Volume 7, Issue 4
A Model of the Signal Transduction Process under a Delay

Jutarat Kongson & Somkid Amornsamankul

East Asian J. Appl. Math., 7 (2017), pp. 741-751.

Published online: 2018-02

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  • 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 pathway, locally asymptotically stable, persistence, ligand-receptor, delay.

  • AMS Subject Headings

34D05, 34D20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-741, author = {}, title = {A Model of the Signal Transduction Process under a Delay}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {4}, pages = {741--751}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.181016.300517a}, url = {http://global-sci.org/intro/article_detail/eajam/10717.html} }
TY - JOUR T1 - A Model of the Signal Transduction Process under a Delay JO - East Asian Journal on Applied Mathematics VL - 4 SP - 741 EP - 751 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.181016.300517a UR - https://global-sci.org/intro/article_detail/eajam/10717.html KW - Signal transduction pathway, locally asymptotically stable, persistence, ligand-receptor, delay. AB -

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.

Jutarat Kongson & Somkid Amornsamankul. (2020). A Model of the Signal Transduction Process under a Delay. East Asian Journal on Applied Mathematics. 7 (4). 741-751. doi:10.4208/eajam.181016.300517a
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