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Recent advances on the Discretizable Molecular Distance Geometry Problem

Author

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  • Lavor, Carlile
  • Liberti, Leo
  • Maculan, Nelson
  • Mucherino, Antonio

Abstract

The Molecular Distance Geometry Problem (MDGP) consists in finding an embedding in R3 of a nonnegatively weighted simple undirected graph with the property that the Euclidean distances between embedded adjacent vertices must be the same as the corresponding edge weights. The Discretizable Molecular Distance Geometry Problem (DMDGP) is a particular subset of the MDGP which can be solved using a discrete search occurring in continuous space; its main application is to find three-dimensional arrangements of proteins using Nuclear Magnetic Resonance (NMR) data. The model provided by the DMDGP, however, is too abstract to be directly applicable in proteomics. In the last five years our efforts have been directed towards adapting the DMDGP to be an ever closer model of the actual difficulties posed by the problem of determining protein structures from NMR data. This survey lists recent developments on DMDGP related research.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:219:y:2012:i:3:p:698-706
    DOI: 10.1016/j.ejor.2011.11.007
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    Citations

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    Cited by:

    1. 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.
    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. 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.
    4. 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.
    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. 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.
    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. Martello, Silvano & Pinto Paixão, José M., 2012. "A look at the past and present of optimization – An editorial," European Journal of Operational Research, Elsevier, vol. 219(3), pages 638-640.
    9. 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.

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