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Bulletin of Mathematical Biology

, Volume 68, Issue 4, pp 735–751 | Cite as

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

  • Maykel Pérez González
  • Julio Caballero
  • Aliuska Morales Helguera
  • Miguel Garriga
  • Gerardo González
  • Michael FernándezEmail author
Original Article

Abstract

The inhibitory activity towards p34 cdc 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.

Keywords

QSAR Autocorrelation vectors Multilinear regression Artificial neural networks Plant hormones 

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References

  1. Aoyama, T., Suzuki, Y., Ichikawa, H., 1990. Neural networks applied to structure–activity relationships. J. Med. Chem. 33, 905–908.CrossRefPubMedGoogle 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.CrossRefPubMedGoogle 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.CrossRefGoogle Scholar
  4. D'Agostino, I.B., Kieber, J.J., 1999. Molecular mechanisms of cytokinin action. Curr. Opin. Plant Biol. 2, 359–364.CrossRefPubMedGoogle 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.Google Scholar
  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.Google Scholar
  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.Google Scholar
  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.CrossRefGoogle 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.CrossRefGoogle Scholar
  10. Frank, J., 1993. Seiler Research Laboratory, MOPAC version 6.0. U.S. Air Force Academy.Google Scholar
  11. Gasteiger, J., Zupan, J., 1995. Neural networks in chemistry. Angew. Chem. Int. Ed. Engl. 32, 503–527.CrossRefGoogle Scholar
  12. Gasteiger, J., Li, X., 1994. Abbildung elektrostatischer Potentiale muscarinischer und nicotinischer Agonisten mit künstlichen neuronalen Netzen. Angew. Chem. 106, 671–674.CrossRefGoogle Scholar
  13. Geary, R.F., 1954. The contiguity ratio and statistical mapping. Incorp. Stat. 5, 115–145.CrossRefGoogle Scholar
  14. González, M.P., Helguera, A.M., González-Díaz, H., 2004. A TOPS-MODE approach to predict permeability coefficients. Polymer 45, 2073–2079.CrossRefGoogle Scholar
  15. González, M.P., Terán, C., 2004a. A TOPS-MODE approach to predict adenosine kinase inhibition. Bioorg. Med. Chem. Lett. 14, 3077–3079.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
  18. Haberer, G., Kieber, J.J., 2002. Cytokinins, new insights into a classic ophytohormone. Plant Physiol. 128, 354–362.CrossRefPubMedGoogle 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.CrossRefPubMedGoogle Scholar
  20. Hawkins, D.M., 2004. The problem of overfitting. J. Chem. Inform. Comput. Sci. 44, 1–12.CrossRefMathSciNetGoogle 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.CrossRefGoogle Scholar
  22. Kohonen, T., 1982. Self-organized formation of topologically correct feature maps. Biol. Cybernet. 43, 59–69.CrossRefMathSciNetzbMATHGoogle Scholar
  23. Kolmogorov, A.N., 1957. Doklady Akademiia Nauk SSSR. 114, 953–954.Google Scholar
  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.Google Scholar
  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.CrossRefPubMedGoogle 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.CrossRefPubMedGoogle 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.CrossRefGoogle Scholar
  29. Moran, P.A.P., 1950. Notes on continuous stochastic processes. Biometrika 37, 17–23.PubMedMathSciNetzbMATHGoogle 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.CrossRefPubMedGoogle 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.CrossRefGoogle 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.Google Scholar
  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.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefPubMedGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2006

Authors and Affiliations

  • Maykel Pérez González
    • 1
    • 2
  • Julio Caballero
    • 3
    • 4
  • Aliuska Morales Helguera
    • 2
    • 5
  • Miguel Garriga
    • 6
  • Gerardo González
    • 6
  • Michael Fernández
    • 3
    • 4
    Email author
  1. 1.Unit of Service, Drug Design DepartmentExperimental Sugar Cane Station “Villa Clara-Cienfuegos,”RanchueloVilla ClaraCuba
  2. 2.Chemical Bioactive CenterCentral University of Las VillasSanta Clara, Villa ClaraCuba
  3. 3.Molecular Modeling Group, Center for Biotechnological Studies, Faculty of AgronomyUniversity of Matanzas, MatanzasMatanzasCuba
  4. 4.Probiotic Group, Center for Biotechnological Studies, Faculty of AgronomyUniversity of Matanzas, MatanzasMatanzasCuba
  5. 5.Department of Chemistry, Faculty of Chemistry and PharmacyCentral University of Las VillasSanta Clara, Villa ClaraCuba
  6. 6.Plant Biotechnology Group, Center for Biotechnological Studies, Faculty of AgronomyUniversity of Matanzas, MatanzasMatanzasCuba

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