INTRODUCTION

The acceleration of industrialization has released a large amount of metals into the aquatic environment (Hendriks 2013). Heavy metals not only pose potential risks to the survival, growth, and reproduction of plants and nonhuman animals (de Oliveira et al. 2018), but they can also affect the fertility and reproduction of humans through the food chain (Zhang et al. 2018). Therefore, how to effectively identify and manage heavy metal pollution is a major issue worldwide.

Previous studies on quantifying chemical toxicity have presented several approaches on the basis of certain theoretical propositions (Vaananen et al. 2018). Among these approaches, the classical dose–response model has frequently been used to relate internal metal concentration with toxicity (Fox and Billoir 2013; King et al. 2015). The dose–response model cannot predict effects in other exposure scenarios, such as long-term exposure, because it relies on a certain exposure endpoint (Delignette-Muller et al. 2017). The toxicokinetic–toxicodynamic (TK–TD) model (Schmitt et al. 2013; Swiatek et al. 2017) is a type of dynamic model that describes the cumulative dynamics of metals in vivo over time (Ducrot et al. 2016). Jager et al. (2011) integrated a kinetic model with different hypotheses of biological individuals into a framework and proposed the general unified threshold model for survival (GUTS) based on the general TK–TD model of mortality threshold. Stochastic death (GUTS–stochastic death) and individual tolerance (GUTS–IT) approaches were the most commonly used TD models in the GUTS framework. The GUTS–stochastic death model assumed that the threshold of lethal effect was fixed and was identical for all individuals. However, the GUTS–IT model assumed that the threshold of the lethal effect was distributed for all individuals and that once an individual threshold was exceeded, mortality immediately followed.

Compared with the dose–response model, the GUTS model took into account both time and concentration simultaneously. Up to now, few studies have compared applicability between the dose–response and GUTS models. Recently, in a study of the time-course survival of Lymnaea stagnalis exposed to cadmium (Cd), the GUTS model was found to produce more conservative estimates and to have lower uncertainty than the dose–response model for visual assessment (Baudrot et al. 2018). Studies are needed to evaluate the performance of these models in determining Cd toxicity in other organisms. In the present study, the model organism zebrafish (Danio rerio) was chosen to assess these models.

In general, heavy metal toxicity is assumed to be caused by binding with carriers or an ion pathway for the uptake of essential elements (Bridges and Zalups 2005). In zebrafish, it was observed that Cd²⁺ was taken up mainly through the potassium (K⁺), calcium (Ca²⁺), and magnesium (Mg²⁺) uptake channel, and that lead (Pb²⁺) was taken up by the Ca²⁺ and Mg²⁺ channels (Feng et al. 2018). Some studies (Hogstrand et al. 1996; Rogers et al. 2003) have demonstrated that Cd and Pb act as Ca analogs. In the present study, we simulated Pb toxicity to zebrafish with the dose–response and GUTS models to verify the reliability of the data and to evaluate model performance. The objective of our study was to model the time-course of survival of zebrafish exposed to Pb or Cd using the dose–response and GUTS models, to evaluate model applicability, and to determine whether Cd and Pb differed in their toxicity to zebrafish.

MATERIALS AND METHODS

Model approach

Dose–response model

In the toxicity experiments, the test organisms were exposed to different levels of metal test solutions, and survival rate was recorded at several time points. The deaths of the organisms were assumed to be independent of one another, and the average survival rate at a target time was expressed as a function of the contaminant concentration (c). The specific model equation followed that of Baudrot et al. (2018), with a slight modification of the log–logistic equation for the 3 parameters described as follows:

(1)

where f(c) is the survival rate of the test organisms at concentration (c) of heavy metal, d is the survival rate of test organisms in the control treatment, LC50 is the lethal concentration at which 50% mortality is observed, and b is the shape of the dose–response curve describing the effect strength of the pollutant. We assumed that d was equal to 1, because there was no mortality under the control treatment. Hence, the equation was transformed into Equation 2:

(2)

TK–TD models

The TK–TD model was applied for toxicological predictions. The GUTS model, a type of TK–TD model, has been widely used to predict the mortality of test organisms due to metal exposure. Of the 2 types of GUTS models (Forfait-Dubuc et al. 2012), GUTS–stochastic death assumes that all the test organisms would tolerate the same threshold concentration and that they would die if the internal concentration exceeded this threshold. The survival rate at exposure time S(t) can be expressed as Equation 3 as follows:

(3)

where t is the exposure time and h(τ) is the hazard rate, which can be expressed as Equation 4.

(4)

where b_w is the lethal rate, Z_w is the threshold concentration that the test organism can tolerate without dying, h_b is the background hazard rate, and is the internal concentration in the organism at a given exposure time (t).

The GUTS–IT model assumes that each organism has its own tolerance threshold, that an individual died immediately after its internal metal concentration exceeded the threshold, and that the tolerance threshold concentrations of metal in the organisms followed a statistical distribution from a population. The survival equation (Equation 5) is as follows:

(5)

where h_b is the background hazard rate, k_d is the discharge rate, α is the median effect concentration, β is the shape of distribution of the threshold, and t is the exposure time.

The model equation and parameter estimations of GUTS–stochastic death and GUTS–IT have been described by Virgile Baudrot (2018).

Statistical analysis

Using a log–logistic model, we analyzed the survival data at a given time (t) with the Morse package in R (Cran.r Project. 2019; Charles et al. 2018). We evaluated the model performance by comparing the R² and root mean square error (RMSE) between observed and predicted survival rates. The R² value was calculated with the following equation, and the RMSE was calculated in R software using the hydroGOF package.

(6)

where Q_{observed value} is the observed survival rate of the zebrafish, and Q_{fitted value} is the fitted survival rate estimated by the dose–response, GUTS–stochastic death, or GUTS–IT models.

RESULTS

Modeling of the required data sets

All the parameters could be estimated by the dose–response and GUTS models for either the Pb or Cd treatments with at least 3 sets of data where 1 set of data included one concentration at different exposure times. The dose–response relationships could be estimated with at least 3 sets of data (Figure 1). Moreover, the parameters that were estimated by the dose–response and GUTS models remained stable once 5 or more sets of data were used, which demonstrated that both the dose–response and GUTS models had identical data requirements.

Prediction of metal toxicity in zebrafish by different models

Prediction of Cd and Pb toxicity by the dose–response model

The parameters at the different exposure times were estimated by the dose–response model, and the results are shown in Table 1. The parameter b indicates the strength of the toxic effect: the b value increased over time up to 72 h, and then decreased slightly at 96 h. Furthermore, the b value at the 72-h exposure time was approximately twice that at 24 h, and thus the results showed that the effect strength of Cd in fish was strongest at the 72-h exposure time. The LC50 decreased gradually over time, as shown in Table 1 (Cd: by 63% decrease). For the Pb treatments, the b value decreased gradually over time, and the toxic effect strength of Pb on zebrafish was the greatest at 24 h. The LC50 value decreased as time increased (Pb: 34% decrease), as shown in Table 1. The findings demonstrate that the survival rate of zebrafish declined with increasing exposure time.

Table 1. Parameters of the dose-response model for zebrafish exposed to cadmium (Cd) and lead (Pb) at different exposure times

		b			LC50 (mg/L)
Metal	Time (h)	Average	Q2.5	Q97.5	Average	Q2.5	Q97.5
Cd	24	1.106	0.700	1.567	1.191	0.855	1.567
	48	1.963	1.420	2.626	0.491	0.393	0.615
	72	2.105	1.523	2.801	0.469	0.377	0.583
	96	2.021	1.464	2.707	0.445	0.356	0.555
Pb	24	2.941	2.091	4.011	1.869	1.568	2.247
	48	2.741	1.987	3.692	1.516	1.267	1.825
	72	2.870	2.083	3.902	1.449	1.215	1.730
	96	2.545	1.857	3.414	1.231	1.025	1.496

• b = effect strength; LC50 = median lethal concentration; Q_2.5 = 2.5% quantile; Q_97.5 = 97.5% quantile.

The predicted dose–response curve of Cd in fish at different exposure times is shown in Figure 2A. Survival rate decreased as exposure concentration increased for all exposure times. The curve for the 24-h exposure time was smoother than the curves for the other exposure times. In addition, the shape of the dose–response curve b was similar among the other exposure times, as shown in Table 1. All the observed survival rates fell into the confidence interval, as predicted by the dose–response model except for that at the 1-mg/L Cd concentration point at 24 h. The toxic effects of Cd on zebrafish exposed to different concentrations were well predicted by the dose–response model.

The toxic effects of Pb on zebrafish exposed to different concentrations were also well predicted by the dose–response model (Figure 2B). Survival rate decreased as exposure concentration increased at all exposure times. Moreover, the shape of the dose–response curve b was similar among the exposure times, as shown in Table 1. All the observed survival rates fell into the confidence interval predicted by the dose–response model except for those for Pb concentrations of 0.50 and 1 mg/L at 24 h.

The fitted performance of the dose–response model was higher for the Pb treatments than for the Cd treatments (Figure 3), with a higher R² value (0.97) and a lower RMSE (0.06) for the Pb treatments than for the Cd treatments (R² = 0.96, RMSE = 0.08). The survival rate of zebrafish was well simulated by the dose–response model.

Prediction of Cd and Pb toxicities by the GUTS models

The K_d estimated by GUTS–stochastic death (Pb: 0.10; Cd: 0.77) was approximately 25 to 30 times that estimated by GUTS–IT (Pb: 0.01; Cd: 0.02), and the background rate (h_b) simulated by GUTS–stochastic death (Pb: 3.70 × 10^–4; Cd: 1.68 × 10^–4) was approximately twice that estimated by GUTS–IT (Pb: 1.27 × 10^–4; Cd: 0.82 × 10^–4; Table 2). For the Cd treatments, the no-effect concentration (Z_w) from the GUTS–stochastic death model and the median effect concentration (α) from the GUTS–IT model were 0.13 and 0.42, respectively, demonstrating a difference in survival rate prediction between these 2 models. The GUTS–IT model assumes differences in sensitivity among individuals, with each individual having a different threshold concentration. A more sensitive individual will die at lower Cd concentrations, which leads to an underestimation of the survival rate at low Cd concentrations.

Table 2. Comparison of the parameters estimated by general unified threshold model for survival–stochastic death (GUTS–SD) and GUTS–individual tolerance (IT)

		GUTS–SD			GUTS–IT
Metal	Parameter	Average	Q2.5	Q97.5	Average	Q2.5	Q97.5
Cd	kd × 10–3	770.2	194.9	1118	20.55	8.808	33.87
	hb × 10–4	1.675	0.114	7.594	0.822	0.045	5.494
	Zw or α	0.127	0.065	0.197	0.416	0.229	0.588
Pb	kd × 10–3	98.900	24.360	122.600	3.590	2.332	5.606
	hb × 10–4	3.700	0.100	10.100	1.266	0.055	8.391
	Zw or α	0.769	0.349	0.918	1.176	0.927	1.506

• Q_2.5 = 2.5% quantile; Q_97.5 97.5% quantile; k_d = discharge rate; h_b = background hazard rate; Z_w = no-effect concentration; a = median effect concentration.

For the Pb treatments, the Z_w in the GUTS–stochastic death model and the α in the GUTS–IT model were 0.77 and 1.18 mg/L, respectively, indicating a difference in survival rate prediction between GUTS–stochastic death and GUTS–IT. In GUTS–stochastic death, when the concentration in the body was lower than 0.77 mg/L, the zebrafish remained alive. However, in GUTS–IT, when it reached 1.18 mg/L, death occurred.

The survival rates of zebrafish at external concentrations of 0 and 0.10 mg/L Cd were adequately estimated by the GUTS–stochastic death model (Figure 4A). For the other exposure concentrations, all survival rates fit well except for the rate at 48 h. As shown in Figure 4B, the survival rate was underestimated at 0.10 mg/L Cd by the GUTS–IT model, yet overestimated at the remaining exposure concentrations except for 1 and 2 mg/L Cd at 24 h.

The GUTS–stochastic death model underestimated the survival rate at 0 mg/L Pb (Figure 4C), because the h_b rate of Pb was not 0 (Table 2). The effective concentration was 0.77 mg/L, and, if the internal concentration in the organism was below the threshold concentration, the predicted survival rate was equal to that in the control treatment. Hence, the predicted survival rate was equivalent across the Pb exposure concentrations of 0, 0.25, and 0.50 mg/L. However, no death occurred at the 0.50 mg/L Pb concentration, which caused overestimation of the survival rate at this concentration by the GUTS–stochastic death model. Survival rate fit perfectly when the external concentration was 1 mg/L Pb, but was underestimated and overestimated at 2 and 4 mg/L Pb exposure concentrations, respectively. For the GUTS–IT model simulation, as shown in Figure 4D, survival rate fit perfectly at 0 and 0.25 mg/L Pb concentrations. However, survival rate was overestimated at 0.50 and 4 mg/L Pb, and underestimated at 1 and 2 mg/L Pb.

Fitted performance of the GUTS model was higher for the Pb treatments than for the Cd treatments. Moreover, the fitted performance of GUTS–stochastic death (R² = 0.94; RMSE = 0.09) was comparable to that of the GUTS–IT model (R² = 0.94; RMSE = 0.09) for the Cd treatments, whereas for the Pb treatments, the fitted performance of GUTS–IT (R² = 0.96; RMSE = 0.07) was better than that of GUTS–stochastic death (R² = 0.94; RMSE = 0.09). It is noteworthy that there was little difference in fitted performance between the dose–response and GUTS models, which had similar R² and RMSE values (Figures 3 and 5).

DISCUSSION

The LC50 in zebrafish decreased gradually as exposure time increased in both Cd and Pb treatments; the same pattern has probably been found in other organisms and under different exposure scenarios, as observed for Gammarus pulex exposed to propiconazole (Nyman et al. 2012). We also noted that the magnitude of LC50 exposed to Pb and Cd treatments was Cd < Pb, which was inconsistent with the findings of Smith et al. (2015). This difference between studies might be due to species specificity in metal uptake. Accordingly, the Cd toxicity to zebrafish was stronger than that of Pb toxicity, indicating greater resistance to Pb than to Cd in the zebrafish. Furthermore, this result indirectly suggests that the no-effect concentration (Z) or median effect concentration (α) of Pb was higher than that of Cd, which was consistent with our results using the GUTS–stochastic death or GUTS–IT models. However, the quantitative relevance of LC50 and the no-effect concentration (Z) or median effect concentration (α) needs further investigation. In addition, the parameters K_d and b were derived by dose-response model and GUTS model, respectively, for Pb and Cd exposures. Our results show that the discharge rate (K_d) of zebrafish exposed to Cd (GUTS–stochastic death: 0.77; GUTS–IT: 0.02) was higher than that of fish exposed to Pb (GUTS–stochastic death: 0.10; GUTS–IT: 0.01), suggesting that Pb was higher in the body of the zebrafish, and indirectly indicating that the effect strength (b) of Pb was stronger than that of Cd. Moreover, the effect strength (b) of Pb was strongest at 72 h, whereas that of Cd was strongest at 24 h, possibly because of different Cd and Pb metabolism in zebrafish. However, the underlying effect mechanism requires investigation.

Our results showed that the data requirements were identical for both the dose–response and GUTS models. Evaluation of the quality of model predictions should be performed from both qualitative and quantitative perspectives. Qualitatively, the overall response pattern in the data was matched by the model outputs (Figures 2 and 4). Quantitatively, the goodness-of-fit of the observed and fitted values was evaluated based on R² and RMSE, which were compared among the different models. The goodness-of-fit of the GUTS models was slightly smaller than that of the dose–response model. This difference was possibly due to the deviation between the observed and fitted values, which was mainly caused by the dominant parameters of the GUTS model (K_d, Z, or α) that had been correlated for laboratories and had an influence on the survival rate over time (Baudrot et al. 2018). However, compared with the dose–response model, the GUTS models had higher predictive ability, which could be extrapolated to predict the survival rate of organisms under other conditions (Ashauer and Escher 2010). Pollutant exposure conditions in the real environment are more complex than those in the laboratory; for example, pulse exposure (Nyman et al. 2012) and multiple metal exposures (Gao et al. 2016) occur in nature. In addition, the dose–response model can fit the survival rate at a given time, but cannot fit the survival rate at another time. However, the GUTS model can not only model the survival rate at a certain time, but can also simulate survival rate at another time based on survival rate at that time, and there would be no need for animals in toxicity testing of metals at another time (Forfait-Dubuc et al. 2012). Considering that animal testing costs €10 billion every year and uses more than 100 million animals, it has been recommended that animal testing be reduced as much as possible (Hartung 2009). The GUTS models had a greater ability than the dose–response model to predict toxicity. Moreover, the dose–response model is empirical, with no information on mechanisms of toxic action, whereas the GUTS model incorporates some mechanistic understanding (Brock et al. 2010; Baudrot et al. 2018).

The current paradigm of GUTS for most metals is spillover, in which metals are bound by metal-binding proteins to a threshold, above which free metals spill over into the cell and cause toxicity (Morcillo et al. 2016). Whereas the metal-binding proteins can be measured with current technology, free metals in the body cannot yet be distinguished and individually measured. The threshold estimated quantitatively by the GUTS model can approximately reflect the mechanism underlying mortality (Ashauer et al. 2015). Thus the GUTS model has greater potentiality for toxicity prediction than the dose–response model.

CONCLUSIONS

The present study demonstrated that Pb toxicity to zebrafish is stronger than Cd toxicity. For either the Pb or Cd treatments, we found that the data requirements were identical for both the dose–response and GUTS models. In addition, there was a negligible difference between the GUTS models and the dose–response model in simulating survival rate. Moreover, compared with the dose–response model, the GUTS model can be extrapolated to predict the survival rate of organisms at any time. The data requirements, fit performance, and applicability indicate that the GUTS model has greater potential than the dose–response model for the prediction of metal toxicity.