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Universal transformation and non-linear connection between experimental and calculated property vectors in QSPR

  • Ramon Carbó-DorcaEmail author
Original Paper
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Abstract

In this paper a well-known data set transformation, the feature scaling, is promoted for QSPR manipulations of input and output property vectors. Such easily reversible transformation converts the QSPR problems into kind of universal procedure, where the experimental and calculated property vectors are defined with dimensionless elements and brought into a subset of the unit interval. When the QSPR vectors are expressed in this way, it is easy to find out a functional relationship connecting them in a two-dimensional plane. An illustrative example about the Cramer steroid set is given. From the obtained results, one can conjecture that the Quantum and Classical QSPR relationships, between computed and experimental vectors, are far from being linear.

Keywords

QSAR QSPR QSTR Molecular space QSPR Quantum QSPR Feature scaling Universal transformation of QSPR vectors Cramer steroid set Experimental-calculated QSPR vectors non-linear relationship 

Notes

Compliance with ethical standards

Conflict of interest

The author declares no conflict of interests.

References

  1. 1.
    R. Carbó-Dorca, A. Gallegos, Á.J. Sánchez, Notes on quantitative structure-properties relationships (QSPR) (1): A discussion on a QSPR dimensionality paradox (QSPR DP) and its quantum resolution. J. Comput. Chem. 30, 1146–1159 (2008)CrossRefGoogle Scholar
  2. 2.
    R. Carbó-Dorca, E. Besalú, L.D. Mercado, Communications on quantum similarity (3): a geometric-quantum similarity molecular superposition (GQSMS) algorithm. J. Comput. Chem. 32, 582–599 (2011)CrossRefGoogle Scholar
  3. 3.
    R. Carbó-Dorca, Notes on quantitative structure-properties relationships (QSPR) (3): density functions origin shift as a source of quantum QSPR (QQSPR) algorithms in molecular spaces. J. Comput. Chem. 34, 766–779 (2013)CrossRefGoogle Scholar
  4. 4.
    R. Carbó-Dorca, D. Barragán, Communications on quantum similarity (4): collective distances computed by means of similarity matrices, as generators of intrinsic ordering among quantum multimolecular polyhedra. WIREs Comput. Mol. Sci. 5, 380–404 (2015)CrossRefGoogle Scholar
  5. 5.
    R. Carbó-Dorca, S. González, Molecular space quantitative structure-properties relations (MSQSPR): a quantum mechanical comprehensive theoretical framework. Int. J. QSPR 1(2), 1–22 (2016)Google Scholar
  6. 6.
    R. Carbó-Dorca, S. González, Notes in QSPR (4): quantum multimolecular polyhedra, collective vectors, quantum similarity and quantum QSPR fundamental equation. Manag. Stud. 4, 33–47 (2016)Google Scholar
  7. 7.
    R. Carbó-Dorca, Toward an universal quantum QSPR operator. Int. J. Quant. Chem. 118(15), e25602 (2018).  https://doi.org/10.1002/qua.25602 CrossRefGoogle Scholar
  8. 8.
    R. Carbó, L. Leyda, M. Arnau, How similar is a molecule to another? An electron density measure of similarity between two molecular structures. Intl. J. Quant. Chem. 17, 1185–1189 (1980)CrossRefGoogle Scholar
  9. 9.
    R. Carbó-Dorca, Quantum similarity, Chapter 17, in Concepts and Methods in Modern Theoretical Chemistry, vol. 1, ed. by S.K. Ghosh, P.K. Chattaraj (CRC Press, Taylor & Francis, Boca Raton, 2013), pp. 349–365Google Scholar
  10. 10.
    R. Carbó-Dorca, E. Besalú, Centroid origin shift of quantum object sets and molecular point clouds: description and element comparisons. J. Math. Chem. 50, 1161–1178 (2012)CrossRefGoogle Scholar
  11. 11.
    L.D. Mercado, R. Carbó-Dorca, Quantum similarity and discrete representation of molecular sets. J. Math. Chem. 49, 1558–1572 (2011)CrossRefGoogle Scholar
  12. 12.
    R. Carbó-Dorca, Quantum similarity matrices column set as holograms of DF molecular point clouds. J. Math. Chem. 50, 2339–2341 (2012)CrossRefGoogle Scholar
  13. 13.
    R. Carbó-Dorca, Multimolecular polyhedra and QSPR. J. Math. Chem. 52, 1848–1856 (2014)CrossRefGoogle Scholar
  14. 14.
    R. Carbó-Dorca, Quantum polyhedra, definitions, statistics and the construction of a collective quantum similarity index. J. Math. Chem. 53, 171–182 (2015)CrossRefGoogle Scholar
  15. 15.
    R. Carbó-Dorca, An isometric representation problem related with quantum multimolecular polyhedra and similarity. J. Math. Chem. 53, 1750–1758 (2015)CrossRefGoogle Scholar
  16. 16.
    R. Carbó-Dorca, An isometric representation problem in quantum multimolecular polyhedra and similarity: (2) synisometry. J. Math. Chem. 53, 1867–1884 (2015)Google Scholar
  17. 17.
    A. Cherkasov, E.N. Muratov, D. Fourches, A. Varnek, I.I. Baskin, M. Cronin, J. Dearden, P. Gramatica, Y.C. Martin, R. Todeschini, V. Consonni, V.E. Kuzmin, R. Cramer, R. Benigni, C. Yang, J. Rathman, L. Terfloth, J. Gasteiger, A. Richard, A. Tropsha, QSAR modeling: where have you been? Where are you going to? J. Med. Chem. 57, 4977–5010 (2014)CrossRefGoogle Scholar
  18. 18.
    S.C. Basak, Mathematical descriptors for the prediction of property, bioactivity, and toxicity of chemicals from their structure: a chemical-cum-biochemical approach. Curr. Comput. Aided Drug Des. 9, 449–462 (2013)CrossRefGoogle Scholar
  19. 19.
    P. Gramatica, Chap. 21 On the development and validation of QSAR models, in Computational Toxicology: Volume II (Methods in Molecular Biology, vol. 930), ed. by B. Reisfeld, A.N. Mayeno (Springer, New York, NY, 2013), pp. 499–526CrossRefGoogle Scholar
  20. 20.
    R. Carbó-Dorca, Least squares estimation of unknown molecular properties and quantum QSPR fundamental equation. J. Math. Chem. 53, 1651–1656 (2015)CrossRefGoogle Scholar
  21. 21.
  22. 22.
    R. Carbó-Dorca, A study on Goldbach conjecture. J. Math. Chem. 54, 1798–1809 (2016)CrossRefGoogle Scholar
  23. 23.
    J.F. Dunn, B.C. Nisula, D. Rodbard, Transport of steroid hormones: binding of 21 endogenous steroids to both testosterone-binding globulin and corticosteroid-binding globulin in human plasma. J. Clin. Endocrin. Metab. 53, 58–68 (1981)CrossRefGoogle Scholar
  24. 24.
    R.D. Cramer III, D.E. Patterson, J.D. Bunce, Comparative molecular field analysis (CoMFA). 1. Effect of shape on binding of steroids to carrier proteins. J. Am. Chem. Soc. 110, 5959–5967 (1988)CrossRefGoogle Scholar
  25. 25.
    M. Wagener, J. Sadowski, J. Gasteiger, Autocorrelation of molecular surface properties for modeling corticosteroid binding globulin and cytosolic Ah receptor activity by neural networks. J. Am. Chem. Soc. 117, 7769–7775 (1995)CrossRefGoogle Scholar
  26. 26.
    D. Robert, Ll Amat, R. Carbó-Dorca, Three-dimensional quantitative structure-activity relationships from tuned molecular quantum similarity measures: prediction of the corticosteroid-binding globulin binding affinity for a steroid family. J. Chem. Inf. Comput. Sci. 39, 333–344 (1999)CrossRefGoogle Scholar
  27. 27.
    Spartan’16; Wavefunction Inc.; Irvine CA Google Scholar
  28. 28.
    Grapher 13; Golden Software; Golden COGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institut de Química Computacional i CatàlisiUniversitat de GironaGironaSpain

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