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Recent results on assigned and unassigned distance geometry with applications to protein molecules and nanostructures

Author

Listed:
  • Simon J. L. Billinge

    (Columbia University
    Brookhaven National Laboratory)

  • Phillip M. Duxbury

    (Michigan State University)

  • Douglas S. Gonçalves

    (Universidade Federal de Santa Catarina)

  • Carlile Lavor

    (University of Campinas)

  • Antonio Mucherino

    (Université de Rennes 1)

Abstract

In the 2 years since our last 4OR review of distance geometry methods with applications to proteins and nanostructures, there has been rapid progress in treating uncertainties in the discretizable distance geometry problem; and a new class of geometry problems started to be explored, namely vector geometry problems. In this work we review this progress in the context of the earlier literature.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:271:y:2018:i:1:d:10.1007_s10479-018-2989-6
    DOI: 10.1007/s10479-018-2989-6
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    References listed on IDEAS

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    1. P. Juhás & D. M. Cherba & P. M. Duxbury & W. F. Punch & S. J. L. Billinge, 2006. "Ab initio determination of solid-state nanostructure," Nature, Nature, vol. 440(7084), pages 655-658, March.
    2. Felipe Fidalgo & Douglas S. Gonçalves & Carlile Lavor & Leo Liberti & Antonio Mucherino, 2018. "A symmetry-based splitting strategy for discretizable distance geometry problems," Journal of Global Optimization, Springer, vol. 71(4), pages 717-733, August.
    3. Antonio Mucherino & Carlile Lavor & Leo Liberti, 2012. "The Discretizable Distance Geometry Problem," Post-Print hal-00756943, HAL.
    4. 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.
    5. 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.
    6. Cláudio P. Santiago & Carlile Lavor & Sérgio Assunção Monteiro & Alberto Kroner-Martins, 2018. "A new algorithm for the small-field astrometric point-pattern matching problem," Journal of Global Optimization, Springer, vol. 72(1), pages 55-70, September.
    7. 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.
    8. Simon J. L. Billinge & Phillip M. Duxbury & Douglas S. Gonçalves & Carlile Lavor & Antonio Mucherino, 2016. "Assigned and unassigned distance geometry: applications to biological molecules and nanostructures," 4OR, Springer, vol. 14(4), pages 337-376, December.
    9. 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.
    10. Leo Liberti & Carlile Lavor, 2018. "Open Research Areas in Distance Geometry," Springer Optimization and Its Applications, in: Panos M. Pardalos & Athanasios Migdalas (ed.), Open Problems in Optimization and Data Analysis, pages 183-223, Springer.
    11. 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.
    12. Jan Leeuw, 1988. "Convergence of the majorization method for multidimensional scaling," Journal of Classification, Springer;The Classification Society, vol. 5(2), pages 163-180, September.
    13. 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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    Cited by:

    1. Carlile Lavor, 2020. "Comments on: 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 340-345, July.
    2. 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).
    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.

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