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The discretizable molecular distance geometry problem

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

Abstract

Given a simple weighted undirected graph G=(V,E,d) with d:E→ℝ+, the Molecular Distance Geometry Problem (MDGP) consists in finding an embedding x:V→ℝ3 such that ‖x u x v ‖=d uv for each {u,v}∈E. We show that under a few assumptions usually satisfied in proteins, the MDGP can be formulated as a search in a discrete space. We call this MDGP subclass the Discretizable MDGP (DMDGP). We show that the DMDGP is NP-hard and we propose a solution algorithm called Branch-and-Prune (BP). The BP algorithm performs remarkably well in practice in terms of speed and solution accuracy, and can be easily modified to find all incongruent solutions to a given DMDGP instance. We show computational results on several artificial and real-life instances.

Keywords

Distance geometry Branch-and-prune Molecular conformation Protein NMR 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Carlile Lavor
    • 1
  • Leo Liberti
    • 2
  • Nelson Maculan
    • 3
  • Antonio Mucherino
    • 4
  1. 1.Department of Applied Mathematics (IMECC-UNICAMP)State University of CampinasCampinasBrazil
  2. 2.LIXÉcole PolytechniquePalaiseauFrance
  3. 3.Federal University of Rio de Janeiro (COPPE–UFRJ)Rio de JaneiroBrazil
  4. 4.CERFACSToulouseFrance

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