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The discretizable molecular distance geometry problem

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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.

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Authors and Affiliations

  1. Department of Applied Mathematics (IMECC-UNICAMP), State University of Campinas, 13081-970, Campinas, SP, Brazil

    Carlile Lavor

  2. LIX, École Polytechnique, 91128, Palaiseau, France

    Leo Liberti

  3. Federal University of Rio de Janeiro (COPPE–UFRJ), C.P. 68511, 21945-970, Rio de Janeiro, RJ, Brazil

    Nelson Maculan

  4. CERFACS, Toulouse, France

    Antonio Mucherino

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  1. Carlile Lavor
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  2. Leo Liberti
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  3. Nelson Maculan
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  4. Antonio Mucherino
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Correspondence to Leo Liberti.

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The present work is based on the preliminary 2006 technical report [37].

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Lavor, C., Liberti, L., Maculan, N. et al. The discretizable molecular distance geometry problem. Comput Optim Appl 52, 115–146 (2012). https://doi.org/10.1007/s10589-011-9402-6

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