BNNmix: A new approach for predicting the mixture toxicity of multiple components based on the back-propagation neural network

Abstract The chemical mixtures in various environmental media not only have concentration diversity but also mixture-ratio diversity. It is impossible to experimentally determine the toxicities of all mixtures; therefore, it is necessary to develop effective methods based on models to predict mixture toxicity. In this study, a new approach (BNNmix) based on the back-propagation neural network (BPNN) was developed and used to predict the toxicities of seven-component mixtures (consisting of two substituted phenols, two pesticides, two ionic liquids, and one heavy metal) on Caenorhabditis elegans. We found that the combined toxicities of various mixtures used in the experiments were neither global concentration-additive nor global response-additive, which implied that it was impossible to accurately predict the toxicities of such mixtures by using common models such as concentration addition (CA) and response addition (independent action, IA). Using the BNNmix approach to estimate or predict the toxicities of the mixtures under test, it was found that the predictive toxicities of various mixtures with different mixture ratios and concentrations were almost in accordance with those observed experimentally. Unlike the CA and IA models, the BNNmix approach can predict not only the toxicities of mixtures having toxicological interactions but also those with global concentration or response additivities.