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Enumerating and indexing many-body intramolecular interactions: a graph theoretic approach.

Penfold R, Wilde PJ - J Math Chem (2015)

Bottom Line: The hierarchical structure of atomic index lists for each interaction order [Formula: see text] is compactly expressed as a directed acyclic graph.With suitable data structures (e.g., edge lists or adjacency matrices), automatic enumeration and indexing of [Formula: see text]-body interactions can be implemented straightforwardly to handle large bio-molecular systems.Explicit examples are discussed, including a chemically relevant effective potential model of taurocholate bile salt.

View Article: PubMed Central - PubMed

Affiliation: Institute of Food Research, Norwich Research Park, Colney, Norwich, NR4 7UA UK.

ABSTRACT

The central idea observes a recursive mapping of [Formula: see text]-body intramolecular interactions to [Formula: see text]-body terms that is consistent with the molecular topology. Iterative application of the line graph transformation is identified as a natural and elegant tool to accomplish the recursion. The procedure readily generalizes to arbitrary [Formula: see text]-body potentials. In particular, the method yields a complete characterization of [Formula: see text]-body interactions. The hierarchical structure of atomic index lists for each interaction order [Formula: see text] is compactly expressed as a directed acyclic graph. A pseudo-code description of the generating algorithm is given. With suitable data structures (e.g., edge lists or adjacency matrices), automatic enumeration and indexing of [Formula: see text]-body interactions can be implemented straightforwardly to handle large bio-molecular systems. Explicit examples are discussed, including a chemically relevant effective potential model of taurocholate bile salt.

No MeSH data available.


Related in: MedlinePlus

Generic structures of -body interactions represented on the directed acyclic graph  are compared with the physical formation from the combination of two bends with atomic indexes  and  respectively. a Construction of the typical proper dihedral index sequence  comprising two triplet repeats arising from the distinct hinge atoms  and  that form the shared bond. A similar sequence  arises for the degenerate -cycle structure as shown in (c), but where the “flap” atoms are also identified to close the ring. b The typical improper dihedral index sequence  with only a single hinge atom
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Fig1: Generic structures of -body interactions represented on the directed acyclic graph are compared with the physical formation from the combination of two bends with atomic indexes and respectively. a Construction of the typical proper dihedral index sequence comprising two triplet repeats arising from the distinct hinge atoms and that form the shared bond. A similar sequence arises for the degenerate -cycle structure as shown in (c), but where the “flap” atoms are also identified to close the ring. b The typical improper dihedral index sequence with only a single hinge atom

Mentions: In a molecular structure, covalently bonded atom pairs are considered to be adjacent. Similarly, a pair of adjacent bonds sharing a common “hinge” atom form a more or less flexible bend. The corresponding -body interaction is often described by an effective potential in terms of the external bond angle supplementary to the angle subtended at the hinge atom [17]. A -body dihedral interaction is associated with a pair of adjacent bends that share a common bond. Two situations are possible [18] (see Fig. 1): “proper” torsions arise when both hinge atoms are distinct, so that one bend is rotated about the other through a dihedral angle ; while “improper” dihedral interactions link two bends through a common hinge atom, and are defined by a wag angle . Proper torsions typically account for geometric restrictions conferred by implicit substituents (usually protons) or lone electron pairs and may be alternatively characterized by a bond lying along the dihedral axis. Conversely, the dihedral axis of an improper torsion does not contain a bond and these interactions are used to constrain planar groups (like rings) or to hinder interconversion of stereocenters.Fig. 1


Enumerating and indexing many-body intramolecular interactions: a graph theoretic approach.

Penfold R, Wilde PJ - J Math Chem (2015)

Generic structures of -body interactions represented on the directed acyclic graph  are compared with the physical formation from the combination of two bends with atomic indexes  and  respectively. a Construction of the typical proper dihedral index sequence  comprising two triplet repeats arising from the distinct hinge atoms  and  that form the shared bond. A similar sequence  arises for the degenerate -cycle structure as shown in (c), but where the “flap” atoms are also identified to close the ring. b The typical improper dihedral index sequence  with only a single hinge atom
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4544505&req=5

Fig1: Generic structures of -body interactions represented on the directed acyclic graph are compared with the physical formation from the combination of two bends with atomic indexes and respectively. a Construction of the typical proper dihedral index sequence comprising two triplet repeats arising from the distinct hinge atoms and that form the shared bond. A similar sequence arises for the degenerate -cycle structure as shown in (c), but where the “flap” atoms are also identified to close the ring. b The typical improper dihedral index sequence with only a single hinge atom
Mentions: In a molecular structure, covalently bonded atom pairs are considered to be adjacent. Similarly, a pair of adjacent bonds sharing a common “hinge” atom form a more or less flexible bend. The corresponding -body interaction is often described by an effective potential in terms of the external bond angle supplementary to the angle subtended at the hinge atom [17]. A -body dihedral interaction is associated with a pair of adjacent bends that share a common bond. Two situations are possible [18] (see Fig. 1): “proper” torsions arise when both hinge atoms are distinct, so that one bend is rotated about the other through a dihedral angle ; while “improper” dihedral interactions link two bends through a common hinge atom, and are defined by a wag angle . Proper torsions typically account for geometric restrictions conferred by implicit substituents (usually protons) or lone electron pairs and may be alternatively characterized by a bond lying along the dihedral axis. Conversely, the dihedral axis of an improper torsion does not contain a bond and these interactions are used to constrain planar groups (like rings) or to hinder interconversion of stereocenters.Fig. 1

Bottom Line: The hierarchical structure of atomic index lists for each interaction order [Formula: see text] is compactly expressed as a directed acyclic graph.With suitable data structures (e.g., edge lists or adjacency matrices), automatic enumeration and indexing of [Formula: see text]-body interactions can be implemented straightforwardly to handle large bio-molecular systems.Explicit examples are discussed, including a chemically relevant effective potential model of taurocholate bile salt.

View Article: PubMed Central - PubMed

Affiliation: Institute of Food Research, Norwich Research Park, Colney, Norwich, NR4 7UA UK.

ABSTRACT

The central idea observes a recursive mapping of [Formula: see text]-body intramolecular interactions to [Formula: see text]-body terms that is consistent with the molecular topology. Iterative application of the line graph transformation is identified as a natural and elegant tool to accomplish the recursion. The procedure readily generalizes to arbitrary [Formula: see text]-body potentials. In particular, the method yields a complete characterization of [Formula: see text]-body interactions. The hierarchical structure of atomic index lists for each interaction order [Formula: see text] is compactly expressed as a directed acyclic graph. A pseudo-code description of the generating algorithm is given. With suitable data structures (e.g., edge lists or adjacency matrices), automatic enumeration and indexing of [Formula: see text]-body interactions can be implemented straightforwardly to handle large bio-molecular systems. Explicit examples are discussed, including a chemically relevant effective potential model of taurocholate bile salt.

No MeSH data available.


Related in: MedlinePlus