Mathematical models for predicting the toxicity of micropollutant mixtures in water

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. 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. 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. 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. 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. 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.

New methods of top-to-down mixture toxicity prediction: A case study of eliminating of the effects of cosolvent from binary mixtures

A comparison of mixture toxicity assessment: Examining the chronic toxicity of atrazine, permethrin and chlorothalonil in mixtures to Ceriodaphnia cf. dubia

Various chemical pollutants are always existing as mixtures in real environment. Currently, the assessment and prediction of chemical mixture toxicity is the hotspots and difficulties in environmental chemistry. To accurately assess and predict the toxicity of a chemical mixture, it is necessary to validate whether the toxicities of various components in the mix- ture is additive or not. Three common additive reference models, the effect summation (ES), concentration addition (CA), and independent action (IA), are available to determine the toxicity interaction. Synergism or antagonism between the compo- nents in a mixture can be identified if the observed toxicity of the mixture deviates from the prediction in terms of ES, CA, or IA. The resulting interaction type (synergism or antagonism) may be inconsistent according to those reference models ap- plied. Although the ES model is the earliest application model proposed to assess and predict mixture toxicity, its application in environmental chemistry was affected due to its limit in the interpretation of the so-called sham combination constructed by the same compound. The IA model is suitable to model the toxicities of mixtures consisting of the components showing dissimilar modes of actions. The CA can predict the toxicities of the mixtures consisting of the chemicals with similar modes of actions and can rationally interpret the sham combination which is impossible to be depicted by the ES model. The CA is therefore often considered as a standard additive model for the toxicity prediction of a chemical mixture. However, the CA is only a pragmatic model because it has no solid theory basis and no direct connection with the mechanism of action resulting in toxicity. Furthermore, there are so-called predictive blind zones in some concentration intervals on the concentration- response curve where the toxicities of mixtures cannot be predicted by the CA. So, it is necessary to carefully use the CA model.

Acute toxicity of binary and ternary mixtures of La, Ce and Dy on Daphnia magna: Toxicity patterns depend on the ratios of the components and the concentration gradient

Development and validation of a metal mixture bioavailability model (MMBM) to predict chronic toxicity of Ni-Zn-Pb mixtures to Ceriodaphnia dubia

Perfluorooctane sulfonic acid (PFOS) and perfluorooctanoic acid (PFOA) have emerged as two concerning contaminants in recent years. However, there is limited information about their mixture toxicity to aquatic organisms. In the present study, the single and mixture toxicity of PFOA and PFOS to zebrafish (Danio rerio) embryo were tested, and the mixture toxicity was predicted by concentration addition (CA) and independent action (IA) models. It is found that PFOS and PFOA have synergistic effect at 96 hpf, while this kind of synergistic effect is not obvious at 72 hpf. CA and IA models both could predict the 72 h mixture toxicity, while underestimate the 96 h mixture toxicity.

The toxicities of chemical mixtures containing 10 compounds, detected in wastewater treatment plant (WWTP) effluents, were investigated using Daphnia magna in a two-step prediction (TSP) model. The 10 chemicals determined by gas chromatography/ mass spectrometry in WWTP effluents included three groups: Three acetylcholinesterase inhibitors, six narcosis inhibitors, and one seedling root inhibitor. In the first step, a concentration addition (CA) model was used to predict the mixture toxicities for the three component groups with similar modes of action; in the second step, an independent action (IA) model was used for the newly developed concentration-response curves from the three CA predictions. The CA predictions did not show a statistically significant difference from the observed results with respect to the three groups of chemicals, whereas the IA model did not conform to the experimental results. Therefore, the concentration-response curves obtained from the mixture toxicity tests in each group was considered as a single curve and applied in the next step of the mixture toxicity prediction. However, the observed toxicity of the 10-chemical mixture showed large differences from the results of the IA and CA model predictions, whereas the TSP model predicted the toxicity well and with statistical significance (p = 0.0501, n = 17). This suggests that the TSP model would provide a valid prediction for a randomly selected chemical mixture having various modes of action if the concentration-response function for an individual component is obtained.

Concentration addition and independent action model: Which is better in predicting the toxicity for metal mixtures on zebrafish larvae

The study aimed to assess the single and joint lethal toxicity, type of interaction and the extent to which simple mathematical model of concentration addition (CA), independent action (IA) and generalized concentration addition (GCA) could predict the joint toxicity of copper hydroxide and glyphosate mixture in Clarias gariepinus. Static bioassay were setup to determine the individual and combined (based on ratio 1:2) lethal concentrations (LCx) of the pesticides. Data from the static bioassays were then fitted into the synergistic ratio (SR), concentration-addition (toxicity unit; TU) and isobologram model to determine the type of interaction between the different classes of pesticides, while the CA, IA and GCA models were used to predicted the observed mixture effects. The estimated 24 h, 48 h, 72 h and 96 h LC50 for copper hydroxide were 198.66 mg/L, 167.51 mg/L, 138.64 mg/L, and 104.82 mg/L; glyphosate were 162.92 mg/L, 103.88 mg/L, 61.95 mg/L, and 52.6l mg/L; while the mixtures were 63.18 mg/L, 59.06 mg/L, 56.42 mg/L, and 50.67 mg/L, respectively. Glyphosate was 2 times more toxic than copper hydroxide to C. gariepinus when acting singly. The SR and RTU was <1 indicate that the interaction between the pesticides was synergistic. Synergism was also corroborated by the isobologram model. The interaction of the mixture of copper hydroxide and glyphosate followed the IA model while the CA and GCA model underestimated the observed mixture effects. The study showed that copper hydroxide was practically non-toxic, while glyphosate and the mixture were slightly toxic to C. gariepinus

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.

Arsenic (As) and lead (Pb) are environmental pollutants found in common sites and linked to similar adverse health effects. Multiple studies have investigated the toxicity of each metal individually or in complex mixtures. Studies defining the joint interaction of a binary exposure to As and Pb, especially during the earliest stages of development, are limited and lack confirmation of the predicted mixture interaction. We hypothesized that a mixture of As (iAsIII) and Pb will have a concentration addition (CA) interaction informed by common pathways of toxicity of the two metals. To test this hypothesis, developing zebrafish (1–120 h post fertilization; hpf) were first exposed to a wide range of concentrations of As or Pb separately to determine 120 hpf lethal concentrations. These data were then used in the CA and independent action (IA) models to predict the type of mixture interaction from a co-exposure to As and Pb. Three titration mixture experiments were completed to test prediction of observed As and Pb mixture interaction by keeping the Pb concentration constant and varying As concentrations in each experiment. The prediction accuracy of the two models was then calculated using the prediction deviation ratio (PDR) and Chi-square test and regression modeling applied to determine type of interaction. Individual metal exposures determined As and Pb concentrations at which 25% (39.0 ppm Pb, 40.2 ppm As), 50% (73.8 ppm Pb, 55.4 ppm As), 75% (99.9 ppm Pb, 66.6 ppm As), and 100% (121.7 ppm Pb, 77.3 ppm As) lethality was observed at 120 hpf. These data were used to graph the predicted mixture interaction using the CA and IA models. The titration experiments provided experimental observational data to assess the prediction. PDR values showed the CA model approached 1, whereas all PDR values for the IA model had large deviations from predicted data. In addition, the Chi-square test showed most observed results were significantly different from the predictions, except in the first experiment (Pb LC25 held constant) with the CA model. Regression modeling for the IA model showed primarily a synergistic response among all exposure scenarios, whereas the CA model indicated additive response at lower exposure concentrations and synergism at higher exposure concentrations. The CA model was a better predictor of the Pb and As binary mixture interaction compared to the IA model and was able to delineate types of mixture interactions among different binary exposure scenarios.

The combined toxicities of binary mixtures of veterinary pharmaceutical active compounds were examined using the bioluminescent bacterium Aliivibrio fischeri as a test organism (Microtox® test). Mixtures were prepared at an equitoxic ratio that corresponded to the inhibitory concentration, 10% (IC10) of individual pharmaceutical active compounds. In addition, the toxicity was determined of a multicomponent mixture that contained all of the investigated pharmaceutical active compounds mixed at a ratio corresponding to their individual predicted no-effect concentration (PNEC) values. The experimental results were successively compared with those obtained by applying the 2 most widely used models for predicting mixture toxicity, the concentration addition (CA) and independent action (IA) models. Although the toxicity of the multicomponent mixture tested was well predicted by the CA and IA models, deviations from the model predictions were found for almost all of the binary mixtures. The deviations from the CA and IA models were greater at lower concentrations, particularly when diclofenac sodium and amoxicillin were present in the mixture. Based on these results, another hypothesis was tested, that of toxicological interactions occurring in binary mixtures (in the direction of synergistic or antagonistic effects), by applying the combination index method, which allowed for computerized quantification of synergism, the additive effect and antagonism. The application of this method confirmed, for at least half of the binary combinations, the clear presence of synergistic deviations at the lowest tested concentrations, with a tendency toward antagonism at the higher ones. In 1 case, a relevant antagonistic interaction was observed. Environ Toxicol Chem 2017;36:815-822. © 2016 SETAC.

The toxicities of the heavy metals (Pb, Cd, Ni, Zn, and Co) and their ternary mixtures with Sodium Dodecyl Sulfate (SDS) to Lysinibacillus fusiformis isolated from Talinum fruticosum farms irrigated with Otamiri River water in Owerri, Imo State, Nigeria, were assessed using dehydrogenase activity (DHA) restriction as an endpoint. Fixed ratio mixtures (arbitrary concentration ratio (ABCR) and equi-effect concentration ratio (EECR) mixtures) were formulated to evaluate the combined toxicities of these toxicants. Toxicities were predicted with concentration addition (CA) and independent action (IA) models and compared with the experimentally observed toxicities. The response of the bacterium to the toxicants’ toxicities was concentration-dependent and gradually inhibited the DHA as the concentration increased, with percentage inhibitions greater than 95% at 0.5 mM for Zn, 1 mM for Ni, 0.3 mM for Pb, 0.08 mM for Cd, 0.7 mM for Co, as well as 10 mM for SDS. The 50% effective concentrations (EC50S) of the individual toxicants differed significantly from one another (P &lt; 0.05). All the dose-response relationships of the ABCR and EECR mixtures and the individual toxicants could be described by a logistic function. In most binary mixtures, predicted toxicities from the CA and IA models were significantly different from the observed toxicities. In ABCR1 mixture ratio of SDS + Cd2+ mixtures, CA and IA models correctly predicted the experimental data at different points, while the IA model correctly predicted the experimental data in the EECR50 mixture ratio of SDS + Pb2+ mixture. In SDS + Co2+ mixtures, EC50S predicted by both models were identical. The effects of the mixtures interactions showed both weak and strong synergism, as well as additive against the soil bacterium. Similarly, in all but ABCR1 and ABCR2 mixture ratios of SDS + Cd + Zn ternary mixtures, the experimentally observed EC50, CA- and IA-predicted EC50S were significantly different from one another (P &lt; 0.05). Furthermore, both models greatly underestimated the mixture toxicity at all tested mixture ratios and were strongly synergistic against the soil bacterium. The use of such contaminated water for irrigation could negatively affect the soil bacterial community and, by extension, soil fertility, going by the possible interaction between heavy metals and SDS.

To develop the risk prediction technology for mixture toxicity, a reliable and extensive dataset of experimental results is required. However, most published literature only provides data on combinations containing two or three substances, resulting in a limited dataset for predicting the toxicity of complex mixtures. Complex mixtures may have different mode of actions (MoAs) due to their varied composition, posing difficulty in the prediction using conventional toxicity prediction models, such as the concentration addition (CA) and independent action (IA) models. The aim of this study was to generate an experimental dataset comprising complex mixtures. To identify the target complex mixtures, we referred to the findings of the HBM4EU project. We identified three groups of seven to ten components that were commonly detected together in human bodies, namely environmental phenols, perfluorinated compounds, and heavy metal compounds, assuming these chemicals to have different MoAs. In addition, a separate mixture was added consisting of seven organophosphate flame retardants (OPFRs), which may have similar chemical structures. All target substances were tested for cytotoxicity using HepG2 cell lines, and subsequently 50 different complex mixtures were randomly generated with equitoxic mixtures of EC10 levels. To determine the interaction effect, we calculated the model deviation ratio (MDR) by comparing the observed EC10 with the predicted EC10 from the CA model, then categorized three types of interactions: antagonism, additivity, and synergism. Dose-response curves and EC values were calculated for all complex mixtures. Out of 50 mixtures, none demonstrated synergism, while six mixtures exhibited an antagonistic effect. The remaining mixtures exhibited additivity with MDRs ranging from 0.50 to 1.34. Our experimental data have been formatted to and constructed for the database. They will be utilized for further research aimed at developing the combined CA/IA approaches to support mixture risk assessment.