Clifford algebra and discretizable distance geometry

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...

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Published in:Mathematical methods in the applied sciences Vol. 41; no. 11; pp. 4063 - 4073
Main Authors: Alves, R., Lavor, C., Souza, C., Souza, M.
Format: Journal Article
Language:English
Published: Freiburg Wiley Subscription Services, Inc 30.07.2018
Subjects:
3D protein structure
Atomic radius
Atomic structure
branch‐and‐prune algorithm
Combinatorial analysis
conformal Clifford algebra
distance geometry
Intersections
Mathematical analysis
NMR
Nuclear magnetic resonance
Organic chemistry
Proteins
Uncertainty
ISSN:0170-4214, 1099-1476
Online Access:Get full text
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Summary: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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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.4422