# Quantitative Representation of Water Quality Biotoxicity by Algal Photosynthetic Inhibition

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## Abstract

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_{abs}), Comprehensive Parameter Index (CPI) and Performance Index of Comprehensive Toxicity Effect (PI

_{cte}), as quantitative toxicity characteristic parameters. The paper compared the univariate curve fitting results with the multivariate data-driven model results and investigated the effectiveness of Back Propagation(BP) Neural Network and Support Vector Machine for Regression (SVR) models to enhance the accuracy and stability of toxicity detection. Using Dichlorophenyl Dimethylurea (DCMU) samples as an example, the mean Relative Root Mean Square Error (RRMSE) corresponding to the optimal parameter PI

_{cte}for the dose-effect curve fitting was 1.246 in the concentration range of 1.25–200 µg/L. On the other hand, the mean RRMSEs corresponding to the results of the BP neural network and SVR models were 0.506 and 0.474, respectively. Notably, BP neural network exhibited excellent prediction accuracy in the medium-high concentration range of 7.5–200 µg/L, with a mean RRSME of only 0.056. Regarding the stability of the results, the mean Relative Standard Deviation (RSD) of the univariate dose-effect curve results was 15.1% within the concentration range of 50–200 µg/L. In contrast, the mean RSDs for both BP neural network and SVR results were less than 5%. In the concentration range of 1.25–200 µg/L, the mean RSDs were 6.1% and 16.5%, with the BP neural network performing well. The experimental results of Atrazine were analyzed to further validate the effectiveness of the BP neural network in improving the accuracy and stability of results. These findings provided valuable insights for the development of biotoxicity detection by using the algae photosynthetic inhibition method.

## 1. Introduction

## 2. Algorithm

#### 2.1. BP Neural Network

_{NNR}is the predicted output of the output layer, the pollutant concentration predicted by the neural network. ${I}_{i}$ represents the inhibition rate of photosynthetic fluorescence parameters after normalization, ${y}_{h}$ is the output of the hidden layer, ${f}_{1}$ is the S-shaped transfer function between the input layer and the hidden layer, ${f}_{2}$ is the linear transfer function between the hidden layer and the output layer, ${W}_{ih}$ is the connection weights between the input layer and the hidden layer, ${W}_{hj}$ is the connection weight between the hidden layer and the output layer. If the obtained output does not match the target output, the difference between the two is backward propagated, and the connection weights between layers are adjusted. The formulas for updating weights are

#### 2.2. Support Vector Machine for Regression

## 3. Experiment Measurement and Parameters Selection

#### 3.1. Experimental Measurement

#### 3.2. Parameters Selection

_{abs}) [12,13,14,15]. Wang et al. [15] examined the stress response of Microcystic aerugionosa and Pseudokirchneriella subcapitata to Tetracycline and concluded that the maximum quantum yield of photosystem PSII (Fv/Fm) is a suitable indicator for Tetracycline toxicity detection. Li et al. [14] presented that Fv/Fm can be used to assess the toxicity of Cu

^{2+}. Strasser [4] constructed PI

_{abs}based on a theoretical model of biofilm energy flow, considering the energy flow during photosynthesis. Sun et al. [16] demonstrated that PI

_{abs}are the most convincing parameters among all fluorescence parameters by comparing the effects of Atrazine on different parameters of Chlorella. Based on the fact that the toxic stress caused the distortion of the algal fluorescence kinetic curve (OJIP), and the degree of change was proportional to the intensity of toxicity (as shown in Figure 2), some researchers extracted information on curve variability and obtained comprehensive fluorescence parameters to characterize the biological toxicity of water bodies, such as Comprehensive Parameter Index (CPI) and Performance Index of Comprehensive Toxicity Effect (PI

_{cte}). Moreover, they proved that the comprehensive parameters were superior in terms of toxicity response, minimum detection limit, maximum response concentration, stability, and reproducibility under stress with DCMU, Dibromothymoquinone (DBMIB), Methyl Viologen (MV), Malathion and Carbofuran [17,18].

_{abs}, comprehensive parameters CPI and PI

_{cte}, would be extracted and used as input parameters for univariate dose–effect curve fitting and multivariate BP neural network and SVR.

## 4. Method and Results

_{abs}, CPI and PI

_{cte}as independent variables, while the sample concentration served as the dependent variable. We established n experimental concentrations and used n-1 of them as the training set and 1 as the test set to obtain predicted results for all samples. We evaluated the accuracy of predictions using the Relative Root Mean Square Error (RRMSE) and the stability using the Relative Standard Deviation (RSD) [19].

#### 4.1. Analysis of Single Parameter for Dose–Effect Curve Fitting

_{abs}, CPI and PI

_{cte}variables were set in a dose–effect curve fitting independently to predict concentration. The results presented that RRMSEs of samples in concentrations of 0.625 µg/L and 0.75 µg/L were greater than 10 and thus not significantly reliable. Only results in the effective concentrations range of 1.25–200 µg/L were included below. Comparing the accuracy of the prediction results for different parameters, RRMSEs corresponding to Fv/Fm, PI

_{abs}, CPI and PI

_{cte}were 2.25, 1.31, 1.54 and 1.25, respectively. The three comprehensive parameters predicted higher accuracy than Fv/Fm alone, with PI

_{cte}having the lowest RRMSE and a 44.9% decrease compared to Fv/Fm. This suggested that the comprehensive parameters reflect the effects of multiple nodes, rather than one node of the photosynthesis process, and provide more valid information and greater accuracy in predicting samples of unknown concentrations. Further analysis of the trend of the RRMSE for each parameter with increasing concentration showed that the RRMSE of the three comprehensive parameters rapidly decreased with increasing concentration and stabilized in the middle and high range. However, the accuracy and the stability of predictions were not high enough, as shown in Figure 3a.

_{abs}, CPI and PI

_{cte}were 35.4%, 19.9%, 17.2% and 15.1%, respectively, while the PI

_{cte}parameter had the smallest RSD, which was reduced by 57.3% relative to Fv/Fm, as shown in Figure 3b.

#### 4.2. Analysis of Multi-Parameters for Data-Driven Model

_{abs}, CPI and PI

_{cte}were used as the independent variables for regression analysis in the data-driven model, and the concentration of samples was used as the dependent variable. Univariate dose–effect curves for PI

_{cte}were compared to multivariate input predictions using BP neural network and SVR, as indicated in Table 2.

_{cte}was 15.1% in the effective concentration interval (50–200 µg/L), while both data-driven models showed mean RSDs of less than 5% in this concentration region. For the effective concentration interval (1.25–200 µg/L), the RSDs of the multivariate BP neural network and SVR predictions decreased with increasing concentration, with mean values of 6.1% and 16.5%, respectively, and the BP neural network predictions were more stable.

#### 4.3. Experimental Verification of the Other Substance

_{abs}, CPI and PI

_{cte}inhibition rate used as independent variables, and with the concentration of the samples used as the dependent variable. The mean RRMSEs in the effective concentration range (1.25–200 µg/L) were obtained for each parameter and were 2.20, 1.59, 1.40 and 1.40, respectively. The predictions of the three comprehensive parameters were found to be more accurate than the common parameter Fv/Fm, and there were the most accurate results for CPI and PI

_{cte}. The mean RSDs corresponding to the parameters Fv/Fm, PI

_{abs}, CPI and PI

_{cte}in the effective concentration interval (50–200 µg/L) were 16.4%, 16.7%, 19.7% and 17.0%, respectively. There was no significant difference in the RSDs of the predicted results for the four parameters using a one-ANOVA analysis of variance.

_{cte}for dose-effect fitting. In the whole concentration region, the RRMSEs of the BP neural network predictions remained basically unchanged with concentration, demonstrating good accuracy. Additionally, in the effective concentration region (50–200 µg/L), the mean RSD of the BP neural network predictions was 9.8%, lower than the dose-effect curve fitting results. These results were consistent with those obtained from DCMU samples in Section 4.2, which further illustrated the ability of BP neural networks to significantly improve the accuracy and stability of toxicity detection of photosynthetic inhibition effects in algae.

## 5. Conclusions

_{abs}, CPI and PI

_{cte}. We compared and analyzed the accuracy and stability of the inversion results of the univariate dose–effect curve and multivariate BP neural network and SVR. Firstly, we analyzed the results of the four parameters entered individually into the dose–effect curve for DCMU samples. The mean RRMSE and RSD values corresponding to the comprehensive parameter PI

_{cte}were 1.26 (1.25–200 µg/L) and 15.1% (50–200 µg/L), respectively, which were better than those of the other parameters but not sufficiently high. We then compared the results of the BP neural network and SVR with multivariate input. The corresponding mean RRMSEs were 0.506 and 0.474, respectively, with a mean RRMSE of only 0.056 in the medium to high concentration range (7.5–200 µg/L) for the BP neural network. The BP neural network also exhibited good stability, with an average RSD of only 6.1% (1.25–200 µg/L). Finally, the experimental finding of Atrazine samples further verified that the BP neural network could effectively improve the accuracy and stability of algal photosynthesis inhibition methods. In the next step, the BP neural network quantitative analysis will be optimized for the practical situation of the algal photosynthetic inhibition method on biotoxicity detection.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 3.**Predictions of DCMU by dose–effect curve-fitting (

**a**) RRMSEs trend with concentration (

**b**) RSDs trend with concentration.

**Figure 4.**Predictions of DCMU by data-driven models (

**a**) RRMSEs trend of concentration (

**b**) RSDs trend of concentration. (Note: BPNN stands for BP neural network).

**Figure 5.**Predictions of Atrazine by data-driven models (

**a**) RRMSEs trend of concentration (

**b**) RSDs trend of concentration.

Toxin | Concentrations Tested | Stress Time |
---|---|---|

DCMU | 0.625, 0.75, 1.25, 1.5, 2.5, 3.75, 5, 7.5, 10, 15, 25, 32.5, 50, 75, 100, 150, 200 μg /L | 15 min |

Atrazine | 0.625, 0.75, 1.25, 1.5, 2.5, 3.75, 5, 7.5, 10, 15, 25, 32.5, 50, 75, 100, 150, 200 μg/L | 15 min |

Sample Groups | Concentration µg/L | RRMSE | RSD | ||||
---|---|---|---|---|---|---|---|

Dose–Effect Curve | SVR | BP Neural Network | Dose–Effect Curve | SVR | BP Neural Network | ||

1 | 0.625 | 16.266 | 9.923 | 8.867 | -- | 0.341 | 0.295 |

2 | 0.75 | 13.389 | 4.913 | 5.318 | -- | 0.390 | 0.385 |

3 | 1.25 | 7.633 | 0.875 | 2.518 | -- | 0.650 | 0.069 |

4 | 2.5 | 3.317 | 0.596 | 2.483 | -- | 0.078 | 0.125 |

5 | 3.75 | 1.878 | 0.435 | 0.959 | -- | 0.251 | 0.030 |

6 | 5 | 1.158 | 0.432 | 0.564 | -- | 0.485 | 0.113 |

7 | 7.5 | 0.439 | 0.831 | 0.072 | - | 0.102 | 0.074 |

8 | 10 | 0.079 | 0.331 | 0.162 | -- | 0.325 | 0.138 |

9 | 15 | 0.281 | 0.565 | 0.048 | -- | 0.121 | 0.048 |

10 | 25 | 0.568 | 0.339 | 0.050 | -- | 0.147 | 0.051 |

11 | 32.5 | 0.667 | 0.254 | 0.015 | 0.002 | 0.075 | 0.008 |

12 | 50 | 0.467 | 0.174 | 0.042 | 0.112 | 0.013 | 0.028 |

13 | 65 | 0.228 | 0.110 | 0.046 | 0.192 | 0.015 | 0.043 |

14 | 100 | 0.323 | 0.392 | 0.080 | 0.313 | 0.041 | 0.082 |

15 | 150 | 0.166 | 0.606 | 0.030 | 0.098 | 0.004 | 0.030 |

16 | 200 | 0.248 | 0.699 | 0.017 | 0.039 | 0.007 | 0.016 |

Average (µg/L) | 1.246 | 0.474 | 0.506 | 0.151 | 0.165 | 0.061 |

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**MDPI and ACS Style**

Hu, L.; Liang, T.; Yin, G.; Zhao, N.
Quantitative Representation of Water Quality Biotoxicity by Algal Photosynthetic Inhibition. *Toxics* **2023**, *11*, 493.
https://doi.org/10.3390/toxics11060493

**AMA Style**

Hu L, Liang T, Yin G, Zhao N.
Quantitative Representation of Water Quality Biotoxicity by Algal Photosynthetic Inhibition. *Toxics*. 2023; 11(6):493.
https://doi.org/10.3390/toxics11060493

**Chicago/Turabian Style**

Hu, Li, Tianhong Liang, Gaofang Yin, and Nanjing Zhao.
2023. "Quantitative Representation of Water Quality Biotoxicity by Algal Photosynthetic Inhibition" *Toxics* 11, no. 6: 493.
https://doi.org/10.3390/toxics11060493