Evaluation of an asymmetry parameter for curve-fitting in single-chemical and mixture toxicity assessment

Modeling mixtures interactions in environmental toxicology

In the environment, organisms are exposed to mixtures of different toxicants, which may interact in ways that are difficult to predict when only considering each component individually. Adapting and expanding tools from pharmacology, the toxicology field uses analytical, graphical, and computational methods to identify and quantify interactions in multi-component mixtures. The two general frameworks are concentration addition, where components have similar modes of action and their effects sum together, or independent action, where components have dissimilar modes of action and do not interact. Other interaction behaviors include synergism and antagonism, where the combined effects are more or less than the additive sum of individual effects. This review covers foundational theory, methods, an in-depth survey of original research from the past 20 years, current trends, and future directions. As humans and ecosystems are exposed to increasingly complex mixtures of environmental contaminants, analyzing mixtures interactions will continue to become a more critical aspect of toxicological research.

Metal Mixture Toxicity of Ni, Cu, and Zn in Freshwater Algal Communities and the Correlation of Single-Species Sensitivities Among Single Metals: A Comparative Analysis

The effects assessment of metals is mainly based on data of single metals on single species, thereby not accounting for effects of metal mixtures or effects of species interactions. Both of these effects were tested in combination, thereby hypothesizing that the sensitivity of a community to synergistic mixture toxicity depends on the correlation of single-species sensitivities among the single metals. Single-metal and metal-mixture effects were tested in full concentration-response experiments (fixed ray of 1:1:3 and 5:1:13 mass ratio Ni:Cu:Zn) on eight single freshwater algal species and 14 algal communities of four species each. The mean correlation of single-species median effect concentrations among the single metals (Ni-Cu, Cu-Zn, and Zn-Ni) for all species in a community (r ̅ ) ranged from -0.4 to 0.9 among the communities; most of these (12/14) were positive. Functional endpoints (total biomass) were overall less sensitive than structural endpoints (Bray-Curtis similarity index) for communities with positively correlated single-species sensitivities among the single metals (r ̅ > 0.33 ), suggesting that such correlations indicate functional redundancy under metal-mixture stress. Antagonistic metal-mixture interactions were predominantly found in single species, whereas metal-mixture interactions were antagonistic and surprisingly synergistic for the communities, irrespective of the reference mixture model used (concentration addition or independent action). The mixture interactions close to the carrying capacity (day 7) of communities gradually shifted from antagonism to more noninteractions with increasing correlation of single-species sensitivities among the single metals. Overall, this suggests that functional redundancy under mixed-metal stress comes at the cost of reduced biodiversity and that synergisms can emerge at the community level without any synergisms on the single-species level. Environ Toxicol Chem 2023;42:2666-2683. © 2023 SETAC.

The Occurrence of Oxidative Stress Induced by Silver Nanoparticles in Chlorella vulgaris Depends on the Surface-Stabilizing Agent

Silver nanoparticles (AgNPs) are of great interest due to their antimicrobial properties, but their reactivity and toxicity pose a significant risk to aquatic ecosystems. In biological systems, AgNPs tend to aggregate and dissolve, so they are often stabilized by agents that affect their physicochemical properties. In this study, microalga Chlorella vulgaris was used as a model organism to evaluate the effects of AgNPs in aquatic habitats. Algae were exposed to AgNPs stabilized with citrate and cetyltrimethylammonium bromide (CTAB) agents and to AgNO₃ at concentrations that allowed 75% cell survival after 72 h. To investigate algal response, silver accumulation, ROS content, damage to biomolecules (lipids, proteins, and DNA), activity of antioxidant enzymes (APX, PPX, CAT, SOD), content of non-enzymatic antioxidants (proline and GSH), and changes in ultrastructure were analyzed. The results showed that all treatments induced oxidative stress and adversely affected algal cells. AgNO₃ resulted in the fastest death of algae compared to both AgNPs, but the extent of oxidative damage and antioxidant enzymatic defense was similar to AgNP-citrate. Furthermore, AgNP-CTAB showed the least toxic effect and caused the least oxidative damage. These results highlight the importance of surface-stabilizing agents in determining the phytotoxicity of AgNPs and the underlying mechanisms affecting aquatic organisms.

Comparison of the Anticancer Effects of Arvanil and Olvanil When Combined with Cisplatin and Mitoxantrone in Various Melanoma Cell Lines-An Isobolographic Analysis

Due to the unique structures of arvanil and olvanil, the drugs combine certain properties of both cannabinoids and vanilloids, which makes them able to stimulate both TPRV1 and CB1 receptors and causes them to be interesting agents in the setting of carcinoma treatment. The aim of this study was to investigate the cytotoxic and anti-proliferative effects of arvanil and olvanil when administered alone and in combination with cisplatin (CDDP) and mitoxantrone (MTX), using various primary (A375, FM55P) and metastatic (SK-MEL 28, FM55M2) human malignant melanoma cell lines. The results indicate that both arvanil and olvanil inhibited (dose-dependently) the viability and proliferation of various malignant melanoma cells, as demonstrated by MTT and BrdU assays. The safety profile of both arvanil and olvanil tested in human keratinocytes (HaCaT) and normal human melanocytes (HEMa-LP) revealed that neither arvanil nor olvanil caused significant cytotoxicity in HaCaT and HEMa-LP cell lines in LDH and MTT assays. Isobolographically, it was found that both arvanil and olvanil exerted additive interactions with MTX and antagonistic interactions with CDDP in the studied malignant melanoma cell lines. In conclusion, the combinations of arvanil or olvanil with MTX may be considered as a part of melanoma multi-drug therapy; however, the combination of these compounds with CDDP should be carefully considered due to the antagonistic interactions observed in the studied malignant melanoma cell lines.

Correlated Ni, Cu, and Zn Sensitivities of 8 Freshwater Algal Species and Consequences for Low-Level Metal Mixture Effects

Predicting metal sensitivities and metal mixture interactions for species within each trophic level is essential to understand the effects of metals at the ecosystem level. The present study was set up to explore the correlations of metal sensitivities among species and if these sensitivities or metal mixture interactions are related to growth or morphological traits. The toxicity of Ni, Cu, and Zn on algal growth was tested for 8 freshwater algal species when dosed singly and in combinations in phosphorus-limiting static systems. The metal sensitivities on specific growth rate (10% effect concentrations expressed as free ion activities) varied 2 to 3 orders of magnitude among species depending on metal. These sensitivities were unrelated (p > 0.05) to their specific growth rate (0.7-1.8 d^-1 ) or cell volume (10⁰ -10³ m³  cell^-1 ). Species-specific differences in one or more toxicokinetic and/or toxicodynamic (TKTD) processes are likely at the basis of this variation. The log-transformed metal sensitivities positively correlated (p < 0.1) among the species in all 3 binary combinations (Ni-Cu, Ni-Zn, and Cu-Zn), suggesting that species have correlated TKTD rates for these metals. Furthermore, they would also predict stronger effects of metal mixtures on algal community biodiversity than what would be expected without a positive correlation. Low-level metal mixture effects varied similarly, largely among species and mixture interactions that were highly variable: ranging from synergistic to antagonistic relative to independent action during exponential growth, whereas mixture interactions at 10% effect shifted toward additivity/synergism relative to concentration addition at carrying capacity. Some evidence was found for stronger synergistic mixture effects in smaller species. Overall, the present study highlights the importance of incorporating more species in sensitivity distributions and accounting for mixture toxicity in risk assessment. Environ Toxicol Chem 2021;40:2015-2025. © 2021 SETAC.

A statistical framework for assessing pharmacological responses and biomarkers using uncertainty estimates

High-throughput testing of drugs across molecular-characterised cell lines can identify candidate treatments and discover biomarkers. However, the cells' response to a drug is typically quantified by a summary statistic from a best-fit dose-response curve, whilst neglecting the uncertainty of the curve fit and the potential variability in the raw readouts. Here, we model the experimental variance using Gaussian Processes, and subsequently, leverage uncertainty estimates to identify associated biomarkers with a new Bayesian framework. Applied to in vitro screening data on 265 compounds across 1074 cancer cell lines, our models identified 24 clinically established drug-response biomarkers, and provided evidence for six novel biomarkers by accounting for association with low uncertainty. We validated our uncertainty estimates with an additional drug screen of 26 drugs, 10 cell lines with 8 to 9 replicates. Our method is applicable to any dose-response data without replicates, and improves biomarker discovery for precision medicine.

New models for the time dependent toxicity of individual and combined toxicants

Time-dependent toxicity data of specific toxicants observed against A. fischeri were analysed using a single time-dependent Weibull cumulative distribution function (CDF). For binary mixtures the individual Weibull parameters provided the marginals for a bivariate copula model, characterised by a single extra parameter, the interaction exponent, θ. The copula model unites both the dose addition (DA, Loewe additivity) and dose independence (DI, Bliss independence) hypotheses of combinations into a single explicit equation and returns both hypotheses as special cases. The model predicts the linear isoboles from sham (like against like) experiments and the linear, concave, convex and mixed concave-convex isoboles from true binary mixtures. Systems are defined as being independent when θ = 1, additive when min(n 1, n 2) ≤ θ ≤ max(n 1, n 2), antagonistic when θ < min(n 1, n 2) and synergistic when θ > max(n 1, n 2), where n i are the individual dose (concentration) exponents. More complex mixtures were analysed by developing n-dimensional copulas: two ternary systems were analysed using a ternary copula that returned the three bivariate marginals and the three individual marginals of the mixture. The general model can also be used for time-independent studies by simply removing the time dependency. Research into combined effects has often assumed that if both the parameters for all the individual components in a mixture and the model for combinations were known then the additive effect of the whole could be predicted. This hypothesis has been shown to be false because without knowing how the components in a mixture interact the predictions from the standard DI or DA models provide only an initial, best guess, analysis.

Optimal designs for asymmetric sigmoidal response curves in bioassays and immunoassays

The 5-parameter logistic (5PL) model is frequently used to model and analyze responses from bioassays and immunoassays which can be skewed. Various types of optimal experimental designs for 2, 3 and 4-parameter logistic models have been reported but not for the more complicated 5PL model. We construct different types of optimal designs for studying various features of the 5PL model and show that commonly used designs in bioassays and immunoassays are generally inefficient for statistical inference. To facilitate use of such designs in practice, we create a user-friendly software package to generate various tailor-made optimal designs for the 5PL model and evaluate robustness properties of a design under a variation of criteria, model forms and misspecification in the nominal values of the model parameters.

Competitive light-initiated chemiluminescent assay: using 5-α-dihydrotestosterone-BSA as competitive antigen for quantitation of total testosterone in human sera

This paper described a homogeneous method, light-initiated chemiluminescent assay (LICA), for quantitation of total testosterone in human sera. The assay was bead based and built on a competitive-binding reaction format, in which 5-α-dihydrotestosterone (5-α-DHT) competed with the testosterone in serum samples in binding with biotinylated anti-testosterone antibody. The more testosterone in the serum sample, the less 5-α-DHT that bonded with biotinylated anti-testosterone antibodies. 5-α-DHT was coupled with emission beads (doped with thioxene derivatives and Eu(III) as a chemiluminescence emitter) via bovine serum albumin as a linker. Once streptavidin-coated sensitizer beads (modified with phthalocyanine as a photosensitizer) were added, the streptavidin/biotin reaction between 5-α-DHT-bound anti-testosterone antibody and sensitizer beads could bring emission and sensitizer beads together, which allowed energy transfer from sensitizer bead to emission bead. As such, an exciting light (680 nm) impinging on the sensitizer beads led to light emission at 520-620 nm by emission beads. The strength of the emitted light was inversely proportional to the testosterone in serum sample. The detection range of this assay was from 13.3 to 1200 ng/dL. The coefficient variation for intra- and inter-assay was lower than 15%. The recovery of this method ranged from 95.5 to 105.9% for different samples. Moreover, the LICA assay was highly specific with low cross-reactivity and interference. The concentration of testosterone from 58 serum samples analyzed by the LICA method significantly correlated (y = 0.97x + 1.87, R² = 0.970, p < 0.001) with those obtained with the SIEMENS Centaur Xp System. Graphical abstract ᅟ.

Assessment of Cu applications in two contrasting soils-effects on soil microbial activity and the fungal community structure

Copper (Cu)-based fungicides have been used in viticulture to prevent downy mildew since the end of the 19th century, and are still used today to reduce fungal diseases. Consequently, Cu has built up in many vineyard soils, and it is still unclear how this affects soil functioning. The present study aimed to assess the short and medium-term effects of Cu contamination on the soil fungal community. Two contrasting agricultural soils, an acidic sandy loam and an alkaline silt loam, were used for an eco-toxicological greenhouse pot experiment. The soils were spiked with a Cu-based fungicide in seven concentrations (0-5000 mg Cu kg^-1 soil) and alfalfa was grown in the pots for 3 months. Sampling was conducted at the beginning and at the end of the study period to test Cu toxicity effects on total microbial biomass, basal respiration and enzyme activities. Fungal abundance was analysed by ergosterol at both samplings, and for the second sampling, fungal community structure was evaluated via ITS amplicon sequences. Soil microbial biomass C as well as microbial respiration rate decreased with increasing Cu concentrations, with EC₅₀ ranging from 76 to 187 mg EDTA-extractable Cu kg^-1 soil. Oxidative enzymes showed a trend of increasing activity at the first sampling, but a decline in peroxidase activity was observed for the second sampling. We found remarkable Cu-induced changes in fungal community abundance (EC₅₀ ranging from 9.2 to 94 mg EDTA-extractable Cu kg^-1 soil) and composition, but not in diversity. A large number of diverse fungi were able to thrive under elevated Cu concentrations, though within the order of Hypocreales several species declined. A remarkable Cu-induced change in the community composition was found, which depended on the soil properties and, hence, on Cu availability.

Evaluation of consistency for multiple experiments of a single combination in the time-dependence mixture toxicity assay

Test-to-test consistency was evaluated for a single binary combination of organic chemicals using an assay that examined toxicity over multiple exposure times. Six experiments were conducted. The toxicities of 3-chloro-2-butanone (3C2B), methyl crotonate (MC) and the mixture of both (MX) were evaluated in each experiment at 15, 30 and 45 min of exposure using the Microtox^® system. Concentration-response (x/y) curves were generated via the five-parameter logistic minus one-parameter (5PL - 1P) curve-fitting function and were used to develop predicted x/y curves for the dose-addition (DA) and independence (I) models of combined effect. A variety of toxicity (e.g. effective concentration, EC₅₀) and time-dependent toxicity (TDT) endpoints, 5PL - 1P parameters and various combined-effects metrics (e.g. MX/DA) were calculated. Test-to-test consistency was evaluated via the coefficient of variation (CV) or, for TDT, the standard deviation of mean values. In the study, CVs obtained for single-chemical and mixture toxicity endpoints (EC₂₅, EC₅₀ and EC₇₅) at each exposure time were <20, as were those for the predicted DA and I curves. For the MX/DA metric, mixture toxicity was consistent with that predicted for DA at each exposure time in each experiment with CVs <6, despite some substantial variation in TDT for MC-alone at the EC₂₅ and for the 30-45 min time-interval. There was a lower variation in TDT for 3C2B and MX. Mean and CV values for 5PL - 1P-derived slope and asymmetry parameters were also assessed to provide bases for comparisons in future reports.

Modeling of pharmaceuticals mixtures toxicity with deviation ratio and best-fit functions models

The present study deals with assessment of ecotoxicological parameters of 9 drugs (diclofenac (sodium salt), oxytetracycline hydrochloride, fluoxetine hydrochloride, chloramphenicol, ketoprofen, progesterone, estrone, androstenedione and gemfibrozil), present in the environmental compartments at specific concentration levels, and their mutual combinations by couples against Microtox® and XenoScreen YES/YAS® bioassays. As the quantitative assessment of ecotoxicity of drug mixtures is an complex and sophisticated topic in the present study we have used two major approaches to gain specific information on the mutual impact of two separate drugs present in a mixture. The first approach is well documented in many toxicological studies and follows the procedure for assessing three types of models, namely concentration addition (CA), independent action (IA) and simple interaction (SI) by calculation of a model deviation ratio (MDR) for each one of the experiments carried out. The second approach used was based on the assumption that the mutual impact in each mixture of two drugs could be described by a best-fit model function with calculation of weight (regression coefficient or other model parameter) for each of the participants in the mixture or by correlation analysis. It was shown that the sign and the absolute value of the weight or the correlation coefficient could be a reliable measure for the impact of either drug A on drug B or, vice versa, of B on A. Results of studies justify the statement, that both of the approaches show similar assessment of the mode of mutual interaction of the drugs studied. It was found that most of the drug mixtures exhibit independent action and quite few of the mixtures show synergic or dependent action.

Evaluation of time-dependent toxicity and combined effects for a series of mono-halogenated acetonitrile-containing binary mixtures

Mixture and time-dependent toxicity (TDT) was assessed for a series of mono-halogenated acetonitrile-containing combinations. Inhibition of bioluminescence in Aliivibrio fischeri was measured after 15, 30 and 45-min of exposure. Concentration-response (x/y) curves were determined for each chemical alone at each timepoint, and used to develop predicted x/y curves for the dose-addition and independence models of combined effect. The x/y data for each binary mixture was then evaluated against the predicted mixture curves. Two metrics of mixture toxicity were calculated per combined effect model: (1) an EC₅₀-based dose-addition (AQ) or independence (IQ) quotient and (2) the mixture/dose-addition (MX/DA) and mixture/independence (MX/I) metrics. For each single chemical and mixture tested, TDT was also calculated. After 45-min of exposure, 25 of 67 mixtures produced curves that were consistent with dose-addition using the MX/DA metric, with the other 42 being less toxic than predicted by MX/DA. Some mixtures had toxicity that was consistent with both dose-addition and independence. In general, those that were less toxic than predicted for dose-addition were also less toxic than predicted for independence. Of the 25 combinations that were consistent with dose-addition, 22 (88%) mixtures contained chemicals for which the individual TDT values were both >80%. In contrast, of the 42 non-dose-additive combinations, only 2 (4.8%) of the mixtures had both chemicals with individual TDT values >80%. The results support previous findings that TDT determinations can be useful for predicting chemical mixture toxicity.

An automated fitting procedure and software for dose-response curves with multiphasic features

In cancer pharmacology (and many other areas), most dose-response curves are satisfactorily described by a classical Hill equation (i.e. 4 parameters logistical). Nevertheless, there are instances where the marked presence of more than one point of inflection, or the presence of combined agonist and antagonist effects, prevents straight-forward modelling of the data via a standard Hill equation. Here we propose a modified model and automated fitting procedure to describe dose-response curves with multiphasic features. The resulting general model enables interpreting each phase of the dose-response as an independent dose-dependent process. We developed an algorithm which automatically generates and ranks dose-response models with varying degrees of multiphasic features. The algorithm was implemented in new freely available Dr Fit software (sourceforge.net/projects/drfit/). We show how our approach is successful in describing dose-response curves with multiphasic features. Additionally, we analysed a large cancer cell viability screen involving 11650 dose-response curves. Based on our algorithm, we found that 28% of cases were better described by a multiphasic model than by the Hill model. We thus provide a robust approach to fit dose-response curves with various degrees of complexity, which, together with the provided software implementation, should enable a wide audience to easily process their own data.

Time-dependence in mixture toxicity prediction

The value of time-dependent toxicity (TDT) data in predicting mixture toxicity was examined. Single chemical (A and B) and mixture (A+B) toxicity tests using Microtox(®) were conducted with inhibition of bioluminescence (Vibrio fischeri) being quantified after 15, 30 and 45-min of exposure. Single chemical and mixture tests for 25 sham (A1:A2) and 125 true (A:B) combinations had a minimum of seven duplicated concentrations with a duplicated control treatment for each test. Concentration/response (x/y) data were fitted to sigmoid curves using the five-parameter logistic minus one parameter (5PL-1P) function, from which slope, EC25, EC50, EC75, asymmetry, maximum effect, and r(2) values were obtained for each chemical and mixture at each exposure duration. Toxicity data were used to calculate percentage-based TDT values for each individual chemical and mixture of each combination. Predicted TDT values for each mixture were calculated by averaging the TDT values of the individual components and regressed against the observed TDT values obtained in testing, resulting in strong correlations for both sham (r(2)=0.989, n=25) and true mixtures (r(2)=0.944, n=125). Additionally, regression analyses confirmed that observed mixture TDT values calculated for the 50% effect level were somewhat better correlated with predicted mixture TDT values than at the 25 and 75% effect levels. Single chemical and mixture TDT values were classified into five levels in order to discern trends. The results suggested that the ability to predict mixture TDT by averaging the TDT of the single agents was modestly reduced when one agent of the combination had a positive TDT value and the other had a minimal or negative TDT value.

A concentration addition model to assess activation of the pregnane X receptor (PXR) by pesticide mixtures found in the French diet

French consumers are exposed to mixtures of pesticide residues in part through food consumption. As a xenosensor, the pregnane X receptor (hPXR) is activated by numerous pesticides, the combined effect of which is currently unknown. We examined the activation of hPXR by seven pesticide mixtures most likely found in the French diet and their individual components. The mixture's effect was estimated using the concentration addition (CA) model. PXR transactivation was measured by monitoring luciferase activity in hPXR/HepG2 cells and CYP3A4 expression in human hepatocytes. The three mixtures with the highest potency were evaluated using the CA model, at equimolar concentrations and at their relative proportion in the diet. The seven mixtures significantly activated hPXR and induced the expression of CYP3A4 in human hepatocytes. Of the 14 pesticides which constitute the three most active mixtures, four were found to be strong hPXR agonists, four medium, and six weak. Depending on the mixture and pesticide proportions, additive, greater than additive or less than additive effects between compounds were demonstrated. Predictions of the combined effects were obtained with both real-life and equimolar proportions at low concentrations. Pesticides act mostly additively to activate hPXR, when present in a mixture. Modulation of hPXR activation and its target genes induction may represent a risk factor contributing to exacerbate the physiological response of the hPXR signaling pathways and to explain some adverse effects in humans.

Mixture toxicity of SN2-reactive soft electrophiles: 3. Evaluation of ethyl α-halogenated acetates with α-halogenated acetonitriles

Mixture toxicity for each of four ethyl α-halogenated acetates with each of three α-halogenated acetonitriles (xANs) was assessed. Inhibition of bioluminescence in Vibrio fischeri was measured after 15, 30, and 45 min of exposure. Concentration-response curves were developed for each chemical at each exposure duration and used to develop predicted concentration-response curves for the dose-addition and independence models of combined effect. Concentration-response curves for each mixture and each exposure duration were then evaluated against the predicted curves using three metrics per model: (1) EC50-based additivity quotient (AQ) or independence quotient (IQ) values; (2) mean AQ (mAQ) or mean IQ (mIQ) values, which were calculated by averaging the EC25, EC50, and EC75 AQ or IQ values; and (3) deviation values from additivity (DV-A) or independence (DV-I). Mixture toxicity for ethyl iodoacetate was dose-additive with each of the xANs at all exposure durations and was also often consistent with independence. The same was true for mixture toxicity of ethyl bromoacetate with each xAN. However, for the two more slowly reactive chemicals, ethyl chloroacetate (ECAC) and ethyl fluoroacetate (EFAC), mixture toxicity with each xAN only became consistent with dose-addition on increasing exposure duration. Consistency with independence for both ECAC and EFAC with the xANs was essentially limited to the EC50-IQ metric, thereby showing the utility of calculating the mean quotient (mAQ, mIQ) and deviation value (DV-A, DV-I) metrics. On review of these findings with those from the first two studies in the series, the results suggest that instances in which mixture toxicity was not consistent with dose-addition relate (1) to differences in the capability of the chemicals to form strong H-bonds with water; and (2) to differences in relative reactivity and time-dependent toxicity levels of the chemicals.