Discretization orders for protein side chains

Costa, Virginia; Mucherino, Antonio; Lavor, Carlile; Cassioli, Andrea; Carvalho, Luiz Mariano; Maculan, Nelson

doi:10.1007/s10898-013-0135-1

Cited by 18 publications

(13 citation statements)

References 16 publications

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“…2 presents a backbone with three amino acids). More details about protein graphs including side chains are given in [16,57,58]. …”

Section: A New Dmdgp Order For Protein Graphsmentioning

confidence: 99%

Minimal NMR distance information for rigidity of protein graphs

Lavor¹,

Liberti²,

Donald³

et al. 2019

Discrete Applied Mathematics

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Nuclear Magnetic Resonance (NMR) experiments provide distances between nearby atoms of a protein molecule. The corresponding structure determination problem is to determine the 3D protein structure by exploiting such distances. We present a new order on the atoms of the protein, based on information from the chemistry of proteins and NMR experiments, which allows us to formulate the problem as a combinatorial search. Additionally, this order tells us what kind of NMR distance information is crucial to understand the cardinality of the solution set of the problem and its computational complexity.

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“…2 presents a backbone with three amino acids). More details about protein graphs including side chains are given in [16,57,58]. …”

Section: A New Dmdgp Order For Protein Graphsmentioning

confidence: 99%

Minimal NMR distance information for rigidity of protein graphs

Lavor¹,

Liberti²,

Donald³

et al. 2019

Discrete Applied Mathematics

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“…iBP is most naturally defined as a recursive tree traversal algorithm [13,7] that uses recursively defined affine transformation matrices [24] for computing embedded coordinates. However, recent use of Clifford algebra has yielded embedding equations that are non-recursive [12], the key results of which are recalled here.…”

Section: Iterative Embedding Relationsmentioning

confidence: 99%

“…Fig. 4 illustrates how the new orders more directly and uniformly sample Ramachandran space than previously published vertex orders [7]. An iBP calculation was performed, using both vertex orders, to find solutions to the iDMDGP instance of a backbone-only tetrapeptide, with the direct distance feasibility (DDF, [5]) and van der Waals (VDW) pruning devices enabled.…”

Section: Ramachandran-defined Vertex Ordersmentioning

confidence: 99%

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Tuning interval Branch-and-Prune for protein structure determination

et al. 2018

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The interval Branch and Prune (iBP) algorithm for obtaining solutions to the interval Discretizable Molecular Distance Geometry Problem (iDMDGP) has proven itself as a powerful method for molecular structure determination. However, substantial obstacles still must be overcome before iBP may be employed as a tractable general-purpose alternative to existing structure determination algorithms. This work introduces an iterative variant of the iBP algorithm that leverages existing knowledge of protein structures in order to reduce the size of the effective search space by many orders of magnitude. These improvements are included in a newly released implementation of the iBP software that aims to provide a solid platform for both research and application of the iDMDGP.

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“…In previous works, discretization orders were either handcrafted (Costa et al., ; Lavor et al., ) or searched over pseudo de Bruijn graphs constructed from sets of cliques of G (Mucherino, ), or obtained by means of a greedy algorithm (Lavor et al., ; Mucherino, ), or even found by formulating a constraint programing problem whose solution was attempted by an answer set programming (ASP) solver (Gonçalves et al., ). In the last cited paper, the idea to search for discretization orders that can satisfy some additional assumptions, which may have an impact on the search domain and make it “easier” to explore, was first proposed.…”

Section: Introductionmentioning

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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Discretization orders for protein side chains

Cited by 18 publications

References 16 publications

Minimal NMR distance information for rigidity of protein graphs

Minimal NMR distance information for rigidity of protein graphs

Tuning interval Branch-and-Prune for protein structure determination

Optimal partial discretization orders for discretizable distance geometry

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