Modeling of acute cadmium toxicity in solution to barley root elongation using biotic ligand model theory

Biotic Ligand Modeling for the Effect of Major Cations on the Uptake of Cadmium in Folsomia candida Exposed in a Sand-Solution Medium

Biotic ligand modeling (BLM) approaches are already applied to predict the bioavailability and possible risk of metals in surface water, but need further development for soils. The present study investigated the effect of major cations (Ca2+ , Mg2+ , Na+ , K+ , and H+ ) on cadmium bioaccumulation in the springtail Folsomia candida. To avoid the complexity of real soils and enable control of elemental speciation in the exposure medium, the animals were exposed to different cadmium concentrations in an inert quartz sand-solution medium. Accumulation of cadmium in the animals was measured after 7 days exposure at different cation concentrations. Among the cations, only Ca2+ significantly affected the uptake of cadmium in the springtails. Mg2+ also had higher effects compared with other selected cations. Using a BLM approach, the uptake of cadmium in the animals predicted by taking into account both Ca2+ and Mg2+ activities correlated well with the measured values (R2  = 0.68). The final estimated conditional binding constants for cadmium (log KCd-BL ), Ca (log KCa-BL ), and Mg (log KMg-BL ) of 1.06, 2.14, and 1.23 L/mol, respectively, were in agreement with previously reported values. The match between predicted and measured uptake data confirms the applicability and usefulness of the BLM for predicting the bioavailability of cadmium to springtails and opens the way for its application in soil. Environ Toxicol Chem 2024;00:1-7. © 2024 SETAC.

Amelioration of cadmium cytotoxicity to human cells by nutrient cation contents and the building of a biotic ligand model

A variety of important major and trace elements may competitively inhibit cadmium (Cd) absorption in human cells and reduce Cd toxicity. However, the impact of essential elements on the cytotoxicity of metals can be difficult to quantify and anticipate. Cd acute toxicity to Caco-2 cell viability was studied in culture solutions and modeled by a biotic ligand model (BLM). The individual effects of the cations potassium (K⁺), calcium (Ca²⁺), magnesium (Mg²⁺), ferrous ion(Fe²⁺), zinc (Zn²⁺) and manganese (Mn²⁺) on Cd toxicity were also investigated. The results indicated that the toxicity of Cd in culture solutions to cell viability declined with increasing concentrations of Zn²⁺ and Mn²⁺ in the solutions, while K⁺, Ca^{2 +}, Mg^{2 +} and Fe²⁺ had no significant effect. Using the BLM, the stability constants for the binding of Cd^{2 +}, Zn²⁺, and Mn²⁺ to biotic ligands were determined to be logK_CdBL = 5.76, logK_ZnBL = 4.39 and logK_MnBL = 5.31, respectively. Moreover, it was calculated that 51% occupancy of the biotic ligand sites for Cd by Cd was required to cause a 50% reduction in Caco-2 cell viability. A BLM was successfully established using the estimated constants to predict the Cd cytotoxicity to Caco-2 cell viability as a function of solution characteristics, so that the effective concentrations that reduced cell viability by 50% (EC50) could be predicted by the BLM within 1.6 fold changes of the observed EC50. The application's viability and precision for foretelling Cd toxicity in Caco-2 cells are discussed.

Assessment soil cadmium and copper toxicity on barley growth and the influencing soil properties in subtropical agricultural soils

Evaluation joint cadmium (Cd) and copper (Cu) phytotoxicity in wide range of subtropical agricultural soils is highly vital for phytoremediation of soils contaminated with Cd and Cu. In this study, barley root elongation assays were performed in 30 representative soils in response to single and combined Cd and Cu inhibition. The single Cd caused nearly 50% inhibition of barley root elongation, and Cu induced more than 50% inhibition in most soils. Mixed Cd + Cu caused significant inhibition on barley growth with average relative root elongation values of 20.0% and 30.4% in soil with a pH < 7 and pH > 7, respectively. An antagonistic interaction was evaluated in combined Cd + Cu toxicity, which was strong in soils containing low soluble Cu and Cd contents. Soil pH was the controlling factor in predicting single and mixed Cd and Cu phytotoxicity, which could explain 44% and 46% variation of single Cd and Cu toxicity, respectively. Soil organic carbon and effective cation exchange capacity were another important factor positively influencing metal toxicity, which further improved empirical prediction models accuracy, with determined coefficient (r²) values of 0.44-0.84. These results provide a theoretical basis for soils Cd and Cu pollution control.

Prediction of Cd Accumulation in Wheat (Triticum aestivum L.) and Simulation Calculation of Lime or Zn Fertilizer Remediated Soil

Soil Cd contamination to wheat raise wide concerns over food safety. It is essential to find the key factors affecting Cd accumulation in wheat and to establish a predictive model. The effects of pH, Zn, Ca, and DOM on the accumulation of Cd in wheat were investigated using hydroponic experiments. The results showed that Zn was the most important factor inhibiting Cd uptake in wheat. Models were developed to predict the Cd contents in wheat tissues based on the ion concentration. Meanwhile, the available Cd contents in soil were predicted using a geochemical multi-surface model (MSM) which is suitable for various soils and conditions. The combination of the hydroponic accumulation model and MSM exhibits good predictions of wheat-Cd (R² = 0.822-0.862, RMSE = 0.317-0.533). The results of this study can quantitatively predict the accumulation of Cd in wheat and provide a reference for soil remediation and safe wheat production.

From speciation to toxicity: Using a "Two-in-One" whole-cell bioreporter approach to assess harmful effects of Cd and Pb

Due to the sheer number of contaminated sites, bioavailability-based measurement and modeling of toxicity is used to triage response; despite advances, both remain relatively cumbersome. Cadmium (Cd) and lead (Pb) are two of the most toxic and globally prevalent pollutants, disproportionately impacting disadvantaged communities. Here we demonstrate the use of high throughput lights-on bioreporter technology to measure both speciation and toxicity. The organism's response is fit-for-purpose to parameterize the Biotic Ligand Model used in risk assessment of aquatic ecotoxicity and setting environmental Water Quality Criteria. Toxicity endpoints for analogous Cd and Pb models reported in literature average 71st and 44th rank-percentile sensitivity of Genus Mean Acute Values for acute toxicity (i.e., insensitive) in comparison to the bioreporter, the unique dual-mode measurement ability of which can predict toxicity endpoints from below the 5th percentile up to the 50th rank-percentile. These results are extensible to other reporters, paving the way to cost-efficient environmental risk assessment of aquatic ecotoxicity for a wide range of priority toxic pollutants.

Modeling of selenite toxicity to wheat root elongation using biotic ligand model: Considering the effects of pH and phosphate anion

It has not been well understood that the binding affinity and potential toxicity of different chemical forms of selenite (Se(IV)), which are predominant forms of selenium with plant availability. The influences of pH and major anions on Se(IV) toxicity to wheat root elongation were determined in solutions and modeled based on the biotic ligand model (BLM) and free ion activity model (FIAM) concepts. Results showed that EC50[Se(IV)]_T values increased from 164 to 273 μM as the pH raised from 4.5 to 8.0, indicating the increase of pH induced weakened Se(IV) toxicity. The EC50{SeO₃^2-} values increased from 0.019 to 71.3 μM while the EC50{H₂SeO₃} values sharply decreased from 2.08 μM to 0.760 nM with the pH increasing from 4.5 to 8.0. The effect of pH on Se(IV) toxicity could be explained by the changes of Se(IV) species in different pH solutions as H₂SeO₃, HSeO₃^- and SeO₃^2- were differently toxic to wheat root elongation. The toxicity of Se(IV) decreased with increasing H₂PO₄^- activity but not for SO₄^2-, NO₃^- and Cl^- activities, indicating that only H₂PO₄^- had a competitive effect with Se(IV) on the binding sites. A site-specific BLM was developed to count in effects of pH and H₂PO₄^-, and stability constants of H₂SeO₃, HSeO₃^-, SeO₃^2- and H₂PO₄^- to the binding sites were obtained: log [Formula: see text]  = 4.96, log [Formula: see text]  = 3.47, log [Formula: see text]  = 2.56 and log [Formula: see text]  = 2.00. Results implied that BLM performed much better than FIAM in the wheat root elongation prediction when coupling toxic species H₂SeO₃, HSeO₃^-, SeO₃^2-, and the competitions of H₂PO₄^- for the binding sites while developing the Se(IV)-BLM.

Intrinsic soil property effects on Cd phytotoxicity to Ligustrum japonicum 'Howardii' expressed as different fractions of Cd in forest soils

A better comprehensive understanding of the influence of soil/solution properties on cadmium (Cd) phytotoxicity is essential for soil Cd ecological risk assessment. The toxicity of soil spiked Cd to Ligustrum japonicum 'Howardii' seedling growth was conducted by the greenhouse pot experiments using 13 typical forest soils selected from mainland of China. The results showed that the ranges of Cd toxicity thresholds of 10% seedling growth inhibition (EC₁₀) and 50% inhibition (EC₅₀) followed the order: soil pore water Cd (EC₁₀ on average 0.88 mg L^-1 with the variation of 54.9 folds and EC₅₀ on average 2.28 mg L^-1 with variation of 41.8 folds), DTPA extractable Cd (EC₁₀ on average 5.4 mg kg^-1 with 20.9 folds variation and EC₅₀ on average 17.86 mg kg^-1 with 6.6 folds variation), total added Cd (EC₁₀ on average 6.55 mg kg^-1 with 16.7 folds variation and EC₅₀ on average 22.11 mg kg^-1 with 5.1 folds variation), which suggested that whatever the available Cd expressed, its toxicity is largely affected by soil properties. The empirical multiple equations were well developed between different fractions of Cd toxicity thresholds ECx (x = 10 or 50) and soil/solution. The results also showed that the pH inversely correlated with EC₁₀ (r² = 0.54, P < 0.01) and EC₅₀ (r² = 0.63, P < 0.001) based on soil pore water, indicating the ECx decreased with more toxicity as pH increased. No single significant soil solution properties were found for ECx in DTPA extractable Cd. For the ECx of DTPA extractable and total Cd, the content of aluminum oxides in soil and soil pH were the two significant factors inversely related with ECx, which explained 68%-79% of the inter-soil variation, respectively. Overall, soil or solution pH was the most important factor controlling Cd toxicity thresholds. Meanwhile, significant negative correlations existed between the soil solution pH and the slopes of parameter (b) of the dose-response curves for different fractions of Cd, implying that the growth of toxic effect enhanced as unit Cd dosage increased in low pH soils. These results will be helpful to evaluate the metal ecological risk in forest soils.

Predicting the combined toxicity of binary metal mixtures (Cu-Ni and Zn-Ni) to wheat

In order to investigate and model toxicity and interactions between metals in mixtures, inhibition of wheat root elongation in response to additions of single-metals of copper (Cu), zinc (Zn), and nickel (Ni) and of binary mixed-metal combinations of Cu-Ni and Zn-Ni was tested, using water culture experiments under different Mg concentrations and pH values. A biotic ligand model (BLM) of single-metal Cu, Zn, and Ni was established. The results showed that the toxicity of Cu, Zn or Ni in isolation decreased with increasing Mg concentration whereas the effects of pH on Cu, Zn, or Ni toxicity were related not only to free Cu²⁺, Zn²⁺, and Ni²⁺ concentrations, but also to inorganic metal complexes. In binary mixtures, the two metals in the Cu-Ni mixture showed a weakly antagonistic effect, whereas the two metals in the Zn-Ni mixture showed greater antagonism. Using data from single-metal Cu, Zn, and Ni BLMs, combined with the toxicity index and the overall amounts of metal ions bound to the biotic ligands, one simple model was developed. This model consisted of the toxic unit (TU_M, no competition included) and two extended BLMs, BLM-TU_f (f as a function of TU, including competition between Mg²⁺ and metal ions) and BLM-f_mix (including the competition between Mg²⁺ and metal ions, as well as between free metal ions). They were then used to predict the joint toxicity of Cu-Ni and Zn-Ni binary mixtures to wheat. Both of the extended BLMs could provide more accurate predictions of toxic effects of Cu-Ni and Zn-Ni than TU_M. BLM-f_mix performed best for the Zn-Ni binary mixture (r² = 0.93; root-mean-square error, RMSE = 9.87). On the other hand, for the Cu-Ni mixture, the predictive effect based on BLM-TU_f (r² = 0.93; RMSE = 9.60) was similar to that of BLM-f_mix (r² = 0.93; RMSE = 9.56). The results provide a theoretical basis for the evaluation and remediation of soils contaminated with mixtures of heavy metals.

Comparison Among Test Substrates in Metal Uptake and Toxicity to Folsomia candida and Hordeum vulgare

The main aim of this short review was to assess the effect of test medium on the bioavailability of metals to the soil invertebrate Folsomia candida and the barley plant Hordeum vulgare. Solution-only exposures and sand-solution media were suitable media with control survival of > 80%. Comparing toxicity and accumulation data, LC₅₀ and/or EC₅₀ values as well as internal concentrations of cadmium (Cd) and copper (Cu) were similar in the tests with different porewater composition for springtails and barley plants. Similar results for toxicity and bioaccumulation of Cd and Cu using different test substrates, suggest the importance of physiological handling of the effects by the organisms rather than the influence of test medium composition.

An improved biotic ligand model (BLM) for predicting Co(II)-toxicity to wheat root elongation: The influences of toxic metal speciation and accompanying ions

In order to explore the effects of pH and accompanying ions on divalent cobalt (Co(II)) toxicity to the wheat root elongation, an improved biotic ligand model (BLM) to predict Co(II) toxicity was developed in solution culture. The results showed that the Co(II)-toxicity decreased with the increases of K⁺, Ca²⁺ and Mg²⁺ activities, and the activity of Na⁺ had no impact on the Co(II)-toxicity. High H⁺ activity reduced the Co(II)-toxicity by the competitive effect of H⁺, while low H⁺ activity affected the toxicity by the change in the type of Co(II) in culture medium. Co²⁺ and CoOH⁺ were toxic to wheat root elongation, and Co(OH)₂ was not. On the basis of BLM theory, the conditional equilibrium constants for Co²⁺, CoOH⁺, H⁺, Mg²⁺, Ca²⁺, K⁺ were obtained: logK_CoBL = 4.65, logK_CoOHBL = 6.62, logK_HBL = 4.53, logK_MgBL = 3.65, logK_CaBL = 2.36 and logK_KBL = 2.17. Free Co²⁺ and CoOH⁺, and the competitions of K⁺, Mg²⁺ and Ca²⁺ were suggested to be considered when developing the Co(II)-BLM.

Development of a coupled model of quantitative ion character-activity relationships-biotic ligand model (QICARs-BLM) for predicting toxicity for data poor metals

The biotic ligand model (BLM) is proposed as a tool to quantitatively evaluate biological toxicity of metals considering both metal speciation and the influence of environmental conditions. The model assumes that biological sites bind to metals as biotic ligands (BLs) and obtains a series of BLM parameters including conditional binding constants (K). However, developing a BLM for each metal and biology takes a lot of experimentation. In the present study, relationships between metal ionic characters and BLM parameter K were respectively investigated for three terrestrial organisms. The results showed that ionization potential was the most strongly related to log K for barley (R2 = 0.845, p <  0.01) and earthworm (R2 = 0.881, p <  0.01), and electronegativity index most significantly related to log K for lettuce (R2 = 0.835, p <  0.01). Based on these relationships, a set of quantitative ion character-activity relationships (QICARs) were developed for predicting log K of metals. Then the QICAR were coupled with BLM and a novel QICAR-BLM was constructed. Finally, the QICAR-BLM was applied to predict EC50 of other unknown-toxicity metals for selected species, and compensate for the lack of toxicity data for a large number of metals in soil.

The effect of major cations on the toxicity of cadmium to Folsomia candida in a sand-solution medium analyzed by biotic ligand modeling

The aim of this study was to assess the effect of major cations (Ca²⁺, Mg²⁺, Na⁺, K⁺, and H⁺) on cadmium toxicity to the springtail Folsomia candida. Survival of the animals was determined after seven days exposure to different cadmium concentrations in an inert sand-solution medium, in different experimental setups with modification of the cation concentrations. Among the cations tested, Ca²⁺ and Mg²⁺ had protective effects on the toxicity of cadmium to the springtails while Na⁺, K⁺, and H⁺ showed less competition with free cadmium ions for binding to the uptake sites of the collembolans. Toxicity predicted with a biotic ligand model agreed well with the observed values. Calculated conditional binding constants and the fraction of biotic ligands occupied by cadmium to show 50% effects were similar to values reported in the literature. The results emphasize the important role of solution chemistry in determining metal toxicity to soil invertebrates.

A multivariate analysis of health risk assessment, phytoremediation potential, and biochemical attributes of Spinacia oleracea exposed to cadmium in the presence of organic amendments under hydroponic conditions

Cadmium (Cd) phytoremediation potential and its accumulation in edible and nonedible plant tissues is the function of various biochemical processes taking place inside plants. This study assessed the impact of organic ligands on Cd phyto uptake and different biophysiochemical processes of Spinacia oleracea L., and associated health hazards. Plants were exposed to Cd alone and chelated with citric acid (CA) and ethylenediaminetetraacetic acid (EDTA). Results revealed that the effect of Cd on lipid peroxidation, H₂O₂ production and pigment contents varied greatly with its applied level and the type of organic ligand. Moreover, the effect was more prominent in root tissues than leaf tissues and for high concentrations of Cd and organic ligands. Cadmium accumulation increased by 90 and 74% in roots and leaves, respectively, with increasing Cd levels (25-100 µM). Cadmium exposure at high levels caused lipid peroxidation in roots only. Application of both CA and EDTA slightly diminished Cd toxicity with respect to pigment contents, lipid peroxidation and hydrogen peroxide (H₂O₂) contents. Hazard quotient (HQ) of Cd was <1.00 for all the treatments. Under nonlinear effect of treatments, multivariate analysis can be an effective tool to trace overall effects/trends.

The prediction of combined toxicity of Cu-Ni for barley using an extended concentration addition model

Environment pollution often occurs as an obvious combined effect involving two (or more) elements, and this effect changes with the concentrations of the different elements. The effects on barley root elongation were studied in hydroponic systems to investigate the toxicity of Cu-Ni combined at low doses and at a fixed concentration ratio. For low doses of Cu-Ni, the addition of Ni (<0.5 μM) to Cu significantly decreased Cu toxicity for barley, but the addition of Cu (<0.25 μM) had no significant effect on Ni toxicity. At a fixed concentration ratio, according to the single effective concentration (EC) (barley root elongation inhibitory concentration) values of Cu and Ni, five sets of Cu-Ni fixed ratios were used: ECn(Cu)+ECm(Ni) (n + m = 100) (ECn and EC_m indicate toxicity unit value for n% and m% inhibition of barley root length, respectively). The calculated toxicity unit value for 50% inhibition of root length ranged from 0.44 to 0.98 (i.e., <1), indicating a synergistic effect. To consider the interactions between the metal ions, the extended concentration addition model (e-CA) was established by integrating the Cu-Ni interaction into the concentration addition model (CA), and the data of two groups (the low doses of Cu-Ni and at a fixed concentration ratio) were respectively fitted. The e-CA accurately predicted the root length of barley under the Cu-Ni combined action. The correlation coefficient (r) and the root-mean-square error (RMSE) between predicted and observed values were 0.97 and 6.6 (low-dose group) and 0.96 and 8.12 (fixed-ratio group), respectively, and e-CA significantly improved the prediction accuracy compared to the traditional CA model without consideration of the Cu-Ni competition (r = 0.89, RMSE = 14.16). The results provided a theoretical basis for evaluation and remediation of soil contaminated with heavy metal composites.

Metabolomic analysis of the toxic effect of chronic exposure of cadmium on rat urine

This study aimed to assess the toxic effect of chronic exposure to cadmium through a metabolomic approach based on ultra-performance liquid chromatography/mass spectrometry (UPLC-MS). Forty male Sprague-Dawley rats were randomly assigned to the following groups: control, low-dose cadmium chloride (CdCl₂) (0.13 mg/kg body weight (bw)), middle-dose CdCl₂ (0.8/kg bw), and high-dose CdCl₂ (4.9 mg/kg bw). The rats continuously received CdCl₂ via drinking water for 24 weeks. Rat urine samples were then collected at different time points to establish the metabolomic profiles. Multiple statistical analyses with principal component analysis and partial least squares-discriminant analysis were used to investigate the metabolomic profile changes in the urine samples and screen for potential biomarkers. Thirteen metabolites were identified from the metabolomic profiles of rat urine after treatment. Compared with the control group, the treated groups showed significantly increased intensities of phenylacetylglycine, guanidinosuccinic acid, 4-pyridoxic acid, 4-aminohippuric acid, 4-guanidinobutanoic acid, allantoic acid, dopamine, LysoPC(18:2(9Z,12Z)), and L-urobilinogen. By contrast, the intensities of creatinine, L-carnitine, taurine, and pantothenic acid in the treated groups were significantly decreased. These results indicated that Cd disrupts energy and lipid metabolism. Meanwhile, Cd causes liver and kidney damage via induction of oxidative stress; serum biochemical indices (e.g., creatinine and urea nitrogen) also support the aforementioned results.

Development and validation of abiotic ligand model for nickel toxicity to wheat (Triticum aestivum)

A terrestrial biotic ligand model (t-BLM) was developed to predict nickel toxicity to wheat (Triticum aestivum) root elongation in hydroponic solutions. The competitive effects of five major cations (Ca²⁺, Mg²⁺, Na⁺, K⁺ and H⁺) on Ni toxicity were investigated and Mg²⁺was found to be a strong competitor, while H⁺ showed less competing effect. Besides free Ni²⁺, the toxicity induced by the species NiHCO₃⁺ was non-neglect able at pH>7 because NiHCO₃⁺ occupied a significant fraction of total Ni under such condition. Thus, a t-BLM including Ni²⁺, NiHCO₃⁺, Mg²⁺, and H⁺ could successfully predict the nickel toxicity to wheat root elongation and it performed better prediction than the conventional free ion activity model. In addition, the model was examined with two sets of independent experiments, which contained multiple cations and low-molecular-weight organic acids to mimic the rhizosphere condition. The developed t-BLM well predicted nickel toxicity in both experiments since it can account in both complexation and competition effects, suggesting its potential to be used in a complicated matrix like soil solution. This study provides direct evidence that the t-BLM is a reliable method for the risk assessment of nickel in terrestrial system.

Extended biotic ligand model for predicting combined Cu-Zn toxicity to wheat (Triticum aestivum L.): Incorporating the effects of concentration ratio, major cations and pH

Current risk assessment models for metals such as the biotic ligand model (BLM) are usually applied to individual metals, yet toxic metals are rarely found singly in the environment. In the present research, the toxicity of Cu and Zn alone and together were studied in wheat (Triticum aestivum L.) using different Ca²⁺ and Mg²⁺ concentrations, pH levels and Zn:Cu concentration ratios. The aim of the study was to better understand the toxicity effects of these two metals using BLMs and toxic units (TUs) from single and combined metal toxicity data. The results of single-metal toxicity tests showed that toxicity of Cu and Zn tended to decrease with increasing Ca²⁺ or Mg²⁺ concentrations, and that the effects of pH on Cu and Zn toxicity were related not only to free Cu²⁺ and Zn²⁺ activity, respectively, but also to other inorganic metal complex species. For the metal mixture, Cu-Zn interactions based on free ion activities were primarily additive for the different Ca²⁺ and Mg²⁺ concentrations and levels of pH. The toxicity data of individual metals derived by the BLM, which incorporated Ca²⁺ and Mg²⁺ competition and toxicity of inorganic metal complexes in a single-metal toxicity assessment, could predict the combined toxicity as a function of TU. There was good performance between the predicted and observed effects (root mean square error [RMSE] = 7.15, R² = 0.97) compared to that using a TU method with a model based on free ion activity (RMSE = 14.29, R² = 0.86). The overall findings indicated that bioavailability models that include those biochemistry processes may accurately predict the toxicity of metal mixtures.

Modeling acute toxicity of metal mixtures to wheat (Triticum aestivum L.) using the biotic ligand model-based toxic units method

The combined toxic effects of copper (Cu) and cobalt (Co) were predicted using the biotic ligand model (BLM) for different concentrations of magnesium (Mg²⁺) and pH levels, with parameters derived from Cu-only and Co-only toxicity data. The BLM-based toxic unit (TU) approach was used for prediction. Higher activities of Mg²⁺ linearly increased the EC₅₀ of Cu and Co, supporting the concept of competitive binding of Mg²⁺ and metal ions in toxic action. The effects of pH on Cu and Co toxicity were related not only to free Cu²⁺ and Co²⁺ activity, respectively, but also to inorganic metal complexes. Stability constants for the binding of Cu²⁺, CuHCO₃⁺, CuCO₃(aq), CuOH⁺, Mg²⁺, Co²⁺, CoHCO₃⁺ and Mg²⁺ with biotic ligands were logK_CuBL 5.87, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{log}\,{K}_{{{\rm{CuHCO}}}_{3}{\rm{BL}}}$$\end{document}logKCuHCO3BL 5.67, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{log}\,{K}_{{{\rm{CuCO}}}_{3}{\rm{BL}}}$$\end{document}logKCuCO3BL 5.44, logK_CuOHBL 5.07, logK_MgBL 2.93, logK_CoBL 4.72, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathrm{log}\,{K}_{{{\rm{CoHCO}}}_{3}{\rm{BL}}}$$\end{document}logKCoHCO3BL 5.81 and logK_MgBL 3.84, respectively. The combinations of Cu and Co showed additive effects under different conditions. When compared with the FIAM-based TU model (root mean square error [RMSE = 16.31, R² = 0.84]), the BLM-based TU model fitted the observed effects better (RMSE = 6.70, R² = 0.97). The present study supports the BLM principles, which indicate that metal speciation and major cations competition need to be accounted for when predicting toxicity of both single metals and mixtures of metals.