Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T17:04:53.816Z Has data issue: false hasContentIssue false
  • English
  • Français

A Model of the Signal Transduction Process under a Delay

Part of: Stability theory

Published online by Cambridge University Press:  31 January 2018

Jutarat Kongson  and
Somkid Amornsamankul
Jutarat Kongson*
Affiliation:
Department of Mathematics, Burapha University, Chonburi 20130, Thailand Centre of Excellence in Mathematics, Bangkok 10400, Thailand
Somkid Amornsamankul
Affiliation:
Department of Mathematics, Mahidol University, Bangkok 10400, Thailand Centre of Excellence in Mathematics, Bangkok 10400, Thailand
*
*Corresponding author. Email address:jutarat.kongson@gmail.com (J. Kongson)
Get access

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.

Keywords

Signal transduction pathwaylocally asymptotically stablepersistenceligand-receptordelay

MSC classification

Secondary: 34D05: Asymptotic properties 34D20: Stability
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 4 , November 2017 , pp. 741 - 751
Copyright
Copyright © Global-Science Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Albert, B., Johnson, A., Lewis, J., Raff, M., Robert, K., and Peter, W., Molecular Biology of the Cell, 5th ed. Garland Science, 2008.Google Scholar
[2] Hunter, T., Signaling-2000 and beyond, Cell 100, 113–127 (2000).Google Scholar
[3] Iglesias, P. A., Feedback control in intracellular signaling pathways: Regulation chemotaxis in dictyostelium discoideum, Eur. J. Control 9, 216–225 (2003).Google Scholar
[4] Levchenko, A. and Iglesias, P., Models of eukaryotic gradient sensing: Application to chemotaxis of amoebae and neutrophils, Biophys. J. 82, 50–63 (2002).Google Scholar
[5] Lodish, H., Berk, A., Zipursky, S. L., Maatsudaira, P., Baltimore, D., and Darnell, J., Molecular Cell Biology, 4th ed., Freeman, W. H., pp. 849–877, 2000.Google Scholar
[6] Norman, A. W. and Litwach, G., Hormones, Academic. Press, California, USA, (1997).Google Scholar
[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, 3063–3071 (2005).Google Scholar
[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, 219–229 (2011).Google Scholar
[9] Spiegel, A. M., G protein defects in signal transduction, Horm. Res. Paediatr. 53, 1–22 (2000).Google Scholar
[10] Zhong, H. and Ncubig, R. R., Regulator of G protein signaling proteins: Novel multi functional drug target, J. Pharmacol. Exp. Ther. 297, 837–845 (2001).Google Scholar