Enumerating and indexing many-body intramolecular interactions: a graph theoretic approach.
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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.
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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 |
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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 |
View Article: PubMed Central - PubMed
Affiliation: Institute of Food Research, Norwich Research Park, Colney, Norwich, NR4 7UA UK.
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.