Can the joint effect of ternary mixtures be predicted from binary mixture toxicity results?

The joint effect of the majority of chemical mixtures can be predicted using the reference model of Concentration Addition (CA). It becomes a challenge, however, when the mixtures include chemicals that synergise or antagonise the effect of each other. In this study we examine if the deviation from CA of seven ternary mixtures of interacting chemicals can be predicted from knowledge of the binary mixture responses involved. We hypothesise that the strongest interactions will take place in the binary mixtures and that the size of the ternary mixture response can be predicted from knowledge of the binary interactions. The hypotheses were tested using a stepwise modelling approach of incorporating the information held in binary mixtures into a ternary mixture model, and comparing the model predictions with observed ternary mixture toxicity data derived from studies of interacting chemical mixtures on the floating plant Lemna minor and the bacteria Vibrio fischeri. The results showed that for both the antagonistic and the synergistic ternary mixtures the ternary model predictions were superior to the conventional CA reference model and provided robust estimations of the size of the experimentally derived ternary mixture toxicity effects.

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► Predicting the joint effect of interacting mixtures is a challenge.
► We present a model to predict the joint effect of ternary mixtures based on their binary interactions.
► The model was validated on experimental data on Lemna minor and Vibrio fischeri.
► The results showed that the ternary model was superior to that of Concentration Addition.