A Branch‐and‐Prune algorithm for the Molecular Distance Geometry Problem

The molecular distance geometry problem can be formulated as the problem of finding an immersion in R 3 of a given undirected, nonnegatively weighted graph G. In this paper, we discuss a set of graphs G for which the problem may also be formulated as a combinatorial search in discrete space. This is theoretically interesting as an example of "combinatorialization" of a continuous nonlinear problem. It is also algorithmically interesting because the natural combinatorial solution algorithm performs much better than a global optimization approach on the continuous formulation. We present a Branch and Prune algorithm which can be used for obtaining a set of positions of the atoms of protein conformations when only some of the distances between the atoms are known.

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“…Section 4 concludes this short paper. Refer to [2,3,4] for more details on the DMDGP and the BP algorithm.…”

Section: Introductionmentioning

confidence: 99%

The discretizable molecular distance geometry problem

et al. 2011

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“…Two columns of Table 1 refer to the BP algorithm [21] applied to the reordered proteins. We report the solution quality in terms of Largest Distance Error (LDE): LDE({x 1 , x 2 , .…”

Section: Computational Resultsmentioning

confidence: 99%

“…The DMDGP and DDGP can both be solved (approximately for a given ε > 0) using a recursive binary exploration following the order < on V : at each rank i, use the already known positions of the adjacent predecessors in Uv to find at most two positions for the i-th vertex, and recurse the search over each of them. Such an algorithm, called Branch-and-Prune (BP), was described in [21], further discussed in [17], and used in several papers [27,19,18,28,29,25,20] to solve different DMDGP variants. Similar algorithms were proposed in [35,3].…”

Section: ⊓ ⊔mentioning

confidence: 99%

“…As long as an order on V is given that ensures that each vertex i > K has at least K adjacent predecessors, it is easy to derive a binary tree search where there are at most two alternatives for placing the next vertex in the sequence (see [16,22]). Search methods based on this principle were proposed in [21,35,3]. The same vertex order for the problem restricted to K = 3 was discussed within the context of the Discretizable Molecular Distance Geometry Problem (DMDGP), see [15], and an application to real proteins discussed in [27,19].…”

Section: Introductionmentioning

confidence: 99%

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Discretization orders for distance geometry problems

et al. 2011

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Given a weighted, undirected simple graph G = (V, E, d) (where d : E → R + ), the Distance Geometry Problem (DGP) is to determine an embeddingAlthough, in general, the DGP is solved using continuous methods, under certain conditions the search is reduced to a discrete set of points. We give one such condition as a particular order on V . We formalize the decision problem of determining whether such an order exists for a given graph and show that this problem is NP-complete in general and polynomial for fixed dimension K. We present results of computational experiments on a set of protein backbones whose natural atomic order does not satisfy the order requirements and compare our approach with some available continuous space searches.

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“…Distance geometry can used to determine the coordinates of a set of objects based on distance information between the objects of interest [7,8]. The input set of distances may consist of exact distances, or they may be specified in the form of distance ranges [9]. In addition, the set of input distances may or may not be sufficient for a unique determination of the coordinates of all the objects of interest [10].…”

Section: Introductionmentioning

confidence: 99%

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2017

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Protein structure determination from experimental NMR spectroscopic data, Comparative Modeling and Protein Design require a search for low energy conformations with specific spatial relationships between different segments of the same molecule. Generation and characterization of the range of molecular conformations that are consistent with a specified set of restraints is a challenging problem. Distance geometry is an efficient method for generation of molecular conformations that are consistent with a set of specified distance restraints. The effects of Energy directed generation of trial distance matrix for use in Distance Geometry are investigated in this study. Potential Energy directed sampling of distances may direct conformational search towards favorable regions of the conformational space. The use of this method has the potential to improve sampling of conformational space and to avoid the tradeoff between the experimental and the knowledge based information in structure determination and structure refinement.

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A Branch‐and‐Prune algorithm for the Molecular Distance Geometry Problem

Cited by 121 publications

References 13 publications

The discretizable molecular distance geometry problem

The discretizable molecular distance geometry problem

Discretization orders for distance geometry problems

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