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Assigned and unassigned distance geometry: applications to biological 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

Considering geometry based on the concept of distance, the results found by Menger and Blumenthal originated a body of knowledge called distance geometry. This survey covers some recent developments for assigned and unassigned distance geometry and focuses on two main applications: determination of three-dimensional conformations of biological molecules and nanostructures.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aqjoor:v:14:y:2016:i:4:d:10.1007_s10288-016-0314-2
    DOI: 10.1007/s10288-016-0314-2
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    References listed on IDEAS

    as
    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. Antonio Mucherino & Carlile Lavor & Leo Liberti, 2012. "The Discretizable Distance Geometry Problem," Post-Print hal-00756943, HAL.
    3. 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.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Yves Crama & Michel Grabisch & Silvano Martello, 2022. "Preface," Annals of Operations Research, Springer, vol. 314(1), pages 1-3, July.
    2. Yves Crama & Michel Grabisch & Silvano Martello, 2018. "Sweet sixteen," 4OR, Springer, vol. 16(1), pages 1-13, March.
    3. 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).
    4. Farid Alizadeh & Douglas Gonçalves & Nathan Krislock & Leo Liberti, 2018. "Preface: Special issue dedicated to Distance Geometry," Journal of Global Optimization, Springer, vol. 72(1), pages 1-4, September.
    5. 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.
    6. Yves Crama & Michel Grabisch & Silvano Martello, 2022. "Sixty-one surveys in operations research," Annals of Operations Research, Springer, vol. 314(1), pages 5-13, July.
    7. 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.
    8. Yves Crama & Michel Grabisch & Silvano Martello, 2021. "4OR comes of age," 4OR, Springer, vol. 19(1), pages 1-13, March.

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