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Frontiers of Environmental Science & Engineering

Front. Environ. Sci. Eng.    2017, Vol. 11 Issue (2) : 10
Toxicity models of metal mixtures established on the basis of “additivity” and “interactions”
Yang Liu1,2,Martina G. Vijver2,Bo Pan1(),Willie J. G. M. Peijnenburg2,3
1. Faculty of Environmental Science and Engineering, Kunming University of Science and Technology, Kunming 650500, China
2. Institute of Environmental Sciences (CML), Leiden University, Leiden 2300 RA, The Netherlands
3. National Institute of Public Health and the Environment (RIVM), Center for Safety of Substances and Products, Bilthoven 3720 BA, The Netherlands
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· No preference is set between CA and IA models to assess toxicity of metal mixtures.

· Increased model complexity does not, by itself, lead to improved performance.

· Not all significant deviations have biological meaning due to poor reproducibility.

· Interactions are suggested to incorporate when they are significant and repeated.

Observed effects of metal mixtures on animals and plants often differ from the estimates, which are commonly calculated by adding up the biological responses of individual metals. This difference from additivity is commonly referred to as being a consequence of specific interactions between metals. The science of how to quantify metal interactions and whether to include them in risk assessment models is in its infancy. This review summarizes the existing predictive tools for evaluating the combined toxicity of metals present in mixtures and indicates the advantages and disadvantages of each method. We intend to provide eco-toxicologists with background information on how to make good use of the tools and how to advance the methods for assessing toxicity of metal mixtures. It is concluded that statistically significant deviations from additivity are not necessarily biologically relevant. Incorporation of interactions between metals in a model does not on forehand mean that the model is more accurate than a model developed based on additivity only. It is recommended to first use a relatively simple method for effect prediction of uninvestigated metal mixtures. To improve the reliability of toxicity modeling for metal mixtures, further efforts should focus on balancing the relationship between the significance of statistics and the biological meaning, and unraveling the toxicity mechanisms of metals and their mixtures.

Keywords Metal      Mixtures      Toxicity      Additivity      Modeling      Interactions     
Corresponding Authors: Bo Pan   
Issue Date: 06 April 2017
 Cite this article:   
Yang Liu,Martina G. Vijver,Bo Pan, et al. Toxicity models of metal mixtures established on the basis of “additivity” and “interactions”[J]. Front. Environ. Sci. Eng., 2017, 11(2): 10.
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Yang Liu
Martina G. Vijver
Bo Pan
Willie J. G. M. Peijnenburg
Fig.1  Diagram of deviation patterns for binary mixtures
species metal mixtures R2 a) RMSE b)/RMSD c) sources
Lactuca sativa Cu-Ni 0.79 13.0 [42]
Lactuca sativa Cu-Cd 0.87 10.9 [42]
Lactuca sativa Ni-Cd 0.81 12.7 [42]
Triticum aestivum Co-Zn 0.88 13.1 [42]
Triticum aestivum Cu-Al 0.86 12.9 [42]
Triticum aestivum Cu-Mn 0.70 17.7 [42]
Escherichia coli Cu-Zn, Cu-Cd, Cd-Zn 0.68 19.0 [70]
Pseudomonas fluorescens Cu-Zn, Cu-Cd, Cd-Zn 0.89 10.0 [70]
Vibrio fischeri Cd-Pb 0.81 15.0 [70]
Lemna aequinoctialis Cu-UO2 0.96 8.0 [70]
Lemna paucicostata Cu-Cd 0.76 18.0 [70]
Ceriodaphnia dubia Zn-Cd 0.77 16.0 [70]
Daphnia ambigua Zn-Cd 0.96 7.0 [70]
Daphnia magna Zn-Cd 0.84 14.0 [70]
Daphnia pulex Zn-Cd 0.88 11.0 [70]
Dreissena polymorpha Cu-Zn, Zn-Cd, Cu-Cd, Cu-Zn-Cd 0.92 11.0 [70]
Oncorhynchus mykiss Al-Cu-Zn d) 5.0 [70]
Daphnia magna Cu-Zn, Cd-Zn, Cd-Cu, Cd-Cu-Zn 0.65 25.0 [71]
Lactuca sativa Cu-Zn, Cu-Ag 0.78 14.0 [71]
Oncorhynchus clarkii lewisi Zn-Pb, Zn-Cd, Zn-Cd-Pb 0.81 17.0 [71]
Oncorhynchus mykiss Zn-Pb, Zn-Cd, Zn-Cd-Pb 0.64 24.0 [71]
Tab.1  Summary of WHAM-FTOX fitting to different mixture toxicity data sets
method and assumption Cu-Ni source method and assumption Cu-Ag source
CA-FIAM (no interaction) R2 e) = 0.49 [8] CA-FIAM (no interaction) R2 = 0.80 [71]
IA-FIAM (no interaction) R2 = 0.85 [8] extended CA-FIAM (Cu2+↔Ag+) R2 = 0.80 [31]
extended CA-FIAM (DR a) or DL b) Cu2+c)Ni2+) R2 = 0.55 [8] WHAM-FTOX
H+, Cu2+↔Ag+
R2 = 0.78 [71]
H+, Cu2+↔Ni2+
R2 = 0.79 [42] WHAM-FTOX
H+, Cu2+↔Ag+
R2 = 0.56 [42]
H+, Cu2+↔Ni2+
R2 = 0.82 [42] BLM-TU (H+) R2 = 0.69 [13]
BLM-TU (H+, Mg2+) R2 = 0.86 [13] BLM-fmix (H+, Cu2+↔Ag+) R2 = 0.58 [13]
BLM-fmix (H+, Mg2+, Cu2+↔Ni2+) R2 = 0.58 [13] BLM-TEF (H+, Cu2+↔Ag+) R2 = 0.74 [13]
BLM-TEF (H+, Mg2+, Cu2+↔Ni2+) R2 = 0.76 [13] BLM-TEF (H+) R2 = 0.69 [31]
d) extended CA-ETM (Cu2+↔Ag+) R2 = 0.80 [31]
Tab.2  Comparison of the predictive power of diverse modeling methods for assessing toxicity of Cu-Ni and Cu-Ag mixtures to L. sativa
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