Two-Compartment Toxicokinetic–Toxicodynamic Model to Predict

Article pubs.acs.org/est

Two-Compartment Toxicokinetic−Toxicodynamic Model to Predict Metal Toxicity in Daphnia magna Qiao-Guo Tan and Wen-Xiong Wang* State Key Laboratory of Marine Environmental Science, College of Environment and Ecology, Xiamen University, Xiamen 361005, China S Supporting Information *

ABSTRACT: Relating the toxicity of metals to their internal concentration is difficult due to complicated detoxification processes within organisms. Only the metabolically available metals are potentially toxic to organisms, while metals in the detoxified form are toxicologically irrelevant. Accordingly, we developed a two-compartment toxicokinetic−toxicodynamic model for metals in a freshwater cladoceran, Daphnia magna. The toxicokinetics simulated the bioaccumulation processes, while the toxicodynamics quantitatively described the corresponding processes of toxicity development. Model parameters were estimated for D. magna and three metals, i.e., cadmium, zinc, and mercury, by fitting the literature data on metal bioaccumulation and toxicity. A range of crucial information for toxicity prediction can be readily derived from the model, including detoxification rate, no-effect concentration, threshold influx rate for toxicity, and maximum duration without toxicity. This process-based model is flexible and can help improve ecological risk assessments for metals.

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INTRODUCTION Predicting the toxicity of trace metals to aquatic organisms is one of the important challenges in ecotoxicological studies. High uncertainty exists in assessing the associated risks by simply measuring the metal concentrations in different environmental compartments (e.g., water, sediment, soil) due to the difficulty in relating exposure to toxicity. The most straightforward and widely used method for establishing the relationship is to conduct the standard toxicity tests. However, the toxicity statistics, such as the concentrations causing toxicity in x% of organisms (ECx) derived by regression analysis using mathematical (e.g., logit, probit) models, are purely descriptive without much biological relevance.1,2 For trace metals in aquatic systems, the great dependence of bioavailability on water chemistry is another obstacle for predicting the toxicity from exposure.3,4 The biotic ligand model (BLM) was accordingly developed in order to consider the effects of the competition of major cations (e.g., Ca2+, Mg2+, H+) and the complexation of natural ligands (e.g., HCO3−, dissolved organic matter) on metal bioavailability and toxicity.4−6 Although this model makes it possible to extrapolate results obtained from laboratory toxicity tests to site-specific conditions, it is essentially doing toxicity tests on a computer, generating the same toxicity statistics (i.e., ECx), and is not process based.1,7 Relating toxicity of contaminants to their concentration in aquatic organisms is apparently more appropriate than relating to their concentration in water, because the former is a better surrogate of contaminant concentration at the site of toxic action which has explicitly considered the effects of bioavailability, routes of exposure, exposure duration, efflux, and so on.8 This is what the critical body residue approach is based on.8,9 For many organic compounds (e.g., narcotic © 2012 American Chemical Society

organics), a relatively constant threshold body concentration corresponding to toxicity was found across a wide range of aquatic organisms.8 However, it is difficult to find such a threshold for metals even in the same biological species, not to mention among different species.10,11 The main reason is that organisms have many mechanisms for metal detoxification, including sequestration in metallothionein and incorporation into insoluble granules or deposits.12 Rainbow12,13 divided the whole-body metals into two compartments: metabolically available and detoxified metals. Toxicity is related to metabolically available metals only. The recently developed subcellular partitioning model further divided metals into five fractions, and only metals bound to organelles and heatsensitive proteins are considered toxic to organisms.14,15 Although these nonparameterized approaches provided valuable insights on metal toxicity mechanisms, they have limited capability for predicting toxicity quantitatively. Toxicokinetic−toxicodynamic (TK−TD) model is a collective name for a group of process-based models for simulating and predicting toxicity over time.16,17 In two steps, TK−TD model relates exposure to toxicity: toxicokinetics simulates the bioaccumulation process (e.g., uptake, biotransformation, efflux), while the toxicodynamics describes the corresponding time-course of hazard and toxicity.18 Compared to the methods using ECx, TK−TD model is more mechanistic and biologically relevant. TK−TD model has been successfully applied for predicting toxicity of organic compounds;18,19 in contrast, very Received: Revised: Accepted: Published: 9709

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few studies employed it for predicting metal toxicity.20,21 On the other hand, the toxicokinetics (also called biokinetics) of metals have been elaborately quantified in a wide range of aquatic organisms using a radiotracer technique;22,23 however, these toxicokinetic data have never been input into a toxicodynamic model to contribute to toxicity prediction, until now. Moreover, in most of previous studies using TK−TD model, toxicity was related to contaminant concentration in the whole body.24 For metals, this simplification may become unacceptable due to the detoxification mechanisms described above. In the present study, we therefore developed a twocompartment TK−TD model for predicting the metal toxicity in aquatic organisms for the first time. Metabolically available and detoxified metals were quantitatively separated, and toxicity can thus be related to the concentration of the former. Daphnia magna was selected as the model organism because it is a species widely used in standard toxicity tests and there are now enough literature data that allow the calibration and validation of the model. Toxicity of both essential (i.e., Zn) and nonessential metals (i.e., Cd and Hg) was modeled in this study.

dC2(t ) = k12 × C1(t ) − k 21 × C2(t ) dt

where Cint(t) is the whole-body metal concentration (μg g ); C1(t) and C2(t) are the concentration of metal distributed in compartment one and two (μg g−1), respectively, both of which are normalized to the weight of the whole organism; Jin(t) is the metal influx rate (μg g−1 h−1); ke1 is the efflux rate constant of metals from compartment one (h−1); and k12 and k21 are the rate constants for metals being transferred from compartment one to two and two to one (h−1), respectively. A growth rate constant should be added into eqs 2 and 3 when there is growth of organisms during the experiment, which can lead to dilution of the accumulated metals.26,27 However, in acute toxicity tests without feeding, growth of animals can be ignored. In the present study, we considered only the aqueous metal exposure since the data we analyzed were from studies on aqueous toxicity. Under environmentally realistic concentrations, there is a proportional increase of metal uptake rate with metal concentration in solution of given water chemistry. Therefore, Jin(t) is expressed as:

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Jin (t ) = k u × Cw(t )

TOXICOKINETIC−TOXICODYNAMIC MODEL Model Concept. The basic concept of a two-compartment model for relating metal accumulation to toxicity has been described by Rainbow and Luoma.25 Briefly, metals in the body of an organism were divided into two compartments: in compartment one, metals are metabolically available; and in compartment two, metals are detoxified (Figure 1). Newly

(4)

where ku is the uptake rate constant (L g−1 h−1); and Cw(t) is the metal concentration in solution (μg L−1). However, higher metal concentrations are usually used in toxicity tests, and saturation of uptake rate is expected to happen. In that case, a Michaelis−Menten equation usually can be used to describe metal uptake kinetics satisfactorily.28 Although we only considered aqueous uptake of metals here, dietary assimilation of metals can be conveniently included into the model by adding an additional component (i.e., ingestion rate × assimilation efficiency × metal concentration in food) to eq 4.26,27 Toxicodynamic Model. The toxicodynamic model used here was modified from the dynamic energy budget toxicology (DEBtox) survival model.20,24,29 The basic principle is that when the metal concentration in compartment one exceeds the threshold concentration (C IT , μg g −1 ), hazard (H(t), dimensionless) caused by internal metal exposure begins to accumulate and the probability of mortality increases as a consequence.

Figure 1. Two-compartment toxicokinetic−toxicodynamic model. For the meaning of symbols, see the explanation for eqs 1−7 in the text.

⎪ k k × (C1(t ) − C IT) + h 0 if C1(t ) > C IT d H (t ) ⎧ =⎨ ⎪ dt ho otherwise ⎩

incorporated metals are initially distributed into compartment one, where the metals would be eliminated from the organism or reversibly transferred into compartment two. If the elimination rate is exceeded by the influx rate, metals in compartment one will build up and toxicity will subsequently occur when a threshold concentration is exceeded. The turnover rate of metals in compartment one is expected to be faster than in compartment two. Toxicokinetic Model. First-order kinetics was assumed for metal efflux and the transfer of metals between the two compartments (Figure 1). Therefore, metal accumulation processes are described as follows: C int(t ) = C1(t ) + C2(t )

(3) −1

S(t ) = e−H(t )

(5) (6)

S0(t ) = e−h0 × t

(7) −1

−1

where kk is the killing rate (g μg h ); S(t) is the survival probability of an organism surviving to time t; h0 is the background hazard rate (h−1); S0(t) is the survival probability of organisms in the negative control treatment. In the present study, h0 is set to zero because the mortality of D. magna due to background hazard during toxicity tests (≤ 48 h) was always negligible. By definition, CIT is the highest concentration of metabolically available metal that organisms can tolerate without causing elevated hazard rate, and the kk is the hazard rate caused by per unit of excess metal above CIT. Therefore, CIT defines the boundary between safe and toxicity, and kk determines how serious the toxicity would be when it occurs.

(1)

dC1(t ) = Jin (t ) − (ke1 + k12) × C1(t ) + k 21 × C2(t ) dt (2) 9710

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Table 1. Estimated Toxicokinetic Parameters (Mean ± Standard Deviation)a metal

f1(0)

k12 (d−1)

k21 (d−1)

ke1 (d−1)

source of data for estimation

Cd Hg Zn

0.333 ± 0.022 0.617 ± 0.010 1

0.133 ± 0.034 0.062 ± 0.017 0

0.039 ± 0.008 0.116 ± 0.015 0

0.791 ± 0.079 1.35 ± 0.06 0.284 ± 0.005

ref 30 ref 33 ref 43

a f1(0): the fraction of metals in compartment one at the beginning of efflux. For the meaning of the other parameters see Figure 1 and the explanation for eqs 1−3 in the text.

data set was approximately [f1(0) × Cint(0) − ΔCint]/[Cint(0) − ΔCint], where ΔCint is the difference in Cint(t) between the first two data points of the original data. The parameters were then estimated by fitting to both data sets together. To further reduce the uncertainty in estimation, the four toxicokinetic parameters were not estimated at the same time. Instead, k21 was first estimated based on prior knowledge. Specifically, at the later stage of the efflux process, nearly all retained metal was in compartment two (i.e., the slow exchange compartment), k21 is thus approximately the efflux rate constant of the whole-body metal. Therefore, k21 is calculated as the slope of the depuration curve after the y axis (percentage of metal retained) is natural log transformed (see Figure 2).30 Subsequently, the other three parameters were estimated by keeping k21 fixed.

The toxicodynamic model (eq 5) corresponds to the threshold hazard model in Ashauer and Brown24 (their eq 17) and the DEBtox survival model in the General Unified Threshold model of Survival.17 This toxicodynamic model assumes very fast, instant recovery of toxicodynamic damage.17,24 Parameter Estimation. The value of model parameters and their standard deviations were estimated by Marquardt type least-squares fitting using the software OpenModel 2.0.0 (University of Nottingham, http://www.nottingham.ac.uk/ environmental-modelling/OpenModel.htm). Parameters were estimated in two steps. First, toxicokinetic parameters (k12, k21, and ke1) were estimated from data on metal efflux over time. Second, keeping these toxicokinetic parameters fixed, the toxicodynamic parameters (kk, CIT) were estimated from time course of survival data from toxicity tests. All the data for model fitting are from papers previously published (Tables 1, 2). Three metals were investigated, i.e., Table 2. Estimated Toxicodynamic Parametersa metal Cd

Hg

Zn

age/ preexposure/ clone 21 d/no/ sensitive 21 d/no/ tolerant 12 d/no/NA 12 d/0.50 μg L−1/NA 12 d/5.0 μg L−1/NA 21 d/no/NA

CIT (μg g−1)

kk (g mg−1 h−1)

source of data for estimation

41.0 ± 3.3

2.67 ± 0.31

ref 41

29.2 ± 4.2

0.658 ± 0.080

ref 41

21.5 ± 12.8 53.8 ± 7.4

0.778 ± 0.124 0.365 ± 0.041

ref 31 ref 31

112 ± 6

0.885 ± 0.133

ref 31

354 ± 3

2.85 ± 0.30

ref 44

Figure 2. Efflux processes of Cd, Hg, and Zn from D. magna. The efflux data were fitted with the two-compartment model (see Figure 1), and the parameters are listed in Table 1. The model for Zn was simplified to a one-compartment model. The dots are measured values and the lines are modeled values. C1(t), C2(t), and Cint(t) are metal concentrations in compartment one, two, and whole body, respectively.

All values are expressed on dry weight basis and are mean ± standard deviation. For the meaning of the parameters see Figure 1 and the explanation for eq 5 in the text. NA: not applicable. a

Cd, Hg, and Zn. All the bioaccumulation and toxicity experiments were conducted with the same clone of D. magna (except noted) under the temperature of 23.5−24 °C. Toxicokinetic Parameters. Besides the three toxicokinetic parameters (i.e., k12, k21, ke1) in eqs 2 and 3, a fourth parameter is needed to initialize the software calculation, which is the fraction of whole-body metal distributed in compartment one at the beginning of the efflux process (or f1(0)). The value of f1(0) is a result of exposure history (e.g., metal concentration, duration of exposure) and is expected to be different under different exposure scenarios; therefore, f1(0) should not be considered as a “true” toxicokinetic parameter. However, the uncertainty of this parameter would affect the estimation of other “true” parameters. Prior knowledge that eliminated metal was nearly all from compartment one at the beginning of depuration was thus employed to reduce the uncertainty. In detail, a new efflux data set was created, which was the original efflux data without the first data point. The f1(0) of the new

Aqueous uptake rate of metal is heavily dependent on water chemistry; therefore, ku quantified in one solution cannot be directly extrapolated to another. It is thus not practical to assign a fixed value to ku in the model. In contrast, k12, k21, and ke1 are mainly determined by biological processes which are species specific and are considered not affected by water chemistry. The values of these parameters can thus be used in different waters. In the present study, ku was either estimated from the values reported in the literatures or back calculated from the bioaccumulation data using the toxicokinetic model of the present study (see Supporting Information (SI) for details). Toxicodynamic Parameters. The two toxicodynamic parameters (CIT and kk) were estimated by fitting the model to the data from the time-to-death toxicity tests. In the software calculation, the values of C1(0) and C2(0) should be assigned to initialize the estimation. If there was no preexposure (i.e., exposure to elevated concentration of the metals before toxicity tests), the concentrations of nonessential metals (e.g., Cd and 9711

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h of exposure, Cd concentration in D. magna would be 46.0 μg g−1, but would be predicted to be 82.7 μg g−1 by using the onecompartment model with ke.26 After a long-term exposure (e.g., 20 d), much higher proportion of metal should be found in compartment two compared to that of the short-term exposure (Figure 3B). If the exposure is pulsed or intermittent, high proportion of metal can be found in compartment two even after a short-term exposure (i.e., 3−4 d, Figure 3C, D). In natural waters where the exposure is long-term, a higher proportion of metals would be expected to be in the slow exchange compartment (or detoxified form) compared to the acute exposure in the laboratory. When the steady state is reached i.e., dC1(t)/dt = dC2(t)/dt = 0, according to eq 3, the fraction of whole-body metal distributed in compartment two can be calculated as:

Hg) in organisms were negligible compared to the subsequent accumulation. Both of the two concentrations were therefore set to zero. However, if there was preexposure or if the metal was essential (e.g., Zn), suitable values need to be assigned to the two concentrations, which were obtained from the literature. For example, C1(0) of Zn was 92 μg g−1 for D. magna.31 For Hg, C1(0) was zero, and C2(0) was 0.506 μg g−1 and 3.80 μg g−1 for D. magna preexposed to 0.50- and 5.0-μg L−1 Hg for 4 d and depurated for another 4 d, respectively.31

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RESULTS AND DISCUSSION Toxicokinetics. The efflux of Cd and Hg can be well described by the two-compartment model (Figure 2). During the first two days, efflux was dominated by compartment one and was very fast. The estimated efflux rate constant, ke1, was 0.791 d−1 for Cd and 1.35 d−1 for Hg (Table 1). After the initial fast elimination, the majority of the retained metals were in the slow exchange compartment (i.e., compartment two). The transfer of metals from compartment two to compartment one became the rate limiting step of efflux. Therefore, k21 is approximately the rate constant for the whole-body metal efflux afterward. The estimated k21 is 12−20 times lower than ke1 (Table 1). By definition, k21 is similar to the efflux rate constant (or ke) reported in previous studies on metal biokinetics.27,32 After a short-term exposure (e.g., 48 h), most of the newly incorporated metal is in compartment one (Figure 3A). Therefore, using ke reported in the literatures (or k21 here) to predict bioaccumulation in an acute exposure would lead to substantial overestimation because the elimination rate of newly incorporated metal was underestimated. For example, assuming a dissolved Cd concentration of 20 μg L−1, the uptake rate is thus 1.79 μg g−1 h−1 (see Figure 3 for the calculation). After 48

fss2 =

k12 k12 + k 21

(8)

The value of fss2 is determined by the two toxicokinetic parameters and is theoretically independent of the exposure metal concentration as long as the parameters are not affected and D. magna can survive. Based on the estimated parameters (Table 1), fss2 is 77.3% and 34.8% for Cd and Hg, respectively. However, after 3−4 d of exposure to Cd and Hg,30,33 which was apparently not long enough for the steady state to be reached, 66.7% of Cd and 38.3% of Hg were found in compartment two (Table 1). The reason was that the exposure was not constant but pulsed or intermittent.30,33 The efflux of Zn did not follow a typical two-compartment pattern, and the one-compartment model can fit the observed data well (Figure 2, see SI Table S1 and Figure S1 for details on model selection). The one-compartment model can be considered as a special case of the two-compartment model, of which k12 = k21 = 0. The efflux rate constant is the sole parameter needed to quantify Zn efflux and was estimated to be 0.284 d−1 (Table 1). Metals in compartment two (or the slow exchanging compartment) are considered to be detoxified;25 therefore, k12 can be deemed as the detoxification rate constant. Besides detoxification, efflux of incorporated metals from compartment one is another way to avoid toxicity, of which the rate is quantified by ke1. For Cd and Hg, the estimated ke1 was 5.9 and 22 times higher than k12 (Table 1), respectively, indicating that efflux was faster and played a more important role than the detoxification mechanisms in coping with the potential toxicity of metals. Detoxification rates of metals in several aquatic invertebrates have been estimated using different methods.25,34 Those estimations were based on the theory that toxicity occurs when the combined rates of efflux and detoxification are exceeded by the influx rate.13,25 Croteau and Luoma34 derived the detoxification rate by deducting efflux rate from influx rate at the onset of toxicity. Although the approach is straightforward, determining the critical influx rate at the onset of toxicity is difficult, which is dependent on the selection of exposure concentrations and the definition of “onset of toxicity”. In contrast to our results, Croteau and Luoma34 estimated that the rates of detoxification of assimilated dietary Cu, Cd, and Ni in snail (Lymnaea stagnalis) were 1−2 orders higher than the efflux rates. This discrepancy may be due to both the differences in methods, which have been described above,

Figure 3. Simulated Cd accumulation in D. magna (right panel) when exposed to Cd concentrations described in the corresponding figures in the left panel. The toxicokinetic parameters used for the simulation were those listed in Table 1. The uptake rate was calculated with the equation obtained from ref 28: Jin(t) = 19.5 × Cw(t)/[198.2 + Cw(t)]. See SI for the code and concentration data for generating the figures. A: short-term exposure to a high Cd concentration; B: long-term exposure to a low Cd concentration; C: pulse exposure to high Cd concentration followed by depuration; D: intermittent exposure. 9712

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and the interspecies difference. Specifically, the snail had much slower rate of metal efflux than D. magna. The ke of Cd in the snail was 0.021 d−1, not only far lower than the ke1 in D. magna (0.791 d−1), but also lower than the efflux rate constant from the slow exchanging compartment of D. magna (k21, 0.039 d−1). Interspecies difference was also reported by Rainbow and Luoma.25 The shrimp (Palaemon elegans) had no significant detoxification (i.e., irreversible storage) of Zn and could only rely on efflux to avoid toxicity. In contrast, the amphipod (Orchestia gammarellus) and the barnacle (Amphibalanus amphitrite) had detoxification rates 2−3 orders of magnitude higher than the efflux rate. The toxicokinetics of Cd is very different among cladoceran species (SI Figure S2, Table S2). D. magna had much lower ke1 and k21 than the other three cladoceran species, i.e., Ceriodaphnia dubia, Daphnia galeata, and Moina macrocopa, indicating that it would take a much longer time for D. magna to eliminate the incorporated Cd. The detoxification rate (i.e., k12) in D. magna was also lower than in D. galeata and M. macrocopa, but was higher than in C. dubia. The sum of ke1 and k12 reflects the capability of the organisms to cope with the incorporated metals by efflux and detoxification, and is the lowest in D. magna. It is thus not surprising that D. magna was the most sensitive to Cd exposure among the four cladoceran species.35 According to the two-compartment model, when a higher proportion of metal is detoxified (into compartment two), the overall efflux rate would be expected to be slower. Not only the metals detoxified into physiologically inert granules had lower efflux rate,36 metals detoxified by binding to MTLP were also found to be eliminated at slower rates. Buchwalter et al.37 found that among 21 species of aquatic insects, the percentage of Cd detoxified in MTLP fraction was negatively correlated with ke. In addition, in five marine bivalves, after 7 d of efflux, the species with higher ke of Cu retained higher percentage of the metal associated with MTLP, suggesting that Cu bound with MTLP was eliminated more slowly than Cu in other forms.38 Toxicodynamics. After the first several hours of exposure to a lethal metal concentration, rapidly increasing mortality of D. magna was observed (Figures 4−6), presumably because the concentration of metals at the site of toxic action had exceeded the threshold.25 This time process of toxicity can be well described by the toxicodynamic model (Figures 4−6), and the estimated parameters (CIT, kk) are listed in Table 2. To understand the differences in tolerance among D. magna of

Figure 5. (A) Survivorship of D. magna during the 48-h exposure to 1000 μg L−1 of Zn.44 Other details as in Figure 4. (B) Comparison between observed and model predicted survivorship at the end of 48-h exposure to different concentrations of Zn (μg L−1), which are indicated beside the dots. The 48-h toxicity tests were independent of the 48-h experiment from which the toxicodynamic parameters were estimated.44.

different clone or with different preexposure history, the same toxicokinetic parameters were assumed for them. Although this assumption is a simplification due to the availability of toxicokinetic data, it is acceptable according to the current knowledge.39−41 Higher toxicity of metals to organisms could be a result of lower CIT, higher kk, or both. Compared to the Cd-sensitive daphnids, the tolerant clone had 4.0 times lower kk. The CIT was more comparable between clones with a difference of 1.4 fold (Table 2). Pre-exposure to elevated concentration of Hg up to 5.0 μg L−1 increased the CIT from the background 21.5 to 112 μg g−1, while kk was less variable among treatments (2.4 fold) and no consistent trend was observed (Table 2). The underlying mechanisms for the different Cd kk in different daphnid clones and elevated Hg CIT in preexposed daphnids are still unclear and warrant further studies. In Table 2, the parameters for each group of daphnids were estimated separately by fitting the model to relevant data only. The parameters were also estimated by fitting the model to all data for different daphnid groups by assuming either the same CIT or kk (SI Table S3). To validate the TK−TD model, we used the model to predict the survivorship of D. magna in independent toxicity tests, i.e., tests independent of those from which the model parameters had been estimated (Figure 5B, SI Figure S3). There was good agreement between the predicted and the observed survivorship of daphnids in the Zn toxicity tests (r2 = 0.981, Figure 5B). As the toxicodynamic parameters for Hg were estimated with 12-d D. magna, in toxicity tests the survivorship was better predicted for daphnids of the same age than for 4-d and 28-d daphnids (SI Figure S3). These results suggest that toxicodynamic parameters vary slightly among daphnids of different ages. The no-effect concentration in water can be easily derived based on CIT; however, the value cannot be directly extrapolated to waters of different water chemistry where metal bioavailability can be very different.3,4 Although BLM is usually known as specifically designed for considering the effects of water chemistry on metal toxicity,4,5 it can also be a good tool for predicting metal bioavailability or uptake rate as a function of water chemistry.6 Using BLM to derive metal uptake rate for the TK−TD model will widen the applicability of the latter model to waters with site-specific conditions. Based on the pattern of the efflux curves (i.e., Figure 2) it is evident that two compartments exist in D. magna for Cd and Hg, which is further supported by the statistical analysis using

Figure 4. Survivorship of two clones of D. magna (i.e., the sensitive clone and the tolerant clone) during the 24-h exposure to 400 μg L−1 of Cd.41 The dots are observed values and the thick lines are modeled values. The estimated toxicodynamic parameters are listed in Table 2. The insets are the comparison between observed and modeled survivorship, the dashed lines are the 1:1 lines, and r2 is the coefficient of dependence of the 1:1 line. 9713

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Figure 6. Survivorship of D. magna during the 20-h exposure to 50 μg L−1 of Hg. The daphnids were pre-exposed to 0 (control), 0.50, and 5.0 μg L−1 of Hg for 4 d and then depurated in clean water for another 4 d.31 Other details as in Figure 4.

Akaike’s Information Criteria (SI Table S1, Figure S1).42 Nevertheless, during an acute exposure (e.g., 24 h), nearly all of the newly accumulated metal is in compartment one (Figure 3A), and the role of compartment two in metal storage and detoxification is not important. The CIT estimated in the present study can also be considered as the whole-body threshold for acute toxicity tests. It is thus not surprising that a one-compartment model can also adequately simulate the bioaccumulation and toxicity of metals in the acute toxicity tests (SI Table S4, Figure S4).20 However, in chronic toxicity tests or under fluctuating exposures, considerable proportion of metal is distributed in compartment two and detoxified (Figure 3B−D). No wholebody threshold concentration for toxicity exists, simply because the fraction of metals in compartment two is very variable at the onset of toxicity. It is thus necessary to separate the metabolically available metal from the detoxified forms to make valid toxicity prediction; and using the two-compartment model is a choice. Casado-Martinez et al.10 exposed the polychaete (Arenicola marina) to two different sediments of very different metal bioavailability. When the polychaetes were exposed to the first sediment, mass mortality was observed after 10 d of exposure; in contrast, no mortality occurred during the 30-d test for the second sediment, although the polychaetes finally showed higher metal concentrations than those worms manifesting toxicity in the first experiment. Taking Zn as an example, we re-analyzed their data with the two-compartment TK−TD model (SI Figure S5). In the first experiment, C1(t) rapidly rose and exceeded C IT before much Zn was incorporated into compartment two; in contrast, C1(t) in the second experiment never reached CIT and allowed the gradual increase of C2(t) to a much higher level. A one-compartment model can adequately describe the bioaccumulation and toxicity of Zn in D. magna in the present study; in contrast, a twocompartment model of Zn is clearly necessary for the polychaete. The choice of model should be based on the actually observed toxicokinetics and toxicodynamics of the metal in the organism of concern; and there should be no model that fits all situations. The two-compartment TK−TD model presented in this study is in essence a process-based model which quantitatively describes metal uptake, internal disposition, elimination, and the processes of toxicity development. By using the model, the toxicologically relevant metal fraction can be separated from the metal in detoxified forms, making it possible to quantify the detoxification processes and to predict toxicity under chronic and fluctuating exposures. The model is a flexible and can be readily adapted according to any further knowledge on metal bioaccumulation and toxicity mechanisms. The framework of the model is theoretically applicable to other aquatic organisms

after slight modification, if necessary. In future studies, there are great potentials for integrating the BLM into the TK−TD model, which will enable the latter to derive site-specific and mechanistic no-effect concentrations for developing water quality criteria and enhance the scientific quality of ecological risk assessments.

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ASSOCIATED CONTENT

S Supporting Information *

Further theoretical considerations including model design, noeffect influx rate, and maximum exposure duration without toxicity; comparison between the one- and two-compartment model and details of model selection; toxicokinetic modeling of Cd for three other cladoceran species; calculation of ku of metals for modeling; computer code for the TK−TD model. This information is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the three anonymous reviewers for their constructive comments. This study was supported by the grant (2011M500072) from China Postdoctoral Science Foundation to Q.-G.T., and by program for Changjiang Scholars and Innovative Research Team in university (PCSIRT, IRT0941).

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REFERENCES

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