An Evaluation of Metal Binding Constants to Cell Surface Receptors in Freshwater Organisms, and Their Application in Biotic Ligand Models to Predict Metal Toxicity

Abstract

Biotic ligand models (BLMs) predict the toxicity of metals in aquatic environments by accounting for metal interactions with cell surface receptors (biotic ligands) in organisms, including water chemistry (metal speciation) and competing cations. Metal binding constants (log K_MBL values), which indicate the affinity of metals for cell surface receptors, are fundamental to BLMs, but have only been reported for a few commonly investigated metals and freshwater species. This review evaluated literature toxicity and uptake data for seven key metals (cadmium (Cd), cobalt (Co), copper (Cu), nickel (Ni), lead (Pb), uranium (U), and zinc (Zn)) and four key competing cations (protons (H), calcium (Ca), magnesium (Mg), and sodium (Na)), to derive average metal binding constants for freshwater organisms/taxa. These constants will improve current BLMs for Cd, Cu, Ni, Pb, and Zn, and aid in developing new BLMs for Co and U. The derived metal binding constants accurately predicted metal toxicity for a wide range of freshwater organisms (75–88% of data were within a factor of two and 88–98% of data were within a factor of three of the ideal 1:1 agreement line), when considering metal speciation, competing cations and the fraction of cell receptors ((f_C)_M^50%) occupied by the metal at the median (50%) effect concentration (EC₅₀). For many organisms, toxicity occurs when 50% of cell surface receptors are occupied by the metal, though this threshold can vary. Some organisms exhibit toxicity with less than 50% receptor occupancy, while others with protective mechanisms show reduced toxicity, even with similar log K_MBL values. For Cu, U, and Pb, the toxic effect of the metal hydroxide (as MOH⁺) must be considered in addition to the free metal ion (M²⁺), as these metals hydrolyse in circumneutral freshwaters (pH 5.5 to 8.5), contributing to toxicity.

1. Introduction

Metal toxicity in aquatic organisms occurs when metals bind to active functional groups (ligands) on the cell surface, such as cell membrane transporters (receptors), thereby impairing their vital functions (Figure 1). For instance, copper (Cu⁺) interferes with sodium (Na⁺) uptake, while cadmium (Cd²⁺), zinc (Zn²⁺), and lead (Pb²⁺) disrupt calcium (Ca²⁺) uptake [1]. Additionally, copper (Cu²⁺) can also disrupt Ca²⁺ uptake [2].

Metal toxicity to aquatic organisms is influenced largely by the following factors, which stem from three key conceptual models for metal–organism interaction—the free ion activity model (FIAM) [3,4], the biotic ligand model (BLM) [5,6], and the electrostatic toxicity model (ETM) [7,8]:

(i)

The metal’s binding affinity to ligands at cell surface receptors: a higher affinity means toxicity will occur at a lower metal concentration;

(ii)

Metal speciation in water: Free metal ions (M^z+) are typically toxic, but other positively charged species (MOH^(z−1)+, MF^(z−1)+) can also cause toxicity (Figure 1), especially for metals that hydrolyse within the pH range of natural freshwaters (pH 5.5–8.5), such as uranium (as uranyl, UO₂²⁺), copper (Cu²⁺), and lead (Pb²⁺). Predicting toxicity is challenging since total or dissolved metal concentrations are not reliable indicators of metal bioavailability [9]. Binding with anions, like bicarbonate or dissolved organic matter, reduces the concentration of free metal ions and reduces toxicity;

(iii)

Metals disrupt essential element uptake at cell surface receptors: however, the presence of essential elements and similar cations, such as Ca²⁺, magnesium (Mg²⁺), sodium (Na⁺), and protons (H⁺), in freshwater can ameliorate metal toxicity (Figure 1);

(iv)

Toxicity depends on the proportion of cell surface receptor sites bound by metals: If a toxic response occurs when 50% of sites are occupied, the TR₅₀ can be calculated from the inverse of the metal concentration causing the effect. If less than 50% of sites are occupied at the TR₅₀, then the metal’s binding affinity depends on both the metal concentration and the fraction of occupied sites.

The existing conceptual models (FIAM, BLM and ETM) that describe metal binding at cell surface receptors (biotic ligands) are widely acknowledged to share a common framework, with metal binding (stability) constants being a central component. However, metal binding constants have generally been reported for only a limited number of freshwater taxa (fish, crustaceans and micro-organisms), and often show considerable variability within and among species [10,11]. The lack of binding constants for metals such as cobalt (Co²⁺), UO₂²⁺ and Pb²⁺, and limited data for nickel (Ni²⁺), Cd²⁺, Cu²⁺ and Zn²⁺, constrains the wider use of these models in predicting metal toxicity across freshwater taxa.

The binding constants of metals with cell surface receptors (represented as log K values) can be measured directly through uptake (accumulation) studies or derived from toxicity data. When using toxicity data, the apparent binding constant (which is the inverse of the free metal ion concentration at the TR₅₀) requires adjustment for ameliorative cation concentrations (H⁺, Na⁺, Mg²⁺, Ca²⁺) and receptor occupancy to obtain the true binding constant. If less than 50% of cell surface receptors are occupied at the TR₅₀, increased toxicity is observed, but the binding constant decreases. Organisms with the ability to bind metals at other high-affinity, low-capacity, receptors can reduce metal toxicity.

This study evaluated the literature on the toxicity and uptake of seven key metals (Cd²⁺, Co²⁺, Cu²⁺, Ni²⁺, Pb²⁺, UO₂²⁺ and Zn²⁺) in freshwater systems. The primary objective was to compile a comprehensive database of metal binding (stability) constants at cell surface receptors (biotic ligands) for a diverse range of freshwater taxa, including fish (e.g., Oncorhynchus mykiss and Pimephales promelas), crustaceans (e.g., Daphnia magna and Ceriodaphnia dubia), microalgae (e.g., Raphidocelis subcapitata) and molluscs (e.g., Lymnaea stagnalis). Binding constants for the ameliorative cations Ca²⁺, Mg²⁺, Na⁺ and H⁺, were also included. Potassium (K⁺) was excluded due to its relatively minor ameliorative effect. A secondary objective was to compare the measured and predicted toxicity (EC/LC₅₀ values) of the seven metals, as a key measure of the reliability of the derived metal binding constants.

The following section outlines the development and unification of the existing conceptual models, providing the foundation for deriving metal binding constants and predicting metal toxicity to aquatic organisms.

2. Conceptual Models of Metal Binding to Biotic Ligands

To cause a toxic response, a metal must first interact with transporters (receptors) on the cell membrane surface, comprising macromolecules dominated by oxygen-containing functional (donor) groups, such as carboxylate (COOH) [12]. These functional groups have an average proton dissociation constant between 4 and 6 [11] and, as such, in most natural waters (circumneutral pH), the cell surface receptors will be deprotonated and consist of negatively charged surface sites, {X–cell⁻}. The transport and binding of soluble metals at cell surface receptors is considered to occur rapidly [12]. The complexation of the metal with the cell surface results in the formation of {M–X–cell}. The seven divalent metals investigated are more likely to bind with oxygen-rich donor groups, like carboxylate (see Section 3.13). In contrast, toxic metals like Ag⁺ and Hg²⁺ show a preference for nitrogen or sulphur-rich donor groups over oxygen.

In the development of the extended FIAM, Brown and Markich [4] demonstrated that the toxic response (TR) of an organism to a metal could be described by Equation (1)

$$\mathrm{TR}={\displaystyle \frac{{\mathrm{TR}}_{\max }{{\left\{\mathrm{X}-\mathrm{cell}\right\}}_{\mathrm{T}}}^n{\left[\mathrm{M}\right]}^n}{{{\left\{\mathrm{X}-\mathrm{cell}\right\}}_{\mathrm{E}}}^n(K_{-1}+[M]{)}^n+{{\left\{\mathrm{X}-\mathrm{cell}\right\}}_{\mathrm{T}}}^n[\mathrm{M}{]}^n}}$$

(1)

where TR_max is the maximum toxic response, {X–cell}_T is the total number of receptor sites on the cell membrane, {X–cell}_E is the concentration of receptor sites bound by metal ions which causes half of the maximal toxic response (TR₅₀), K₋₁ is the inverse of the binding (or stability) constant (which will be defined as K_MBL, so K₁ = 1/K₋₁ = K_MBL) between the metal and the receptor sites on the cell membrane surface and n determines the slope of the concentration-response curve.

Equation (1) is the product of two processes: (1) the reaction of the metal with receptor sites on the cell membrane surface and (2) the response of the organism to the presence of the toxic metal. In the first process, an explicit equation can be derived for the concentration of the total number of surface receptor sites bound by the metal (i.e., {M–X–cell}), using the law of mass action [4], as described by Equation (2).

$$\{\mathrm{M}–\mathrm{X}–\mathrm{cell}\}={\displaystyle \frac{\{\mathrm{X}-\mathrm{cell}{\}}_{\mathrm{T}}[\mathrm{M}]}{K_{-1}+\left[\mathrm{M}\right]}}$$

(2)

Similarly, the response of the organism to the interaction of the metal with receptor sites on the cell membrane surface is described by Equation (3).

$$\mathrm{TR}={\displaystyle \frac{{\mathrm{TR}}_{\max }{\left\{\mathrm{M}–\mathrm{X}–\mathrm{cell}\right\}}^n}{{{\left\{\mathrm{X}-\mathrm{cell}\right\}}_{\mathrm{E}}}^n+\{\mathrm{M}–\mathrm{X}–\mathrm{cell}{\}}^n}}$$

(3)

The substitution of Equation (2) into (3) leads to Equation (1). Equation (3), through the exponent n, accounts for the fact that concentration-response curves are generally sigmoidal in shape and have large slopes (i.e., n ≥ 5) [4,13].

A closer inspection of Equation (1) is useful as it contains important information. Moving TR_max to the left-hand side of Equation (1), inverting followed by simplification leads to Equation (4):

$${\displaystyle \frac{{\mathrm{TR}}_{\max }}{\mathrm{TR}}}={\displaystyle \frac{1}{f_{\mathrm{TR}}}}={\displaystyle \frac{{{\left\{\mathrm{X}-\mathrm{cell}\right\}}_{\mathrm{E}}}^n{\left(K_{-1}+\left[\mathrm{M}\right]\right)}^n}{{{\left\{\mathrm{X}-\mathrm{cell}\right\}}_{\mathrm{T}}}^n{\left[\mathrm{M}\right]}^n}}+1$$

(4)

where f_TR is the ratio of the toxic response to the maximum response (e.g., TR₅₀/TR_max = f₅₀ = 0.5). The rearrangement of Equation (4) gives

$$\left({\displaystyle \frac{1}{f_{\mathrm{TR}}}}-1\right){{\left\{\mathrm{X}–\mathrm{cell}\right\}}_{\mathrm{T}}}^n[\mathrm{M}{]}^n={{\left\{\mathrm{X}–\mathrm{cell}\right\}}_{\mathrm{E}}}^n(K_{-1}+[\mathrm{M}]{)}^n$$

(5)

Equation (4) can be simplified, by taking the n-th root, and following rearrangement gives

$${\left({\displaystyle \frac{1}{f_{\mathrm{TR}}}}-1\right)}^{1/n}{\displaystyle \frac{\{\mathrm{X}-\mathrm{cell}{\}}_{\mathrm{T}}}{{\left\{\mathrm{X}-\mathrm{cell}\right\}}_{\mathrm{E}}}}={\displaystyle \frac{(K_{-1}+[\mathrm{M}\left]\right)}{\left[\mathrm{M}\right]}}={\displaystyle \frac{\left(1+K_1\left[\mathrm{M}\right]\right)}{K_1\left[\mathrm{M}\right]}}$$

(6)

Further rearrangement leads to Equation (7),

$$[\mathrm{M}]={\displaystyle \frac{K_{-1}}{{\left(1/f_{\mathrm{TR}}-1\right)}^{1/n}(1/{\left(f_C\right)}_{\mathrm{M}}^{50\%})-1}}$$

(7)

where (f_C)_M^50% (= {X–cell}_E/{X–cell}_T) is the fraction of receptor sites occupied at the TR₅₀. If the TR₅₀ (i.e., f_TR = 0.5) is considered, then Equation (7) can be reduced to

$$[\mathrm{M}]={\displaystyle \frac{{\left(f_C\right)}_{\mathrm{M}}^{50\%}{K}_{-1}}{1-{\left(f_C\right)}_M^{50\%}}}$$

(8)

In the absence of competing ions, such as protons (H⁺), Na⁺ and the hardness cations, Ca²⁺ and Mg²⁺, Equation (8) is identical to that given by De Schamphelaere and Janssen [9] in the development of a BLM to predict the effects of such ions (hardness and protons) on acute copper (Cu²⁺) toxicity. Additionally, if the TR₅₀ occurs when half of the receptor sites are occupied, then (f_C)_M^50% is equivalent to (1 − (f_C)_M^50%) [i.e., (f_C)_M^50% = 0.5] and the metal concentration at the TR₅₀ is given by

[M] = K₋₁ = 1/K₁ = 1/K_MBL

(9)

Alternatively, if less than half of the receptor sites are occupied at the TR₅₀, then the fraction ((f_C)_M^50%/(1 − (f_C)_M^50%) in Equation (8) is less than unity since (f_C)_M^50% < 0.5 and, as such, K₋₁ is larger than the metal concentration which causes the TR₅₀. It is not possible for more than 50% of the receptor cells to be occupied at the TR₅₀. To demonstrate these behaviours, Figure S1 shows the calculated TR when the following parameter values are used in Equation (1): TR_max = 100; K₋₁ = 0.5; n = 10; {X–cell}_T = 1 and (f_C)_M^50% = 0.2, 0.5 and 0.8 (units are not provided for brevity and the values used are for simplicity and the purpose of the demonstration). It is clear from Figure S1 that it is not possible to achieve the true TR_max if more than half the receptor sites are occupied at the TR₅₀, thereby invalidating such scenarios. Consequently, the minimum value K₋₁ can have is the metal concentration that occurs at the TR₅₀ and this would happen when the biological response causing the TR₅₀ occurs when 50% of the receptor sites are occupied. Conversely, when (f_C)_M^50% ≤ 0.5, the true TR_max is attained; however, as (f_C)_M^50% continues to decrease below 0.5, the TR₅₀ moves progressively to lower metal concentrations, as indicated by Equation (8).

Brown and Markich [4] showed that the FIAM could be adapted to systems where metal ion binding to surface sites is ameliorated by protons (H⁺). In this scenario, the expression for {M–X–cell} is modified to

$$\left\{\mathrm{M}–\mathrm{X}–\mathrm{cell}\right\}={\displaystyle \frac{K_{\mathrm{MBL}}{\left\{\mathrm{X}-\mathrm{cell}\right\}}_{\mathrm{T}}\left[\mathrm{M}\right]}{1+K_{\mathrm{MBL}}\left[\mathrm{M}\right]+K_{\mathrm{HBL}}\left[\mathrm{H}\right]}}$$

(10)

(i.e., an extension of Equation (2)), where K_MBL has replaced K₁ and K_HBL is the binding constant of H⁺ with receptor sites on the cell membrane surface. The extension of the sequence of Equation (2) to Equation (10) above, in the case of amelioration by H⁺, leads to the metal concentration (free ion) at the TR₅₀:

$$[\mathrm{M}]={\displaystyle \frac{{\left(f_C\right)}_{\mathrm{M}}^{50\%}}{1-{\left(f_C\right)}_{\mathrm{M}}^{50\%}}}{\displaystyle \frac{1}{K_{\mathrm{MBL}}}}\left(1+K_{\mathrm{HBL}}\left[\mathrm{H}\right]\right)$$

(11)

The expansion of Equation (11) to include amelioration by Na⁺, and the hardness ions, Ca²⁺ and Mg²⁺, gives (the metal concentration at the TR₅₀)

$$[\mathrm{M}]={\displaystyle \frac{{\left(f_C\right)}_{\mathrm{M}}^{50\%}}{1-{\left(f_C\right)}_{\mathrm{M}}^{50\%}}}{\displaystyle \frac{1}{K_{\mathrm{MBL}}}}\left(1+K_{\mathrm{HBL}}\left[\mathrm{H}\right]+K_{\mathrm{NaBL}}\left[\mathrm{Na}\right]+K_{\mathrm{CaBL}}\left[\mathrm{Ca}\right]+K_{\mathrm{MgBL}}\left[\mathrm{Mg}\right]\right)$$

(12)

where K_NaBL, K_CaBL and K_MgBL are the binding constants of Na, Ca and Mg cations, respectively, with receptor sites on the cell membrane surface (Figure 1). Equation (12) is identical to that given by De Schamphelaere and Janssen [9] in the development of a BLM to predict the effects of such ions on acute metal toxicity. Most studies have found that the potassium ion (K⁺) does not provide an ameliorative affect to metal toxicity and, as such, is not considered further.

It has frequently been found that toxicity is not only caused by the free metal ion, but other cationic metal–ligand species, ML (such as metal hydroxide (MOH) or fluoride (MF)), can also elicit a toxic response. Brown and Markich [4] extended the FIAM to account for the toxicity caused by such species. Again, the model equations extend Equation (2):

$$\left\{\mathrm{M}–\mathrm{X}–\mathrm{cell}\right\}+\left\{\mathrm{LM}–\mathrm{X}–\mathrm{cell}\right\}={\displaystyle \frac{\{\mathrm{X}-\mathrm{cell}{\}}_{\mathrm{T}}\left(K_1+K_3{K}_4\left[\mathrm{L}\right]\right)[\mathrm{M}]}{1+\left(K_1+K_3{K}_4\left[\mathrm{L}\right]\right)\left[\mathrm{M}\right]}}$$

(13)

where K₁ is again used for K_MBL, K₃ is the binding constant of ML with receptor sites on the cell membrane surface and K₄ is the binding constant of the metal (M) and the ligand (L). The rearrangement of Equation (13) and combination of it with a version of Equation (3) that contains both {M–X–cell} and {LM–X–cell} gives the following:

$$K_{\mathrm{MBL}}\left[\mathrm{M}\right]+K_{\mathrm{LMBL}}\left[\mathrm{ML}\right]={\displaystyle \frac{{\left(f_C\right)}_{\mathrm{M}}^{50\%}}{1-{\left(f_C\right)}_{\mathrm{M}}^{50\%}}}\left(1+K_{\mathrm{HBL}}\left[\mathrm{H}\right]+K_{\mathrm{NaBL}}\left[\mathrm{Na}\right]+K_{\mathrm{CaBL}}\left[\mathrm{Ca}\right]+K_{\mathrm{MgBL}}\left[\mathrm{Mg}\right]\right)$$

(14)

Rearrangement of Equation (14), leads to:

$$\left[\mathrm{M}\right]+{\displaystyle \frac{K_{\mathrm{LMBL}}}{K_{\mathrm{MBL}}}}\left[\mathrm{ML}\right]={\displaystyle \frac{{\left(f_C\right)}_{\mathrm{M}}^{50\%}}{1-{\left(f_C\right)}_{\mathrm{M}}^{50\%}}}{\displaystyle \frac{1}{K_{\mathrm{MBL}}}}\left(1+K_{\mathrm{HBL}}\left[\mathrm{H}\right]+K_{\mathrm{NaBL}}\left[\mathrm{Na}\right]+K_{\mathrm{CaBL}}\left[\mathrm{Ca}\right]+K_{\mathrm{MgBL}}\left[\mathrm{Mg}\right]\right)$$

(15)

Markich et al. [14,15] demonstrated that the toxic response of bivalves to dioxouranium(II) or copper(II) was best described by combining the activities of [M²⁺] and [MOH⁺], where [M²⁺] had twice the effect of [MOH⁺] (i.e., [M²⁺] + [MOH⁺]/2). Reanalysis of Cu(II) toxicity data for D. magna from De Schamphalaere and Janssen [9] revealed a similar relationship (i.e., [Cu²⁺] + [CuOH⁺]/2) (refer to Supplementary Information). Crémazy et al. [16] reported that scandium (Sc(III)) uptake by the microalga Chlamydomonas reinhardtii was best explained by a combination of Sc³⁺ and its hydroxide complexes (such as ScOH²⁺ and Sc(OH)₂⁺) above pH 6.5. Wilkinson et al. [17] found that both [M³⁺] and [MF²⁺] were needed to describe the toxicity of aluminium(III) to Atlantic salmon (O. mykiss), with the activity of [Al³⁺] being 1.5 times that of [AlF²⁺] [4]. Similarly, Crémazy et al. [18] reported that both [Sc³⁺] and [ScF²⁺] were necessary for explaining Sc(III) uptake in C. reinhardtii, with binding constants having a ratio of 1.9 (see Equation (15)). It can be seen from these examples that the toxic response induced by [ML] is related to that of [M] by dividing [ML] by the ratio of the charges of the two species. This behaviour then allows the metal concentration at the TR₅₀ to be described by the following:

$$\left(\left[\mathrm{M}\right]+\mathsf{\Sigma }{\displaystyle \frac{z_{\mathrm{ML}}}{z_{\mathrm{M}}}}\left[\mathrm{ML}\right]\right)={\displaystyle \frac{{\left(f_C\right)}_{\mathrm{M}}^{50\%}}{1-{\left(f_C\right)}_{\mathrm{M}}^{50\%}}}{\displaystyle \frac{1}{K_{\mathrm{MBL}}}}\left(1+K_{\mathrm{HBL}}\left[\mathrm{H}\right]+K_{\mathrm{NaBL}}\left[\mathrm{Na}\right]+K_{\mathrm{CaBL}}\left[\mathrm{Ca}\right]+K_{\mathrm{MgBL}}\left[\mathrm{Mg}\right]\right)$$

(16)

where z_M is the charge of the metal ion, and z_ML is the charge of each ML species that also causes a toxic response (the summation is used to define the number of ML species that may cause a toxic response). A comparison of Equations (15) and (16) indicates that K_LMBL must be less than K_MBL because z_ML/z_M is less than one (i.e., for M²⁺ and MOH⁺, K_HOMBL/K_MBL = 0.5). The use of charge alone in Equation (16) might be overly simplistic. Binding constants generally consist of two components: an intrinsic term and an electrostatic term. This approach has been successfully used to explain metal binding to natural dissolved organic matter (DOM), such as humic and fulvic acids [19]. The surfaces of natural DOM resemble those of cell membrane surfaces. Equation (16) may imply that the intrinsic terms for M and ML are similar (see Section 7 for more detail).

The model development outlined above demonstrates that the formulation of the BLM can be derived directly from rearrangement of the formulation of the FIAM, and both can be equally utilised to describe the toxic response of organisms to metals. The models show that toxic response is a function of the strength of binding that metals have at organism cell surface receptors, a response that can be ameliorated by the presence of several cations in aqueous systems, such as, H⁺, Na⁺, Ca²⁺ and Mg²⁺. The concentration at which a toxic response occurs is also related to the fraction of sites on the cell surface that are bound by the metal at the TR₅₀; the lower the fraction of sites on the cell surface that are bound, the lower the metal concentration that elicits the TR₅₀. It is also important to understand that the toxic response is caused by the free metal ion as well as other cationic species of the metal when bound to various ligands (e.g., MOH and MF).

Metals bound to other ligands (such as sulphate, chloride, carbonate, phosphate or organic macromolecules) in solution do not typically cause a toxic response and, as such, the total metal concentration at the TR₅₀ will generally be greater than the concentration of metal species that cause the toxic response (e.g., M, MOH, MF, etc.). The combination of the two conceptual models also demonstrates how concentration-response curves are frequently sigmoidal in shape and have large slopes (i.e., n ≥ 5). Importantly, the extended FIAM demonstrates a cascade of effects that includes (a) the reaction of a metal with receptor sites on the cell membrane surface, (b) the response of an organism to the presence of the toxic metal and (c) the magnification of toxicity depending on the fraction of cell surface sites occupied at the TR₅₀ (Figure 2).

In addition to the BLM and FIAM, ETMs have been used to describe metal and metalloid uptake and toxicity to plants [7,8]. These models describe an electrical double layer above the cell membrane surface with three key electrical properties of the cell membrane [20]. There is a transmembrane electrical potential (E_m) that describes the electrical potential difference between the cell interior and the bulk phase medium. The second is a negative electrical potential (ψ₀) on the cell membrane surface, due to acidic amino acids in membrane proteins and the phosphate groups of membrane phospholipids [20]. Finally, there is the electrical potential difference (E_m,surf) from surface to surface, which is the driving force of metal transport across the cell membrane. Classical electrostatic theory is used together with ion binding through definition of the cell membrane surface charge density (σ) and the electrical potential of the exterior surface of the cell membrane (ψ₀). The model provides an elegant depiction of binding at cell surfaces that can be utilised to describe the toxicity and uptake of metals in plants and that could equally be utilised to describe the toxicity of metals to aquatic organisms.

An important difference between ETMs and BLMs (including the FIAM) is that the former describes two distinct binding sites, with metal binding defined by the following two reactions:

$${\mathrm{M}}^{\mathrm{z}+}+\mathrm{X}–{\mathrm{cell}}^{-} \leftrightharpoons \mathrm{M}–\mathrm{X}–{\mathrm{cell}}^{(\mathrm{z}-1)+}$$

(17)

$${\mathrm{M}}^{\mathrm{z}+}+\mathrm{Y}–\mathrm{cell} \leftrightharpoons \mathrm{M}–\mathrm{Y}–{\mathrm{cell}}^{\mathrm{z}+}$$

(18)

with Equation (17) representing a reaction with a negatively charged site (as described above) and Equation (18) defining the reaction of a metal with an uncharged site. These sites likely describe carboxylic acid (-COOH) binding and amine (-NH₂) binding, respectively. As such, the binding of an amine group will occur at a greater pH. In some studies of aquatic organisms, the toxicity of a metal has been found to have an inflexion point as the pH is increased. Such an inflexion point may be the result of the binding of metals to a second cell surface site at the increased pH (see Section 8).

3. Metal Binding Constants

This section provides the binding (or stability) constants (log K_MBL values) for seven environmentally important metals (Zn²⁺, Ni²⁺, Cd²⁺, Co²⁺, Cu²⁺, UO₂²⁺ and Pb²⁺;

Table 1. Binding constants (log K_MBL) for zinc (Zn²⁺), nickel (Ni²⁺), cadmium (Cd²⁺), cobalt (Co²⁺), copper (Cu²⁺), uranium (UO₂²⁺) and lead (Pb²⁺) at cell surface receptor sites (biotic ligands) in freshwater organisms.

Taxa	Organism a	log KMBL
		Zn2+	Ni2+	Cd2+	Co2+	Cu2+	UO22+	Pb2+
Fish c	Acipenser transmontanus	6.1		7.3		8.2		7.3
	Cottus bairdii	6.1 (3) b		7.2		8.1
	Ctenopharyngodon idella	5.7
	Danio rerio					7.7
	Mogurnda mogurnda	6.1				7.3	7.4
	Neogobius melanostomus		4.7
	Oncorhynchus clarkii	5.8				7.8
	Oncorhynchus kisutch					7.8
	Oncorhynchus mykiss	5.9 (13)	4.7 (3)	7.5 (13)	5.3 (3)	7.9 (12)	7.3	7.1 (3)
	Oncorhynchus nerka					7.7
	Oncorhynchus tshawytscha	6.1		7.6		7.7 (2)
	Oreochromis mossambicus			7.0
	Perca flavescens			7.2
	Pimephales promelas	5.7 (3)	4.7 (3)	7.1 (3)	5.7	7.6 (11)	7.4	6.8 (5)
	Prosopium williamsoni	5.5
	Salmo trutta			7.6
	Salvelinus confluentus	5.7		7.2
	Average (fish)	5.9	4.7	7.3	5.5	7.8	7.4	7.1
Crustaceans (cladocerans)	Acantholeberis curvirostris					7.8
	Acroperus elongatus					8.2
	Acroperus harpae					8.3
	Alona sp.					8.1
	Alona affinis		4.7
	Alona quadrangularis					8.0
	Bosmina coregoni		5.0
	Bosmina longirostris					7.9 (2)
	Camptocercus lilljeborgi		4.9
	Ceriodaphnia cornuta					7.9
	Ceriodaphnia dubia	5.9 (8)	5.2 (4)	7.0 (3)	5.5	8.0 (15)	7.4	7.0 (7)
	Ceriodaphnia pulchella		4.8			7.7 (2)
	Ceriodaphnia quadrangula		4.8
Crustaceans (cladocerans)	Ceriodaphnia reticulata	6.2		6.5		8.1 (3)
	Ceriodaphnia rigaudi			7.0
	Ceriodaphnia silvestri			6.9
	Chydorus ovalis		4.7			7.9
	Chydorus sphearicus					8.1 (2)
	Daphnia ambigua					7.9
	Daphnia carinata	5.7				7.4		6.9 (2)
	Daphnia exilis					7.8
	Daphnia galeata					7.6 (3)
	Daphnia longispina		4.9			7.8 (2)
	Daphnia magna	5.8 (9)	4.9 (6)	6.9 (7)	5.4 (2)	7.8 (13)	8.0	6.7 (4)
	Daphnia obtusa					7.8
	Daphnia pulex	5.9 (2)	4.7 (2)	6.6 (2)		7.9 (4)
	Daphnia similis							6.8
	Daphnia thomsoni	6.3
	Disparalona rostrata					7.7
	Eurycercus lamellatus					8.1
	Moina affinis	6.2		7.0		8.0
	Moinodaphnia macleayi	6.3				7.7	8.2
	Peracantha truncata		4.6
	Pleuroxus truncatus					7.7
	Pseudosida ramosa			7.2
	Pseudosida variabilis					8.3
	Scapholeberis microcephala					8.2
	Scapholeberis mucronata					8.1
	Simocephalus expinosus					7.8 (2)
	Simocephalus serrulatus		5.0	6.9
	Simocephalus vetulus		4.8	6.9		7.9 (3)
	Average (cladocerans)	6.0	4.8	6.9	5.5	7.9	7.9	6.8
Crustaceans (amphipods)	Gammarus sp.						7.5
	Gammarus pseudolimnaeus			6.5
	Gammarus pulex		4.7
	Hyalella azteca	5.9 (2)	5.1 (4)	7.3 (2)	5.8	7.8	7.4	6.9
Crustaceans (copepod)	Notodiaptomus iheringi			7.4		7.5
Crustaceans (ostracod)	Cypridopsis vidua						7.8
Crustaceans (decapod)	Macrobrachium rosenbergi	5.6
	Average (crustaceans)	6.0	4.9	6.9	5.6	7.9	7.7	6.9
Molluscs d (bivalves)	Alathyria profuga	5.9	4.8	6.6	5.9	7.4		6.4
	Cambarunio iris					8.1 (3)
	Corbicula fluminea					7.7	7.6
	Cucumerunio novaehollandiae	6.0	5.0	6.8	6.1	7.7		6.6
	Echyridella menziesii	5.7				8.1
	Epioblasma rangiana					7.9
	Epioblasma triquetra					8.2
	Hyridella australis	6.0	5.0	6.8	6.1	7.6		6.6
	Hyridella depressa	6.0	4.9	6.7	6.0	7.5		6.5
Molluscs (bivalves)	Hyridella drapeta	5.9	4.9	6.6	6.0	7.5		6.5
	Lampsilis abrupta					7.9
	Lampsilis fasciola					8.0 (2)
	Lampsilis rafinesqueana	6.3		7.4		7.8		6.8
	Lampsilis siliquoidea	6.3		7.5		7.8 (3)		6.7
	Obovaria subrotunda					7.8
	Ortmanniana ligamentina					7.6 (2)
	Paetulunio fabalis					8.2
	Potamilus ohiensis					7.9
	Velesunio sp.					8.2
	Velesunio anbiguus	5.8	4.8	6.6	5.9	7.4		6.4
	Velesunio angasi	6.3
	Venustaconcha ellipsiformis					8.1
	Average (bivalves)	6.0	4.9	6.9	6.0	7.8	7.6	6.6
Molluscs (gastropods)	Amerianna cumingi	6.2				7.9	8.1
	Filopaludina bengalensis					7.9
	Fluminicola sp.					8.2
	Fontigens aldrichi					7.9
	Lymnaea stagnalis		4.9 (3)	6.6 (2)	5.9	8.0 (4)
	Physella acuta					8.3
	Physella gyrina					7.7
	Planorbella pilsbryi					8.2
	Pomacea paludosa	5.8
	Potamopyrgus antipodarum			7.3
	Pyrgulopsis robusta					8.0
	Racesina luteola			6.5		8.2
	Taylorconcha serpenticola					8.1
	Average (gastropods)	6.0	4.9	6.8	5.9	8.0	8.1	—
	Average (molluscs)	6.0	4.9	6.8	6.0	7.9	7.9	6.6
Rotifers	Anuraeopsis fissa	5.8
	Brachionus calicyflorus		4.6					7.4
	Brachionus rubens	5.5
	Euchlanis dilatata	6.1				7.9
	Lecane inermis	6.3				8.0
	Lecane quadridentata	6.2						7.5
	Average (rotifers)	6.0	4.6	—	—	8.0	—	7.4
Microalgae (Chlorophyceae)	Ankistrodesmus arcuatus		4.6			8.0
	Chlamydomonas reinhardtii						7.7 (2)
	Chlorella sp.	5.8 (4)	5.0 (2)			7.8 (11)	7.8 (4)
	Raphidocelis subcapitata	6.1 (9)	4.7 (6)	7.0 (7)	5.7 (2)	7.8 (8)	8.1	7.0 (2)
	Average (microalgae)	6.0	4.8	7.0	5.7	7.9	7.9	7.0
Macrophytes	Ceratophyllum demersum					7.2	7.7
	Lemna aequinoctialis					7.7	7.4 (3)
	Lemna minor	6.2	4.7 (3)	7.1	6.1 (2)	7.4	7.8 (2)	7.2
Hydra	Hydra circumcincta			7.1
	Hydra viridissima	6.1	5.2			7.7 (2)	7.3 (3)
Insects	Chironomus tentans						7.6
	Tanytarsus dissimilis	6.1		7.3		7.5		6.6
Euglenid	Euglena gracilis						7.7
Annelid	Aeolosoma sp.				5.4
Bacteria	Erwinia sp.					7.7
	Average (all)	6.0	4.8	7.0	5.8	7.9	7.7	6.8
	95% confidence limit	0.1	0.1	0.1	0.2	0.1	0.1	0.1
	Number of organisms (n)	42	31	37	15	84	20	21

Note(s): ^a Taxonomic classification as per the Catalogue of Life [21]. ^b Values with parentheses (n) are averages (individual organism log K_MBL values and references are provided in Table S1). ^c Fish are all teleostei, except for Acipenser transmontanus (chondrostei). ^d Bivalves are all unionids, except for Corbicula fluminea (venerid).

) and four key ameliorative cations (H⁺, Na⁺, Ca²⁺ and Mg²⁺;

Table 2. Binding constants (log K_MBL) for the ameliorative cations (calcium (Ca²⁺), magnesium (Mg²⁺), sodium (Na⁺) and protons (H⁺)) at cell surface receptor sites (biotic ligands) in freshwater organisms.

Taxa	Organism a	log KMBL
		Ca2+	Mg2+	Na+	H+
Fish	Ctenopharyngodon idella		2.8
	Mogurnda mogurnda				5.8
	Oncorhynchus mykiss	3.5 (7) b	3.0	2.4	5.8 (5)
	Oreochromis mossambicus	3.5
	Perca flavescens	3.7
	Pimephales promelas	3.2 (4)			5.6 (2)
	Average (fish)	3.5	2.9	2.4	5.7
Crustaceans (cladocerans)	Ceriodaphnia dubia	3.2 (2)	2.6	2.4 (2)	5.6
	Ceriodaphnia pulchella			2.4
	Ceriodaphnia reticulata			2.1
	Daphnia galeata			2.2
	Daphnia longispina			2.1
	Daphnia magna	3.2 (5)	2.8 (6)	2.2 (5)	5.8 (3)
	Daphnia pulex	3.5 (2)	3.0 (2)	2.1	5.7
	Simocephalus expinosus			2.0
	Simocephalus vetulus			2.4
	Ten species of cladocerans c	3.2	2.6
	Average (cladocerans)	3.3	2.7	2.2	5.7
Crustaceans (amphipod)	Hyalella azteca	3.4 (3)	2.8 (2)		5.8
	Average (crustaceans)	3.3	2.8	2.2	5.7
Molluscs (bivalves)	Corbicula fluminea	3.5
	Velesunio angasi		2.7
	Average (molluscs)	3.5	2.7	—	—
Micoalgae	Chlamydomonas reinhardtii	3.7	2.8		6.2
	Chlorella sp.				5.8 (2)
	Raphidocelis subcapitata	3.1	2.9 (2)	2.2	5.7 (3)
	Average (microalgae)	3.4	2.8	2.2	5.9
Macrophyte	Ceratophyllum demersum	3.2	2.7
Hydra	Hydra circumcincta	3.7	2.8
	Average	3.4	2.8	2.2	5.8
	95% confidence limit	0.1	0.1	0.1	0.1
	Number of organisms (n)	14	12	11	10

Note(s): ^a Taxonomic classification as per Catalogue of Life [21]. ^b Values with parentheses (n) are averages (individual organism log K_MBL values and references are provided in Table S2). ^c Group average calculated by Deleebeeck et al. [22].

) with cell surface receptors (biotic ligands) in freshwater organisms. For Zn, Ni, Cd and Co, it is assumed that only the free metal ion (M²⁺) induces a toxic response in circumneutral (pH 5.5 to 8.5) oxic freshwaters. However, for Cu, UO₂ and Pb, it is assumed that both the free metal ion (M²⁺) and the cationic hydrolysed species, MOH⁺, induces a toxic response. The Supplementary Materials include a summary of each study used to derive the log K_MBL values for the seven divalent metals (Table S1) and four ameliorative cations (Table S2). A summary of the relative binding affinities of these metals/cations to biotic ligands, along with comparisons between different freshwater taxa and key organisms, is provided in Section 3.12.

3.1. Methodology

A comprehensive literature review on the toxicity and uptake of Cd²⁺, Co²⁺, Cu²⁺, Ni²⁺, Pb²⁺, UO₂²⁺ and Zn²⁺ (and Ca²⁺, Mg²⁺, Na⁺ and H⁺) in freshwater organisms was conducted using the Web of Science, Scopus, Google Scholar and ECOTOX databases (up to July 2024). For toxicity studies, the median effect concentrations (TR₅₀) were assessed using ecologically relevant endpoints such as survival (LC₅₀), reproduction and growth (EC₅₀), since TR₅₀ values are necessary for deriving log K_MBL values (see Section 2). Both acute and chronic exposures, as defined by Warne et al. [23], were considered. Only studies reporting the concentrations of (i) key complexing ligands (bicarbonate (alkalinity), sulphate, chloride, phosphate (microalgae/macrophytes) and/or DOC), and (ii) ameliorative cations (protons (pH), Ca²⁺, Mg²⁺ (or hardness) and Na⁺) in test waters (natural or reconstituted) were considered, as these are necessary for determining metal speciation (e.g., free metal ions) and competition with test metals at cell surface biotic ligands, respectively. These studies also needed to demonstrate a robust experimental design (e.g., sufficient controls, test concentrations, replicates and control acceptability criteria) and data analysis (established statistical tests to derive EC/LC₅₀ values), with quality scores ≥ 75% (see Warne et al. [23]). Preference was given to studies that measured test metal concentrations, and data were excluded if the solubility of the test metal was exceeded (and concentrations were not measured).

The speciation, or chemical form, of Cd, Co, Cu, Ni, Pb, UO₂ and Zn (and Na, Ca and Mg) in test waters was predicted using the WHAM (v7.05) chemical speciation code [24]. Inorganic equilibrium constants were taken from Markich and Brown [25] and corrected for ionic strength using the Davies equation. Metal binding to natural DOM was estimated using the Humic Ion Binding Model (HIBM) VII (a component of WHAM), assuming DOM contained 50% carbon with 65% active cation binding sites [26], represented as fulvic acid (FA). For example, a DOC concentration of 1 mg/L was modelled as 1.3 mg/L FA. The model also assumed that iron(III) and aluminium(III) activities were controlled by hydroxide solubility. Adjustments to the default FA binding constants (log K_MA and ∆LK₂) for Cd, Co, Cu, Ni, Pb, UO₂ and Zn were made to improve the accuracy of the free metal ion (M²⁺) activity predictions in natural freshwaters, which HIBM VII tends to underestimate for Cd, Cu, Pb and UO₂, or overestimate for Ni, Co and Zn [27,28,29,30,31,32,33]. These adjustments, based on previous research, aimed to improve the accuracy of metal binding with natural DOM and provide better estimates of M²⁺ and/or MOH⁺ needed to derive log K_MBL values. The modelling incorporated physicochemical parameters from the test waters as input data.

For toxicity experiments, log K_MBL values were derived by adjusting TR₅₀ values according to the percentages of M²⁺ and/or MOH⁺ (from speciation modelling) and accounting for the competitive (or ameliorative) effects of H⁺, Ca²⁺, Mg²⁺ and Na⁺, as outlined in Section 2. For metal uptake experiments, log K_MBL values were derived using the inverse of the Michaelis–Menton constant (1/K_m), as outlined in Section 2). Metal uptake is usually described by Michaelis–Menton kinetics (i.e., fast Langmuirian adsorption of M²⁺ and/or MOH⁺ at cell surface receptor sites), followed by a first-order rate-limiting internalisation step [34]. It is essential to include only intracellular metal (i.e., metal taken up via the cell surface receptor sites/transporters; Figure 1), ensuring that surface-bound (extracellular) metal is excluded (often using EDTA washes; see Hassler et al. [35] for more information on chemical extractions).

When log K_MBL values were derived from both uptake and toxicity experiments under the same test conditions, (f_C)_M^50% values (the fraction of receptor sites occupied at the TR₅₀; Section 2) were directly determined (see Section 6). The (f_C)_M^50% values were also derived using the methodology described by De Schamphalaere and Janssen [9]. Frequently, it was necessary to use a derived (f_C)_M^50% value across multiple studies for the same metal/organism, or for multiple metals with the same organism.

A one-way analysis of variance (ANOVA) was used to determine if average log K_MBL values differed significantly (p ≤ 0.05) among (i) taxa (e.g., fish vs. crustaceans vs. molluscs), (ii) key individual species (e.g., C. dubia vs. D. magna vs. O. mykiss vs. P. promelas vs. R. subcapitata vs. Chlorella sp.) and (iii) metals (e.g., Cd²⁺ vs. Co²⁺ vs. Cu²⁺ vs. Ni²⁺ vs. Pb²⁺ vs. UO₂²⁺ vs. Zn²⁺). The Tukey Honest Significant Difference test was used to compare average log K_MBL values where ANOVA indicated significant (p ≤ 0.05) differences. ANOVA assumptions [36] were tested and model adequacy was confirmed using either raw or transformed (log₁₀) data. The overall consistency of log K_MBL values across uptake and toxicity studies allowed for the combination of values for each metal (Table S3). Both acute and chronic toxicity data (as defined by Warne et al. [23]) were employed to derive metal binding constants (log K_MBL values)—see Section 5 for further discussion.

To simplify terminology, the unified conceptual model of metal–organism interaction (Section 2) will hereafter be referred to as the BLM. The capacity of the BLM to predict metal toxicity (EC/LC₅₀) was assessed using the factor of two rule, which allows for a range of four around the ideal 1:1 agreement line in comparisons between measured and predicted toxicity. Additionally, a factor of three assessment was considered, in line with analyses by Peters et al. [37] and Price et al. [38]. This assessment method has shown broad applicability to organisms across different freshwater taxa, including fish, crustaceans and microalgae [38,39].

For trace metals, binding constants (log K_MBL) can be determined directly, but for ameliorative cations, these constants are generally derived through competition experiments. In these experiments, the metal binding to cell surface receptors varies as a function of the ameliorative cation concentration. As the concentration of an ameliorative cation increases (or pH decreases), the metal concentration required to reach the TR₅₀ rises. Binding constants for ameliorative cations are derived from the change in TR₅₀ with respect to ameliorative cation concentrations. For Mg, binding constants were also derived directly from toxicity tests, corroborating the findings from competition experiments.

It might be expected that the binding constants for ameliorative cations would differ depending on the metal being examined (e.g., the binding constant for Ca²⁺ may differ between experiments with Cd²⁺ and Pb²⁺). However, the binding constants for each of the four ameliorative cations (Ca²⁺, Mg²⁺, H⁺ and Na⁺) are consistent across all metals (see Section 3.9, Section 3.10, Section 3.11 and Section 3.12), indicating that the biotic ligand binding these metals is either the same or very similar for all seven metals examined.

3.2. Zinc

Table 1 provides the Zn²⁺ binding constants for 42 freshwater organisms from eight taxa, with an average log K_ZnBL value of 6.0 ± 0.1 (95% confidence limit). Additional information is provided in Table S1 and the Supplementary Materials. The log K_ZnBL values were uniformly distributed across molluscs (12 species), fish (10 species) and crustaceans (10 species), followed by the rotifers (five species) and microalgae (two species). The average log K_ZnBL values were not significantly (p > 0.05) different across molluscs (6.0 ± 0.2), fish (5.9 ± 0.2), crustaceans (6.0 ± 0.2), rotifers (6.0 ± 0.4) and microalgae (6.0 ± 0.1) (Table 1). The average log K_ZnBL values for the cladocerans C. dubia (5.9 ± 0.2) and D. magna (5.8 ± 0.3), the two most studied crustaceans, were comparable. For the two most studied fish species, the average log K_ZnBL value for rainbow trout O. mykiss (5.9 ± 0.1) was consistent with that of the fathead minnow P. promelas (5.7 ± 0.4). Likewise, the average log K_ZnBL values were similar for the two most-studied microalgae, R. subcapitata (6.1 ± 0.1) and Chlorella sp. (5.8 ± 0.1) (Table 1). The average log K_ZnBL value of 6.0 ± 0.1 (all organisms) is higher than the reported range of 5.3–5.6 used for fish and crustaceans in Zn BLMs [10], but consistent with the average log K_ZnBL value of 5.8 derived directly from uptake experiments (Table S3).

3.3. Nickel

Table 1 provides the Ni²⁺ binding constants for 31 freshwater organisms from seven taxa, with an average log K_NiBL value of 4.8 ± 0.1 (95% confidence limit). Additional information is provided in Table S1 and the Supplementary Materials. Most log K_NiBL values were determined for crustaceans (16 species), followed by molluscs (seven species), fish (three species) and microalgae (three species). The average log K_NiBL values were not significantly (p > 0.05) different across crustaceans (4.9 ± 0.1), molluscs (4.9 ± 0.1), microalgae (4.8 ± 0.2) and fish (4.7 ± 0.2) (Table 1). Among molluscs, the average log K_NiBL values for bivalves (4.9 ± 0.1) and gastropods (4.9 ± 0.5) were identical. Similarly, among fish, the average log K_NiBL value for O. mykiss (4.7 ± 0.5) was identical to P. promelas (4.7 ± 0.7) and Neogobius melanostomus (4.7). Although the average log K_NiBL value for C. dubia (5.2 ± 0.5) was not significantly (p > 0.05) different to D. magna (4.9 ± 0.3) (Table 1), the 0.3 log unit difference between the two cladoceran species may stem from an overestimation in two of the four derived log K_NiBL values for C. dubia, with values of 5.4 [40] and 5.5 [37] being higher than 5.0 [41] and 4.9 [42] (Table S1). This is likely due to the use of (f_C)_Ni^50% values that were too high (see Supplementary Materials for further details).

The average log K_NiBL value of 4.8 (all organisms) exceeds the value of 4.0 used by Santore et al. [43] in a recent analysis of the Ni BLM for a range of freshwater taxa. The authors also report log K_MBL values for Ca (4.3), Mg (3.6), Na (1.0) and H (4.7), which are inconsistent with those provided in the present study. They also report a log K_NiOHBL value of −5.5, which is irrelevant for circumneutral freshwaters (pH 5.5–8.5), as Ni does not hydrolyse until pH 9.5 (~10%). It seems that the toxicity data were used to “re-calibrate” the log K_MBL values. However, the average log K_NiBL value of 4.8 from the present study is comparable to the value of 4.9 used for crustaceans in the Ni BLM of Kozlova et al. [44], and in close agreement with the average log K_NiBL value of 4.7 derived directly from uptake experiments (Table S3).

3.4. Cadmium

Table 1 provides the Cd²⁺ binding constants for 37 freshwater organisms from seven taxa, with an average log K_CdBL value of 7.0 ± 0.1 (95% confidence limit). Additional information is provided in Table S1 and the Supplementary Materials. The majority of log K_CdBL values were determined for crustaceans (13 species), followed by molluscs (11 species) and fish (9 species). The average log K_CdBL value for fish (7.3 ± 0.1) was significantly (p ≤ 0.05) higher than that of crustaceans (6.9 ± 0.2), molluscs (6.8 ± 0.2) and microalgae (7.0 ± 0.4) (Table 1). Among fish, the average log K_CdBL value for O. mykiss (7.5 ± 0.1) was higher than that of P. promelas (7.1 ± 0.2). In contrast, the average log K_CdBL values for the cladocerans C. dubia (7.0 ± 0.9) and D. magna (6.9 ± 0.3) were comparable (Table 1). Likewise, the average log K_CdBL values for bivalves (6.9 ± 0.3) and gastropods (6.8 ± 0.6) were similar. Although fish had a higher average log K_CdBL value compared to other taxa, their ranges still overlapped (fish: 7.0–7.6, crustaceans: 6.5–7.4, molluscs: 6.5–7.5). The average log K_CdBL value of 7.0 is lower than the range of 7.3–7.6 used for fish in Cd BLMs [10], but comparable to the value of 7.0 used for crustaceans in the Cd BLM of Clifford and McGeer [45], and consistent with the average log K_CdBL value of 7.2 derived directly from uptake studies (Table S3).

3.5. Cobalt

Table 1 provides the Co²⁺ binding constants for 15 freshwater organisms from six taxa, with an average log K_CoBL value of 5.8 ± 0.2 (95% confidence limit). Additional information is provided in Table S1 and the Supplementary Materials. Most log K_CoBL values were determined for molluscs (seven species), followed by crustaceans (three species) and fish (two species). The average log K_CoBL values for crustaceans (5.6 ± 0.5), fish (5.5 ± 0.4) and microalgae (5.7 ± 0.1) were similar, but all were significantly (p ≤ 0.05) lower than the average log K_CoBL value for molluscs (6.0 ± 0.1) (Table 1). Among molluscs, the average log K_CoBL values for bivalves (6.0 ± 0.1) and gastropods (5.9) were comparable. Cobalt has the least amount of data among the seven metals, with most of it derived from only two studies [46,47] with single values per organism, making taxa comparisons less reliable. At present, no Co BLM exists for aquatic organisms.

3.6. Copper

Table 1 provides the Cu²⁺ binding constants for 87 freshwater organisms from nine taxa, with an average log K_CuBL value of 7.9 ± 0.1 (95% confidence limit). Additional information is provided in Table S1 and the Supplementary Materials. Most log K_CuBL values were determined for crustaceans (32 species) and molluscs (32 species), followed by fish (ten species), microalgae (three species) and rotifers (two species). The average log K_CuBL values were not significantly (p > 0.05) different across crustaceans (7.9 ± 0.1), molluscs (7.9 ± 0.1), fish (7.8 ± 0.2), microalgae (7.9 ± 0.1) and rotifers (8.0 ± 0.1) (Table 1). The average log K_CuBL value for C. dubia (8.0 ± 0.2) was similar to that of D. magna (7.8 ± 0.1), and the cladoceran group (7.9 ± 0.1) (Table 1). Among molluscs, the average log K_CuBL values for bivalves (7.8 ± 0.1) and gastropods (8.0 ± 0.1) were comparable. The average log K_CuBL values were identical for the two microalgae, Chlorella sp. (7.8 ± 0.1) and R. subcapitata (7.8 ± 0.2). The average log K_CuBL value for fish (7.8 ± 0.2) largely reflects the difference between O. mykiss (7.9 ± 0.1) and P. promelas (7.6 ± 0.1). The average log K_CuBL value of 7.9 is at the upper end of the reported range of 7.4–8.0 used for fish and crustaceans in Cu BLMs [10], but is in excellent agreement with the average log K_CuBL value of 7.9 derived directly from uptake studies (Table S3).

3.7. Uranium

Table 1 provides the UO₂²⁺ (uranyl) binding constants for 20 freshwater organisms from eight taxa, with an average log K_UO2BL value of 7.7 ± 0.1 (95% confidence limit). Additional information is provided in Table S1 and the Supplementary Materials. Most log K_UO2BL values were determined for crustaceans (six species), followed by fish, microalgae and macrophytes (three species) and molluscs (two species). The average log K_UO2BL values were not significantly (p > 0.05) different across crustaceans (7.7 ± 0.4), fish (7.4 ± 0.1), microalgae (7.9 ± 0.1), macrophytes (7.6 ± 0.2) and molluscs (7.9 ± 0.9) (Table 1). Most organisms are represented by a single log K_UO2BL value, hindering sensible comparisons. The average log K_UO2BL value of 7.7 is in excellent agreement with the average log K_UO2BL value of 7.7 derived directly from uptake studies (Table S3). At present, no UO₂ BLM exists for aquatic organisms.

3.8. Lead

Table 1 provides the Pb²⁺ binding constants for 21 freshwater organisms from seven taxa, with an average log K_PbBL value of 6.8 ± 0.1 (95% confidence limit). Additional information is provided in Table S1 and the Supplementary Materials. Most log K_PbBL values were determined for molluscs (eight species), followed by crustaceans (five species), fish (three species), rotifers (two species) and microalgae (one species). The average log K_PbBL value for molluscs (6.6 ± 0.1) was significantly (p ≤ 0.05) lower than that of crustaceans (6.9 ± 0.2), fish (7.1 ± 0.2) and microalgae (7.0 ± 0.2) (Table 1).

It should be noted that six of the eight data points for mollucs were from one study (average log K_PbBL of 6.5) with unionid bivalves [46], which skewed the overall average downward, particularly when compared to the average (6.8) of the other two other unionid species. The average log K_PbBL value for O. mykiss (7.1 ± 0.6) was similar than that of P. promelas (6.8 ± 0.2) (Table 1). The average log K_PbBL value for C. dubia (7.0 ± 0.4) was comparable with that of D. magna (6.7 ± 0.3). More toxicity data/log K_PbBL values are required for molluscs to re-assess comparisons with other taxa. The average log K_PbBL value of 6.8 is generally consistent with the value of 6.7 used for a range of freshwater taxa in the Pb BLM of DeForest et al. [48], and the average log K_PbBL value of 7.0 derived directly from uptake studies (Table S3).

3.9. Calcium

Calcium binding constants (log K_CaBL) can be derived from experimental studies where freshwater organisms exposed to metals at varying Ca²⁺ concentrations show reduced metal toxicity as the Ca²⁺ concentration increases. Table 2 provides the Ca²⁺ binding constants for 14 freshwater organisms from six taxa, with an average log K_CaBL value of 3.4 ± 0.1 (95% confidence limit). Additional information is provided in Table S2 and the Supplementary Materials. Most log K_CaBL values were determined for crustaceans (five species), followed by fish (four species) and microalgae (two species). The average log K_CaBL values were not significantly (p > 0.05) different among crustaceans (3.3 ± 0.1), fish (3.5 ± 0.1) and microalgae (3.4 ± 1.4) (Table 2). These values align with those currently used in BLMs for invertebrates (3.5) and fish (3.4) [49].

The average log K_CaBL values from metal-specific studies were found to be 3.3 ± 0.2 for Zn²⁺, 3.3 ± 0.2 for Ni²⁺, 3.5 ± 0.1 for Cd²⁺, 3.3 ± 0.2 for Cu²⁺, 3.2 for UO₂²⁺ and 3.2 for Pb²⁺, with no data available for Co²⁺ (uncertainties apply where studies reported five or more values). These averages align with the overall value of 3.4 ± 0.1 (Table 2), with no significant differences observed (p > 0.05) across metals, indicating metal binding occurs at the same or similar receptor sites on the cell surface.

3.10. Magnesium

Magnesium binding constants (log K_MgBL) can be derived from experimental studies where freshwater organisms exposed to metals at varying Mg²⁺ concentrations show reduced metal toxicity as the Mg²⁺ concentration increases. Table 2 provides the Mg²⁺ binding constants for 12 freshwater organisms from six taxa, with an average log K_MgBL value of 2.8 ± 0.1 (95% confidence limit). Additional information is provided in Table S2 and the Supplementary Materials. Most log K_MgBL values were determined for crustaceans (five species), followed by fish and microalgae (two species). Two of the Mg²⁺ binding constants were determined directly from toxicity studies [50,51] rather than from reduced metal toxicity with increasing Mg²⁺ concentration. The EC/LC₅₀ values from the two studies were corrected for Mg speciation (e.g., fraction of Mg occurring as Mg²⁺) and further adjusted for the concentrations of the other ameliorative cations (Ca²⁺, Na⁺ and H⁺). The log K_MgBL values obtained were consistent with those derived from the ameliorative effect of Mg (see Table S2). The average log K_MgBL values were not significantly (p > 0.05) different among crustaceans (2.8 ± 0.1), fish (2.9 ± 0.3) and microalgae (2.8 ± 0.3) (Table 2). These values are lower than those currently used in BLMs for invertebrates (3.5) and fish (4.0) [49].

The average log K_MgBL values from metal-specific studies were found to be 2.9 ± 0.2 (Zn²⁺), 2.8 ± 0.2 (Ni²⁺), 2.8 ± 0.2 (Cd²⁺), 2.8 (Cu²⁺) and 2.7 (UO₂²⁺), with no data available for Co²⁺ or Pb²⁺ (uncertainties apply where studies reported five or more values). These averages align with the overall value of 2.8 ± 0.1 (Table 2), with no significant differences observed (p > 0.05) across metals, indicating metal binding occurs at the same or similar receptor sites on the cell surface. The two log K_MgBL values obtained from toxicity studies averaged 2.7, which matches the group average.

3.11. Sodium

Sodium binding constants (log K_NaBL) can be derived from experimental studies where freshwater organisms exposed to metals at varying Na⁺ concentrations show reduced metal toxicity as the Na⁺ concentration increases. Table 2 provides the Na⁺ binding constants for 11 freshwater organisms from three taxa, with an average log K_NaBL value of 2.2 ± 0.1 (95% confidence limit). Additional information is provided in Table S2 and the Supplementary Materials. Most log K_NaBL values were determined for crustaceans (nine species), followed by fish and microlagae (one species). The average log K_NaBL values were not significantly (p > 0.05) different among crustaceans (2.2 ± 0.1), fish (2.4) and microalgae (2.2) (Table 2). These values are lower than those currently used in BLMs for invertebrates (2.7) and fish (3.0) [49]. The binding capacities of Ca²⁺, Mg²⁺ and Na⁺ to organic carboxylate ligands [25] suggest that these metals would bind to biotic ligands in the order Ca²⁺ > Mg²⁺ > Na⁺, a sequence that is corroborated by the present study.

The average log K_NaBL values from metal-specific studies were found to be 2.2 ± 0.3 for Zn²⁺, 2.1 for Cd²⁺ and 2.3 ± 0.1 for Cu²⁺, with no data available for the four other divalent metals (uncertainties apply where studies reported five or more values). These averages align with the overall value of 2.2 ± 0.1 (Table 2), with no significant differences observed (p > 0.05) across metals, indicating metal binding occurs at the same or similar receptor sites on the cell surface.

Sodium transporters on cell surfaces are widely recognised as essential for Na⁺ uptake by freshwater organisms [52], much like Ca and Mg transporters, providing a mechanistic basis for using Na⁺ binding constants. Moreover, Na transporters, including electrogenic Na⁺ channels and Na⁺/H⁺ exchangers found on the apical cell surface, are also capable of transporting non-essential metals of a similar size to Na, such as lithium (Li⁺). Of the four ameliorative cations, Na⁺ has the weakest binding affinity (or lowest average log K_ML value), being 3–4 orders of magnitude lower than H⁺, 16 times lower than Ca, and four times lower than Mg²⁺, at cell surface receptors. Some researchers have suggested that the “Na-effect” may be due to changes in activity coefficients and/or a charge screening effect on cell surface receptors, rather than from Na binding at Na receptors (transporters). This hypothesis is still largely untested, but it could offer a valuable complementary perspective.

3.12. Protons (H⁺)

Proton binding constants (log K_HBL) can be derived from experimental studies where freshwater organisms exposed to metals at varying pH levels show reduced metal toxicity as pH decreases. Table 2 provides the proton binding constants for ten freshwater organisms from three taxa, with an average log K_HBL value of 5.8 ± 0.1 (95% confidence limit). Additional information is provided in Table S2 and the Supplementary Materials. The log K_HBL values were evenly distributed across the three major taxa: four crustacean species, three fish species and three microalgal species. The average log K_HBL values were not significantly (p ≤ 0.05) different among crustaceans (5.7 ± 0.1), fish (5.7 ± 0.2) and microalgae (5.9 ± 0.2) (Table 2). These values are within the range previously reported for invertebrates (5.4–6.1) and fish (5.0–6.7) [10].

The average log K_HBL values from metal-specific studies were found to be 5.9 ± 0.1 for Zn²⁺, 5.7 for Ni²⁺, 5.8 ± 0.1 for Cd²⁺, 5.6 ± 0.2 for Cu²⁺, 5.9 for UO₂²⁺ and 5.8 for Pb²⁺, with no data available for Co²⁺ (uncertainties apply where studies reported five or more values). These averages align with the overall value of 5.8 ± 0.1 (Table 2), with no significant differences observed (p > 0.05) across metals, indicating metal binding occurs at the same or similar receptor sites on the cell surface. The magnitude of the proton (H⁺) binding constant indicates that the cell surface receptor is a carboxylate group [10].

3.13. Overview

The average log K_MBL values for all freshwater taxa indicate the following ranking of metal binding affinity to biotic ligands: Cu²⁺ > UO₂²⁺ > Cd²⁺ ≈ Pb²⁺ > Zn²⁺ ≈ Co²⁺ > Ni²⁺ (see Table 1). Copper had the highest binding affinity (log K_CuBL = 7.9), while Ni had the lowest (log K_NiBL = 4.8), with a ~1000-fold difference. This relative ranking largely reflects the four major taxa, which are highly consistent: fish (Cu²⁺ > UO₂²⁺ ≈ Cd²⁺ ≈ Pb²⁺ > Zn²⁺ ≈ Co²⁺ > Ni²⁺), crustaceans (Cu²⁺ ≈ UO₂²⁺ > Cd²⁺ ≈ Pb²⁺ > Zn²⁺ ≈ Co²⁺ > Ni²⁺), molluscs (Cu²⁺ ≈ UO₂²⁺ > Cd²⁺ ≈ Pb²⁺ > Zn²⁺ ≈ Co²⁺ > Ni²⁺), and microalgae (Cu²⁺ ≈ UO₂²⁺ > Cd²⁺ ≈ Pb²⁺ > Zn²⁺ ≈ Co²⁺ > Ni²⁺). For the ameliorative cations, the ranking of the average log K_MBL values across all freshwater taxa was: H⁺ >> Ca²⁺ > Mg²⁺ > Na⁺. Protons (H⁺) had the highest binding affinity (log K_HBL = 5.8), while Na⁺ had the lowest (log K_NaBL = 2.2), with a ~4000-fold difference.

An average binding constant (log K_ML) for a specific metal can be applied across all freshwater taxa, though taxa- or species-specific log K_ML values may be applied if available. The uncertainty (error), or variability, in the average log K_ML values is relatively small (typically ± 0.1 log units; Table 1 and Table 2) and unlikely to significantly affect the overall accuracy or reliability of the BLM for predicting metal toxicity. For Cu, data from 42 species across nine phyla, resulted in an average log K_ML value with a relatively small uncertainty (8.0 ± 0.1), while for Co, data from only 15 species across six phyla led to a higher uncertainty for the average log K_ML value (5.8 ± 0.2). For new freshwater organisms (not yet part of the database) that are highly sensitive to certain metals, the use of average metal binding constants may be constrained due to unknown (f_C)_M^50% factors. The accuracy or reliability of the BLM is most likely to be influenced by metal speciation (calculated via speciation models), specifically the percentage of free metal ions (M²⁺) for Zn, Ni, Cd and Co, or the percentages of M²⁺ and MOH⁺ for Cu, UO₂ and Pb. Metal speciation is largely governed by key water chemistry parameters such as alkalinity, dissolved organic carbon (DOC) concentration and pH.

A key challenge in applying the BLM to less-studied metals like Co and UO₂ is the limited toxicity and uptake data (compared to the other five metals studied) across freshwater species, which increases uncertainty (or error) in the binding constants (log K_ML values). This can lead to greater variability between measured and predicted toxicity, resulting in fewer data points within a factor of two of the 1:1 agreement line (as shown for Co and UO₂ in Section 4). Both Co and UO₂ tend to interact with the same cell surface receptors or transporters as other divalent metals like Cd, Pb, Ni and Zn, but with different binding affinities, affecting toxicity. Section 4 evaluates the reliability of the log K_MBL values in predicting metal toxicity, and Section 5 explores the link between metal binding constants/affinity and toxicity.

The ameliorative cations (H⁺, Ca²⁺, Mg²⁺ and Na⁺) compete with trace metals (like Zn²⁺, Ni²⁺, Cd²⁺ and Co²⁺) for binding sites on cell surface receptors (biotic ligands) in aquatic organisms. The ability to influence (or modulate) metal binding is determined by their binding affinity at these biotic ligands (i.e., H⁺ >> Ca²⁺ > Mg²⁺ > Na⁺; Table 2). The binding constants (log K_MBL values) for each ameliorative cation were shown to be independent of the trace metal examined. However, a key distinction is that H⁺, Ca²⁺, Mg²⁺ and Na⁺ compete with both M²⁺ and MOH⁺ for Cu²⁺, UO₂²⁺ and Pb²⁺, while they only compete with M²⁺ for Zn²⁺, Ni²⁺, Cd²⁺ and Co²⁺. In practical terms, as water hardness increases (i.e., the concentrations of Ca and/or Mg increase), Ca²⁺, and to a lesser extent Mg²⁺, will more effectively compete with trace metals like Cd²⁺, Zn²⁺ and Pb²⁺ at cell surface receptors. Likewise, as conductivity increases, Na⁺ will compete more effectively with trace metals, including Cu²⁺. When pH decreases, the higher proton (H⁺) concentration (a ten-fold increase for every unit drop in pH) will increasingly compete with trace metals at cell surface receptors.

The seven divalent metals investigated bind to an oxygen-containing donor ligand, such as carboxylate (-COOH). However, their binding affinities vary considerably, spanning three orders of magnitude, with Ni exhibiting the lowest affinity and Cu the highest (Table 1). Each metal’s binding affinity for cell surface receptors is influenced by its affinity for carboxylate. This is illustrated in Figure S2, which shows a strong positive linear regression (r² = 0.97; p ≤ 0.001) between the binding affinity of six of the divalent metals (log K_MBL) with cell surface receptors and acetate, a common monocarboxylic acid (carboxylate ligand). Uranium (UO₂²⁺) is excluded from this analysis because its two oxygen atoms cause steric hinderance, which reduces its binding to cell surface receptors and results in a lower log K_ML value than expected based on its affinity for acetate. The linear free energy relationship (LFER) shown in Figure S2 indicates that the binding constants of metals to biotic ligands are proportional to their binding with simple carboxylate ligands. Carbonaro and Di Toro [53] further explored LFERs between metal and proton (H⁺) binding constants of carboxylate, phenolic and hydroxo-ligands, deriving Irving-Rossotti slopes, which aligned well with metal binding constants for natural DOM (humic and fulvic acids). Given the similar metal binding behaviour of humic and fulvic acids to that of cell membrane surfaces, LFERs are a useful tool for determining metal binding constants to carboxylate-based receptors on cell surfaces.

To determine if the log K_MBL values derived for freshwater organisms could extend to other organisms, a selection of metal toxicity studies was evaluated for marine and terrestrial organisms (see Supplementary Materials). The log K_MBL values were consistent with those from freshwater organisms, suggesting a wider relevance of the data, although a more detailed comparison is necessary.

4. Comparison of Measured and Predicted Metal Toxicity

Figure 3 illustrates the comparison between the measured and predicted toxicity values (EC/LC₅₀) for Zn²⁺, Ni²⁺, Cd²⁺ and Co²⁺, while Figure 4 shows the comparison for Cu²⁺, UO₂²⁺ and Pb²⁺. Predicted EC/LC₅₀ values were derived using Equation (12), incorporating the average log K_MBL values for Ca²⁺, Mg²⁺, Na⁺ and H⁺ (Table 2) and adjustments for M²⁺ for all seven metals, plus 0.5 × MOH⁺ for Cu²⁺, UO₂²⁺ and Pb²⁺, in each water quality scenario. The comparisons assess the accuracy of the derived log K_MBL values, as well as those for the ameliorative cations (Ca²⁺, Mg²⁺, Na⁺ and H⁺) and the derived (f_C)_M^50% values. Although previous studies have compared Cd²⁺, Cu²⁺ and Zn²⁺, this study uses 2–3 times more toxicity data, whilst maintaining or improving predictive accuracy. The Ni²⁺ and Pb²⁺ datasets are comparable to those from Santore et al. [43] and DeForest et al. [48], respectively. Additionally, this study provides the first comparisons for Co²⁺ and UO₂²⁺. The accuracy of the predictions is reflected by how closely the measured and predicted toxicity values match. This study found that 75 to 88% of toxicity values fell within a factor of two of the ideal 1:1 agreement line (

Table 3. A comparison of measured versus predicted metal toxicity using the conceptual model.

Metal	% of Data within a Factor of Two of the 1:1 Agreement Line	% of Data within a Factor of Three of the 1:1 Agreement Line	Number of Water Quality Scenarios	Number of Organisms (Species)	Number of Studies
Zinc	81	94	142	7	13
Nickel	83	97	256	10	14
Cadmium	88	98	83	6	7
Cobalt	75	92	12	9	4
Copper	79	91	383	12	15
Uranium	75	88	52	10	6
Lead	80	95	110	5	8

and Figure 3 and Figure 4). The best agreement was observed for Cd²⁺ (88%), while the worst was for Co²⁺ and UO₂²⁺ (75%), which had the smallest datasets and the largest uncertainties in their log K_MBL values (Table 1, Table 2 and Table 3). Furthermore, 89 to 98% of toxicity values were within a factor of three of the ideal 1:1 agreement line (Table 3 and Figure 3 and Figure 4). Overall, the strong alignment between measured and predicted toxicity for all seven metals supports the reliability of the derived log K_MBL and (f_C)_M^50% values. An overview for each metal is provided in Section 4.1, Section 4.2, Section 4.3, Section 4.4, Section 4.5, Section 4.6 and Section 4.7.

The comparisons presented in Figure 4 for Cu, UO₂, and Pb are based on predicted toxicity that considers both M²⁺ and (0.5×) MOH⁺. Among the seven metals, MOH⁺ occurs in test solutions only for these three metals. The significance of including MOH⁺ in toxicity assessments is most evident with uranium (UO₂), as UO₂OH⁺ has a higher concentration than UO₂²⁺ in nearly all studies (since it hydrolyses at about pH 5). A reanalysis of the predicted toxicity of uranium using only UO₂²⁺ (rather than UO₂²⁺ plus 0.5 × UO₂OH⁺) in Figure 5 shows that just one out of the 52 data points (2% of data) falls within a factor of two of the ideal 1:1 line, with eight data points within a factor of three (15%), but the majority (85%) fall well outside the factor of three line. This suggests that uranium would be much more toxic than observed.

The differences for Cu and Pb are less pronounced because they hydrolyse around pH 7, resulting in substantial pH regions (pH 5.5–7.5) where the M²⁺ ion dominates. However, toxicity is still predicted to increase significantly for both metals, leading to notable discrepancies between measured and predicted toxicity. For Pb, the average log K_PbBL value increased significantly (p ≤ 0.05) from 6.8 ± 0.1, when both Pb²⁺ and PbOH⁺ are considered, to 7.2 ± 0.2, when only Pb²⁺ is considered. Consequently, the average predicted Pb toxicity would increase (EC/LC₅₀ values would decrease), by a factor of 2.5, indicating that fewer data points would lie above the 1:1 line, with many falling below the lower factor of three line. Similarly for Cu, the average log K_CuBL value increased significantly (p ≤ 0.05) from 7.9 ± 0.1, when both Cu²⁺ and CuOH⁺ are considered, to 8.2 ± 0.1, when only Cu²⁺ is considered. Consequently, the average predicted Cu toxicity would increase (EC/LC₅₀ values would decrease), by a factor of two, again indicating that a significant portion of the data would fall below the lower factor of three line when comparing measured and predicted data. Therefore, it is evident that in environmental pH ranges where MOH⁺ forms, both M²⁺ and MOH⁺ need to be accounted for as contributors to toxicity. Consulting with BLM practitioners is necessary to identify the best approach for integrating this into current software. The simplest solution would be to use the sum of the concentrations of M²⁺ and 0.5 × MOH⁺ from speciation modelling calculations for Cu and Pb (at pH ≥ 7.0) or UO₂ (at pH ≥ 5.0) to improve, or optimise, the BLM.

The conceptual model demonstrates how a cascade of effects result in the concentration at which metals become toxic. Understanding these effects is vital for quantifying the varying toxicity metals impose on aquatic organisms. In many aquatic organisms, toxicity occurs when 50% of biotic ligands are occupied ((f_C)_M^50%). However, in some cases, toxicity can be higher (i.e., lower TR₅₀) because of lower ligand occupancy at the TR₅₀, while other organisms experience reduced toxicity (due to protective mechanisms), despite a constant metal binding constant. These organisms might have additional low-affinity, high-capacity receptors that effectively reduce the effect of the metal. Further research is needed on the underlying physiological mechanisms governing (f_C)_M^50% (i.e., why is organism sensitivity enhanced?), as well as the relationship between toxicity and (f_C)_M^50%.

The (f_C)_M^50% factor may be applied to multiple metals for a single species or to the same metal across related species. Further research is needed to quantify (f_C)_M^50% for a wider range of freshwater species. Collaboration between BLM practitioners is required to determine the most effective way to integrate an adjustable (f_C)_M^50% factor into existing software.

4.1. Zinc

Figure 3a compares the measured and predicted EC/LC₅₀ values for 142 water quality scenarios across seven organisms from 13 studies. The predicted EC/LC₅₀ values incorporate the average log K_MBL values for Zn²⁺ (Table 1), Ca²⁺, Mg²⁺, Na⁺ and H⁺ (Table 2), and adjustments for Zn²⁺ activity in each scenario. Figure 3a shows that the predicted EC/LC₅₀ values align closely with the measured values over nearly three orders of magnitude, with 81% of data points within a factor of two, and 94% within a factor of three, of the ideal 1:1 line. The data points appear to be uniformly distributed around the 1:1 line.

The sensitivity factor ((f_C)_Zn^50%) was applied to eight organisms (two fish species, four crustacean species and a microalgae and insect), ranging from 0.0521 to 0.45 (Table S4)—with the default maximum of 0.5 being applied to all other species. According to Equation (12), as (f_C)_Zn^50% decreases, the Zn EC/LC₅₀ should also decrease. Figure 6 illustrates the relationship between (f_C)_Zn^50% and the corresponding EC/LC₅₀ values. Despite the small dataset (n = 8) leading to an insignificant (p > 0.05) linear relationship, the data still suggest that a decrease in (f_C)_Zn^50% is associated with a decrease in EC/LC₅₀.

4.2. Nickel

Figure 3b compares the measured and predicted EC/LC₅₀ values for 256 water quality scenarios across ten organisms from 14 studies. The predicted EC/LC₅₀ values incorporate the average log K_MBL values for Ni²⁺ (Table 1), Ca²⁺, Mg²⁺, Na⁺ and H⁺ (Table 2), and adjustments for Ni²⁺ activity in each scenario. Figure 3b shows that the predicted EC/LC₅₀ values align closely with the measured values over nearly five orders of magnitude, with 83% of data points within a factor of two, and 97% within a factor of three, of the ideal 1:1 line. The data points appear to be uniformly distributed around the 1:1 line.

The sensitivity factor ((f_C)_Ni^50%) was applied to 17 organisms (two fish species, eight crustacean species, two mollusc species, two microalgal species, two macrophyte species and a rotifer), ranging from 0.0033 to 0.499 (Table S4)—with the default maximum of 0.5 being applied to all other species. According to Equation (12), as (f_C)_Ni^50% decreases, the Ni EC/LC₅₀ should also decrease. Figure 6 illustrates the positive linear relationship (r² = 0.76; p < 0.001) between (f_C)_Ni^50% and the corresponding EC/LC₅₀ values. Therefore, as (f_C)_Ni^50% decreases, freshwater organisms become more sensitive to Ni.

4.3. Cadmium

Figure 3c compares the measured and predicted EC/LC₅₀ values for 83 water quality scenarios across six organisms from seven studies. The predicted EC/LC₅₀ values incorporate the average log K_MBL values for Cd²⁺ (Table 1), Ca²⁺, Mg²⁺, Na⁺ and H⁺ (Table 2), and adjustments for Cd²⁺ activity in each scenario. Figure 3c shows that the predicted EC/LC₅₀ values align closely with the measured values over two orders of magnitude, with 88% of data points within a factor of two, and 98% within a factor of three, of the ideal 1:1 line. The data points appear to be uniformly distributed around the 1:1 line.

The sensitivity factor ((f_C)_Cd^50%) was applied to two organisms (O. mykiss and Hyalella azteca), ranging from 0.00676 to 0.216 (Table S4)—with the default maximum of 0.5 being applied to all other species. Two of the three (f_C)_Cd^50% values that were less than 0.5 were based on studies investigating the Cd toxicity and/or uptake in O. mykiss [77,109]. Liao et al. [77] reported a (f_C)_Cd^50% value of 0.0128, with a range of 0 to 0.0634. A re-analysis of their data produced a (f_C)_Cd^50% of 0.00676. Niyogi et al. [77] determined a log K_CdBL of 7.5 from uptake measurements, but a log K_CdBL of 8.0 from toxicity measurements (see Section 6). To harmonise the binding constant between these measurements, a (f_C)_Cd^50% value of 0.216 was attributed to the toxicity data. Additionally, a (f_C)_Cd^50% value of 0.184 was derived using data from Schroeder [72] for the toxicity of Cd²⁺ to H. azteca. The (f_C)_Cd^50% value derived from Liao et al. [109] is substantially lower than corresponding values derived from Niyogi et al. [77] or Schroeder [72].

4.4. Cobalt

Figure 3d compares the measured and predicted EC/LC₅₀ values for 12 water quality scenarios across nine organisms from four studies. The predicted EC/LC₅₀ incorporate the average log K_MBL values for Co²⁺ (Table 1), Ca²⁺, Mg²⁺, Na⁺ and H⁺ (Table 2), and adjustments for Co²⁺ activity in each scenario. This calculation accounts for both the competitive/ameliorative effects of Ca²⁺, Mg²⁺, Na⁺ and H⁺ and the effect of speciation (complexation). Figure 3d shows that the predicted EC/LC₅₀ values align closely with the measured values over two orders of magnitude, with 75% of data points within a factor of two, and 92% within a factor of three, of the ideal 1:1 line. There appears to be a slight bias of data points below the 1:1 line, but the dataset is limited.

The sensitivity factor ((f_C)_Co^50%) was applied to only one organism (the crustacean, C. dubia), with a value of 0.0521 (Table S4)—with the default maximum of 0.5 being applied to all other species.

4.5. Copper

Figure 4a compares the measured and predicted EC/LC₅₀ values for 383 water quality scenarios across 12 organisms from 15 studies. The predicted EC/LC₅₀ values incorporated the average log K_MBL values for Cu²⁺ (Table 1), Ca²⁺, Mg²⁺, Na⁺ and H⁺ (Table 2), and adjustments for Cu²⁺ and (0.5×) CuOH⁺ activities in each scenario. Figure 4a shows that the predicted EC/LC₅₀ values align closely with the measured values over three orders of magnitude, with 79% of data points within a factor of two, and 91% within a factor of three, of the ideal 1:1 line. The data points appear to be uniformly distributed around the 1:1 line.

The sensitivity factor ((f_C)_Cu^50%) was applied to 12 organisms (nine crustacean species, two microalgal species and an insect), ranging from 0.002 to 0.499 (Table S4)—with the default maximum of 0.5 being applied to all other species. According to Equation (12), as (f_C)_Cu^50% decreases, the Cu EC/LC₅₀ should also decrease. Figure 6 illustrates the positive linear relationship (r² = 0.73; p ≤ 0.01) between (f_C)_Cu^50% and the corresponding EC/LC₅₀ values. Therefore, as (f_C)_Cu^50% decreases, freshwater organisms become more sensitive to Cu. Interestingly, the slope obtained for the linear regression for Cu (4.2 ± 0.8) is similar to that found for nickel (3.0 ± 0.4), within uncertainty. Both metals also have an extremely low (f_C)_M^50% value in their dataset, which seems to depart from the rest of the linear relationship obtained for each metal (see Figure 6).

4.6. Uranium

Figure 4b compares the measured and predicted EC/LC₅₀ values for 52 water quality scenarios across ten organisms from six studies. The predicted EC/LC₅₀ values incorporate the average log K_MBL values for UO₂²⁺ (Table 1), Ca²⁺, Mg²⁺, Na⁺ and H⁺ (Table 2), and adjustments for UO₂²⁺ and (0.5×) UO₂OH⁺ activities in each scenario. Figure 4b shows that the predicted EC/LC₅₀ values align closely with the measured values over two orders of magnitude, with 75% of data points within a factor of two, and 88% within a factor of three, of the ideal 1:1 line. The data points appear to be uniformly distributed around the 1:1 line.

The sensitivity factor ((f_C)_UO2^50%) was applied to only two organisms (the crustacean, C. dubia, and the macrophyte, Ceratophyllum demersum), with values of 0.0521 and 0.47 (Table S4), respectively—with the default maximum of 0.5 being applied to all other species. The (f_C)_UO2^50% value of 0.052 was used for the toxicity data of Goulet et al. [95] where C. dubia was studied (the same value as used for other metals, except Cd).

4.7. Lead

Figure 4c compares the measured and predicted EC/LC₅₀ values for 110 water quality scenarios across five organisms from eight studies. The predicted EC/LC₅₀ values incorporate the average log K_MBL values for Pb²⁺ (Table 1), Ca²⁺, Mg²⁺, Na⁺ and H⁺ (Table 2), and adjustments for the Pb²⁺ and (0.5×) PbOH⁺ activities in each scenario. Figure 4c shows that the predicted EC/LC₅₀ values align closely with the measured values over three orders of magnitude, with 80% of data points within a factor of two, and 95% within a factor of three, of the ideal 1:1 line. The data points are evenly distributed around the 1: 1 line.

The sensitivity factor ((f_C)_Pb^50%) was applied to only three organisms (the crustaceans, C. dubia, D. magna and Daphnia similis), with values between 0.0521 and 0.24 (Table S4)—with the default maximum of 0.5 being applied to all other species.

5. Relationships between Metal Binding Constants and Toxicity

Since both acute and chronic toxicity endpoints are commonly used in aquatic ecotoxicology, it was important to incorporate all available metal toxicity data to derive metal binding constants (log K_ML values) for the BLM. The toxicity endpoints, which ranged from acute lethal effects (e.g., 2-day survival for crustaceans) to chronic sublethal effects (e.g., 28-day growth for gastropod molluscs), exhibited a bimodal distribution across taxa. Metal binding constants were largely derived from acute toxicity data for fish (84%), crustaceans (85%) and rotifers (75%), while chronic toxicity data dominated for molluscs (90%), microalgae (100%) and macrophytes (100%). No significant (p > 0.05) differences in Zn, Cu or Pb binding constants were observed between acute and chronic exposures in the cladoceran C. dubia (the only species where sufficient data were available for a direct comparison), with similar results for Zn across eight cladoceran species and for Cu in gastropods. Although more data are needed for other species/taxa comparisons, the current findings support combining acute and chronic toxicity (LC/EC₅₀) data to derive metal binding constants. Moreover, metal binding to cell surface receptors should be consistent irrespective of the exposure duration or type (lethal or sublethal effects).

The log K_MBL values for seven freshwater organisms (O. mykiss, P. promelas, C. dubia, D. magna, H. azteca, R. subcapitata and Lemna minor) were derived for all seven metals (Cd²⁺, Co²⁺, Cu²⁺, Ni²⁺, Pb²⁺, UO₂²⁺ and Zn²⁺). For these organisms, the measured toxicity of each metal is a function of the derived log K_MBL value, the (f_C)_M^50% value, and the concentrations of ameliorative cations. An assessment of metal toxicity can be made through the linear regression of the log K_MBL values among the organisms. Table S5 presents the coefficients of determination (r² values) and slopes of the linear regressions fitted to the log K_MBL values across the seven organisms. All regressions showed strong positive linear relationships (p < 0.01), with r² values between 0.82 and 0.99 (average of 0.93), and slopes ranging from 0.79 to 1.23 (average of 1.00 ± 0.12). The average slope met the expected slope of unity, within uncertainty.

Given that (f_C)_M^50% values and the concentrations of ameliorative cations can strongly affect log K_MBL values, it is important to apply a consistent (f_C)_M^50% value when comparing toxicity across various organisms for all seven metals. Linear regressions of metal toxicity (expressed as 1/[M], where [M] is the toxicity concentration in µmol/L) and metal binding constants (log K_MBL values) were fitted for C. dubia (with a (f_C)_M^50% value of 0.0521), D. magna and O. mykiss (both with a (f_C)_M^50% value of 0.5). Figure 7 shows the positive linear regressions (p ≤ 0.01) for these species, with r² values ranging from 0.91 for C. dubia to 0.97 for O. mykiss, indicating that log K_MBL values explain between 91% and 97% of the variability in metal toxicity. As predicted by Equation (19), the slope of the relationship between log K_MBL and log (1/[M]) should be one. The regression slopes for C. dubia, D. magna and O. mykiss ranged from 0.88 to 1.10, with an average slope of 1.02, which is in close agreement with the expected slope of 1.00. Overall, the results indicate that higher log K_MBL values correspond to increased metal toxicity in these freshwater organisms.

The linear regression for C. dubia (Figure 7a) omits a Cd²⁺ value because its (f_C)_M^50% value was 0.5, while the other six metals had a value of 0.052. Similarly, O. mykiss lacks a Cd²⁺ value in the regression (Figure 7b) due to its (f_C)_M^50% value of 0.216, compared to 0.5 for the other six metals. To illustrate the effect of (f_C)_M^50% on metal toxicity, Cd²⁺ values were added as an overlay on Figure 7b using both the uncorrected (0.216; open red circle) and corrected (i.e., × (1 − 0.216)/0.216); open purple circle) (f_C)_M^50% value. The correction brings Cd²⁺ in line with the other six metals.

6. Organism Sensitivity and Its Relationship to the Fraction of Cells Bound at the TR₅₀ ((f_C)_M^50%)

The toxic response of aquatic organisms to metals is driven by a sequence, or cascade, of effects, as described in Equation (2). This cascade is a key feature of the extended FIAM, but is not explicit in the BLM. The extended FIAM highlights two distinct and sequential processes in the toxic response to metals. Additionally, a third mechanism is revealed in the cascade when the TR₅₀ is reached with less than 50% of cell surface receptor sites occupied (Equation (8)). Figure 2 illustrates this cascade, showing the key terms (or parameters) at each stage.

Altszyler et al. [110] demonstrated that a cascade of interactions can result in an ultrasensitive response. In the context of the metal toxicity in aquatic organisms, the (f_C)_M^50% parameter can serve as an indicator of an organism’s sensitivity to metals. Altszyler et al. [110] showed that a cascade of effects can amplify toxicity, making organisms more sensitive. Changes in the sensitivity could lead to significant variation in an organism’s response to metal toxicants. Sensitive organisms may transport metals into cells more rapidly than less sensitive organisms, even though the metal binding affinity is equivalent. This behaviour suggests that organisms can employ defensive mechanisms, such as mucous coatings to reduce metal binding at cell surface receptors, providing protection from toxicity. Such effects can be further elucidated from studies that have examined both metal uptake by, and toxicity to, freshwater organisms.

Niyogi et al. [77] investigated the uptake and toxicity of Cd in rainbow trout (O. mykiss). From their uptake data, they calculated a log K_CdBL value of 7.5 (Table S1), and also determined a 96 h LC₅₀ value of 10.3 nmol/L (corrected for the effects of Ca and DOC) from toxicity tests. Using Equation (9), this LC₅₀ value results in a log K_Cd-tox of 8.0, which the authors referred to as the “true estimate” of Cd binding affinity at the biotic ligand. However, metal uptake measurements reflect the true binding affinity of metals for biotic ligands. The concentration at which LC₅₀ or EC₅₀ values are observed is related to the binding constant through the sensitivity factor, (f_C)_M^50%, as defined in Equation (8), and re-expressed below in terms of K_MBL and K_M-tox:

$$\left[\mathrm{M}\right]={\displaystyle \frac{{\left(f_C\right)}_{\mathrm{M}}^{50\%}}{1-{\left(f_C\right)}_{\mathrm{M}}^{50\%}}}{\displaystyle \frac{1}{K_{\mathrm{MBL}}}}={\displaystyle \frac{1}{K_{\mathrm{M}-\mathrm{tox}}}}$$

(19)

The log K_CdML (termed log K_Cd-gill by the authors]) and log K_Cd-tox values from Niyogi et al. [52] can be equated using Equation (19) and a (f_C)_M^50% of 0.249 was calculated (i.e., almost a quarter of the cell surface binding sites are occupied at the LC₅₀).

Niyogi et al. [111] previously investigated Cd uptake and toxicity in O. mykiss, deriving a log K_CdML value of 7.3 from uptake data (listed in Table S1), which aligned with their later findings. The toxicity tests produced an LC₅₀ of 169 nmol/L for total Cd, which when corrected for Cd speciation and the concentrations of Ca and DOM resulted in an adjusted value of 27.1 nmol/L. This led to a log K_Cd-tox of 7.6, larger than the log K_CdML value. From these results, a (f_C)_M^50% of 0.372 was calculated. The log K_CdML, log K_Cd-tox and (f_C)_Cd^50% values are in good agreement across both studies. The study also investigated Cd uptake and toxicity in yellow perch (Perca flavescens), obtaining a log K_CdML value of 7.2 from the uptake data (listed in Table S1), which is similar to the value for O. mykiss (7.5). Based on Cd toxicity data, P. flavescens had an LC₅₀ of 72,420 nmol/L, more than 400 times higher than for O. mykiss. After accounting for Cd speciation and concentrations of Ca and DOM, the corrected LC₅₀ value for P. flavescens was 6140 nmol/L, resulting in a log K_Cd-tox value of 5.2, two orders of magnitude lower than for O. mykiss.

Although both fish species share a similar Cd binding capacity, P. flavescens appears to have developed a defence mechanism that protects against Cd exposure. This is reflected in the substantially higher 3 h and 24 h LA₅₀ values (17.80 and 31.67 nmol per g wet gill tissue, respectively) compared to O. mykiss (0.34 and 0.55 nmol per g wet gill tissue, respectively). For O. mykiss, both LA₅₀ values were well within the concentration of saturable sites at the gill (0.85 nmol per g wet gill tissue) whereas for P. flavescens, both LA₅₀ values were considerably larger than the concentration of saturable sites (0.67 nmol per g gill wet tissue). Consequently, in P. flavescens, in addition to filling up to 50% of the saturable binding sites (at the LA₅₀), a substantial amount of other low-affinity, high-capacity sites were filled [111], which enables the species to protect itself from Cd exposure, even though the binding affinity for the saturable sites is very similar to that of O. mykiss. It appears that P. flavescens has another layer in the cascade of interactions that enables it to reduce the effect of exposure to Cd. Conversely, for O. mykiss, the two LA₅₀ values occur around the concentration at which at least half of the receptor (saturable) sites are occupied, with only a small fraction of other sites also being occupied. Similar behaviour for Cu was previously reported by Taylor et al. [112].

Leonard et al. [113] investigated Ni uptake and toxicity in two species of fish, O. mykiss and the round goby (Neogobius melanostomus). They found that the log K_NiBL values derived from uptake data were up to an order of magnitude (one log unit) higher than those derived from toxicity data for both species. However, these results need to be reassessed. For N. melanostomus, the authors found a K_d value of 17.8 μmol/L for Ni uptake, corresponding to a log K_NiBL value of 4.8, which is in good agreement with the values listed in Table 1. Using toxicity data, the authors measured an LC₅₀ of 104.1 μmol/L, which reduced to 80.2 μmol/L after adjusting for Ni speciation. After further adjustments for pH and the concentrations of Ca²⁺, Mg²⁺ and Na⁺, applying average binding constants from this study, the LC₅₀ reduced to 21.1 μmol/L. This corresponds to a log K_NiBL value of 4.7, which aligns with their uptake data and the results of this study (Table 1).

For O. mykiss, Leonard et al. [113] found a K_d value of 46.5 μmol/L from whole fish uptake data, which was unusual as the value for N. melanostomus was derived only from the gills. The K_d corresponds to a log K_NiBL of 4.3, lower than measurements from other studies on O. mykiss (4.5–4.9; Table S1) and other freshwater taxa (4.6–5.2; Table 1). Based on toxicity data for O. mykiss, the LC₅₀ concentration of 228.1 μmol/L was reduced to 175.6 μmol/L after adjustment for Ni speciation (Ni²⁺), and further to 46.9 μmol/L after accounting for the ameliorative cations. This final concentration corresponds to a log K_NiBL value of 4.3, matching the uptake data. This analysis underscores the importance of accounting for the free metal ion in toxicity tests (but not uptake tests), and the ameliorative effects of cations (Ca²⁺, Mg²⁺, Na⁺, H⁺) when comparing log K_MBL values derived from metal uptake and toxicity data.

7. The Binding Mechanism of MOH⁺

While free metal ions are often considered the best predictors of metal uptake and toxicity in freshwater organisms, several studies have shown that metal hydroxide complexes (e.g., UO₂OH⁺, CuOH⁺ and Sc(OH)₂⁺/Sc(OH)²⁺) improve the prediction of free metal ion behaviour [9,14,15,16]. Hydroxide complexes become important in freshwater systems after metal hydrolysis, typically starting around pH 5.0 for UO₂²⁺ and pH 7.0 for Cu²⁺ and Pb²⁺. Although PbOH⁺ has yet to be empirically confirmed as complementary to Pb²⁺, it is expected to behave similarly to Cu, based on its first hydrolysis constant [25].

Equations (15) and (16) were formulated based on empirical evidence that K_LMBL/K_MBL = 0.5 [9,14,15], indicating that the relative effects of M and ML at cell surface receptors correlate to their charges. The binding of M and ML at cell surface receptors (biotic ligands) can be described by the following equations:

$$\mathrm{M}+\mathrm{BL} \leftrightharpoons \mathrm{MBL}$$

(20)

$$\mathrm{ML}+\mathrm{BL} \leftrightharpoons \mathrm{LMBL}$$

(21)

where BL (biotic ligand) is the binding site, M is the free metal ion and ML is the complexed metal ion with ligand L (with OH as L in this study). Chemical binding reactions are often divided into intrinsic (chemical affinity) and coulombic (electrostatic interactions) components [19]. For reactions (20) and (21), the intrinsic binding constants (K_int) are likely similar, given that both reactions involve the same ligand (cell surface receptor) and metal. However, the coulombic binding constants (K_coul), or electrostatic interactions, will vary due to charge differences between M and ML.

Brown and Sylva [114] developed a theoretical model to describe metal–ligand interactions, including those at cell surface receptors. Their model predicts that when ML binds to a cell surface receptor (biotic ligand), it will have a similar intrinsic binding constant to that of M binding to the same receptor, but with different electrostatic interactions. This difference is determined by the ratio of two factors: (i) the number of binding groups to the central metal ion (M interacts solely with the receptor (one group), while the metal ion in ML interacts with both L (such as OH) and the receptor (two groups), creating a 2:1 ratio), and (ii) a proportionality constant (k), which applies specifically to ML binding. Thus, the ratio between these two factors is 2/k, and for this ratio to reflect the observed two-fold binding difference between ML and M at cell surface receptors, the value of k must be one.

8. A Second Cell Surface Binding Site at a Moderately Alkaline pH?

According to ETMs, a second neutral site on the cell surface could bind metals in moderately alkaline (pH 7.0 to 8.5) environments [7,8]. This interaction is described by Equation (18). At these pH values, metals are more likely to bind with an amine group (-NH₂) on the cell surface, while at a lower pH (5.5–7.0), metal binding with a carboxyl group (-COOH) is most likely. Analysis of the data from these studies shows both a second (higher) proton binding constant, consistent with binding at a higher pH, and higher metal binding constants to the second cell binding site—consistent with the correlation between binding stability and proton dissociation [25].

Deleebeeck et al. [69] observed a pH breakpoint in their study on Ni toxicity to O. mykiss (Figure S3). At or below a pH of 6.8, the log K_HBL value was 5.7, consistent with other data. Above this pH, the log K_HBL value increased to 6.8. This is the only study on this species that extensively examines the role of proton (H⁺) concentration in Ni toxicity, and one of three studies that explore the effect of pH (all three studies are reviewed here). Deleebeeck et al. [68] later observed similar behaviour in Ni toxicity to R. subcapitata (Figure S4), with a pH breakpoint at 7.2. Below this pH, a log K_HBL value of 5.7 was derived, and above it, a value of 6.7, consistent with the value from their previous study. Similarly, Schroeder [72] reported comparable behaviour for H. azteca (Figure S5), although the pH breakpoint occurred at a higher pH of 8.0. Below this pH, a log K_HBL value of 5.5 was derived, and above it, a value of 6.9, consistent with earlier studies by Deleebeeck et al. [68,69]. The trend in pH breakpoints corresponds with the (f_C)_Ni^50% values across the studies: as the pH breakpoint increases, the (f_C)_Ni^50% value decreases. The average log K_HBL value from the three studies, possibly related to an amine site, is 6.8.

Heijerick et al. [61] investigated the toxicity of Zn to R. subcapitata and observed a similar pH-dependent behaviour as that found by Deleebeeck et al. [68] for Ni. Below and at a pH of 6.8, a log K_HBL value of 5.8 was derived from their data, while above this pH, a larger log K_HBL value of 8.3 was obtained (Figure S6). Wilde et al. [115] found a less distinct pH breakpoint (Figure S7), likely occurring around the same pH as Heijerick et al. [61]. Analysis of their data above pH 6.8 yielded a log K_HBL value of 8.3, matching the earlier study of Heijerick et al. [61]. Van Regenmortel et al. [59], using a different model to assess Zn toxicity to R. subcapitata, could not identify a clear pH breakpoint but derived a high-pH log K_HBL value of 7.9, reasonably consistent with the other two values. The average log K_HBL value from these Zn studies is 8.2, significantly higher than the value obtained for Ni.

Few studies have identified a pH-dependent breakpoint in metal toxicity to freshwater organisms, and only for Ni and Zn, the metals with two of the lowest log K_MBL values. This could imply that amine group binding is possible only when carboxyl group binding is relatively weak. However, given the limited research showing a pH-related toxicity breakpoint, additional studies are necessary to confirm this phenomenon. Although there is good agreement in log K_HBL values for each metal individually (Ni or Zn), there is less agreement between these two metals. Consistent log K_HBL values have been found for carboxyl binding sites across all seven metals, but the lack of consistency of log K_HBL values reported for amine binding sites raises doubts about the reliability of the data. This reinforces the need for further research on this effect with Ni and Zn.

9. Conclusions and Recommendations

This study presents the integration of the extended free ion activity model (FIAM), biotic ligand model (BLM) and electrostatic toxicity model (ETM) into a unified conceptual framework to describe metal interactions at cell surface receptor sites (biotic ligands). The integrated model shows that (i) the free metal ion (M^z+) is primarily responsible for toxicity in aquatic organisms, although other cationic species (e.g., MOH^(z−1)+, MF^(z−1)+) may also contribute, (ii) toxicity can be ameliorated by major cations, including Ca²⁺, Mg²⁺, Na⁺ and H⁺ and (iii) toxicity is strongly influenced by the proportion of receptor sites (biotic ligands) occupied at the TR₅₀ ((f_C)_M^50%), where toxicity increases as (f_C)_M^50% decreases. The key factor determining toxicity is the binding affinity of metals for biotic ligands; the stronger the affinity (or higher the binding constant, log K_MBL), the greater the toxicity to aquatic organisms.

A comprehensive literature evaluation on the toxicity and uptake of seven key metals (Ni²⁺, Zn²⁺, Co²⁺, Cd²⁺, Cu²⁺, UO₂²⁺ and Pb²⁺) and four ameliorative cations (H⁺, Na⁺, Ca²⁺ and Mg²⁺) has produced an extensive database of binding constants (log K_MBL values) for freshwater organisms. This database is a key tool for predicting metal toxicity to aquatic organisms. The binding constants incorporate the competitive effects of the ameliorative cations, the fraction of cells occupied by a metal at the TR₅₀ ((f_C)_M^50%) and metal speciation. For metals like Cu²⁺, UO₂²⁺ and Pb²⁺ that hydrolyze in circumneutral freshwater (pH 5.5–8.5), MOH⁺ was included by adding half of its activity at the TR₅₀ to that of M^z+. The average binding constants (log K_MBL values) for Ca²⁺ (3.4), Mg²⁺ (2.8) and Na⁺ (2.2) are notably lower than those of the seven selected metals (4.8–7.9). The proton (H⁺) binding constant (5.8) is similar to, or higher than, those of Ni²⁺ (4.8), Zn²⁺ (6.0) and Co²⁺ (5.8), but lower than those for Cd²⁺ (7.0), Cu²⁺ (7.9), Pb²⁺ (6.8) or UO₂²⁺ (7.7). There is a 1000-fold difference in binding affinity between Ni²⁺ (lowest) and Cu²⁺ (highest) for biotic ligands. In general, the average binding constants (log K_MBL values) derived from toxicity studies were consistent with those derived directly from uptake studies. The derived binding constants will improve current BLMs for Cd²⁺, Cu²⁺, Ni²⁺, Pb²⁺ and Zn²⁺ and aid in developing new BLMs for Co²⁺ and UO₂²⁺.

The derived metal binding constants accurately predicted metal toxicity for a wide range of freshwater organisms, where 75–88% of data were within a factor of two, and 88–98% of data were within a factor of three, of the ideal 1:1 agreement line. The best agreement was observed for Cd²⁺ (88%) while the worst was for Co²⁺ and UO₂²⁺ (75%), which had the smallest datasets and the largest uncertainties in their log K_MBL values (Table 1, Table 2 and Table 3). Overall, the strong alignment between measured and predicted toxicity for all seven metals supports the reliability of the derived log K_MBL and (f_C)_M^50% values. Additional toxicity and uptake experiments are required for Co²⁺, UO₂²⁺ and Pb²⁺, under a range of water chemistry conditions, to provide further data on binding constants for comparing measured versus predicted toxicity. Experiments designed to evaluate the fraction of cells occupied by a metal at the TR₅₀ ((f_C)_M^50%) for key organisms across freshwater taxa are much needed, as some organisms show great variability in derived (f_C)_M^50% values. It was generally concluded that higher log K_MBL values correspond to increased metal toxicity in freshwater.