Integrated fuzzy concentration addition–independent action (IFCA–IA) model outperforms two-stage prediction (TSP) for predicting mixture toxicity

Mixture toxicities were determined for 12 industrial organic chemicals bearing four different modes of toxic action (MOAs) to Vibrio fischeri, to compare the predictability of the integrated fuzzy concentration addition–independent action (IFCA–IA) model and the two-stage prediction (TSP) model. Three mixtures were designed: The first and second mixtures were based on the ratios of each component at the 1% and 50% effect concentrations (EC1 and EC50), respectively; and the third mixture contained an equimolar ratio of individual components. For the EC1, EC50 and equimolar ratio, prediction errors from the IFCA–IA model at the 50% experimental mixture effects were 0.3%, 6% and 0.6%, respectively; while for the TSP model, the corresponding errors were 2.8%, 19% and 24%, respectively. Thus, the IFCA–IA model performed better than the TSP model. The IFCA–IA model calculated two weight coefficients from the molecular structural descriptors, which weigh the relation between concentration addition (CA) and independent action (IA) through the fuzzy membership functions. Thus, MOAs are not pre-requisites for mixture toxicity prediction by the IFCA–IA approach, implying the practicability of this method in toxicity assessment of mixtures.