**3. Metal bioaccumulation**

Since metals in the environment are not always available, assessing metal accumulation in sentinel species is one of the most effective methods for evaluating effects of metals on biota. The tendency of chemicals to be accumulated in organisms is usually expressed by the bioaccumulation factor (BAF) and the bioconcentration factor (BCF). These factors represent the ratio of the residue in the organisms versus the concentration in water at equilibrium, including or excluding the uptake from dietary sources, respectively. For metals, BCF and BAF vary widely and are inversely related to the external water concentration [57–59]. These characteristics of the accumulation factors for metals are attributed to the complex mechanisms of metal uptake and accumulation [60]. In a number of studies, uptake via saturable kineticsexhibiting mechanisms has been shown to be more common and toxicologically relevant than passive diffusion [61–65]. The concentration of metals accumulated in organisms is further influenced by different physiological and anatomical mechanisms in response to metal exposure [6]. For essential metals, organisms are able to actively regulate metal bioaccumula‐ tion and maintain homeostasis over a range of exposure via exclusion or increased elimination [11, 57, 65]. Organisms have also developed different mechanisms to sequester, detoxify, or store excess metals [11, 62, 66]. The dependence of BCF and BAF on exposure conditions as well their inverse relationship with the exposure concentration invalidates the use of these factors in risk assessment [6, 57, 59].

Biodynamic models have been recommended as an alternative to single and generic values of BCF or BAF in the assessment of metal bioaccumulation [67]. Such models allow for integrating and distinguishing different exposure routes (e.g., water vs. diet) and the dynamic nature of bioaccumulation processes [6, 68, 69]. The models provide a better understanding of the extent of and the contributors to the variability in the bioaccumulation among metals in various species and at different conditions [67, 70]. The biodynamic models are based on the concept of biodynamics that the accumulation of chemicals occurs as a result of a balance of different fluxes. The models assume that the rate of the fluxes can be realistically determined in controlled experiments with varying concentrations and conditions [67]. Uncertainties are inherent in the application of these empirical rates to different conditions, especially those that are extremely different from the conditions in which the rates have been derived. This limitation can be eliminated by integrating inverse phenomena into unifying concepts. The biokinetic model based on a unifying concept is considered 'mechanistic' from the perspective that physiological rates are estimated from chemical-specific properties of substances and species-specific physiological characteristics of organisms [71, 72]. This method facilitates extrapolation to a wide range of chemicals, organisms, and environmental conditions, without the necessity for case-specific calibration. Quantitative relations between uptake and elimina‐ tion rate constants, on the one hand, and metal-specific properties and species-specific physiological characteristics, on the other hand, are required for the development of a mechanistic model. Some potential for meeting this requirement has been revealed from the findings during the last decades. Specifically, metal absorption and elimination rates have been related to the filtration rate and species weight, respectively [71, 73]. The affinity of metals for proteins, which are intensively involved in trafficking processes of metals, may explain the uptake rate constant from the dissolved phase [72]. The affinity of metals for the proteins depends on metal charge and atomic radius and reflects the preferences for coordination and ligands [72, 74, 75]. The suggestion on a potential correlation between uptake kinetics and the affinity of metals for protein has been substantiated by the reported relationship between the absorption efficiency and the binding of metals to membrane transport proteins [76]. Efforts have been put in developing bioaccumulation and toxicity models based on the affinity of metals for biological ligands [69, 72, 77]. Different indicators of metal binding to biological ligands and bioaccumulation have been related to various chemical properties of metals [78– 82].

The accumulation of metals in organisms occurs as a result of a balance of the uptake from food as well as water and losses. Moreover, metal concentrations in organisms are affected by the growth dilution. Taking these factors into consideration, the concentration of metals accumulated in organisms (*C*; µg/g dw) can be expressed by the following equation:

$$\frac{dC}{dt} = \left(k\_u \times C\_w\right) + \left(IR \times AE \times C\_f\right) - \left(k\_{av} + k\_{q'} + \mathbf{g}\right) \times C \tag{5}$$

where *k*<sup>u</sup> (L/g dw/d) is the absorption rate; *C*w (µg/*L*) is the dissolved metal concentration; IR (g/g dw/d) is the ingestion rate; AE (/) is the assimilation efficiency; *C*<sup>f</sup> (µg/g) is the metal concentration in food; *k*ew (1/d) is the excretion rate; *k*ef (1/d) is the egestion rate; and *g* (1/d) is the growth rate. The instant concentration of metals in organisms can be solved from Equation 5:

$$C = \frac{\left(k\_u \times C\_w\right) + \left(IR \times AE \times C\_f\right)}{k\_{\circ w} + k\_{\circ f} + \mathbf{g}} \times \left(1 - e^{-\left(k\_{\circ \circ} + k\_{\circ f} \circ \mathbf{g}\right) \circ t}\right) \tag{6}$$

The first factor in Equation 5 represents the uptake from the dissolved phase and can be further elaborated based on the absorption efficiency and the filtration rate [69]. In the study of Le et al. [69], the filtration, ingestion, and growth rates were related to the species weight while the absorption and assimilation efficiency was considered metal specific. In addition, elimination rates were parameterised based on both chemical properties of metals and mussel size.

Such a mechanistic model has shown good potential for predicting metal accumulation in the zebra mussel with different size and from various sites. A mechanistic model, which is based on chemical properties of metals and physiological characteristics of organisms while taking site-specific contamination levels into consideration, facilitates a wide extrapolation to different conditions and metals. However, a number of disadvantages are inherent in the current model. The modelling is based on the dissolved metal concentrations without a specification of chemical species and forms of metals in the environment. Although different uptake pathways are included in the model, a distinction of tissue-specific accumulation of metals is not accounted for. Another disadvantage of the model is related to the derivation of the relationship between the rate of physiological processes and the chemical properties of metals. Despite the potential correlation between the uptake kinetics and some chemical properties of metals shown recently, quantitative relationships established between these two factors have hardly been validated. Moreover, relationships between uptake kinetics and chemical properties of metals have usually been derived based on limited experimental data, thereby leading to intrinsic uncertainties in the application of the derived relationships.
