Empirical modeling of an in vitro activity of polychlorinated biphenyl congeners and mixtures.

The goal of this research is to predict an in vitro activity of polychlorinated biphenyl (PCB) congeners and their mixtures and to describe the relationship between this activity and chemical structure. The test system used multiple PCB concentrations on each cell culture plate in a repeated measures design, which improved precision for comparing between concentration levels. A weighted regression that accounted for this experimental design feature was used in fitting a nonlinear dose-response exponential model to the PCB concentration-activity data from an in vitro test system in which 3H-phorbol ester binding was measured in cerebellar granule cells exposed to different PCB congeners to test for their effects on protein kinase C translocation. The model allowed for the minimum level to be less than control, a common slope, and the estimation of the log of the concentration that produces an activity 50% above the control activity (E50) for 36 congeners and 3 commercial mixtures. Next, a weighted logistic regression using a second order response model in the variables Clortho, Clpara, and Clmeta was used to relate the estimated log E50s to indicators of chemical structure. This model was preferred over models that might seem more mechanistically based because in internal validation, it attained a smaller PRESS statistic (the sum of squares between all observed and predicted observations) than other models. Evidently, this second order model makes more efficient use of parameters than other models considered. Plots of the predictions of the logistic second order response model versus log Kow confirm the usual pattern that congeners with intermediate levels of log Kow are the more active. The data of three commercial mixtures were included in this regression by assuming a common combination index (ratio of observed E50 to predicted E50, assuming dose addition). The logistic model suggests that congeners with one, two, or three chlorine substitutions at the ortho position are more active than other congeners. Also, congeners with log Kow between 5.2 and 6.6 are generally more active. The estimated combination index indicated that the joint action of PCB congeners in the three commercial mixtures was less than dose additive. The error sum of squares was significantly large, which may indicate a lack of fit of the logistic model. Empirical Bayes estimates (EBE) are weighted averages of model predictions and observations of E50s and can be better estimates than the fitted model when there is a lack of fit. The PRESS statistic for the EBE indicated larger prediction error than for the logistic model, but the EBE provided better estimates of commercial mixture E50s based on dose addition. This may indicate that the logistic model is not incorporating all the information in the single congener data needed to predict mixtures.