P53- mdm2环稳定性和振荡动力学与mdm2诱导的延迟效应

IF 0.7 Q2 MATHEMATICS Tamkang Journal of Mathematics Pub Date : 2021-02-05 DOI:10.5556/J.TKJM.52.2021.3714
M. Y. Baba, M. Saleem, Abdur Raheem
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引用次数: 0

摘要

本文认为P53-Mdm2负反馈回路是基因组的核心回路。我们研究了回路的稳定性和振荡动力学。许多研究通过p53诱导的Mdm2产生的转录延迟的延迟-微分方程来模拟这个循环。然而,我们强调Mdm2诱导的P53蛋白降解延迟的重要性。我们考虑两种形式的P53蛋白,即普通P53和活性P53及其主要拮抗剂蛋白Mdm2,以制定一个最小模型。活跃的P53发现它包含在由布尔变量“s”表示的DNA损伤中。模型的分析使用Nyquist准则提供了延迟的阈值,使得P53的降解延迟低于这些阈值,使得所有蛋白(plain P53、active P53和Mdm2)都接近稳定的平衡状态,从而保证了环路的稳定性。蛋白质中的振荡动力学,如果有的话,将存在于这些阈值之外。
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P53-Mdm2 Loop Stability and Oscillatory Dynamics with Mdm2-Induced Delay Effect in P53
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 ‘s’. 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.
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来源期刊
CiteScore
1.50
自引率
0.00%
发文量
11
期刊介绍: To promote research interactions between local and overseas researchers, the Department has been publishing an international mathematics journal, the Tamkang Journal of Mathematics. The journal started as a biannual journal in 1970 and is devoted to high-quality original research papers in pure and applied mathematics. In 1985 it has become a quarterly journal. The four issues are out for distribution at the end of March, June, September and December. The articles published in Tamkang Journal of Mathematics cover diverse mathematical disciplines. Submission of papers comes from all over the world. All articles are subjected to peer review from an international pool of referees.
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