Application and validation of a biotic ligand model for calculating acute toxicity of lead to Moina dubia in lakes of Hanoi, Vietnam

It is increasingly being recognized that biotic ligand models (BLMs) can successfully predict the toxicity of divalent metals toward aquatic biota applied to temperate freshwater ecosystems. However, studies on the eutrophic lakes in tropical regions toward native tropical organisms, including Moina, are relatively limited. In this study, Moina dubia, the native organism of the Hanoi eutrophic urban lakes, were used in toxicological studies of lead (Pb); 24-h EC50 value of Pb was 523.19 µg/L under optimal living conditions for M. dubia in the laboratory. The constant binding of Pb2+ on M. dubia surface sites (log KPbBL = 2.38) was significantly low. Other stability constants were obtained under experiments as logKCaBL = 2.48, logKMgBL = 2.80, logKNaBL = 2.35, logKKBL = 2.49, and logKHBL = 3.026. A BLM was developed to calculate the acute toxicity (EC50-24 h) of lead on M. dubia based on the condition of the urban lakes of Hanoi. Validation with toxicity data in synthetic medium showed a coefficient determination of 79.16% and a mean absolute percentage error (MAPE) of 10.2%, while the validation with the toxicity data with natural water medium from 11 Hanoi lakes showed a coefficient determination of 73.7% and a MAPE of 13.66%. The BLM worked well with water at a pH of 7.0 to 8.0, but failed with water at a pH above 8.0. Eutrophic conditions proved to have a significant effect on the toxicity of lead on local zooplankton.


Introduction
Lead (Pb) is one of the most toxic non-essential metals to organisms (Pareja-Carrera et al. 2021). Lead is used widely in battery manufacturing, the aluminum industry, coating technology, printing, and mining, and metallurgy. Lead emissions in traffic and the burning of fossil fuels in industrial zones also cause lead pollution in the environment when it is deposited in water or soil (Borase et al. 2021). In many areas, lead pollution happens on the water surface. The concentration of lead in the surface water of Bangladeshi rivers ranges from 17 to 10,180 μg/L (Uddin and Jeong 2021). In China's Honghu, Guchenghu, and Taihu rivers, lead deposits are as high as 37.5-48.75 mg/kg (Yao et al. 2009). In Vietnam, lead concentrations in the surface waters of Hanoi, such as in the To Lich and Kim Nguu rivers, were in the range of 100-220 µg/L due to untreated wastewater (Nguyen et al. 2007). In another study in Vietnam of the northern rivers near the mining areas, Thai Nguyen, found the lead concentration in water used for agricultural irrigation ranged from 93.4 to 111.5 µg/L (Kikuchi et al. 2009). Communicated by Bruno Nunes. Lead is considered a dangerous element and may directly affect the growth and reproduction of organisms. The International Agency for Research on Cancer (IARC) has listed lead and its compounds as potentially carcinogenic substances in humans. The question is how to assess the risk of metal to aquatic ecosystems. The biotic ligand model (BLM) was developed more than 20 years to predict ecotoxicology, and it has been officially applied in many countries (DeForest et al. 2017(DeForest et al. , B.C 2019. In Asia, the BLM was developed for aquatic species in China in 2012 ) and more recently in 2017 (Zhou et al. 2011;Wang et al. 2017). Studies on BLM have been carried out in Japan since 2013, based mainly on toxicological data in other countries (Naito et al. 2010;Hayashi 2013). Most studies on the BLM in tropical regions used toxicological data collected from the temperate zone (Shoji and Taniguchi 2016).
BLMs have been developed for Cu , Ni (Deleebeeck et al. 2008), and Cd (Clifford and McGeer 2010). Lead is one of the metals studied by USEPA in the BLM development center (DeForest et al. 2017). The BLM has been evolving for a long time, but mostly on common species in Europe and America such as Baetis tricaudatus (mayfly), Ceriodaphnia dubia (cladoceran) (Niyogi and Wood 2004), Daphnia magna (DeForest et al. 2017), and Pimephales promelas (Mager et al. 2011). Due to the differences in the body size, metabolism rate, and adsorption ability of the surface of individual species, the application of model constants of European and American species is possibly inaccurate for species in tropical regions. The characteristic of surface water in tropical areas would affect the ability to predict the acute toxicology of metal. However, there are still limited studies on BLM in eutrophic lakes.
Moina dubia is a widely distributed zooplankton in aquatic bodies in Vietnam (Tam et al. 1999), Thailand, the Philippines, Indonesia (Korovchinsky 2013), and Sri Lanka (Fernando 1980). Eutrophic lakes play an important role in controlling the fertility of toxic algae. M. dubia is an important zooplankton in the food chain for maintaining species diversity in the lakes' food chain (Adeyemo et al. 1994). Moina in general and M. dubia, in particular, are very sensitive to pesticides and metals (von der Ohe and Liess 2004). Many studies have selected Moina to study metal toxicity (Zou and Bu 1994;Gama-Flores et al. 2008;Borase et al. 2021). Moina was recommended for the toxicity test in the application of BLM for guiding water quality control in Australia and New Zealand (Batley et al. 2014). Moina was also used in many metal availability and ecotoxicology studies (de Paiva Magalhães et al. 2015). Although Moina was sensitive to metal, few studies to develop BLM in tropical areas used Moina as the model's ligand. This paper discusses BLM model development for urban eutrophic lakes using M. dubia native zooplankton in Vietnam.

Study species and EC 50 determination
Moina dubia were collected from Truc Bach Lake (+ 21° 02′ 40.8″ N; + 105° 5′ 22.1″ E) located in Hanoi. They are abundant in this small urban and highly eutrophic lake (Hoang et al. 2017;Pham et al. 2018). In the laboratory, M. dubia were isolated using a Pasteur pipette. They were cultured in a common basal medium (Conklin and Provasoli 1977) at a temperature of ~ 24 °C, pH = ~ 7.5, under ambient light and a photoperiod of 12-h light: 12-h dark cycle. The acclimation period lasted 1 month (ca. 5-7 generations) to minimize the lake environmental background on the toxicity test results (Oh and Choi 2012). M. dubia were fed ad libitum with Chlorella vulgaris. C. vulgaris were centrifuged and washed to remove culture nutrients before feeding M. dubia at a 10 6 cells/mL density. The newborn M. dubia (< 24 h old) were elected randomly from the culture for toxicity tests.

Water characteristics of eutrophic urban lakes
Water samples were collected from eleven urban lakes in Hanoi city, Vietnam. These lakes are eutrophic and strongly affected by the process of rapid urbanization. The pH of the lakes was always high, mostly from 7.0 to 8.5. The sediment layers of these lakes were around 0.5 to 1 m with high metal contamination (Thuc and Dong 2020). The urban lakes serve as flooding control and wastewater purification for the city, thus containing many substances that affect metal toxicology in the water. Collective sampling in five places in each lake was applied. Samples were transferred to the laboratory and stored at 4 °C. The physical and chemical parameters included pH, DOC, chlorophyll-a, Ca 2+ , Mg 2+ , Na + , and K + . We conducted monitoring and water collection from January 2018 to May 2019. Water samples from two natural suburban lakes were also collected to test the impact of high pH on toxicity of lead on M.dubia.

Experimental design
To investigate the effects independently of the main cations including Ca 2+ , Mg 2+ , Na + , K + , and H + on lead toxicity, we adjusted one cation concentration while keeping all other concentrations as low as possible. The selection of the range adjustment of Ca 2+ , Mg 2+ , Na + , K + , and pH to perform toxicological experiments was based on the range of the main metal ions in Hanoi lakes observed in water quality monitoring and referenced the study of de Schamphelaere and Janssen (2002). The Ca 2+ concentration was adjusted from 3.36 to 115 mg/L, the Mg 2+ concentration was adjusted from 2.99 to 71.2 mg/L, the Na + concentration was adjusted from 3.5 to 74 mg/L, and K + was adjusted from 2.28 to 30.6 mg/L, while pH was kept at 7.5. The pH changed from 7 to 8.5 once M. dubia adapted to the basic condition, so pH < 7 would cause a problem for the metabolism of M. dubia. The composition of the experimental sets is described in supplementary data. Each cation set was adjusted to the pH and kept at room temperature until it met stability conditions before being used for acute tests. Each set was repeated four times and comprised at least five different cation concentrations. The selected cation concentrations represented a range of water surface characteristics of the urban lakes of Hanoi.

Preparation of the synthetic medium
CaCl 2 , MgSO 4 , NaCl, KCl, HCl, and NaOH (purity > 98%, Merck, Germany) were used to make the control medium following the guideline of OECD (2004). In the control medium, these necessary ions were in the lowest concentration to maintain M. dubia comfortably but did not affect the test in the impacts of Ca 2+ , Mg 2+ , Na + , K + , and pH. After adjusting in range of each ion selected, we added Pb 2+ to make up the concentration series of lead from 50 to 1500 µg. Except for the pH set, the medium was adjusted to pH 7.5 in the range of the eutrophic lakes. The buffer MOSP was used for the stability of the solution. All the medium was put into a 25 °C room 1 day before being used for the acute tests to reach near-equilibrium conditions.

Acute toxicity tests
The 24-h immobilization assay was conducted with neonate M. dubia (< 24 h-old age) following OECD Guidelines 202 (OECD 1984). The organisms were acclimated in the laboratory for 5-6 generations before being used for toxicology tests. Six treatments (control and five different lead concentrations) were performed for each test from the lowest to the highest lead concentration with four replications. The medium was filled to 50 mL in each cup. After 24 h exposure at 25 °C and 12 h light: 12 h dark, the number of immobilized neonates in each cup was checked and counted.

Estimating the equilibrium condition of ion and biotic ligand
A Pb 2+ adsorbent solution with four different concentrations of 50 µg/L, 100 µg/L, 200 µg/L, and 300 µg/L were prepared with standard solution Pb(NO 3 ) 2 1 g/L (Merk, Germany) in a soft water environment (hardness in Ca was 50 µg/L, with minimum nutritional ingredients). Since the adsorption of Pb 2+ on the ligand followed Langmuir's adsorption equilibrium equation (Playle et al. 1993), the equilibrium coefficient found was based on the different Pb 2+ adsorbent solutions. Each adsorption equilibrium statement depends on the different initial concentrations of Pb 2+ , which was selected in the range 0.27 to 1.02 µM following Tao et al. (2002). The amount of Pb 2+ adsorbed on the surface of the ligand depends on different pH conditions. The amount of Pb 2+ occupied on the surface of M. dubia varied directly with the concentration of Pb2 + in the water. The concentration of Pb 2+ in the water increases in acidic conditions; thus, the pH for this experiment should remain around 7.0. According to Playle et al. (1992), the pH of the micro-environment of the biotic ligand is slightly lower than the pH of the water environment; therefore, three scenarios of pH were adjusted by NaOH or HCl to three levels of 6.5, 6.8, and 7.0. The reconstituted solution was allowed to stabilize for 30 min before placing 10 M. dubia (< 24 h old) neonates in beakers with different lead concentrations and the lead-free solution as the control medium. The volume of the adsorbent solution was 250 mL. Samples of 10 ml were collected every 15 min at the initial adsorption stage for 1-h and then every 30 min. Samples taken were then measured for Pb 2+ concentration to find the adsorption equilibrium coefficient. Metal adsorption on the contact surface of living organisms is a form of complex bonds between metals and functional groups on the surface of biological cells. The adsorption equilibrium coefficient was calculated by the Langmuir adsorption equilibrium equation (Pham et al. 2018).

Model validation
The acute toxicity tests of lead to M. dubia were conducted with natural water collected from 11 lakes as the natural medium. The acute tests were performed with six lead treatments (one control and five different lead concentrations) and replicated four times (see the "Water characteristics of

Mathematical description of the BLM
The mathematical description of BLM following the approach of De Schamphelaere et al. (2002) applied in Pb according to Nolan et al. (2003), the speciation of Pb 2+ mainly caused toxicity to the aquatic organisms. In this model, only Pb 2+ was considered the cause of metal toxicity to M.dubia. The explanation of the equation is as follows: If CC BL is the total number of ions binding on the biotic ligand, the mass balance equation on the biotic ligand can be written as: (1) At the equilibrium statement of each ion (Me) on the surface biotic ligand, the equilibrium equation for binding of each cation can be written in form as: where Me is the Pb 2+ or Ca 2+ or Mg 2+ or Na + or K + or H + binding on the biotic ligand, and K MeBL is the stability constant for each Me to binding on the biotic ligand.
Combining Eqs. (1) and (2), the concentration of the Pb 2+ binding to the biotic ligand can be expressed as: = 1+K PbBL (Pb 2+ )+K CaBL (Ca 2+ )+K MgBL (Mg 2+ )+K NaBL (Na + )+K KBL (K + )+K HBL (K + ), Assuming that the complexation capacity is independent of the water quality characteristics, the fraction of the total amount of lead occupied on the biotic ligand (f PbBL ) Combining Eqs. (3) and (4), the total amount of lead occupied on the biotic ligand, with the BLM assumptions, to determine the magnitude of toxic effect and with a constant at 50% effect (f PbBL 50%), Eq. (4) can be expressed as: where EC 50-Pb2+ is the free lead ion activity resulting in 50% of M. dubia immobilized after 24 h of exposure. (Ca 2+ ), (Mg 2+ ), (Na + ), (K + ), and (H + ) are the concentrations of described ions in the water bodies. The stability constants K CaBL , K MgBL , K NaBL , K KBL , and K HBL for the binding of these cations to the BL were calculated from the relation between pH, Ca 2+ , Mg 2+ , Na + , K + , and EC 50Pb2+ . Assumption of the BLM concept is the linear relationships observed between EC 50 -Pb2+ and the mentioned ions.
Equation (5) showed that, there is a linear regression relationship between EC 50s and each ion (Ca 2+ ), (Mg 2+ ), (Na + ), (K + ), and (H + ) written in the form of y = a*x + b. In the case of Ca, the equation can be written as y = a Ca * Similar equations can be done with the other ions. The K HBL , K MgBL , K CaBL , K NaBL , and K KBL can be found if the solution of the following matrix was found:

Data treatment and statistics
Speciation calculations were conducted using the Windermere Humic Aqueous Model (WHAM) Ver 7.02 (http:// www. ceh. ac. uk/ produ cts/ softw are/ wham/). Speciation calculations were performed for all experimental treatments. EC 50-24 h expressed as dissolved lead were calculated from observed immobility at each lead concentration. Twenty-four hours expressed as free lead ion activity were calculated from observed immobility at each calculated free lead ion activity. EC 50 values were calculated using the trimmed Spearman-Karber method (Hamilton et al., 1977). All linear regressions were calculated using SPSS 20. The stability constants were received by solving the system of equation coding in Matlab environment.

Characteristics of water in the trophic lakes
The water temperature in eutrophic lakes varied widely from 16 to 35.4 °C. The temperature dropped from 15.5 to 16.5 °C in the winter but increased to 35.4 °C on summer days. The median pH value of eutrophic lakes in Hanoi in the database deviated from neutral to slightly basic (7.0-8.2). Many factors would affect the change in the pH of water bodies. First, the algae take up bicarbonate during photosynthesis and can disturb the H + balance in the water, causing pH variation between day and night (Acuña-Alonso et al., 2020). Second, anthropogenic activities, including discharging untreated domestic wastewater, would also affect the pH of urban lakes. The pH of water strongly affects metal toxicology since it affects the metal availability in water. Since the distribution of metal speciation depends on the pH of water, the variation of pH of water would cause transforming metals from sediment to water which may increase the effect of metal on aquatic organisms (Zhang et al. 2014). pH also causes discomfort to aquatic organisms as they live in permanently alkaline environments (Sakamoto et al., 2018). The data on nutrients (N total from 2.01 to 43.21 mg/L; P total from 0.24 to 1.03 mg/L; and chlorophyll-a from 67.8 to 230.6 mg/ m 3 ) in the eutrophic lakes was in agreement with a previous study (von der Ohe and Liess 2004) ( Table 1). The algae blooming would significantly change the pH value and the daily dissolved oxygen (DO) in the surface water. The DO varied widely from 4.06 to 11.24 mg/L depending on the metabolism of the algae (Cook and Gale 2005). The calcium and magnesium concentrations varied from 20.56 to 56.3 mg/L, and 4.24 mg/L to 12.98 mg/L, respectively.

Effect of major cation on acute Pb toxicity
An increase in Ca 2+ , Mg 2+ , Na + , and K + concentrations resulted in an elevated 24-h EC 50-Pb2+ . In these bioassay sets, observed EC 50s ranged from 283 to 518 nM for free lead ion activity. The results show a positive linear relation (p < 0.05) between the activities of Ca 2+ , Mg 2+ , Na + , and K + (Fig. 1b-e).
A positive linear regression between calcium concentration and the value of EC 50 indicated that calcium could reduce the toxic effect of lead on M. dubia. The impact of calcium on metal toxicity has been observed in many different aquatic species (Markich and Jeffree 1994;Chun-Sang 2016). According to Riethmuller et al. (2001), hardness does not directly affect the types speciation of lead in the medium but is influenced by significant changes in the acid-base balance of the solution, thereby indirectly changing the existence of the lead in the solution. The mobility lead concentration decreased when increasing the concentration of calcium in the medium. In addition, when Ca 2+ and Pb 2+ are highly concentrated in the ligand surface, M. dubia will prioritize absorption of calcium over the lead during metabolism and cell charge balance. High calcium concentration on the cell membranes of organisms can decrease the transport rate of the Pb across the cell membrane, thereby reducing the penetration of the Pb into the body (Favus et al.1989;Markich and Jeffree 1994).
The Mg 2+ concentration on the surface of the ligand creates a positive charge potential on the surface of the organism, which can limit lead absorption into the body (Shen et al., 2016). Experimental results showed that when the magnesium concentration in the environment increased, the amount of lead entering the organism decreased, reducing the toxicity of lead to M. dubia. Na + and K + were two metals that competed strongly with Pb 2+ on the organism's surface (Gramigni et al., 2009). The density of Na + and K + create a positive electric potential on the biological absorption surface, which reduces the possibility of Pb 2+ transport inside the organism. During the transportation of a Pb 2+ ion through the cell membrane, two Na + or K + ions are pumped out to maintain the charge balance on the membrane. Thus, Na + and K + also play a crucial role in regulating lead absorption into the body. An increase in Na + or K + concentration makes it difficult to absorb Pb 2+ , thus reducing the lead toxicity.

Effect of pH on lead toxicity
A pH test was conducted in the range of 7-8.5 to give an observed EC 50-24 h range from 241 to 518 nM for dissolved lead. The linear relationship between H + and EC 50 -Pb2+ would indicate the possibility of proton competition at the ligand surface (Fig. 1a). Two possible mechanisms are proposed. First, pH can affect the speciation of lead in the medium. When pH > 7.5, lead exists in the flexible forms Pb 2+ , and Pb(OH) 2 or PbCO 3 , and these forms would affect the amount of Pb 2+ speciation, which cause the main toxicity to M. dubia (Nolan et al. 2003). When the pH is low, there is mainly Pb 2+ , which is highly interactive with functional groups on the ligand surface. Second, the pH in the medium would affect the micro-environment of the biotic ligand, such as for fish (Playle 1998) or invertebrates (Gensemer and Playle, 1999). This can affect the interaction between the speciation of lead at the organism-water interface (Playle et al., 1992). In this study, the linear relation between H + and EC 50-Pb2+ was found in the pH range from 7.0 to 8.0 but not pH above 8.0. There may be a limitation in using pH to predict EC 50 -Pb2+ in the water with pH above 8.0 (Table 3). This could be because when pH exceeds 8.2, the lead in the medium is mainly in PbCO 3 or Pb (OH) 2 forms reducing the number of Pb 2+ ions in the water environment. In this case, not only Pb 2+ but other speciation of lead is bound to the ligand and transported to the organism. Other speciations of lead such as PbCO 3 or Pb(OH) 2 would disturb the prediction of lead toxicity to the biotic ligand. Other studies reported that Pb(OH) 2 or PbCO 3 had lower toxicity than the flexible form (Antunes and Kreager 2014). For this reason, we used the formula that expressed the relationship between pH in the range from 7.0 to 8.0 and EC 50 to calculate the constants K HBL , K MgBL , K CaBL , K NaBL , and K KBL .

Estimation of BLM parameters
The intercept and slope were obtained by conducting a linear regression analysis of the relationship between EC 50(Pb2+) and cation activity Ca 2+ , Mg 2+ , Na + , K + , and H + . The combination of the effect of the main cations was expressed in the matrix in Eq. (6). The solution of the matrix after speciation calculations and linear regression analyses ( Fig. 1) resulted in the estimation of the stability constants logK CaBL = 2.48, logK MgBL = 2.80, logK NaBL = 2.35, logK KBL = 2.49, and logK HBL = 3.026. These logKs were under the range of the constants reported by Playle et al. (1993) and but in the constant range reported from Paquin et al. (2002) described in Table 2, except for the K-constant, which has not been included in the current BLMs so far (McGeer et al. 2000). In this study, with the constant of K KBL = 2.49, we found that K + also caused a significant reduction of the toxicity of Pb 2+ . According to De , this is due to the presence of Na + and K + , which reduces the lead toxicity not only due to competition on the ligand surface but also by preventing the loss of plasma electrolytes . The constants for Ca 2+ , Mg 2+ , and Na + were slightly lower than those obtained for fish gills used in the BLM (Clifford and McGeer 2010). A higher K HBL showed H + had a significant contribution in proton competition to lead on the ligand surface.
The logK PbBL of Pb 2+ occupated on the biotic ligand was 2.38, one unit less than the logK HBL ∼ 5.4 for fish. The constant binding of lead to the biotic ligand surface (logK PbBL = 2.38) was conducted in a base pH toxicity test based on the Langmuir equation. The binding between lead and the surface of M. dubia as the biotic ligand was lower than the K PbBL = 6.0 of lead binding to gill fish reported by Macdonald et al. (2002) and K PbBL = 5.9 binding between Pb 2+ and algae (Chen et al., 2010). This may be because there are differences in binding Pb 2+ to specific biogenic chelating ligands such as aspartate and citrate on the surface of different biotic ligands (Flora and Pachauri, 2010). Significant differences in Ks for M. dubia and other species like algae, fish gill, and daphnia show the need to continue developing BLM for different types of species to achieve a better BLM performance.

BLM development and validation
Besides factors belonging to water solution effects, the f 50 PbBL in the model was assumed to EC 50 calculation would affect the variation of the BLM calculation. f 50 PbBL was the fraction of the total lead occupied on the biotic ligand, causing a 50% M. dubia effect in the toxic test. The fraction would be different among different biotic ligands and the different physical statements of the biotic ligand (Crémazy et al. 2013;Lock et al. 2006). The f 50 PbBL is slightly based on the references of previous results of different biotic ligands to obtain a better performance. In this study, the f 50 PbBL was adjusted from 0.27 to 0.38 and received the best performance at 0.34 (Fig. 2a). The coefficient of determination of the model describing the explainability of the model is 79.6%, indicating that using the model may determine 79.6% of the variation of EC 50 ; the rest was the factors the model cannot control. When using the model to determine the EC 50 value, the mean absolute percentage error (MAPE) was 10.2%. Thus, the model can calculate the acute toxicity of lead for Moina dubia with high accuracy.
Although the M. dubia BLM developed shows promise, there is still a need to further MAPE validate the data from experiments with a broader range of exposure conditions in the field with variations of DOC concentrations. For validation with natural water, the ANOVA analysis results show that the experimental EC 50 value significantly correlated with the EC 50 value calculated from the model (P-value = 0.0001) (Fig. 3). Comparison between the predicted EC 50 and observed EC 50 from synthetic waters was demonstrated in Fig. 3a.
Natural water samples were collected from 11 urban lakes in Hanoi, Vietnam, to validate the BLM. A single overall intrinsic density to Pb toxicity was used for all the data sets. The model has been calibrated with coefficient f 50 PbBL = 0.28 (range 0.25-0.35) (Fig. 2b). Calculation results of the model after adjustment showed the coefficient determination was 74%, and the MAPE was 13.66% (Fig. 3b). The results (b) f=0.28 R 2 =73.7% (a) f=0.34 R 2 = 79.16% Fig. 3 Predictive capacity of the BLM as shown by the relation between predicted and experimented 24-h EC 50 values of lead to M. dubia tested in a synthetic water medium and b 11 Hanoi lakes' water showed a larger dispersion between EC 50s obtained in the lab experiments with natural water and the calculated EC 50s from the model.
The reason is that, in the urban lake water environment, in addition to the main cations considered to affect the EC 50 values for M. dubia such as Ca 2+ , Mg 2+ , Na + , and K + , there are other cations and anions with complex properties and high concentrations. The magnitude also increases lead toxicity to M. dubia. In addition, the integration of other metals such as arsenic, cadmium, and copper, present in natural water will increase the toxicity of lead when conducting experiments with natural water. Besides, SO 4 2− and Cl − existing at higher concentrations may create bonds and affect the mobility of metals in the environment before directly participating in toxicity to organisms. Besides, these urban lakes sometimes received domestic wastewater or overflow containing high organic concentration, which will affect the model's prediction. Organic matter in natural water has function groups such as -COOH, -CHO, and -OH, which might change the speciation of ions and Pb 2+ , consequently affecting the calculation. In the BLM model, the ratio of humic: fulvic was 50:50 in the medium used. However, this ratio would be different in natural eutrophic water which causes the differences in the result of EC 50 s between experiment and calculation.
The results showed that, although BLM can successfully predict the EC 50 s for lakes with pH range 7.0 to 8.0, the BLM cannot predict lakes with high pH values above 8. We tested samples from the Tuy Lai and Quan Son lakes, located near limestone mountains that have pH above 8.2. The results showed that 24-h EC 50 calculated from the model was significantly higher than the experimental values even after model calibration (Table 3). Other reasons would be that the two lakes have higher hardness levels than other lakes, affecting the calculation of Pb speciation and the value of the EC 50 s calculated by the BLM.

Conclusion
The biotic ligand model (BLM) was developed to calculate the acute toxicity of Pb on natural zooplankton Moina dubia in the lakes of Hanoi with high accuracy. The constants of the main cations occupied on the surface of M. dubia obtained were slightly lower compared with those in the case of Daphnia in the previous studies. The BLMs have proven their usefulness in predicting acute metal toxicity in natural waters based on water characteristics, including pH and concentration of Ca 2+ , Mg 2+ , Na + , and K + ions. Based on the results presented in this study, we found that the BLM cannot predict the water environment with high pH, which happened in some hypereutrophic lakes. The BLM concept can be used to support the development of regulations to protect the aquatic environment. The study illustrates that the incorporation of bioavailability of metals in current water quality guidelines and risk assessments is indispensable. Based on this concept, further BLMs can be developed to investigate the toxicity of different metals on different aquatic organisms. These research studies can provide helpful information to address the risk of heavy metals in the ecology of surface waters.