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Combinatorics of Reaction-Network Posets

[ Vol. 11 , Issue. 9 ]


Douglas J. Klein, Teodora Ivanciuc, Anton Ryzhov and Ovidiu Ivanciuc   Pages 723 - 733 ( 11 )


Reaction networks are viewed as derived from ordinary molecular structures related in reactant-product pairs so as to manifest a chemical super-structure. Such super-structures then are candidates for applications in a general combinatoric chemistry. Notable additional characterization of a reaction super-structure occurs when such reaction graphs are directed, as for example when there is progressive substitution (or addition) on a fixed molecular skeleton. Such a set of partially ordered entities is in mathematics termed a poset, which further manifests a number of special properties, as then might be utilized in different applications. Focus on the overall “super-structural” poset goes beyond ordinary molecular structure in attending to how a structure fits into a (reaction) network, and thereby brings an extra “dimension” to conventional stereochemical theory. The possibility that different molecular properties vary smoothly along chains of interconnections in such a super-structure is a natural assumption for a novel approach to molecular property and bioactivity correlations. Different manners to interpolate/ extrapolate on a poset network yield quantitative super-structure/activity relationships (QSSARs), with some numerical fits, e.g., for properties of polychlorinated biphenyls (PCBs) seemingly being quite reasonable. There seems to be promise for combinatoric posetic ideas.


Posets, partial orderings, reaction networks, substitution reactions, QSAR, QSSAR


Texas A University at Galveston, Galveston, Texas 77553-1675, USA.

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