An interaction model for estimating in vitro estrogenic and androgenic activity of chemical mixtures

There is a need to better understand and predict the biological activity and interaction of chemical constituents in mixtures. Many existing methods assume that the mixture components are additive, and in the case of endocrine disruption, deviation from additivity may occur and render predictions inconclusive. In this study, an alternate index, aRP, which enables the quantification of an antagonistic interaction from analytically derived concentrations of chemical constituents within a mixture that act upon the same molecular target is described. The index is calculated by measuring the degree to which the test compound modulates the activity of a standard hormone as a function of mixture proportions. The aRP was shown to be valid for additive mixtures. It theoretically estimates the product of the relative potential and the interaction index inverse for nonadditive mixtures. The aRP values were computed for agonists and antagonists of both the estrogen and androgen receptors by using yeast-based methods (YES and YAS). The resulting aRP estimates were then validated using higher order mixtures of agonists and antagonists. The use of aRP led to improved predictions compared to estimates based on the toxicity equivalent factor (TEF) approach. The aRP model yielded estimates that were statistically indistinguishable (α = 0.01) from the measured responses in 75% of the 32 mixtures tested. By the same criteria, the TEF approach successfully predicted 34% of the mixtures. Both the aRP and TEF approach correlated well with the observed responses (Pearson R = 0.98 and 0.84, respectively); however, the TEF estimates produced higher percent errors, particularly in mixtures with higher proportions of antagonists. It is suggested that the use of the aRP index allows for a better approximation of the net activity captured by the bioassays through the use of chemically derived concentrations.