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.
Keywords: Aliivibrio fischeri; antagonism; antibiotics; co-toxicity coefficient; concentration addition; cross point hypothesis; isobole; mixture hormesis.