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Supplemental data S2.
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Calculation of the intrinsic sensitivity, i.e. EA50, for D. magna.
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To obtain toxicity predictions, the BLMs were applied in two modes. First, they were run in
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speciation mode to obtain an ‘average’ intrinsic sensitivity for D. magna, i.e. EA50. This
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‘average’ intrinsic sensitivity was calculated in different steps. (1) For each test medium i, the
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[𝐸𝐶50𝐶𝑢2+ ]0,𝑖 was calculated (Eqn. S2.1).
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[𝐸𝐶50𝐶𝑢2+ ]0,𝑖 =
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Where KCuBL = the stability constant for the binding of copper to the biotic ligand (L ∙ mol−1 )
ƒ50%
𝐶𝑢𝐵𝐿
(Eqn. S2.1)
(1− ƒ50%
𝐶𝑢𝐵𝐿 ) ∙ 𝐾𝐶𝑢𝐵𝐿
[Total Gill−Cu]
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and ƒ50%
CuBL =
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ligand concentration of copper’ (nmol ∙ g −1). This is the amount of accumulation of copper to
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the biotic ligand that results in a well-defined effect (here: 50% reduction of reproduction
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relative to a control without copper). For the UGent BLM, the [Total BL-Cu] = [BL-Cu] + [BL-
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CuOH] + [BL-CuCO3] because the BLM accounts for binding of Cu2+, CuOH+ and CuCO3 to
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the biotic ligand and thus assumes that Cu2+, CuOH+ and CuCO3 all contribute to toxicity. For
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the HydroQual BLM, the [Total BL-Cu] = [BL-Cu] + [BL-CuOH] because the BLM accounts
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for binding of Cu2+ and CuOH+ to the biotic ligand and thus assumes that only Cu2+ and CuOH+
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and not CuCO3 contribute to toxicity. Furthermore, the 30 in ƒ50%
CuBL =
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total copper binding capacity of the biotic ligand of 30 nmol Cu/ g wet weight. This means for
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example that a critical fractional biotic ligand occupancy (ƒ50%
CuBL ) of 30% would correspond to
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a critical accumulation of 9 nmol/g wet weight when using the BLM software. (2) In a second
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step, the geometric mean of all the [𝐸𝐶50𝐶𝑢2+ ]0,𝑖 values (across all n test media) was calculated.
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𝑔𝑒𝑜𝑚𝑒𝑎𝑛([𝐸𝐶50𝐶𝑢2+ ]0,𝑖 ) = 𝑛√∏𝑛𝑖[𝐸𝐶50𝐶𝑢2+ ]0,𝑖
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(3)The final ‘average’ ƒ50%
𝐶𝑢𝐵𝐿 (across all media) was calculated.
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. Here, [Total BL-Cu] is the ‘critical gill-concentration’ or ‘biotic
[Total BL−Cu]
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refers to the
(Eqn. S2.2)
𝑔𝑒𝑜𝑚𝑒𝑎𝑛([𝐸𝐶50𝐶𝑢2+ ]
) ∙ 𝐾𝐶𝑢𝐵𝐿
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ƒ50%
𝐶𝑢𝐵𝐿 = (1+𝑔𝑒𝑜𝑚𝑒𝑎𝑛([𝐸𝐶50
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(4) This value was multiplied by 30 to obtain the [Total BL-Cu], i.e. EA50, which was entered
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as parameter value into the BLMs.
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After this, in a second phase, the BLMs were run in toxicity mode (using this parameter value)
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to obtain the predictions of toxicity (EC50s) as µg/L dissolved Cu.
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0,𝑖
𝐶𝑢2+ ]0,𝑖 ) ∙ 𝐾𝐶𝑢𝐵𝐿
)
(Eqn. S2.3)