2D Autocorrelation Modelling of the Inhibitory Activity of Cytokinin-Derived Cyclin-Dependent Kinase Inhibitors

Abstract

The inhibitory activity towards p34cdc 2/cyclin b kinase (CBK) enzyme of 30 cytokinin-derived compounds has been successfully modelled using 2D spatial autocorrelation vectors. Predictive linear and non-linear models were obtained by forward stepwise multi-linear regression analysis (MRA) and artificial neural network (ANN) approaches respectively. A variable selection routine that selected relevant non-linear information from the data set was employed prior to networks training.

The best ANN with three input variables was able to explain about 87% data variance in comparison with 80% by the linear equation using the same number of descriptors. Similarly, the neural network had higher predictive power. The MRA model showed a linear dependence between the inhibitory activities and the spatial distributions of masses, electronegativities and van der Waals volumes on the inhibitors molecules. Meanwhile, ANN model evidenced the occurrence of non-linear relationships between the inhibitory activity and the mass distribution at different topological distance on the cytokinin-derived compounds. Furthermore, inhibitors were well distributed regarding its activity levels in a Kohonen self-organizing map (SOM) built using the input variables of the best neural network.

This is a preview of subscription content, log in to check access.

References

  1. Aoyama, T., Suzuki, Y., Ichikawa, H., 1990. Neural networks applied to structure–activity relationships. J. Med. Chem. 33, 905–908.

    Article  PubMed  Google Scholar 

  2. Arris, C.E., Boyle, F.T., Calvert, A.H., Curtin, N.J., Endicott, J.A., Garman, E.F., Gibson, A.E., Golding, B.T., Grant, S., Griffin, R.J., Jewsbury, P., Johnson, L.N., Lawrie, A.M., Newell, D.R., Noble, M.E.M., Sausville, E.A., Schultz, R., Yu, W., 2000. Identification of novel purine and pyrimidine cyclin-dependent kinase inhibitors with distinct molecular interactions and tumor cell growth inhibition profiles. J. Med. Chem. 43, 2797–2804.

    Article  PubMed  Google Scholar 

  3. Bauknecht, H., Zell, A., Bayer, H., Levi, P., Wagener, M., Sadowski, J., Gasteriger, J., 1996, Locating biologically active compounds in medium-sized heterogeneous datasets by dopological autocorrelation vectors: Dopamine and benzodiazepine agonist. J. Chem. Inform. Comput. Sci. 36, 1205–1213.

    Article  Google Scholar 

  4. D'Agostino, I.B., Kieber, J.J., 1999. Molecular mechanisms of cytokinin action. Curr. Opin. Plant Biol. 2, 359–364.

    Article  PubMed  Google Scholar 

  5. Demuth, H., Beale, M., 2003a. Neural Network Toolbox User's Guide for Use with MATLAB, 4th edn. The Mathworks Inc., Massachusetts, pp. 51–61, Chapter 5.

  6. Demuth, H., Beale, M., 2003b. Neural Network Toolbox User's Guide for Use with MATLAB, 4th edn. The Mathworks Inc., Massachusetts, pp. 9–23, Chapter 8.

  7. Devillers, J., 1999. Autocorrelation descriptors for modelling (eco)toxicological endpoints. In: Devillers, J., Balaban, A.T. (Eds.), Topological Indices and Related Descriptors in QSAR and QSPR. Gordon and Breach Science Publishers, pp. 595–612.

  8. Devillers, J., Domine, D., 1997. Comparison of rehability of log P values calculated from a group contribution approach and from the autocorrelation method. SAR QSAR Environ. Res. 7, 195–232.

    Article  Google Scholar 

  9. Dewar, M.J.S., Zoebisch, E.G., Healy, E.T., Stewart, J.J.P., 1985. AME: New general purpose quantum mechanical molecular model. J. Am. Chem. Soc. 107, 3902–3910.

    Article  Google Scholar 

  10. Frank, J., 1993. Seiler Research Laboratory, MOPAC version 6.0. U.S. Air Force Academy.

  11. Gasteiger, J., Zupan, J., 1995. Neural networks in chemistry. Angew. Chem. Int. Ed. Engl. 32, 503–527.

    Article  Google Scholar 

  12. Gasteiger, J., Li, X., 1994. Abbildung elektrostatischer Potentiale muscarinischer und nicotinischer Agonisten mit künstlichen neuronalen Netzen. Angew. Chem. 106, 671–674.

    Article  Google Scholar 

  13. Geary, R.F., 1954. The contiguity ratio and statistical mapping. Incorp. Stat. 5, 115–145.

    Article  Google Scholar 

  14. González, M.P., Helguera, A.M., González-Díaz, H., 2004. A TOPS-MODE approach to predict permeability coefficients. Polymer 45, 2073–2079.

    Article  Google Scholar 

  15. González, M.P., Terán, C., 2004a. A TOPS-MODE approach to predict adenosine kinase inhibition. Bioorg. Med. Chem. Lett. 14, 3077–3079.

    Article  Google Scholar 

  16. González, M.P., Terán, C., 2004b. QSAR study of N6-(substituted-phenylearbamoyl) adenosine-5′-uronamides as agonist for A1 adenosine receptors. Bull. Math. Biol. 66, 907–920.

    Article  Google Scholar 

  17. Guo-Zheng, L., Jie, Y., Hai-Feng, S., Shang-Sheng, Y., Wen-Cong, L., Nian-Yi, C., 2004. Semiempirical quantum chemical method and artificial neural networks applied for λmax. Computation of some azo dyes. J. Chem. Inform. Comput. Sci. 44, 2047–2050.

    Article  Google Scholar 

  18. Haberer, G., Kieber, J.J., 2002. Cytokinins, new insights into a classic ophytohormone. Plant Physiol. 128, 354–362.

    Article  PubMed  Google Scholar 

  19. Havlíček, I., Hanuš, J., Veselý, J., Leclere, S., Meijer, I., Shaw, G., Strnad, M., 1997. Cytokinin-derived cyclin-dependent kinase inhibitors: Synthesis and cdc2 inhibitory activity of olomoucine and related compounds. J. Med. Chem. 40, 408–412.

    Article  PubMed  Google Scholar 

  20. Hawkins, D.M., 2004. The problem of overfitting. J. Chem. Inform. Comput. Sci. 44, 1–12.

    Article  MathSciNet  Google Scholar 

  21. Hemmateenejad, B., Akhond, M., Miri, R., Shamsipur, M., 2003. Genetic algorithm applied to the selection of factors in principal component-artificial neural networks: Application to QSAR study of calcium channel antagonist activity of 1,4-dihydropyridines (nifedipine analogous). J. Chem. Inform. Comput. Sci. 43, 1328–1334.

    Article  Google Scholar 

  22. Kohonen, T., 1982. Self-organized formation of topologically correct feature maps. Biol. Cybernet. 43, 59–69.

    Article  MathSciNet  MATH  Google Scholar 

  23. Kolmogorov, A.N., 1957. Doklady Akademiia Nauk SSSR. 114, 953–954.

  24. Kowalsky, R.B., Wold, S., 1982. Pattern recognition in chemistry. In: Krishnaiah, P.R., Kamal, L.N. (Eds.), Handbook of Statistics. North-Holland, Amsterdam, pp. 673–697.

  25. Kubinyi, H., 1993. QSAR: Hansch Analysis and Related Approaches. VCH, New York.

    Google Scholar 

  26. Meijer, L., Raymond, E., 2003. Roscovitine and other purines as kinase inhibitors from starfish oocytes to clinical trials. Acc. Chem. Res. 36, 417–425.

    Article  PubMed  Google Scholar 

  27. Meijer, L., Leelere, S., Leost, M., 1999. Properties and potential applications of chemical inhibitors of cyclin-dependent kinases. Pharmacol. Ther. 82, 279–284.

    Article  PubMed  Google Scholar 

  28. Mok, M.C., Martin, R.C., Mok, D.W., 2000. Cytokinins: Biosynthesis, metabolism and perception. In Vitro Cell. Dev. Biol. Plant. 36, 102–107.

    Article  Google Scholar 

  29. Moran, P.A.P., 1950. Notes on continuous stochastic processes. Biometrika 37, 17–23.

    PubMed  MathSciNet  MATH  Google Scholar 

  30. Moreau, G., Broto, P., 1980a. Autocorrelation of a topological structure: A new molecular descriptor. Nouv. J. Chim. 4, 359–360.

    Google Scholar 

  31. Moreau, G., Broto, P., 1980b. Autocorrelation of Molecular structures: Application to SAR studies. Nouv. J. Chim. 4, 757–764.

    Google Scholar 

  32. So, S., Richards, W.G., 1992. Application of neural network: Quantitative structure–activity relationships of the derivatives of 2,4-diamino-5-(substituted-benzyl)pyrimidines as DHFR inhibitors. J. Med. Chem. 35, 3201–3207.

    Article  PubMed  Google Scholar 

  33. StatSoft Inc, 2001. STATISTICA (data analysis software system), version 6. www.statsoft.com.

  34. StatSoft Inc, 2004. Electronic Statistics Textbook. StatSoft, Tulsa, OK, web: http://www.statsoft.com/textbook/stathome.html.

  35. Sumpter, B.G., Getino, C., Noid, D.W., 1994. Theory and applications of neural computing in chemical science. Annu. Rev. Phys. Chem. 45, 439–481.

    Article  Google Scholar 

  36. The MathWorks Inc. (2002). MATLAB version 6.5. www.mathworks.com.

  37. Todeschini, R., Consonni, V., 2000. Handbook of Molecular Descriptors. Wiley-VCH, Weinheim.

    Google Scholar 

  38. Todeschini, R., Consonni, V., Pavan, M., 2003. DRAGON, version 2.1.

  39. Vanyúr, R., Héberger, K., Jakus, J., 2003. Prediction of anti-HIV-I activity of a series of tetrapyrrole molecules. J. Chem. Inform. Comput. Sci. 43, 1829–1836.

    Article  Google Scholar 

  40. Wagener, M., Sadowski, J., Gasteiger, J., 1995. Autocorrelation of molecular properties for modelling corticosteroid binding globulin and cytosolic Ah receptor activity by neural networks. J. Am. Chem. Soc. 117, 7769–7775.

    Article  Google Scholar 

  41. Werner, T., Motyka, V., Strnad, M., Schmülling, T., 2001. Regulation of plant growth by cytokinin. Proc. Natl. Acad. Sci. U.S.A. 98, 10487–10492.

    Article  PubMed  Google Scholar 

  42. Yasri, A., Hartsough, D., 2001. Toward an optimal procedure for variable selection and QSAR model building. J. Chem. Inform. Comput. Sci. 41, 1218–1227.

    Article  Google Scholar 

  43. Zahouily, M., Rhihil Bazoui, A., Sebti, S., Zakarya, D., 2002. Structure–cytotoxicity relationships for a series of HEPT derivatives. J. Mol. Model. 8, 168–172.

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Michael Fernández.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

González, M.P., Caballero, J., Helguera, A.M. et al. 2D Autocorrelation Modelling of the Inhibitory Activity of Cytokinin-Derived Cyclin-Dependent Kinase Inhibitors. Bull. Math. Biol. 68, 735–751 (2006). https://doi.org/10.1007/s11538-005-9006-3

Download citation

Keywords

  • QSAR
  • Autocorrelation vectors
  • Multilinear regression
  • Artificial
  • neural networks
  • Plant hormones