An integrated addition and interaction model for assessing toxicity of chemical mixtures

The high propensity for simultaneous exposure to multiple environmental chemicals necessitates the development and use of models that provide insight into the toxicity of chemical mixtures. In this study, we developed a mathematical model that combines concepts of concentration addition, response addition, and toxicokinetic chemical interaction to assess toxicity of chemical mixtures. A ternary mixture of acetylcholinesterase inhibiting organophosphates (malathion and parathion) and the P450 inhibitor piperonyl butoxide was used to model toxicity. Concentration-response curves were generated for individual chemicals as well as for mixtures of the chemicals using acute toxicity tests with Daphnia magna. The toxicity of binary combinations of malathion and parathion adhered to the principles of concentration addition. The contribution of piperonyl butoxide to mixture toxicity was integrated using a model for response addition. Piperonyl butoxide also modified the toxicity of the organophosphates by inhibiting their metabolic activation. The antagonistic effects of piperonyl butoxide towards the organophosphates were quantified as coefficients of interactions (K-functions) and incorporated into the mixture model. Finally, toxicity of the ternary mixture was modeled at 30 different mixture formulations using three additive models that assumed no interaction (concentration addition, response addition, and integrated addition) and using the integrated addition and interaction (IAI) model. Toxicity of the 30 mixtures was then experimentally determined and compared to model results. Only the IAI model accurately predicted the toxicity of the mixtures. The IAI model holds promise as a means for assessing hazard of complex chemical mixtures.