Quantitative Description of Mixture Toxicity: Effect of Level of Response on Interactions

Haas, Charles N.; Cidambi, Kaushik; Kersten, Sean; Wright, Kenneth P.

doi:10.1897/1551-5028(1996)015<1429:qdomte>2.3.co;2

Cited by 15 publications

(24 citation statements)

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“…Most other analytical approaches to the toxicity of mixtures of chemicals are also based on the 2 reference models: the CA and the IA models. One of the most general mathematical methods, the concentration–response surface model , involves formulation of biases of mixture responses from predictions by 1 of the reference models. This model allows straightforward prediction of mixture toxicity with arbitrary strengths of interactions among components.…”

Section: Discussionmentioning

confidence: 99%

“…In addition, there is seldom enough information about the mode of action of synthetic chemicals . At higher tiers of risk assessment, however, more elaborate modeling schemes, which include arbitrary interactive effects , may be relevant if the proper reference model can be identified and enough toxicity data on mixtures are available. Second, some substances may truly cause synergistic or antagonistic effects with other chemicals.…”

Section: Introductionmentioning

confidence: 99%

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Generalized concentration addition approach for predicting mixture toxicity

Tanaka

Tada

2016

Enviro Toxic and Chemistry

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A new mathematical model for analyzing data and predicting the effect of mixtures of toxic substances is presented as a generalized form of the concentration addition model. The proposed method, the generalized concentration addition (GCA) model, can be applied to mixtures with arbitrary strengths of interactions (synergistic or antagonistic). It requires mixture effect data for least 1 exposure concentration of the mixture in which fractions of all components and concentration-response functions for each component are known. The GCA model evaluates the interaction between components by introducing a novel response function, which is independent of the response functions for each individual components, to describe the effect of addition between different components. The GCA method was applied to published mixture toxicity data, and it was found to fit the mixture effect better than both the concentration addition model and the independent action model, the implication being that the proposed approach is widely applicable. Environ Toxicol Chem 2017;36:265-275. © 2016 SETAC.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalized concentration addition approach for predicting mixture toxicity

Tanaka

Tada

2016

Enviro Toxic and Chemistry

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“…Mixture effects were analyzed by applying the computational framework proposed by Jonker [16] and Haas et al [17]. Following their derivations, the binary TU mixture model can be generalized to where c 1 and c 2 denote the concentrations of the individual chemicals in the mixture, Y indicates the biological response, and f 1 −1 and f 2 −1 indicate the inverse dose‐response functions of the individual compounds in the mixture, here quantified by a log‐logistic model [18].…”

Section: Methodsmentioning

confidence: 99%

Toxicity of simple mixtures to the nematode Caenorhabditis elegans in relation to soil sorption

Jonker

Sweijen

Kammenga

2004

Enviro Toxic and Chemistry

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Single and combined toxicity of copper-zinc, copper-cadmium, cadmium-lead, copper-carbendazim, and copper-carbendazimiprodione to the nematode Caenorhabditis elegans in soil was studied. The one-week population increase was estimated as the toxicity endpoint. The aim was to study the relationship between mixture interactions in the soil and the combined toxic effect. Soil sorption was quantified using the Freundlich adsorption constant. Joint toxicity patterns were quantified by comparing mixture effects to the effect of individual constituents and were related to total metal concentrations in the soil, water-soluble concentrations, and 0.01 M CaCl2-extractable concentrations. The metal with the highest adsorption constant influenced the sorption of metal with the lowest adsorption constant when both were combined, indicating interaction. Consequently, both the composition of the mixture as well as the relative toxicity of individual mixture constituents differed between total, water-soluble, and CaCl2-extractable concentrations, which was taken into account in the data quantification procedure that was applied. Both the additive and the independent model were generally inadequate to describe the effects of metal mixtures. Compared to the additive model, synergism was observed at dose levels higher than the median effect isobole. A general relationship between mixture interactions in the soil and the combined toxicity was not found.

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“…Such models, describing possible patterns of deviation from the reference, have been developed (Carter 1995;Greco et al 1995;Haas et al 1996;Jonker et al 2004), and are usually termed response surface models. Essentially a dose-response relation for each chemical applied separately is combined with a functional relationship between the concentrations of the individual chemicals in the mixture, and the single-chemical concentrations needed to obtain the same effect.…”

Section: Introductionmentioning

confidence: 99%

An isobole-based statistical model and test for synergism/antagonism in binary mixture toxicity experiments

et al. 2007

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Synergism and antagonism are often defined in relation to the model of Concentration Addition (CA). Hence, it is vital for the conclusion of mixture toxicity studies to be able to test whether an observed deviation from CA reflects a true deviation or whether it is simply due to random variation. In this paper we consider a non-linear regression model for the classical ray designs for binary mixture experiments. The model combines dose-response curves for each mixture in the experiment with an isobole model, describing possible deviations from CA. The method allows us to test whether the chosen isobole model is reasonable for the data and to test the hypothesis of CA. Furthermore, it provides us with a measure of the degree of synergism/antagonism. The method is flexible since both the dose-response relationships and the isobole model can be chosen arbitrarily. We demonstrate the use of the method on datasets where combinations of pesticides are tested on a floating plant, Lemna minor, and an algae, Pseudokirchneriella subcapitata. Furthermore, we conduct a simulation study in order to explore the power with which a specific deviation from CA can be distinguished in different test-systems.

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Quantitative Description of Mixture Toxicity: Effect of Level of Response on Interactions

Cited by 15 publications

References 0 publications

Generalized concentration addition approach for predicting mixture toxicity

Generalized concentration addition approach for predicting mixture toxicity

Toxicity of simple mixtures to the nematode Caenorhabditis elegans in relation to soil sorption

An isobole-based statistical model and test for synergism/antagonism in binary mixture toxicity experiments

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