The complex network induced by a sequence of substitution reactions on a chemical structure generates a partially ordered set (or poset) oriented graph. Such a poset can be used to develop network-QSAR models to predict various molecular properties with quantitative superstructure-activity relationships (QSSARs). These novel network- QSAR models look beyond simple molecular structure and chemical descriptors, and predict molecular properties from the topology of a poset network and from the embedding of a chemical compound into a reaction network. We demonstrate this novel quantitative structure-activity relationship (QSAR) approach for the prediction of chromatographic retention properties of polychlorinated biphenyls (PCBs). PCBs have become worldwide pollutants due to their presence in the environment. Exposure to PCBs can permanently damage the nervous, reproductive, and immune systems. PCBs are known carcinogens and have been linked with the development of various forms of cancer including skin and liver. To predict the chromatographic properties for PCBs we generate the substitution reaction poset, which is a formal chlorosubstitution network which progresses from biphenyl to decachlorobiphenyl. Three network-QSAR models are compared, namely poset-average, splinoid poset, and cluster expansion QSSAR models, to estimate the chromatographic properties in different conditions (of column, temperature, or detector) for all 209 PCB congeners. Excellent results are obtained for all QSSAR chromatographic models. Based on the poset reaction diagram, all these three QSSAR models reflect in distinct ways the topology of the network describing the interconversion of chemical species. QSSAR equations based on poset reaction networks add a supramolecular dimension to QSAR models.
Keywords: Quantitative structure-activity relationship (QSAR), network-QSAR, quantitative superstructure-activity relationships (QSSARs), polychlorinated biphenyls (PCBs), reaction network, partially ordered set (poset), Hasse diagram, chromatographic retention time, high-resolution gas chromatography, polychlorinated biphenyls, supramolecular dimension, decachlorobiphenyl, electron capture detectors, chloro-substitution network
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