由microRAN介导的具有时滞负反馈环的基因振荡表达

数学季刊 ›› 2013, Vol. 28 ›› Issue (2): 303-310.

由microRAN介导的具有时滞负反馈环的基因振荡表达

1. Institute of Applied Mathematics, College of Mathematics and Information Sciences, Henan University 2. Hospital of Henan University

收稿日期:2012-10-15 出版日期:2013-06-30 发布日期:2023-03-03
作者简介:ZHANG Feng-pan(1974-), male, native of Nanyang, Henan, an associate professor of Henan University, Ph.D., engages in mathematical biology.
基金资助:
Supported by the National Natural Science Foundation of China(11105040)； Supported by the Natural Science Foundation of Henan University(2010YBZ010)

Oscillatory Gene Expression by the microRAN Mediating Delayed Negative Feedback Loop

1. Institute of Applied Mathematics, College of Mathematics and Information Sciences, Henan University 2. Hospital of Henan University

Received:2012-10-15 Online:2013-06-30 Published:2023-03-03
About author:ZHANG Feng-pan(1974-), male, native of Nanyang, Henan, an associate professor of Henan University, Ph.D., engages in mathematical biology.
Supported by:
Supported by the National Natural Science Foundation of China(11105040)； Supported by the Natural Science Foundation of Henan University(2010YBZ010)

摘要/Abstract

摘要： More and more experiments show that microRNAs can regulate gene expression by stimulating degradation of mRNA or repression of translation of mRNA. In this paper, we incorporate the microRNA into a previous mathematical model of gene expression through forming a microRNA-induced silencing complex(RISC). Our findings demonstrate the dynamical behavior of the constructed system. By Hopf theories, we derive the theoretical results of globally asymptotical stability and provide the sufficient conditions for the oscillation of the simple gene regulatory system, and by numerical simulation further demonstrate how the amplitudes against the change of delay in the gene regulatory network.

关键词: gene regulatory network, microRNA, time delay, Hopf bifurcation, oscillation

Abstract: More and more experiments show that microRNAs can regulate gene expression by stimulating degradation of mRNA or repression of translation of mRNA. In this paper, we incorporate the microRNA into a previous mathematical model of gene expression through forming a microRNA-induced silencing complex(RISC). Our findings demonstrate the dynamical behavior of the constructed system. By Hopf theories, we derive the theoretical results of globally asymptotical stability and provide the sufficient conditions for the oscillation of the simple gene regulatory system, and by numerical simulation further demonstrate how the amplitudes against the change of delay in the gene regulatory network.

Key words: gene regulatory network, microRNA, time delay, Hopf bifurcation, oscillation

中图分类号:

张丰盘, 路金瑞, 刘志广. 由microRAN介导的具有时滞负反馈环的基因振荡表达[J]. 数学季刊, 2013, 28(2): 303-310.

ZHANG Feng-pan, LU Jin-rui, LIU Zhi-guang. Oscillatory Gene Expression by the microRAN Mediating Delayed Negative Feedback Loop[J]. Chinese Quarterly Journal of Mathematics, 2013, 28(2): 303-310.

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