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The combined toxic effects of Cd and Pb in the presence of different concentrations of Ca(2+) were predicted using the biotic ligand model (BLM), with the parameters derived from the Cd-only and Pb-only toxicity data. The BLM-based toxic unit (TU) approach and the proposed BLM-based f(mix) approach were used for prediction. The predicted mixture toxic effects using the BLM-based f(mix) approach were closer to the observed mixture effects (root mean square error [RMSE] = 9.7 at 25 mM Ca(2+) ) than that using the BLM-based TU approach (RMSE = 25.6 at 25 mM Ca(2+) ). This can be attributed to the fact that the BLM-based TU approach only considers the competition between Ca(2+) and Cd or Pb, whereas the BLM-based f(mix) approach considers both the competition between Cd and Pb and the competition between Ca(2+) and Cd or Pb for biotic ligand sites. In addition, the parameters derived from the Cd-only and Pb-only solutions in the presence of the background Ca(2+) concentration (0.025 mM) could be used to predict the mixture toxic effects at higher Ca(2+) concentrations. The BLM-based f(mix) approach proposed in the current study suggests a new way of predicting the Cd-Pb mixture toxicity from the single metal toxicity data by adopting the f(mix) values.

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