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Combinatorics of Reaction-Network Posets

[ Vol. 11 , Issue. 9 ]

Author(s):

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

Abstract:


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.

Keywords:

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

Affiliation:

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



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