Predicting the hormesis and toxicological interaction of mixtures by an improved inverse distance weighted interpolation

Abstract

The prediction of toxicological interactions and hormesis of chemical mixtures is important because organisms are mostly exposed to numerous contaminants and typically to low dose of these mixtures, and it is still a challenge. Although many models have been developed to predict the mixture toxicities such as concentration addition (CA) and independent action (IA), they cannot solve these challenges perfectly. This study has developed an improved inverse distance weighted (IDW) interpolation for prediction of the mixture toxicities. IDW uses the mixture and the single compound as scatter points in space, and the space can be constructed by the concentration axes of various components in the mixture system. Some known mixtures (or the single compound) closest to the unknown mixture are selected as interpolation nodes. To be more accurate in calculation, a new normalization method for concentration has been proposed through dividing the concentration of the mixture and the single compound by the respective EC50 values. Sixteen binary mixture systems are selected for leave-one-out cross-validation and three binary mixture systems are selected for external validation. The results show that the accuracy of IDW is ≥95% for three types of mixtures including no hormetic component, one hormetic component (show no toxicological interaction), and two hormetic components. The IDW also show higher prediction accuracy than that of CA and IA. The IDW developed in this study can be used to predict the toxicity of various mixture systems, thus providing predictive information for chemical mixtures risk assessment. Keywords: Combined toxicity, Euclidean distance, Multi-component, Normalization, Cross validation