Chemical Mixtures: An Unsolvable Riddle?

It is difficult to overstate the complexity of assessing risks from chemical mixtures. For every valid reason to assess risks from mixtures, there appears an equally valid question as to whether it is possible to do so in a scientifically rigorous and relevant manner. Because so few data exist for mixtures, current mixture assessment methods must rely on untested assumptions and simplifications. That the accuracy of risk estimates improve with the number of chemicals assessed together as mixtures is a valid assumption only if assessment methods for mixtures are better than those based on individual chemicals. On the other hand, arbitrarily truncating a mixture assessment to make it manageable may lead to irrelevant risk estimates. Ideally, mixture assessments should be as broad as necessary to improve accuracy and reduce uncertainty over assessments that only use toxicity data for single chemicals. Further broadening the scope may be ill advised because of the tendency to increase rather than decrease uncertainty. Risk assessment methods that seek to be comprehensive at the expense of increased uncertainty can hardly be viewed as improvements. It would be prudent to verify that uncertainty can be reduced before burdening the risk assessment process with more complexity.     

Evaluating Chemical Interaction Studies for Mixture Risk Assessment

We describe a set of criteria to evaluate the quality of data and interpretations in chemical interaction studies. These criteria reflect the consensus of the literature on interaction analysis developed over decades of research in pharmacology, toxicology, and biometry; address common pitfalls in published interaction studies; and can be easily applied to common methods of interaction analysis. The criteria apply broadly to interaction data for drugs, pesticides, industrial chemicals, food additives, and natural products and are intended to assist risk assessors who must evaluate interaction studies for use in component-based mixture risk assessments. The criteria may also assist researchers interested in conducting interaction studies to inform mixture risk assessment. The criteria are also intended to serve larger scientific goals, including increasing the repeatability of results obtained in chemical interaction studies, enhancing the reliability of conclusions drawn from interaction data, providing greater consistency of interpretations among various analysts, and decreasing uncertainty in using interaction data in risk assessments. We describe the basis for each criterion and demonstrate their utility by using them to evaluate interaction studies from the recent toxicological and pharmacological literature, which serve as examples of different types of data sets that the risk assessor may encounter.     

Theory of antimicrobial combinations: biocide mixtures - synergy or addition?

AIMS: To demonstrate the effect that non-linear dose responses have on the appearance of synergy in mixtures of antimicrobials. METHODS AND RESULTS: A mathematical model, which allows the prediction of the efficacy of mixtures of antimicrobials with non-linear dose responses, was produced. The efficacy of antimicrobial mixtures that would be classified as synergistic by time-kill methodology was shown to be a natural consequence of combining antimicrobials with non-linear dose responses. CONCLUSIONS: The effectiveness of admixtures of biocides and other antimicrobials with non-linear dose responses can be predicted. If the dose response (or dilution coefficient) of any biocidal component, in a mixture, is other than one, then the time-kill methodology used to ascertain the existence of synergy in antimicrobial combinations is flawed. SIGNIFICANCE AND IMPACT OF THE STUDY: The kinetic model developed allows the prediction of the efficacy of antimicrobial combinations. Combinations of known antimicrobials, which reduce the time taken to achieve a specified level of microbial inactivation, can be easily assessed once the kinetic profile of each component has been obtained. Most patented cases of antimicrobial synergy have not taken into account the possible effect of non-linear dose responses of the component materials. That much of the earlier literature can now be predicted, suggests that future cases will require more thorough proof of the alleged synergy.     

Effects of Metal Mixtures on Aquatic Biota: A Review of Observations and Methods

A brief review of the historical development of metal mixture interaction analyses is presented. The two major classifications of mixture models are outlined, the “Concentration Addition” and the “Response Addition” approaches. Within these two categories, a number of graphical, mathematical and statistical methods have been used, such as the toxic unit approach, relative potencies, toxicity equivalence factors, and dose-response relationships that have been described using several methods such as probit, logit, and regression analyses. A database was generated to evaluate the frequency of occurrence of less than additive, strictly additive, and more than additive responses to metal mixture effects reported in the literature. The three responses occurred at 43, 27, and 29%, respectively. The database is available electronically from the lead author. The research required to determine the most appropriate methods to quantify the effects of metal mixtures in an ecological risk assessment (ERA) framework is discussed. Until this research is completed, ERAs should use existing models such as the toxic unit or the effects addition approach. Bioaccumulation measurements by organisms for which the accumulation to response relationship is known would also be a useful complement.     

Concentration Addition,Independent Action and Generalized Concentration Addition Models for Mixture Effect Prediction of Sex Hormone Synthesis In Vitro

Humans are concomitantly exposed to numerous chemicals. An infinite number of combinations and doses thereof can be imagined. For toxicological risk assessment the mathematical prediction of mixture effects, using knowledge on single chemicals, is therefore desirable. We investigated pros and cons of the concentration addition (CA), independent action (IA) and generalized concentration addition (GCA) models. First we measured effects of single chemicals and mixtures thereof on steroid synthesis in H295R cells. Then single chemical data were applied to the models; predictions of mixture effects were calculated and compared to the experimental mixture data. Mixture 1 contained environmental chemicals adjusted in ratio according to human exposure levels. Mixture 2 was a potency adjusted mixture containing five pesticides. Prediction of testosterone effects coincided with the experimental Mixture 1 data. In contrast, antagonism was observed for effects of Mixture 2 on this hormone. The mixtures contained chemicals exerting only limited maximal effects. This hampered prediction by the CA and IA models, whereas the GCA model could be used to predict a full dose response curve. Regarding effects on progesterone and estradiol, some chemicals were having stimulatory effects whereas others had inhibitory effects. The three models were not applicable in this situation and no predictions could be performed. Finally, the expected contributions of single chemicals to the mixture effects were calculated. Prochloraz was the predominant but not sole driver of the mixtures, suggesting that one chemical alone was not responsible for the mixture effects. In conclusion, the GCA model seemed to be superior to the CA and IA models for the prediction of testosterone effects. A situation with chemicals exerting opposing effects, for which the models could not be applied, was identified. In addition, the data indicate that in non-potency adjusted mixtures the effects cannot always be accounted for by single chemicals.     

Implications of a statistical occurrence model for mixture toxicity estimation

This study provides a method for characterizing the effects of concentration variability and correlation among co-acting compounds on mixture toxicity, considering the implications of missing chemical data. The method is explored by developing a set of multiple occurrence scenarios for mixtures of related chemicals. The calculations are performed for hypothetical mixtures of a group of ten synthetic antibiotics that have been tested on marine bacterium to fit dose-response relationships for long-term bioluminescence inhibition of Vibrio fischeri. Mixture toxicities are computed and compared for the assumptions of independent joint action theory and concentration/dose addition theory. The study results show that higher variability in concentrations is associated with higher effective (average) mixture toxicity, in this application by as much as a factor of ten for mixtures with highly variable component concentrations. Moreover, omitting the most toxic compounds caused mixture toxicities to be underestimated by a factor of approximately two. We recommend a pre-assessment of the effect of different chemical occurrence patterns and variability on mixture toxicity to help prioritize needs for further co-occurrence data and toxicity studies.     

Risk-Based Management of Site Soils Contaminated with a Mixture of Hazardous Substances: Methodological Approach and Case Study

A novel approach to improve the accuracy and to reduce the uncertainty associated with the assessment of ecotoxicological risks and the determination of remedial objectives was developed herein for a scenario involving multiple contaminants in soil. This approach used laboratory-derived site-specific toxicological data (i.e., obtained from toxicity testing using species in direct contact with soil such as plants and invertebrates) instead of the more traditional approach using generic toxicological benchmarks for corresponding groups of organisms. Inherent to this approach were the data exploration and reduction; the use of generalized linear models to integrate the data for stressors (site-specific chemical and edaphic characteristics with the potential for influencing toxicity) and effects (biological responses for multiple species and multiple endpoints); and the derivation of tools that could predict the level of impairment associated with any combination of metals’ concentrations measured on site and compare it to a pre-specified acceptable threshold. A case study is presented whereby this method was applied to a large site contaminated with a mixture of metals. Ultimately, the distributions of predicted levels of risk for both soil invertebrates and plants were determined for the entire site and compared to those obtained using the traditional approach using benchmarks.     

Synergy between verapamil and other multidrug-resistance modulators in model membranes

Various cationic lipophilic compounds can reverse the multidrug resistance of cancer cells. Possible interaction between these compounds, which are known as modulators, has been assessed by measuring leakage of Sulphan blue from anionic liposomes, induced both by verapamil alone and by verapamil in combination with diltiazem, quinine, thior idazine or clomipramine. An equation was derived to quantify the permeation doses and Hill coefficients of the drugs and mixtures between them by simultaneous fitting of the experimental data. The interaction was tested by two methods, the competition plot and the isobole method; both showed synergy between verapamil and each of diltiazem, qui nine and thioridazine. The dose factor of potentiation for verapamil determined within membranes was 4.0 ± 0.4 with diltiazem, 3.2 ± 0.4 with quinine and 2.4 ± 0.3 with thior idazine. The results suggest that the effectiveness of reversing multidrug resistance may be increased with modulators such as verapamil and diltiazem that have a much greater effect in combination than what would be expected from their effects when considered separately.     

The similarity between odors and their binary mixtures in Drosophila

How are odor mixtures perceived? We take a behavioral approach toward this question, using associative odor-recognition experiments in Drosophila. We test how strongly flies avoid a binary mixture after punishment training with one of its constituent elements and how much, in turn, flies avoid an odor element if it had been a component of a previously punished binary mixture. A distinguishing feature of our approach is that we first adjust odors for task-relevant behavioral potency, that is, for equal learnability. Doing so, we find that 1) generalization between mixture and elements is symmetrical and partial, 2) elements are equally similar to all mixtures containing it and that 3) mixtures are equally similar to both their constituent elements. As boundary conditions for the applicability of these rules, we note that first, although variations in learnability are small and remain below statistical cut-off, these variations nevertheless correlate with the elements' perceptual "weight" in the mixture; thus, even small differences in learnability between the elements have the potential to feign mixture asymmetries. Second, the more distant the elements of a mixture are to each other in terms of their physicochemical properties, the more distant the flies regard the elements from the mixture. Thus, titrating for task-relevant behavioral potency and taking into account physicochemical relatedness of odors reveals rules of mixture perception that, maybe surprisingly, appear to be fairly simple.     

Risk assessment for quantitative responses using a mixture model

A problem that frequently occurs in biological experiments with laboratory animals is that some subjects are less susceptible to the treatment than others. A mixture model has traditionally been proposed to describe the distribution of responses in treatment groups for such experiments. Using a mixture dose-response model, we derive an upper confidence limit on additional risk, defined as the excess risk over the background risk due to an added dose. Our focus will be on experiments with continuous responses for which risk is the probability of an adverse effect defined as an event that is extremely rare in controls. The asymptotic distribution of the likelihood ratio statistic is used to obtain the upper confidence limit on additional risk. The method can also be used to derive a benchmark dose corresponding to a specified level of increased risk. The EM algorithm is utilized to find the maximum likelihood estimates of model parameters and an extension of the algorithm is proposed to derive the estimates when the model is subject to a specified level of added risk. An example is used to demonstrate the results, and it is shown that by using the mixture model a more accurate measure of added risk is obtained.     

Decomposition of spruce litter needles of different quality by Setulipes androsaceus and Thysanophora penicillioides

Different components of functional biodiversity, such as functional type richness and composition, have been reported to affect the decomposition of litter mixtures. In spite of the numerous reports of these effects, mechanisms underlying patterns of decomposition in litter mixtures are still unclear. We analyzed whether mixture decomposition was affected by: (a) the number of species in the mixture (mixture richness); and (b) the mixture’s functional composition (% of fast- vs. slow-decomposing species included in the mixture). We then tested if variation between observed and expected values of decomposition in mixtures was associated to: (c) the initial litter characteristics of the component species (initial nitrogen, lignin, cellulose and hemicellulose content of litters); and (d) the chemical heterogeneity of the mixtures (variation in the same chemical compounds between the components in each mixture). When up to 5 species representing different functional types were included, both species richness and functional composition showed statistically significant non-additive, and in general positive, effects on litter mixture decomposition. The positive effect of mixture richness on decomposition did not disappear, but was much less marked, when considering mixture with slow-decomposing species only. Although the main driver of decomposition in a mixture is still the average decomposability of the component species (itself largely determined by litter quality), the species interactions in a mixture add a consistent source of variability that is worth considering when predicting the decomposability of a given mixture. We showed that a greater positive difference between observed decomposition rates and that expected from its component species alone was found in mixtures with higher mean nitrogen content and a higher heterogeneity in non-labile compounds. Our results offer quantitative proof that litter chemical heterogeneity, as well as the mean quality of the mixture, can affect the decomposability in litter mixtures.     

Testing for Absence of Qualitative Interactions Between Risk Factors and Treatment Effects

The problem of investigating qualitative interactions (QI's) between subsets of patients defined by means of some risk factors, and treatment effects in clinical trials is considered from a viewpoint which leads to interchanging the hypotheses of the testing problem dealed with in the existing literature on QI's. A natural way of approaching this reverse problem is to apply one of the tests available for the original problem of detecting QI's at level 1 — α and to reject the null hypothesis of the new problem if and only if this test accepts. Unfortunately, this would require unbiasedness of the level 1 — α test for existence of QI's to start with, a property which exhibits neither the likelihood ratio procedure derived in the seminal paper of GAIL and SIMON (1985), nor the test based on the extreme order statistics which was introduced by several authors in 1993. Nevertheless we show that there is a valid test for absence of QI's which depends on the extreme values only and coincides with the maximum likelihood ratio procedure for the same problem. Furthermore, the procedure is generalized to the problem of testing for absence of relevant QI's, i.e. of qualitative interactions exceeding some specified tolerance ε > 0.     

Optimum Design of PIλDμ Controller for an Automatic Voltage Regulator System Using Combinatorial Test Design

Combinatorial test design is a plan of test that aims to reduce the amount of test cases systematically by choosing a subset of the test cases based on the combination of input variables. The subset covers all possible combinations of a given strength and hence tries to match the effectiveness of the exhaustive set. This mechanism of reduction has been used successfully in software testing research with t-way testing (where t indicates the interaction strength of combinations). Potentially, other systems may exhibit many similarities with this approach. Hence, it could form an emerging application in different areas of research due to its usefulness. To this end, more recently it has been applied in a few research areas successfully. In this paper, we explore the applicability of combinatorial test design technique for Fractional Order (FO), Proportional-Integral-Derivative (PID) parameter design controller, named as FOPID, for an automatic voltage regulator (AVR) system. Throughout the paper, we justify this new application theoretically and practically through simulations. In addition, we report on first experiments indicating its practical use in this field. We design different algorithms and adapted other strategies to cover all the combinations with an optimum and effective test set. Our findings indicate that combinatorial test design can find the combinations that lead to optimum design. Besides this, we also found that by increasing the strength of combination, we can approach to the optimum design in a way that with only 4-way combinatorial set, we can get the effectiveness of an exhaustive test set. This significantly reduced the number of tests needed and thus leads to an approach that optimizes design of parameters quickly.     

Biodegradation kinetics of select polycyclic aromatic hydrocarbon (PAH) mixtures by <Emphasis Type="Italic">Sphingomonas paucimobilis</Emphasis> EPA505

Many contaminated sites commonly have complex mixtures of polycyclic aromatic hydrocarbons (PAHs) whose individual microbial biodegradation may be altered in mixtures. Biodegradation kinetics for fluorene, naphthalene, 1,5-dimethylnaphthalene and 1-methylfluorene were evaluated in sole substrate, binary and ternary systems using Sphingomonas paucimobilis EPA505. The first order rate constants for fluorene, naphthalene, 1,5-dimethylnaphthalene, and 1-methylfluorene were comparable; yet Monod parameters were significantly different for the tested PAHs. S. paucimobilis completely degraded all the components in binary and ternary mixtures; however, the initial degradation rates of individual components decreased in the presence of competitive PAHs. Results from the mixture experiments indicate competitive interactions, demonstrated mathematically. The generated model appropriately predicted the biodegradation kinetics in mixtures using parameter estimates from the sole substrate experiments, validating the hypothesis of a common rate-determining step. Biodegradation kinetics in mixtures were affected by the affinity coefficients of the co-occurring PAHs and mixture composition. Experiments with equal concentrations of substrates demonstrated the effect of concentration on competitive inhibition. Ternary experiments with naphthalene, 1,5-dimethylnaphthalene and 1-methylfluorene revealed delayed degradation, where depletion of naphthalene and 1,5-dimethylnapthalene occurred rapidly only after the complete removal of 1-methylfluorene. The substrate interactions observed in mixtures require a multisubstrate model to account for simultaneous degradation of substrates. PAH contaminated sites are far more complex than even ternary mixtures; however these studies clearly demonstrate the effect that interactions can have on individual chemical kinetics. Consequently, predicting natural or enhanced degradation of PAHs cannot be based on single compound kinetics as this assumption would likely overestimate the rate of disappearance.     

A rapid method for assessing the suitability of quenching agents for individual biocides as well as combinations

AIMS: To develop a novel, rapid method for testing the ability of quenching agents to neutralize disinfectants. METHODS AND RESULTS: Tests were performed to determine the suitability of different neutralizers for a range of disinfectants, using a new method based on the Bioscreen optical density analyser. Results showed that during disinfection tests, efficacy could be over-estimated due to poor, or no, neutralization of the disinfectant after a specified time of exposure to the bacteria. The failure to distinguish adequately between bacteriostatic and bactericidal effects can lead to false results during disinfectant testing. Experiments also showed that dilution of the disinfectant, following exposure to the bacteria, was not always sufficient to stop the activity of the disinfectant for chemicals with low dilution coefficients. CONCLUSIONS: The quench test proved to be very quick and easy to perform, with results being available within 18 h. Using the Bioscreen, the test is automated and determines whether dilution into a particular neutralizer is able to inactivate a disinfectant within 30 s. SIGNIFICANCE AND IMPACT OF THE STUDY: This new approach allows the efficacy of quenching agents to be determined, prior to undertaking each disinfection study, and can help in the development of more suitable quenching solutions. The test has also been used to find suitable neutralizers for mixtures of disinfectants which might be used during studies on synergistic biocide combinations.     

Reliable predictive computational toxicology methods for mixture toxicity: toward the development of innovative integrated models for environmental risk assessment

A main objective in the field of mixture toxicity is to determine how well combined effects are predictable based on the known effects of mixture constituents. Conducting toxicity tests for all conceivable combinations of chemicals, to understand all mechanisms in the combined toxicity of environmental pollutants, is virtually unfeasible due to cost- and time-consuming procedures. Therefore, predictive tools for mixture toxicity are required to be developed within the applicable range of predictive toxicology. The concept of concentration addition (CA) model is often considered a general method for estimating mixture toxicity at the regulatory level. In the long run, however, the possibility of toxicological synergism between mixture components actually occurs, especially from the no-effect level or non-toxic substances. This is ignored under the CA concept, and needs to be examined and integrated into existing addition models at a scientific level, this paper reviews existing integrated models for estimating the toxicity of complex mixtures in literature. Current approaches to assess mixture toxicity and the need for new research concepts to overcome challenges which recent studies have confronted are discussed, particularly those involved in computational approaches to predict mixture toxicity in an environment risk assessment based on mixture components.     

Bisphenol A and Risk Management Ethics

It is widely recognized that endocrine disrupting compounds, such as Bisphenol A, pose challenges for traditional paradigms in toxicology, insofar as these substances appear to have a wider range of low‐dose effects than previously recognized. These compounds also pose challenges for ethics and policymaking. When a chemical does not have significant low‐dose effects, regulators can allow it to be introduced into commerce or the environment, provided that procedures and rules are in place to keep exposures below an acceptable level. This option allows society to maximize the benefits from the use of the chemical while minimizing risks to human health or the environment, and it represents a compromise between competing values. When it is not possible to establish acceptable exposure levels for chemicals that pose significant health or environmental risks, the most reasonable options for risk management may be to enact either partial or complete bans on their use. These options create greater moral conflict than other risk management strategies, leaving policymakers difficult choices between competing values.     

Synergistic efficacy of botanical blends with and without synthetic insecticides against Aedes aegypti and Culex annulirostris mosquitoes.

Increasing insecticide resistance requires strategies to prolong the use of highly effective vector control compounds. The use of combinations of insecticides with other insecticides and phytochemicals is one such strategy that is suitable for mosquito control. In bioassays with Aedes aegypti and Culex annulirostris mosquitoes, binary mixtures of phytochemicals with or without synthetic insecticides produced promising results when each was applied at a LC25 dose. All mixtures resulted in 100% mortality against Cx. annulirostris larvae within 24 h rather than the expected mortality of 50%. All mixtures acted synergistically against Ae. aegypti larvae within the first 24 h except for one mixture that showed an additive effect. We conclude that mixtures are more effective than insecticides or phytochemicals alone and that they enable a reduced dose to be applied for vector control potentially leading to improved resistance management and reduced costs.