Much ado about interaction: A combination of linear processes yields non-linear toxic effects in chemical mixtures

Predicting chemical mixture toxicity is an important issue for risk assessment. Loewe's concentration addition (CA) is a major model for predicting such toxicity. The CA is an additivity-based model, and if the results of toxicity test deviate from the CA prediction, it is considered that the toxic effect of the mixture is non-additive, and that "interaction" has played some role. In the present study, using as an example a biotic ligand model (BLM), which predicts metal toxicities, we theoretically investigated the toxic effect of mixture and found that the effects are almost always non-additive if the effects are evaluated by total metal concentrations, and the non-additivity is not derived by interactions among metals but by a combination of processes of metal kinetics. Once non-additive effects are observed in chemical mixture, it is often expected that there should be some complex toxic mechanisms or some toxic interaction. Our results suggest that the expectation may not be always true. Since at least two processes are entrained in the metal toxicity (metal speciation and binding of metals to biotic ligand in BLM framework), there is a possibility that the non-additivity is generated by the combination of processes and interaction is nothing to do with it. Our results imply that toxic effects of metal mixture can be predicted more easily than we generally expected.