Assigned and unassigned distance geometry: applications to biological molecules and nanostructures

Billinge, Simon J. L.; Duxbury, Phillip M.; Gonçalves, Douglas; Lavor, Carlile; Mucherino, Antonio

doi:10.1007/s10288-016-0314-2

Cited by 51 publications

(45 citation statements)

References 76 publications

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“…Let us see what happens, considering a small example. More specifically, the instance we want to solve is defined by the graph G D .V, E, d/, given by the following: 3 , v 4 g, fv 3 , v 5 g, fv 3 , v 6 g, fv 4 , v 5 g, fv 4 , v 6 g, fv 5 , v 6 gg, The first three vertices can be fixed at positions In the example, distance d 1,4 is a precise value, which implies that there are two possible positions (instead of two arcs) for v 4 . Because both are feasible, we choose one of them, given by However, distance d 2,5 is represented by the interval OEd 2,5 , N d 2,5 , implying two possible arcs for the position of v 5 .…”

Section: Ibp and The Classical Approachmentioning

confidence: 99%

“…Because the distance d 1,5 is available, it must be used to validate the positions. However, the selected values f2.3, 2.5g do not satisfy the restriction given by d 1,5 (Figure 2a). Even trying a more refined sample, f2.25, 2.35, 2.45, 2.55g, no solution is found (Figure 2b).…”

Section: Ibp and The Classical Approachmentioning

confidence: 99%

“…( 6 ) From (4), (5), and (6), we obtain C n . 4 , : : : , n 1 / D X b n 2 0.5d 2 n 2,n e 1 ^ X b n 1 0.5d 2 n 1,n e 1 D .…”

Section: Ibp and The Conformal Clifford Algebramentioning

confidence: 99%

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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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Section: Ibp and The Classical Approachmentioning

confidence: 99%

Section: Ibp and The Classical Approachmentioning

confidence: 99%

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Clifford algebra and discretizable distance geometry

Alves

Lavor

Souza

et al. 2017

Math Methods in App Sciences

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“…Recent surveys on Distance Geometry (DG) are given in [7,48], an edited book with different applications can be found in [54], two very recent books are given in [38,45], and some historical notes on DG are presented in [44]. …”

Section: Introduction: Distance Geometrymentioning

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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“…A chemical shift driven genetic algorithm for biased Molecular dynamics has been applied for protein structure refinement [6]. 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].…”

Section: Introductionmentioning

confidence: 99%

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2017

RJLBPCS

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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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Assigned and unassigned distance geometry: applications to biological molecules and nanostructures

Cited by 51 publications

References 76 publications

Clifford algebra and discretizable distance geometry

Clifford algebra and discretizable distance geometry

Minimal NMR distance information for rigidity of protein graphs

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