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While in vitro testing is used to identify hazards of chemicals, nominal in vitro assay concentrations may misrepresent potential in vivo effects and do not provide dose–response data which can be used for a risk assessment. We used reverse dosimetry to compare in vitro effect concentrations-to-in vivo doses causing toxic effects related to endocrine disruption. Ten compounds (acetaminophen, bisphenol A, caffeine, 17α-ethinylestradiol, fenarimol, flutamide, genistein, ketoconazole, methyltestosterone, and trenbolone) have been tested in the yeast estrogen screening (YES) or yeast androgen-screening (YAS) assays for estrogen and androgen receptor binding, as well as the H295R assay (OECD test guideline no. 456) for potential interaction with steroidogenesis. With the assumption of comparable concentration–response ratios of these effects in the applied in vitro systems and the in vivo environment, the lowest observed effect concentrations from these assays were extrapolated to oral doses (LOELs) by reverse dosimetry. For extrapolation, an eight-compartment Physiologically Based Toxicokinetic (PBTK) rat model based on in vitro and in silico input data was used. The predicted LOEL was then compared to the LOEL actually observed in corresponding in vivo studies (YES/YAS assay versus uterotrophic or Hershberger assay and steroidogenesis assay versus pubertal assay or generation studies). This evaluation resulted in 6 out of 10 compounds for which the predicted LOELs were in the same order of magnitude as the actual in vivo LOELs. For four compounds, the predicted LOELs differed by more than tenfold from the actual in vivo LOELs. In conclusion, these data demonstrate the applicability of reverse dosimetry using a simple PBTK model to serve in vitro–in silico-based risk assessment, but also identified cases and test substance were the applied methods are insufficient.

Tree-like polyphenyl systems form an important class of compounds in chemistry, in particular material science and polymers. The importance can be seen in LEDs, transmitters, and electronics. In recent years, many extremal results regarding such systems under specific constraints have been reported. More specifically are the sub-categories of such systems with extremal Wiener indices. In this article, we provide a labelling of the vertices on each hexagon (i.e., the corresponding benzene ring), which facilitates the illustration of a treelike polyphenyl system with its corresponding tree structure. This approach helps to characterize the extremal tree-like polyphenyl systems with respect to the Wiener index and compare such systems in general within isometric molecules and between molecules of different underlying tree structures. The results can be used to order these systems, which will aid in predicting the physical properties of compounds. We also briefly examined tree-like polyphenyl systems that resulted from different tree structures.