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Modelling periodic oscillation in gene regulatory networks by cyclic feedback systems

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Abstract

In this paper, we develop a new methodology to analyze and design periodic oscillators of biological networks, in particular gene regulatory networks with multiple genes, proteins and time delays, by using negative cyclic feedback systems. We show that negative cyclic feedback networks have no stable equilibria but stable periodic orbits when certain conditions are satisfied. Specifically, we first prove the basic properties of the biological networks composed of cyclic feedback loops, and then extend our results to general cyclic feedback network with less restriction, thereby making our theoretical analysis and design of oscillators easy to implement, even for large-scale systems. Finally, we use one circadian network formed by a period protein (PER) and per mRNA, and one biologically plausible synthetic gene network, to demonstrate the theoretical results. Since there is less restriction on the network structure, the results of this paper can be expected to apply to a wide variety of areas on modelling, analyzing and designing of biological systems.

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Authors and Affiliations

  1. Osaka Sangyo University, Nakagaito 3-1-1, Daito, Osaka, 574-8530, Japan

    Ruiqi Wang

  2. Hunan Normal University, Changsha, Hunan, 410081, China

    Zhujun Jing

  3. Department of Electrical Engineering and Electronics, Osaka Sangyo University, Nakagaito 3-1-1, Daito, Osaka, 574-8530, Japan

    Luonan Chen

  4. Academy of Mathematics and System Sciences, CAS, Beijing, 100080, China

    Ruiqi Wang & Zhujun Jing

Authors
  1. Ruiqi Wang
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  2. Zhujun Jing
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  3. Luonan Chen
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Correspondence to Luonan Chen.

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Wang, R., Jing, Z. & Chen, L. Modelling periodic oscillation in gene regulatory networks by cyclic feedback systems. Bull. Math. Biol. 67, 339–367 (2005). https://doi.org/10.1016/j.bulm.2004.07.005

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  • DOI: https://doi.org/10.1016/j.bulm.2004.07.005

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