An algorithm to enumerate all possible protein conformations verifying a set of distance constraints

Cassioli, Andrea; Bardiaux, Benjamin; Bouvier, Guillaume; Mucherino, Antonio; Alves, Rafael; Liberti, Leo; Nilges, Michaël; Lavor, Carlile; Malliavin, Thérèse E.

doi:10.1186/s12859-015-0451-1

Cited by 46 publications

(34 citation statements)

References 66 publications

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“…This class of problems was, in fact, initially inspired by calculations of 3D protein backbones. However, the DMDGP is actually a general problem that can have other applications [16], not only in structural biology (for this particular application, the reader can make reference to [2]). Although we restrict our discussion to the case K = 3, all presented theoretical results can be trivially extended to any dimension K > 0.…”

Section: Strict Triangular Inequalitiesmentioning

confidence: 99%

A symmetry-based splitting strategy for discretizable distance geometry problems

et al. 2018

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In memory of our esteemed colleague, Chris Floudas.Abstract Discretizable distance geometry problems consist in a subclass of distance geometry problems where the search space can be discretized and reduced to a tree. Such problems can be tackled by applying a branch-andprune algorithm, which is able to perform an exhaustive enumeration of the solution set. In this work, we exploit the concept of symmetry in the search tree for isolating subtrees that are explored only one time for improving the algorithm performances. The proposed strategy is based on the idea of dividing an original instance of the problem into sub-instances that can thereafter be solved (almost) independently. We present some computational experiments on a set of artificially generated instances, with exact distances, to validate the theoretical results.

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Section: Strict Triangular Inequalitiesmentioning

confidence: 99%

A symmetry-based splitting strategy for discretizable distance geometry problems

et al. 2018

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“…But imagine we have just a little bigger instance and that only at vertex v 8 , for example, an additional distance d i ,8 , i <5, is available. In this case, we do not know how refined the sample from

[{\underset{d}{false}}_{2, 5}, {\overset{d}{true}}_{2, 5}]

should be in order to obtain a position for v 8 that satisfies

{\underset{true_}{d}}_{i, 8} ⩽ | | x_{8} - x_{i} | | ⩽ {\bar{d}}_{i, 8} .

The main problem of the classical approach is that if we sample many values, the search space increases drastically, and for small samples, no solution is found . To avoid sampling process, we should manipulate arcs in a continuous way.…”

Section: Ibp and The Classical Approachmentioning

confidence: 99%

“…The main problem of the classical approach is that if we sample many values, the search space increases drastically, and for small samples, no solution is found [29]. To avoid sampling process, we should manipulate arcs in a continuous way.…”

Section: Ibp and The Classical Approachmentioning

confidence: 99%

Clifford algebra and discretizable distance geometry

Alves

Lavor

Souza

et al. 2017

Math Methods in App Sciences

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Protein structure calculations using nuclear magnetic resonance (NMR) experiments are one of the most important applications of distance geometry. The chemistry of proteins and the NMR data allow us to define an atomic order, such that the distances related to the pairs of atoms {i−3,i},{i−2,i},{i−1,i} are available, and solve the problem iteratively using a combinatorial method, called branch‐and‐prune. The main step of BP algorithm is to intersect three spheres centered at the positions for atoms i−3,i−2,i, with radius given by the atomic distances di−3,i,di−2,i,di−1,i, respectively, to obtain the position for atom i. Because of uncertainty in NMR data, some of the distances di−3,i may not be precise or even not be available. Using conformal Clifford algebra, in addition to take care of NMR uncertainties, which implies that we have to calculate sphere intersections considering that their centers and radius may not be fixed anymore, we consider a more flexible atomic order, where distances di−3,i are replaced by dj,i, where j⩽i−3. Copyright © 2017 John Wiley & Sons, Ltd.

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“…The branch and prune (BP) is a general framework for the solution of DGP K for which the search domain can be discretized (Lavor et al., ; Liberti et al., ). The main idea is to recursively construct the search tree the search tree, and check the feasibility of candidate vertex positions as soon as these positions are computed (Cassioli et al, ; Gonçalves and Mucherino, ). In fact, while assumption 2 ensures that the number of reference distances is at least K , more than K references could be actually available.…”

Section: Definitions and Preliminariesmentioning

confidence: 99%

Optimal partial discretization orders for discretizable distance geometry

Gonçalves

Mucherino

2016

Int Trans Operational Res

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The distance geometry problem (DGP) studies whether a simple weighted undirected graph G = (V, E, d ) can be embedded in a given space so that the weights of the edges of G, when available, are the same as the distances between pairs of embedded vertices. The DGP can be discretized when some particular assumptions are satisfied, which are strongly dependent on the vertex ordering assigned to G. In this paper, we focus on the problem of identifying optimal partial discretization orders for the DGP. The solutions to this problem are in fact vertex orders that allow the discretization of the DGP. Moreover, these partial orders are optimal in the sense that they optimize, at each rank, a given set of objectives aimed to improve the structure of the search space after the discretization. This ordering problem is tackled from a theoretical point of view, and some practical experiences on sets of artificially generated instances, as well as on real-life instances, are provided.

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An algorithm to enumerate all possible protein conformations verifying a set of distance constraints

Cited by 46 publications

References 66 publications

A symmetry-based splitting strategy for discretizable distance geometry problems

A symmetry-based splitting strategy for discretizable distance geometry problems

Clifford algebra and discretizable distance geometry

Optimal partial discretization orders for discretizable distance geometry

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