Characteristics of concentration–inhibition curves of individual chemicals and applicability of the concentration addition model for mixture toxicity prediction

Abstract

The concentration addition (CA) model has been widely applied to predict mixture toxicity. However, its applicability is difficult to evaluate due to the complexity of interactions among substances. Considering that the concentration–response curve (CRC) of each component of the mixture is closely related to the prediction of mixture toxicity, mathematical treatments were used to derive a characteristic index kECx (k was the slope of the tangent line of a CRC at concentration ECx). The implication is that the CA model would be applicable for predicting the mixture toxicity only when chemical components have similar kECx in the whole or part of the concentration range. For five selected chemicals whose toxicity was detected using luminescent bacteria, sodium dodecyl benzene sulfonate (SDBS) showed much higher kECx values than the others and its existence in the binary mixtures brought about overestimation of the mixture toxicity with the CA model. The higher the mass ratio of SDBS in a multi-mixture was, the more the toxicity prediction deviated from measurements. By applying the method proposed in this study to analyze some published data, it is confirmed that some components having significantly different kECx values from the other components could explain the large deviation of the mixture toxicity predicted by the CA model.