Abstract
Hormesis is a concentration-response phenomenon characterized by low-concentration stimulation and high-concentration inhibition, which typically has a nonmonotonic J-shaped concentration-response curve (J-CRC). The concentration addition (CA) model is the gold standard for studying mixture toxicity. However, the CA model had the predictive blind zone (PBZ) for mixture J-CRC. To solve the PBZ problem, we proposed a segmented concentration addition (SCA) method to predict mixture J-CRC, which was achieved through fitting the left and right segments of component J-CRC and performing CA prediction subsequently. We selected two model compounds including chlortetracycline hydrochloride (CTCC) and oxytetracycline hydrochloride (OTCC), both of which presented J-CRC to Aliivibrio fischeri (AVF). The seven binary mixtures (M1–M7) of CTCC and OTCC were designed according to their molar ratios of 12:1, 10:3, 8:5, 1:1, 5:8, 3:10, and 1:12 referring to the direct equipartition ray design. These seven mixtures all presented J-CRC to AVF. Based on the SCA method, we obtained mixture maximum stimulatory effect concentration (ECm) and maximum stimulatory effect (Em) predicted by SCA, both of which were not available for the CA model. The toxicity interactions of these mixtures were systematically evaluated by using a comprehensive approach, including the co-toxicity coefficient integrated with confidence interval method (CTCICI), CRC, and isobole analysis. The results showed that the interaction types were additive and antagonistic action, without synergistic action. In addition, we proposed the cross point (CP) hypothesis for toxic interactive mixtures presenting J-CRC, that there was generally a CP between mixture observed J-CRC and CA predicted J-CRC; the relative positions of observed and predicted CRCs on either side of the CP would exchange, but the toxic interaction type of mixtures remained unchanged. The CP hypothesis needs to be verified by more mixtures, especially those with synergism. In conclusion, the SCA method is expected to have important theoretical and practical significance for mixture hormesis.
Highlights
Hormesis is a concentration-response phenomenon characterized by low-concentration stimulation and high-concentration inhibition [1], which typically has a nonmonotonic concentration-response curve (CRC) [2]
The J-shaped concentration-response curve (J-CRC) can be fitted by the five-parameter BP function with the root-mean-square error (RMSE) less than 0.05 and the coefficient of determination (R2) greater than 0.98
Speaking, the concentration addition (CA) model basically achieved the whole prediction of mixture J-CRC, there was a very small predictive blind zone (PBZ) notably in M7, which was caused by the Em difference between chlortetracycline hydrochloride (CTCC) and oxytetracycline hydrochloride (OTCC)
Summary
Hormesis is a concentration-response phenomenon characterized by low-concentration stimulation and high-concentration inhibition [1], which typically has a nonmonotonic CRC [2]. Antibiotics in low concentration promoted yeast growing, while presenting inhibitory effects in high concentration, which were observed by the father of hormesis Schulz as early as 1888 [20]. Since the IA model would lose its probabilistic meaning when negative values (often referred to as a stimulatory response) were included [27], IA was once considered unfit to predict mixture J-CRC. Martin-betancor et al [32] reported a prediction method for mixture inverted U-CRC. Predicting mixture whole J-CRC was achieved through the docking between left and right curves. This method can be called the segmented concentration addition (SCA) model
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