Geometric Algebra to Model Uncertainties in the Discretizable Molecular Distance Geometry Problem

The discretizable molecular distance geometry problem (DMDGP) is related to the determination of 3D protein structure using distance information detected by nuclear magnetic resonance (NMR) experiments. The chemistry of proteins and the NMR distance information allow us to define an atomic order v 1...

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Veröffentlicht in:Advances in applied Clifford algebras Jg. 27; H. 1; S. 439 - 452
Hauptverfasser: Alves, Rafael, Lavor, Carlile
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.03.2017
Springer Nature B.V
Schlagworte:
Algebra
Algorithms
Applications of Mathematics
Intervals
Mathematical and Computational Physics
Mathematical Methods in Physics
NMR
Nuclear magnetic resonance
Physics
Physics and Astronomy
Proteins
Real numbers
Theoretical
Uncertainty
Distance geometry
Conformal geometric algebra
3D protein structure
Branch and prune algorithm
ISSN:0188-7009, 1661-4909
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Zusammenfassung:The discretizable molecular distance geometry problem (DMDGP) is related to the determination of 3D protein structure using distance information detected by nuclear magnetic resonance (NMR) experiments. The chemistry of proteins and the NMR distance information allow us to define an atomic order v 1 , … , v n such that the distances related to the pairs { v i - 3 , v i } , { v i - 2 , v i } , { v i - 1 , v i } , for i > 3 , are available, which implies that the search space can be represented by a tree. A DMDGP solution can be represented by a path from the root to a leaf node of this tree, found by an exact method, called branch-and-prune (BP). Because of uncertainty in NMR data, some of the distances related to the pairs { v i - 3 , v i } may not be precise values, being represented by intervals of real numbers [ d ̲ i - 3 , i , d ¯ i - 3 , i ] . In order to apply BP algorithm in this context, sample values from those intervals should be taken. The main problem of this approach is that if we sample many values, the search space increases drastically, and for small samples, no solution can be found. We explain how geometric algebra can be used to model uncertainties in the DMDGP, avoiding sample values from intervals [ d ̲ i - 3 , i , d ¯ i - 3 , i ] and eliminating the heuristic characteristics of BP when dealing with interval distances.
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ISSN:0188-7009
1661-4909
DOI:10.1007/s00006-016-0653-2