How to analyse and account for interactions in mixture toxicity with toxicokinetic-toxicodynamic models

The assessment of chemical mixture toxicity is one of the major challenges in ecotoxicology. Chemicals can interact, lead-ing to more or less effects than expected, commonly named synergism and antagonism respectively. The classic ad hoc approach for the assessment of mixture effects is based on dose-response curves at a single time point, and is limited to identifying a mixture interaction but cannot provide predictions for untested exposure durations, nor for scenarios where exposure varies in time. We here propose a new approach using toxicokinetic-toxicodynamic modelling: The General Unified Threshold model of Survival (GUTS) framework, recently extended for mixture toxicity assessment. We designed a dedicated mechanistic interaction module coupled with the GUTS mixture model to i) identify interactions, ii) test hy-potheses to identify which chemical is likely responsible for the interaction, and finally iii) simulate and predict the effect of synergistic and antagonistic mixtures. We tested the modelling approach experimentally with two species (Enchytraeus crypticus and Mamestra brassicae) exposed to different potentially synergistic mixtures (composed of: prochloraz, imidacloprid, cypermethrin, azoxystrobin, chlorothalonil, and chlorpyrifos). Furthermore, we also tested the model with previously published experimental data on two other species (Bombus terrestris and Daphnia magna) exposed to pesticide mixtures (clothianidin, propiconazole, dimethoate, imidacloprid and thiacloprid) found to be synergistic or antagonistic with the classic approach. The results showed an accurate simulation of synergistic and antagonistic effects for the different tested species and mixtures. This modelling approach can identify interactions accounting for the entire time of exposure, and not only at one time point as in the classic approach, and provides predictions of the mixture effect for untested mixture exposure scenarios, including those with time-variable mixture composition.