Study of the joint action of multi-component mixtures based on parameter σ2(k∙ECx) characterizing the shape difference of concentration-response curves.

A previous study has revealed that the parameter k∙ECx, characterizing the shape of concentration-response curves (CRCs), could predict the combined toxicity of binary mixtures. This study further explored the predictability of multi-component mixtures. Eleven component mixtures were designed using the uniform design ray, and the acute toxicity of the eleven environmental pollutants and their mixtures to Vibrio fischeri was determined using microplate toxicity analysis. We used independent action (IA) and the effect residual ratio (ERRx) models to evaluate the combined toxicity of multi-component mixtures and ascertain the functional relationship between σ2(k∙ECx), a parameter characterizing the CRC morphological difference of multi-component mixtures, and combined toxicity. The variance σ2(k∙ECx) of each component characteristic parameter of multi-component mixtures gradually increased in the concentration range, and the relationship between σ2(k∙ECx) and ERRx was consistent with the exponential function. The literature verification showed that this rule is generally applicable to the acute toxicity of multi-component mixtures to luminescent bacteria. The exponential function showed the variation rule of the joint action of multi-component mixtures. In the present study, the joint toxicity of multi-component mixtures can be predicted from single toxicity and small amount of multiple toxicity, circumventing complex multi-component toxicity experiments.