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P53-Mdm2 Loop Stability and Oscillatory Dynamics with Mdm2-Induced Delay Effect in P53
- Source :
- Tamkang Journal of Mathematics. 52
- Publication Year :
- 2021
- Publisher :
- Tamkang Journal of Mathematics, 2021.
-
Abstract
- In this paper, we consider P53-Mdm2 negative feedback loop supposed to be the core circuit of genome. We study stability and the oscillatory dynamics of the loop. Many of the studies modeled this loop by delay-differential equations with P53-induced transcrip- tional delay in the production of Mdm2. We, however, highlight the importance of Mdm2- induced delay in the degradation of P53 protein. We consider two forms of P53 protein i.e., plain P53 and active P53 along with its principal antagonist protein Mdm2 to formulate a minimal model. Active P53 finds its inclusion in the loop in the presence of DNA damage represented by a Boolean variable āsā. The analysis of the model provides thresholds on delays using Nyquist criterion such that delays in the degradation of P53 lower than these thresholds guarantee stability of the loop in that all proteins plain P53, active P53 and Mdm2 approach to stable equilibrium state. The oscillatory dynamics in proteins, if any, would exist beyond these thresholds.
- Subjects :
- Applied Mathematics
General Mathematics
010102 general mathematics
Dynamics (mechanics)
01 natural sciences
Stability (probability)
Loop (topology)
Minimal model
Control theory
Nyquist stability criterion
Negative feedback
0101 mathematics
Boolean data type
Mathematics
Degradation (telecommunications)
Subjects
Details
- ISSN :
- 20739826 and 00492930
- Volume :
- 52
- Database :
- OpenAIRE
- Journal :
- Tamkang Journal of Mathematics
- Accession number :
- edsair.doi...........12866d5db2816f0a70d64cc7db2fcda8