Stability and Hopf bifurcation analysis of lac Operon model with distributed delay and nonlinear degradation rate.

IF 0.8 4区 数学 Q4 BIOLOGY Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2019-12-04 DOI:10.1093/imammb/dqy018
Zenab Alrikaby
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引用次数: 3

Abstract

We propose a simple model of lac operon that describes the expression of B-galactosidase from lac Z gene in Escherichia coli, through the interaction among several identical mRNA. Our goal is to explore the complex dynamics (i.e. the oscillation phenomenon) of this architecture mediated by this interaction. This model was theoretically and numerically investigated using distributed time delay. We considered the average delay as a bifurcation parameter and the nonlinear degradation rate as a control parameter. Sufficient conditions for local stability were gained by using the Routh-Hurwitz criterion in the case of a weak delay kernel. Then we proved that Hopf bifurcation happened and the direction of the periodic solution was determined using multiple time scale technique. Our results suggest that the interaction among several identical mRNA plays the main role in gene regulation.

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具有分布延迟和非线性退化率的lac操纵子模型的稳定性和Hopf分岔分析。
我们提出了一个简单的lac操纵子模型,该模型通过几个相同的mRNA之间的相互作用来描述lac Z基因在大肠杆菌中b -半乳糖苷酶的表达。我们的目标是探索这种相互作用介导的建筑的复杂动力学(即振荡现象)。利用分布式时滞对该模型进行了理论和数值研究。我们将平均延迟作为分岔参数,将非线性退化率作为控制参数。利用Routh-Hurwitz准则,得到了弱延迟核局部稳定的充分条件。然后利用多时间尺度技术证明了Hopf分岔的存在,并确定了周期解的方向。我们的研究结果表明,几个相同的mRNA之间的相互作用在基因调控中起主要作用。
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
15
审稿时长
>12 weeks
期刊介绍: Formerly the IMA Journal of Mathematics Applied in Medicine and Biology. Mathematical Medicine and Biology publishes original articles with a significant mathematical content addressing topics in medicine and biology. Papers exploiting modern developments in applied mathematics are particularly welcome. The biomedical relevance of mathematical models should be demonstrated clearly and validation by comparison against experiment is strongly encouraged. The journal welcomes contributions relevant to any area of the life sciences including: -biomechanics- biophysics- cell biology- developmental biology- ecology and the environment- epidemiology- immunology- infectious diseases- neuroscience- pharmacology- physiology- population biology
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