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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

Effective coarse grained bile salt model of Vila Verde and Frenkel [24]. The molecular graph  is shown along with the iterated line graphs  and . Vertices and edges are labelled
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Fig3: Effective coarse grained bile salt model of Vila Verde and Frenkel [24]. The molecular graph is shown along with the iterated line graphs and . Vertices and edges are labelled

Mentions: A chemically relevant example, central to the hydrolysis and solubilisation of lipid associated with food digestion in the human lower gastrointestinal tract, are the bile salt and bile acid surfactants. Vila Verde and Frenkel [24] have proposed an effective coarse-grained model of trihydroxy bile salts (taurocholate) for a molecular dynamics study of micelle formation that is related to the rate and extent of nutrient absorption by intestinal cells. The authors proposed a “three-to-one” mapping scheme, that groups three carbon or nitrogen atoms into a single bead, to arrive at the molecular graph shown in Fig. 3. Iterated line graphs up to are collected in Figs. 3 and 4. Table 1 lists the vertices for the corresponding DAG description of the hierarchy as sequences of bead indexes.Fig. 3


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

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

Effective coarse grained bile salt model of Vila Verde and Frenkel [24]. The molecular graph  is shown along with the iterated line graphs  and . Vertices and edges are labelled
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

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

Fig3: Effective coarse grained bile salt model of Vila Verde and Frenkel [24]. The molecular graph is shown along with the iterated line graphs and . Vertices and edges are labelled
Mentions: A chemically relevant example, central to the hydrolysis and solubilisation of lipid associated with food digestion in the human lower gastrointestinal tract, are the bile salt and bile acid surfactants. Vila Verde and Frenkel [24] have proposed an effective coarse-grained model of trihydroxy bile salts (taurocholate) for a molecular dynamics study of micelle formation that is related to the rate and extent of nutrient absorption by intestinal cells. The authors proposed a “three-to-one” mapping scheme, that groups three carbon or nitrogen atoms into a single bead, to arrive at the molecular graph shown in Fig. 3. Iterated line graphs up to are collected in Figs. 3 and 4. Table 1 lists the vertices for the corresponding DAG description of the hierarchy as sequences of bead indexes.Fig. 3

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