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 (EC_m) and maximum stimulatory effect (E_m) 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.

Chirality is an important property of molecules. The study of biological activity and toxicity of chiral molecules has important theoretical and practical significance for toxicology, pharmacology, and environmental science. The toxicological significance of chiral ionic liquids (ILs) has not been well revealed. In the present study, the enantiomeric joint toxicities of four pairs of chiral ILs 1-alkyl-3-methylimidazolium lactate to Allivibrio fischeri were systematically investigated by using a comprehensive approach including the co-toxicity coefficient (CTC) integrated with confidence interval (CI) method (CTCICI), concentration-response curve (CRC), and isobole analysis. The direct equipartition ray (EquRay) design was used to design five binary mixtures of enantiomers according to molar ratios of 1:5, 2:4, 3:3, 4:2, and 5:1. The toxicities of chiral ILs and their mixtures were determined using the microplate toxicity analysis (MTA) method. Concentration addition (CA) and independent action (IA) were used as the additive reference models to construct the predicted CRC and isobole of mixtures. On the whole, there was an enantioselective toxicity difference between [BMIM]D-Lac and [BMIM]L-Lac, and [HMIM]D-Lac and [HMIM]L-Lac, while no enantioselective toxicity difference was observed for [EMIM]D-Lac and [EMIM]L-Lac, and [OMIM]D-Lac and [OMIM]L-Lac. Thereinto, the enantiomer mixtures of [BMIM]D-Lac and [BMIM]L-Lac, and [HMIM]D-Lac and [HMIM]L-Lac presented antagonistic action, and the enantiomer mixtures of [EMIM]D-Lac and [EMIM]L-Lac, and [OMIM]D-Lac and [OMIM]L-Lac overall presented additive action. Moreover, the greatest antagonistic toxicity interaction occurred at the equimolar ratio of enantiomers. Based on these results, we proposed two hypotheses, (1) chiral molecules with enantioselective toxicity difference tended to produce toxicity interactions, (2) the highest or lowest toxicity was usually at the equimolar ratio and its adjacent ratio for the enantiomer mixture. These hypotheses will need to be further validated by other enantiomer mixtures.

The joint toxicities of [BMIM]BF₄, [BMIM]PF₆, and [HMIM]BF₄ on acetylcholinesterase (AChE) were systematically investigated by using a progressive approach from 1D single effect point, 2D concentration-response curve (CRC), to 3D equivalent-surface (ES) level. The equipartition equivalent-surface design (EESD) method was used to design 10 ternary mixtures, and the direct equipartition ray (EquRay) design was used to design 15 binary mixtures. The toxicities of ionic liquids (ILs) and their mixtures were determined using the microplate toxicity analysis (MTA) method. The concentration addition (CA), independent action (IA), and co-toxicity coefficient (CTC) were used as the additive reference model to analyze the toxic interaction of these mixtures. The results showed that the Weibull function fitted well the CRCs of the three ILs and their mixtures with the coefficient of determination (R²) greater than 0.99 and root-mean-square error (RMSE) less than 0.04. According to the CTC integrated with confidence interval (CI) method (CTCICI) developed in this study, the 25 mixtures were almost all additive action at 20% and 80% effect point levels. At 50% effect, at least half of the 25 mixtures were slightly synergistic action, and the remaining mixtures were additive action. Furthermore, the ESs and CRCs predicted by CA and IA were all within the CIs of mixture observed ESs and CRCs, respectively. Therefore, the toxic interactions of these 25 mixtures were actually additive action. The joint toxicity of the three ILs can be effectively evaluated by the ES method. We also studied the relationship between the mixture toxicities and component concentration proportions. This study can provide reference data for IL risk assessment of combined pollution.

The predicted toxicity of mixtures of imidazolium and pyridinium ionic liquids (ILs) in the ratios of their EC₅₀, EC₁₀, and NOEC (no observed effect concentration) were compared to the observed toxicity of these mixtures on luciferase. The toxicities of EC₅₀ ratio mixture can be effectively predicted by two-stage prediction (TSP) method, but were overestimated by the concentration addition (CA) model and underestimated by the independent action (IA) model. The toxicities of EC₁₀ ratio mixtures can be basically predicted by TSP and CA, but were underestimated by IA. The toxicities of NOEC ratio mixtures can be predicted by TSP and CA in a certain concentration range, but were underestimated by IA. Our results support the use of TSP as a default approach for predicting the combined effect of different types of ILs at the molecular level. In addition, mixtures of ILs mixed at NOEC and EC₁₀ could cause significant effects of 64.1% and 97.7%, respectively. Therefore, we should pay high attention to the combined effects in mixture risk assessment.