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Unassigned distance geometry and molecular conformation problems

Author

Listed:
  • Phil Duxbury

    (Michigan State University)

  • Carlile Lavor

    (IMECC-Unicamp)

  • Leo Liberti

    (CNRS LIX)

  • Luiz Leduino Salles-Neto

    (Federal University of Sao Paulo)

Abstract

3D protein structures and nanostructures can be obtained by exploiting distance information provided by experimental techniques, such as nuclear magnetic resonance and the pair distribution function method. These are examples of instances of the unassigned distance geometry problem (uDGP), where the aim is to calculate the position of some points using a list of associated distance values not previoulsy assigned to the pair of points. We propose new mathematical programming formulations and a new heuristic to solve the uDGP related to molecular structure calculations. In addition to theoretical results, computational experiments are also provided.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:83:y:2022:i:1:d:10.1007_s10898-021-01023-0
    DOI: 10.1007/s10898-021-01023-0
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    References listed on IDEAS

    as
    1. Leonardo Fontoura & Rafael Martinelli & Marcus Poggi & Thibaut Vidal, 2018. "The minimum distance superset problem: formulations and algorithms," Journal of Global Optimization, Springer, vol. 72(1), pages 27-53, September.
    2. 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.
    3. 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.
    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. Antonio Mucherino & Carlile Lavor & Leo Liberti & Nelson Maculan, 2012. "The Discretizable Molecular Distance Geometry Problem," Post-Print hal-00756940, HAL.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Antonio Mucherino & Carlile Lavor & Leo Liberti, 2012. "The Discretizable Distance Geometry Problem," Post-Print hal-00756943, HAL.
    11. 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.
    12. 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).
    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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