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A Model of the Signal Transduction Process under a Delay

  • Jutarat Kongson (a1) (a2) and Somkid Amornsamankul (a3) (a2)
Abstract

The signal transduction pathway is the important process of communication of the cells. It is the dynamical interaction between the ligand-receptor complexes and an inhibitor protein in second messenger synthesis. The signaling molecules are detected and bounded by receptors, typically G-Protein receptors, across the cell membrane and that in turns alerts intracellular molecules to stimulate a response or a desired consequence in the target cells. In this research, we consider a model of the signal transduction process consisting of a system of three differential equations which involve the dynamic interaction between an inhibitor protein and the ligand-receptor complexes in the second messenger synthesis. We will incorporate a delay τ in the time needed before the signal amplification process can take effect on the production of the ligand-receptor complex. We investigate persistence and stability of the system. It is shown that the system allows positive solutions and the positive equilibrium is locally asymptotically stable under suitable conditions on the system parameters.

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Corresponding author
*Corresponding author. Email address:jutarat.kongson@gmail.com (J. Kongson)
References
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[1] Albert, B., Johnson, A., Lewis, J., Raff, M., Robert, K., and Peter, W., Molecular Biology of the Cell, 5th ed. Garland Science, 2008.
[2] Hunter, T., Signaling-2000 and beyond, Cell 100, 113127 (2000).
[3] Iglesias, P. A., Feedback control in intracellular signaling pathways: Regulation chemotaxis in dictyostelium discoideum, Eur. J. Control 9, 216225 (2003).
[4] Levchenko, A. and Iglesias, P., Models of eukaryotic gradient sensing: Application to chemotaxis of amoebae and neutrophils, Biophys. J. 82, 5063 (2002).
[5] Lodish, H., Berk, A., Zipursky, S. L., Maatsudaira, P., Baltimore, D., and Darnell, J., Molecular Cell Biology, 4th ed., Freeman, W. H., pp. 849877, 2000.
[6] Norman, A. W. and Litwach, G., Hormones, Academic. Press, California, USA, (1997).
[7] Ramanathan, S., Detwiler, P. B., Sengupta, A. M., and Shraiman, B. I., G-protein-coupled enzyme cascades have intrinsic properties that improve signal localization and fidelity, Biophys. J. 58, 30633071 (2005).
[8] Rattanakul, C., Sungkaworn, T., Lenbury, Y., Chudoung, M., Chatsudthipong, V., Triampo, W., and Novaprateep, B., Nonlinear spatiotemporal analysis and modeling of signal transduction pathways involving G protein coupled receptors, IJMMMAS 3, 219229 (2011).
[9] Spiegel, A. M., G protein defects in signal transduction, Horm. Res. Paediatr. 53, 122 (2000).
[10] Zhong, H. and Ncubig, R. R., Regulator of G protein signaling proteins: Novel multi functional drug target, J. Pharmacol. Exp. Ther. 297, 837845 (2001).
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East Asian Journal on Applied Mathematics
  • ISSN: 2079-7362
  • EISSN: 2079-7370
  • URL: /core/journals/east-asian-journal-on-applied-mathematics
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