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Recent advances on the interval distance geometry problem

Author

Listed:
  • Douglas S. Gonçalves

    (Universidade Federal de Santa Catarina)

  • Antonio Mucherino

    (Université de Rennes 1)

  • Carlile Lavor

    (University of Campinas (IMECC-UNICAMP))

  • Leo Liberti

    (CNRS LIX, École Polytechnique)

Abstract

We discuss a discretization-based solution approach for a classic problem in global optimization, namely the distance geometry problem (DGP). We focus our attention on a particular class of the DGP which is concerned with the identification of the conformation of biological molecules. Among the many relevant ideas for the discretization of the DGP in the literature, we identify the most promising ones and address their inherent limitations to application to this class of problems. The result is an improved method for estimating 3D structures of small proteins based only on the knowledge of some distance restraints between pairs of atoms. We present computational results showcasing the usefulness of the new proposed approach. Proteins act on living cells according to their geometric and chemical properties: finding protein conformations can be very useful within the pharmaceutical industry in order to synthesize new drugs.

Suggested Citation

  • Douglas S. Gonçalves & Antonio Mucherino & Carlile Lavor & Leo Liberti, 2017. "Recent advances on the interval distance geometry problem," Journal of Global Optimization, Springer, vol. 69(3), pages 525-545, November.
    • Handle: RePEc:spr:jglopt:v:69:y:2017:i:3:d:10.1007_s10898-016-0493-6
    DOI: 10.1007/s10898-016-0493-6
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    References listed on IDEAS

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    1. Antonio Mucherino & Carlile Lavor & Leo Liberti & Nelson Maculan, 2012. "The Discretizable Molecular Distance Geometry Problem," Post-Print hal-00756940, HAL.
    2. Joonghyun Ryu & Deok-Soo Kim, 2013. "Protein structure optimization by side-chain positioning via beta-complex," Journal of Global Optimization, Springer, vol. 57(1), pages 217-250, September.
    3. Antonio Mucherino & Carlile Lavor & Leo Liberti, 2012. "The Discretizable Distance Geometry Problem," Post-Print hal-00756943, HAL.
    4. Carlile Lavor & Leo Liberti & Nelson Maculan & Antonio Mucherino, 2012. "The discretizable molecular distance geometry problem," Computational Optimization and Applications, Springer, vol. 52(1), pages 115-146, May.
    5. Virginia Costa & Antonio Mucherino & Carlile Lavor & Andrea Cassioli & Luiz Carvalho & Nelson Maculan, 2014. "Discretization orders for protein side chains," Journal of Global Optimization, Springer, vol. 60(2), pages 333-349, October.
    6. Carlile Lavor & Leo Liberti & Antonio Mucherino, 2013. "The interval Branch-and-Prune algorithm for the discretizable molecular distance geometry problem with inexact distances," Journal of Global Optimization, Springer, vol. 56(3), pages 855-871, July.
    7. Lavor, Carlile & Liberti, Leo & Maculan, Nelson & Mucherino, Antonio, 2012. "Recent advances on the Discretizable Molecular Distance Geometry Problem," European Journal of Operational Research, Elsevier, vol. 219(3), pages 698-706.
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    Citations

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    Cited by:

    1. Lavor, Carlile & Souza, Michael & Carvalho, Luiz M. & Gonçalves, Douglas S. & Mucherino, Antonio, 2021. "Improving the sampling process in the interval Branch-and-Prune algorithm for the discretizable molecular distance geometry problem," Applied Mathematics and Computation, Elsevier, vol. 389(C).
    2. Maurizio Bruglieri & Roberto Cordone & Leo Liberti, 2022. "Maximum feasible subsystems of distance geometry constraints," Journal of Global Optimization, Springer, vol. 83(1), pages 29-47, May.
    3. Phil Duxbury & Carlile Lavor & Leo Liberti & Luiz Leduino Salles-Neto, 2022. "Unassigned distance geometry and molecular conformation problems," Journal of Global Optimization, Springer, vol. 83(1), pages 73-82, May.
    4. Leo Liberti, 2020. "Distance geometry and data science," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 271-339, July.
    5. Simon J. L. Billinge & Phillip M. Duxbury & Douglas S. Gonçalves & Carlile Lavor & Antonio Mucherino, 2018. "Recent results on assigned and unassigned distance geometry with applications to protein molecules and nanostructures," Annals of Operations Research, Springer, vol. 271(1), pages 161-203, December.
    6. Bradley Worley & Florent Delhommel & Florence Cordier & Thérèse E. Malliavin & Benjamin Bardiaux & Nicolas Wolff & Michael Nilges & Carlile Lavor & Leo Liberti, 2018. "Tuning interval Branch-and-Prune for protein structure determination," Journal of Global Optimization, Springer, vol. 72(1), pages 109-127, September.
    7. Moira MacNeil & Merve Bodur, 2022. "Integer Programming, Constraint Programming, and Hybrid Decomposition Approaches to Discretizable Distance Geometry Problems," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 297-314, January.

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