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From a theoretical point of view, it has often been argued that the model of independent action (IA) is the most correct reference model to use for predicting the joint effect of mixtures of chemicals with different molecular target sites. The theory of IA, however, relies on a number of assumptions that are rarely fulfilled in practice. It has even been argued that, theoretically, the concentration addition (CA) model could be just as correct. In the present study, we tested the accuracy of both IA and CA in describing binary dose-response surfaces of chemicals with different molecular targets using statistical software. We compared the two models to determine which best describes data for 158 data sets. The data sets represented 98 different mixtures of, primarily, pesticides and pharmaceuticals tested on one or several of seven test systems containing one of the following: Vibrio fischeri, activated sludge microorganisms, Daphnia magna, Pseudokirchneriella subcapitata, Lemna minor, Tripleurospermum inodorum, or Stellaria media. The analyses showed that approximately 20% of the mixtures were adequately predicted only by IA, 10% were adequately predicted only by CA, and both models could predict the outcome of another 20% of the experiment. Half of the experiments could not be correctly described with either of the two models. When quantifying the maximal difference between modeled synergy or antagonism and the reference model predictions at a 50% effect concentration, neither of the models proved significantly better than the other. Thus, neither model can be selected over the other on the basis of accuracy alone. [ABSTRACT FROM AUTHOR]

For plants, pigment content has shown to be a remarkably consistent biomarker across chemicals with different modes of action. In this study, we evaluated the use of pigment content as endpoint in binary mixture toxicity studies compared to three growth endpoints on the floating plant Lemna minor. Six binary combinations of six herbicides with different mode of action were used. Data were tested against both the concentration addition (CA) and independent action (IA) reference models. For CA, two statistical approaches were used. The study showed that for some herbicide combinations the mixture toxicity measured on pigment content did not reflect the results measured on plant population growth, emphasizing the importance of measuring growth in parallel with biomarkers. CA explained the data just as well as IA, and the two different statistical models used to test the data in relation to CA showed very similar results. [Copyright &y& Elsevier]

Binary-mixture studies often are conducted with the aim of elucidating the effect of one specific chemical on the biological action of another. The results can be interpreted in relation to reference models by the use of response-surface analyses and isobolograms. The amount of data needed for these analyses is, however, extensive, and the experiments therefore rarely are repeated. In the present study, we investigate the reproducibility of isobole shapes of binary-mixture toxicity experiments in terms of deviation from the reference model of concentration addition (CA), dose-level dependence, and isobole asymmetry. We use data from four herbicide mixtures tested in three to five independent experiments on the aquatic test plant Lemna minor and the terrestrial plant Tripleurospermum inodorum. The results showed that the variation both within and among experiments was approximately half the size for the aquatic test system compared to the terrestrial system. As a consequence, a consistent deviation from CA could be obtained in three of four herbicide mixtures for L. minor, whereas this was only the case for one or two of the herbicide mixtures tested on T. inodorum. For one mixture on T. inodorum, both CA synergism and antagonism were detected. Dose-dependent effects could not be repeated consistently, just as the asymmetry found in some isoboles could not. The study emphasizes the importance of repeating mixture toxicity experiments, especially for test systems with large variability, and using caution when drawing biological conclusions from the test results. [ABSTRACT FROM AUTHOR]

Abstract: Binary mixture studies are well established for mixtures of pollutants, pesticides, or allelochemicals and sound statistical methods are available to evaluate the results in relation to reference models. The majority of mixture studies are conducted to investigate the effect of one compound on the inhibitory action of another. However, since stimulatory responses to low concentrations of chemicals are gaining increased attention and improved statistical models are available to describe this phenomenon of hormesis, scientists are challenged by the question of what will happen in the low concentration range when all or some of the chemicals in a mixture induce hormesis? Can the mixture effects still be predicted and can the size and concentration range of hormesis be predicted? The present study focused on binary mixtures with one or both compounds inducing hormesis and evaluated six data sets of root length of Lactuca sativa L. and areal growth of Lemna minor L., where substantial and reproducible hormetic responses to allelochemicals and herbicides have been found. Results showed that the concentration giving maximal growth stimulatory effects (M) and the concentration where the hormetic effect had vanished (LDS) could be predicted by the most-used reference model of concentration addition (CA), if the growth inhibitory concentrations (EC50) followed CA. In cases of deviations from CA at EC50, the maximum concentration M and the LDS concentration followed the same deviation patterns, which were described by curved isobole models. Thus, low concentration mixture effects as well as the concentration range of hormesis can be predicted applying available statistical models, if both mixture partners induce hormesis. Using monotonic concentration–response models instead of biphasic concentration–response models for the prediction of joint effects, thus ignoring hormesis, slightly overestimated the deviation from CA at EC20 and EC50, but did not alter the general conclusion of the mixture study in terms of deviation from the reference model. Mixture effects on the maximum stimulatory response were tested against the hypothesis of a linear change with mixture ratio by constructing 95% prediction intervals based on the single concentration–response curves. Four out of the six data sets evaluated followed the model of linear interpolation reasonably well, which suggested that the size of the hormetic growth stimulation can be roughly predicted in mixtures from knowledge of the concentration–response relationships of the individual chemicals. [Copyright &y& Elsevier]