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QSAR model for predicting the toxicity of organic compounds to fathead minnow

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Abstract

In this work, a new norm descriptor is proposed based on atomic properties. A quantitative structure-activity relationship (QSAR) model for predicting the toxicity of organic compounds to fathead minnow is further developed by norm descriptors. Results indicate that this new model based on the norm descriptors has satisfactory predictive results with the squared correlation coefficient (R2) and squared relation coefficient of the cross validation (Q2) of 0.8174 and 0.7923, respectively. Combining with Y-randomization test, applicability domain test, and comparison with other references, calculation results indicate that the QSAR model performs well both in the stability and the accuracy with wide application domain, which might be further used effectively for the safe and risk assessment of various organics.

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Funding

This work was supported by the National Natural Science Foundation of China (21676203 and 21808167).

Author information

Authors and Affiliations

  1. School of Marine and Environmental Science, Tianjin University of Science and Technology, 13 St. 29, TEDA, 300457, Tianjin, People’s Republic of China

    Qingzhu Jia & Yunpeng Zhao

  2. School of Chemical Engineering and Material Science, Tianjin University of Science and Technology, 13 St. 29, TEDA, 300457, Tianjin, People’s Republic of China

    Fangyou Yan & Qiang Wang

Authors
  1. Qingzhu Jia
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  2. Yunpeng Zhao
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  3. Fangyou Yan
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  4. Qiang Wang
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Corresponding author

Correspondence to Qiang Wang.

Additional information

Responsible editor: Marcus Schulz

Electronic supplementary material

Table S1

(XLSX 74 kb)

Appendix

Appendix

The 364th molecule (acetic acid) was shown as an example and the molecular structure was as follows and structure of chemicals were optimized and obtained the most stable molecule structure.

figure a

Firstly, by Eqs. (1)–(4), the position matrices (Mm, m = 1,2,3,4) were calculated and shown as follow:

$$ {M}_{1=}\left[\begin{array}{cccccccc}0& 1& 1& 1& 2& 2& 2& 2\\ {}1& 0& 2& 2& 1& 1& 1& 3\\ {}1& 2& 0& 2& 3& 3& 3& 3\\ {}1& 2& 2& 0& 3& 3& 3& 1\\ {}2& 1& 3& 3& 0& 2& 2& 4\\ {}2& 1& 3& 3& 2& 0& 2& 4\\ {}2& 1& 3& 3& 2& 2& 0& 4\\ {}2& 3& 3& 1& 4& 4& 4& 0\end{array}\right] $$
$$ {M}_{2=}\left[\begin{array}{cccccccc}0& 1& 1& 1& 0& 0& 0& 0\\ {}1& 0& 0& 0& 1& 1& 1& 0\\ {}1& 0& 0& 0& 0& 0& 0& 0\\ {}1& 0& 0& 0& 0& 0& 0& 1\\ {}0& 1& 0& 0& 0& 0& 0& 0\\ {}0& 1& 0& 0& 0& 0& 0& 0\\ {}0& 1& 0& 0& 0& 0& 0& 0\\ {}0& 0& 0& 1& 0& 0& 0& 0\end{array}\right] $$
$$ {M}_{3=}\left[\begin{array}{cccccccc}0& 0& 0& 0& 2& 2& 2& 2\\ {}0& 0& 2& 2& 0& 0& 0& 0\\ {}0& 2& 0& 2& 0& 0& 0& 0\\ {}0& 2& 2& 0& 0& 0& 0& 0\\ {}2& 0& 0& 0& 0& 2& 2& 0\\ {}2& 0& 0& 0& 2& 0& 2& 0\\ {}2& 0& 0& 0& 2& 2& 0& 0\\ {}2& 0& 0& 0& 0& 0& 0& 0\end{array}\right] $$
$$ {M}_{4=}\left[\begin{array}{cccccccc}0& 0.6496& 0.8221& 0.7187& 0.4619& 0.4621& 0.4621& 0.5262\\ {}0.6496& 0& 0.4056& 0.4119& 0.9219& 0.9205& 0.9205& 0.3072\\ {}0.8221& 0.4056& 0& 0.4388& 0.3025& 0.3555& 0.3555& 0.4384\\ {}0.7187& 0.4119& 0.4388& 0& 0.4096& 0.3174& 0.3174& 1.0099\\ {}0.4619& 0.9219& 0.3025& 0.4096& 0& 0.5644& 0.5644& 0.2931\\ {}0.4621& 0.9205& 0.3555& 0.3174& 0.5644& 0& 0.5674& 0.2563\\ {}0.4621& 0.9205& 0.3555& 0.3174& 0.5644& 0.5674& 0& 0.2563\\ {}0.5262& 0.3072& 0.4384& 1.0099& 0.2931& 0.2563& 0.2563& 0\end{array}\right] $$

Then, by Eqs. (5)–(9), the property matrices (MEn, n = 1, 2, 3, 4, 5) were calculated and shown as follows:

  • ME1 = [5.6549 5.6549 4.3982 4.3982 3.7699 3.7699 3.7699 3.7699]T

  • ME2 = [2.5500 2.5500 3.4400 3.4400 2.2000 2.2000 2.2000 2.2000]T

  • ME3 = [0.0183 0.0067 0.1353 0.0498 0.1353 0.1353 0.1353 0.1353]T

  • ME4 = [0.2078 0.2078 0.2018 0.2018 0.2323 0.2323 0.2323 0.2323]T

  • ME5 = [1.0865 1.0865 1.3139 1.3139 1.3120 1.3120 1.3120 1.3120]T

The combinatorial matrices were performed by Eqs. (10)–(12). Finally, the value of the descriptors were obtained by Eqs. (13)–(15) and the largest eigenvalue of the matrix (MB,m,n) also need to calculate. The descriptors were shown in the Table 4 which were selected to predict the toxicity to fathead minnow.

Table 4 Descriptors for predicting the toxicity to fathead minnow
Full size table

Based on above, the pLC50 was calculated by Eq. (16).

$$ {\displaystyle \begin{array}{l}\mathrm{p}L{C}_{50}=1.3402+\sum \limits_{k=1}^{10}{b}_k{\left\Vert {V}_k\right\Vert}_1+\sum \limits_{k=11}^{19}{b}_k{\left\Vert {V}_k\right\Vert}_2\\ {}\kern5.25em +\sum \limits_{k=20}^{33}{b}_k{\left\Vert {V}_k\right\Vert}_{\mathrm{F}}+\sum \limits_{k=34}^{35}{b}_k{\left\Vert {V}_k\right\Vert}_{\lambda}\kern13.5em \\ {}\kern2.25em =2.690\left(\mathrm{mol}/\mathrm{L}\right)\end{array}} $$

The predicted toxicity value for fathead minnow was 2.690 mol/L, and the experimental value was 2.850 mol/L.

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Jia, Q., Zhao, Y., Yan, F. et al. QSAR model for predicting the toxicity of organic compounds to fathead minnow. Environ Sci Pollut Res 25, 35420–35428 (2018). https://doi.org/10.1007/s11356-018-3434-8

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