A new effect residual ratio (ERR) method for the validation of the concentration addition and independent action models

Background, aim, and scope Glutaraldehyde (GA) often acts as an effective sterilant, disinfectant, and preservative in chemical products. It was found that GA had clearly acute toxicity to aquatic organisms. Furthermore, GA in natural environment could not exist as single species but as complex mixtures. To explore the toxicity interaction between GA and the other environmental pollutant, it is necessary to determine the mixture toxicities of various binary mixtures including GA. Two reference models, concentration addition (CA) and independent action (IA), are often employed to evaluate the mixture toxicity, which can be finished by comparing the concentration-response curves (CRCs) predicted by the reference models with the experimental CRC of the mixture. However, the CRC-based method cannot effectively denote the degree of the deviations from the reference models, especially at very low effect levels. Though the model deviation ratio (MDR) can be used to quantitatively evaluate the deviation of a mixture at EC50 level from the reference model, it is difficult to evaluate the deviations at the lower effect levels. Therefore, the primary aim of this study was to develop a new effect residual ratio (ERR) method to validate the deviations from the reference models at various effect levels. Materials and methods Four chemicals having possible dissimilar mode of actions with GA, acetonitrile (ACN), dodine (DOD), simetryn (SIM), and metham sodium (MET), were selected as another component in the binary mixtures including GA, which constructed four binary mixtures, GA-ACN, GA-DOD, GA-SIM, and GA-MET ones. For each binary mixture, two equipotent mixture rays where the concentration ratios of GA to another mixture component are respectively EC50 and EC5 ones were designed and their toxicities (expressed as a percent inhibition to Photobacterium phosphoreum) were determined by microplate toxicity analysis. The observed concentration-response curve (CRC) of a ray was compared with that predicted by CA or IA model to qualitatively assess the toxicity interaction of the mixture ray. To quantitatively and effectively examine the deviations at various effect levels from the reference models, a new concept, ERR at an effect, was defined, and the ERR was employed to evaluate the deviation at various effects with confidence intervals. Results For three binary mixtures, GA-ACN, GA-DOD, and GA-SIM, the CRCs predicted by IA models were almost located in the 95% confidence intervals of the experimental CRCs for both equipotent mixture rays, which indicated the independent actions between binary mixture components. However, two rays of GA-MET binary mixture displayed a little synergistic action because both CRCs predicted by CA and IA were lower than the experimental CRC. ERR showed the same results as MDR, but ERR results at low effect area were clearer than MDR ones. Discussion In CRC comparison, the deviation of CA (for GA-ACN, GA-DOD, and GA-SIM combinations) or IA (for GA-MET) model from the experimental values could be obviously observed at medium area of the CRC. However, at very low effect levels, both deviations of CA and IA and difference between CA and IA model predictions were not very apparent. Thus, it was difficult to confirm which model, CA or IA, had better predicted power at very low effect levels. MDR in many literatures often refers to a ratio at EC50 level. It was also difficult to reflect not only the deviation fact at the other ECx but also the deviation uncertainty. After we extended the definition of MDR to all ECx and examined the 95% confidence intervals based on observation, the plot of the redefined MDRs at many effect levels could better explain the deviations of CA or IA model from the observation. However, MDRs at very low effect levels did not still reflect the high uncertainty there. The ERRs defined in our paper could explicitly explain the degree of deviation from the reference models and especially reflect the high uncertainty at very low effects. It could be said that the ERR is a better indicator than MDR. Conclusions The new ERR validation method developed in our laboratory could provide us with the information about the toxicity interaction between the mixture components and quantitatively assess the accuracy of the reference models (CA or IA) at whole effect levels. The ERR method conquered the invalidation of the classical CRC comparison method on the deviation decision at low effect levels and also got the advantage over the MDR methods. Recommendations and perspectives It holds promise to become an effective method of hazard and risk assessments of chemical mixtures by well characterizing the uncertainty at very low effect levels.