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Contribution of Modified Harary Index to Predict Kováts Retention Indices for a Set of PAHs

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Abstract

A quantitative structure–retention relationship (QSRR) study was performed to correlate descriptors representing molecular structures to the Kováts retention indices of polycyclic aromatic hydrocarbon compounds. The complete set of 37 compounds was divided randomly into a training set of 26 compounds and a test set of 11 compounds. In the pool of descriptors calculated using Dragon and Hyperchem software, the modified Harary index (\( H^{\prime\prime} \)) developed by our team was added. The best selected descriptors by genetic algorithm to build the three linear models were: the first-order Randić connectivity index (\( {}^{1}\chi \)), \( H^{\prime\prime} \) and the third-order valence connectivity index (\( {}^{3}\chi_{p}^{v} \)). The selected model was compared with the one built with \( {}^{1}\chi \), the first Harary index (implanted in Dragon H) and \( {}^{3}\chi_{p}^{v} \). Statistical analysis showed that the model with modified Harary index (R 2 = 99.25, SD 5.82, F = 1517.74) produces better correlation with Kováts retention indices than the one implanted in Dragon (R 2 = 98.20, SD 9.02, F = 626.09). The final QSRR was internally and externally validated. The leave-one-out, cross-validation, bootstrapping, and y-randomization test indicated that the final model is robust and has no chance correlation. The external validations indicated that the model with modified Harary index showed a good predictive power. The mechanistic interpretation of QSRR model was carried out according to the definition of descriptors. Therefore, the result meets the five principles recommended by the Organization for Economic Co-operation and Development for validation of QSRR model.

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References

  1. Karelson M, Lobanov VS, Katritzky AR (1996) Quantum-chemical descriptors in QSAR/QSPR studies. Chem Rev 96:1027–1044

    Article  CAS  Google Scholar 

  2. Santos FJ, Galceran MT (2002) The application of gas chromatography to environmental analysis, TrAC. Trends Anal Chem 21:672–685

    Article  CAS  Google Scholar 

  3. Kaliszan R, Foks H (1977) The relationship between the RM values and the connectivity indices for pyrazine carbothioamide derivatives. Chromatographia 10:346–349

    Article  CAS  Google Scholar 

  4. Kaliszan R (1977) Correlation between the retention indices and the connectivity indices of alcohols and methyl esters with complex cyclic structure. Chromatographia 10:529–531

    Article  CAS  Google Scholar 

  5. Michotte Z, Massart DL (1977) Molecular connectivity and retention indexes. J Pham Sci 66:1630–1632

    Article  CAS  Google Scholar 

  6. Héberger K (2007) Quantitative structure-(chromatographic) retention relationships. J Chromatogr A 1158:273–305

    Article  Google Scholar 

  7. Ivanciuc O, Ivanciuc T, Balaban AT (1998) Quantitative structure-property relationship study of normal boiling points for halogen-/oxygen-/sulfur-containing organic compounds using the CODESSA program. Tetrahedron 54:9129–9142

    Article  CAS  Google Scholar 

  8. Pompe M, Novic M (1999) Prediction of gas chromatographic retention indices using topological descriptors. J Chem Inf Comput Sci 39:59–67

    Article  CAS  Google Scholar 

  9. Junkes BS, Amboni RDMC, Yunes RA, Heinzen VEF (2003) Prediction of the chromatographic retention of saturated alcohols on stationary phases of different polarity applying the novel semi-empirical topological index. Anal Chim Acta 477:29–39

    Article  CAS  Google Scholar 

  10. Lu C, Guo W, Yin C (2006) Quantitative structure-retention relationship study of the gas chromatographic retention indices of saturated esters on different stationary phases using novel topological indices. Anal Chim Acta 561:96–102

    Article  CAS  Google Scholar 

  11. Payares P, Diaz D, Olivero J, Vivas R, Gomez I (1997) Prediction of the gas chromatographic relative retention times of flavonoids from molecular structure. J Chromatogr A 771:213–219

    Article  CAS  Google Scholar 

  12. Tulasamma P, Reddy KS (2006) Quantitative structure and retention relationships for gas chromatographic data: application to alkyl pyridines on apolar and polar phases. J Mol Graph Model 25:507–513

    Article  CAS  Google Scholar 

  13. Randić M (1997) On characterization of chemical structure. J Chem Inf Comput Sci 37:672–687

    Article  Google Scholar 

  14. Kier L, Hall L (2002) The meaning of molecular connectivity: a bimolecular accessibility model. Croat Chem Acta 75:371–382

    CAS  Google Scholar 

  15. Drosos JC, Rhenals MV, Reyes RV (2010) Quantitative structure-retention relationships of polycyclic aromatic hydrocarbons gas-chromatographic retention indices. J Chromatogr A 1217:4411–4421

    Article  CAS  Google Scholar 

  16. Ghavami R, Faham S (2010) QSRR Models for Kováts’ retention indices of a variety of volatile organic compounds on Polar and apolar GC stationary phases using molecular connectivity indexes. Chromatographia 72:893–903

    Article  CAS  Google Scholar 

  17. Polyakova Y, Long MJ, Kyung HR (2006) Linear regression based QSPR models for the prediction of the retention mechanism of some nitrogen containing heterocycles. J Liq Chromatogr Rel Technol 29:533–552

    Article  CAS  Google Scholar 

  18. Mihalić Z, Trinajstić N (1992) A graph-theoretical approach to structure-property relationships. J Chem Educ 69:701–712

    Article  Google Scholar 

  19. Wiener H (1947) Structural determination of paraffin boiling points. J Am Chem Soc 69:17–20

    Article  CAS  Google Scholar 

  20. Ivanciuc O, Balaban TS, Balaban AT (1993) Design of topological indices. Part 4. Reciprocal distance matrix, related local vertex invariants and topological indices. J Math Chem 12:309–318

    Article  CAS  Google Scholar 

  21. Plavšić D, Nikolić S, Trinajstić N, Mihalić Z (1993) On the Harary index for the characterization of chemical graphs. J Math Chem 12:235–250

    Article  Google Scholar 

  22. Lučić B, Miličević A, Nikolić S, Trinajstić N (2002) Harary Index—twelve years later. Croat Chem Acta 75:847–868

    Google Scholar 

  23. Zhou B, Cai X, Trinajstić N (2008) On Harary index. J Math Chem 44:611–618

    Article  CAS  Google Scholar 

  24. XX Li, YZ Fan (2012) The connectivity and the Harary Index of a graph. arXiv:1207.2393 [math.CO]

  25. Todeschini R, Consonni V (2000) Handbook of molecular descriptors. Wiley, Weinheim, p 70, 6

    Book  Google Scholar 

  26. Dragon 5.5 (2009) TALETE. http://www.talete.mi.it

  27. Lee M, Vassilaros D, White C, Novotny M (1979) Retention indices for programmed-temperature capillary-column gas chromatography of polycyclic aromatic hydrocarbons. Anal Chem 51:768–773

    Article  CAS  Google Scholar 

  28. Marvin 5.9.0 (2012) Chem Axon. http://www.chemaxon.com

  29. Hyperchem 6.02 (2000) Hypercube. http://www.hyper.com

  30. SIMCA-P 10.0.4 (2003) Umetrics AB, Umeå. http://www.umetrics.com

  31. MobyDigs 1.1 (2009) TALETE. http://www.talete.mi.it

  32. Abdi H (2003) Partial least squares (PLS) regression; multivariate analysis. In: Lewis-Beck M (ed) Encyclopedia of social sciences research methods. Sage, pp 792–795. http://www.utdallas.edu/~herve/Abdi-PLS-pretty.pdf

  33. Tobias RD (1997) An introduction to partial least squares regression. SAS Institute, Cary. http://www.ats.ucla.edu/stat/sas/library/pls.pdf

  34. Eriksson L, Hermens J, Johansson E, Verhaar H, Wold S (1995) Multivariate analysis of aquatic toxicity data with PLS. Aquat Sci 57:217–241

    Article  Google Scholar 

  35. Golbraikh A, Tropsha A (2002) Beware of q2! J Mol Graph Mod 20:269–276

    Article  CAS  Google Scholar 

  36. Ojha PK, Mitra I, Das RN, Roy K (2011) Further exploring r2 m metrics for validation of QSPR models. Chemom Intell Lab Syst 107:194–205

    Article  CAS  Google Scholar 

  37. Randić M (1975) On characterization of molecular branching. J Am Chem Soc 97:6609–6615

    Article  Google Scholar 

  38. Kier LB, Hall LH (1981) Derivation and significance of valence molecular connectivity. J Pharm Sci 70:583–589

    Article  CAS  Google Scholar 

  39. (2004) OECD principles for the validation of (Q)SARs, adopted by 37th Joint Meeting of Chemicals Committee and Working Party on chemicals, pesticides and biotechnology; Paris 17–19. https://eurl-ecvam.jrc.ec.europa.eu/laboratories-research/predictive_toxicology/background/oecd-principles

  40. Tenenhaus M, La régression PLS (1998) Théorie et pratique, Paris Éditions Technip

  41. Wold S (1995) PLS for multivariate linear modeling. In: van de Waterbeemd H (ed) QSAR: chemometric methods in molecular design, methods and principles in medicinal chemistry, 2nd edn. Verlag Chemie, Weinheim, pp 195–218

    Google Scholar 

  42. Wold S, William J (1983) Dunn III multivariate quantitative structure-activity relationships (QSAR): conditions for their applicability. J Chem Inf Comput Sci 23:6–13

    Article  CAS  Google Scholar 

  43. Eriksson L, Johansson E, Kettaneh-Wold N, Trygg J, Wikström C, Wold S (2006) Multi and megavariate data analysis Part I: basic principles and applications, 2nd edn. Umetrics Academy, Umea

    Google Scholar 

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Acknowledgments

The authors thank the general directorate for scientific research and technological development of the Algerian ministry of high education and scientific research for supporting this work and Kim Koffolt for her help to improve the write-up quality of this paper.

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Authors and Affiliations

  1. Environmental and Food Safety Laboratory, LASEA, BADJI Mokhtar University, El Hadjar, BP12, 23000, Annaba, Algeria

    Imen Touhami, Hamza Haddag, Mabrouka Didi & Djelloul Messadi

  2. Preparatory School for Science and Technology, EPSTA, BP 21, 23000, Annaba, Algeria

    Imen Touhami

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  1. Imen Touhami
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  2. Hamza Haddag
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  3. Mabrouka Didi
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  4. Djelloul Messadi
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Correspondence to Djelloul Messadi.

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This study was funded by the general directorate for scientific research and technological development of the Algerian ministry of high education and scientific research.

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All authors declared that they have no conflict of interest.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Touhami, I., Haddag, H., Didi, M. et al. Contribution of Modified Harary Index to Predict Kováts Retention Indices for a Set of PAHs. Chromatographia 79, 1023–1032 (2016). https://doi.org/10.1007/s10337-016-3120-2

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  • DOI: https://doi.org/10.1007/s10337-016-3120-2

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