRio de JaneiroBrazil

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