IDEAS home Printed from https://ideas.repec.org/a/hin/complx/1409865.html
   My bibliography  Save this article

Bifurcations and Dynamics of the Rb-E2F Pathway Involving miR449

Author

Listed:
  • Lingling Li
  • Jianwei Shen

Abstract

We focused on the gene regulative network involving Rb-E2F pathway and microRNAs (miR449) and studied the influence of time delay on the dynamical behaviors of Rb-E2F pathway by using Hopf bifurcation theory. It is shown that under certain assumptions the steady state of the delay model is asymptotically stable for all delay values; there is a critical value under another set of conditions; the steady state is stable when the time delay is less than the critical value, while the steady state is changed to be unstable when the time delay is greater than the critical value. Thus, Hopf bifurcation appears at the steady state when the delay passes through the critical value. Numerical simulations were presented to illustrate the theoretical results.

Suggested Citation

  • Lingling Li & Jianwei Shen, 2017. "Bifurcations and Dynamics of the Rb-E2F Pathway Involving miR449," Complexity, Hindawi, vol. 2017, pages 1-20, October.
    • Handle: RePEc:hin:complx:1409865
    DOI: 10.1155/2017/1409865
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/8503/2017/1409865.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/8503/2017/1409865.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2017/1409865?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Xu, Yong & Zhu, Ya-nan & Shen, Jianwei & Su, Jianbin, 2014. "Switch dynamics for stochastic model of genetic toggle switch," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 461-466.
    2. Shen, Jianwei & Liu, Zengrong & Zheng, Weixing & Xu, Fengdan & Chen, Luonan, 2009. "Oscillatory dynamics in a simple gene regulatory network mediated by small RNAs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2995-3000.
    3. Luis Mier-y-Terán-Romero & Mary Silber & Vassily Hatzimanikatis, 2010. "The Origins of Time-Delay in Template Biopolymerization Processes," PLOS Computational Biology, Public Library of Science, vol. 6(4), pages 1-15, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. T.V., Binil Shyam & Sharma, Rati, 2024. "mRNA translation from a unidirectional traffic perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    2. Zhdanov, Vladimir P., 2012. "Periodic perturbation of genetic oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 45(5), pages 577-587.
    3. Liu, Yuting & Shan, Meijing & Lian, Xinze & Wang, Weiming, 2016. "Stochastic extinction and persistence of a parasite–host epidemiological model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 586-602.
    4. Xu, Yong & Wu, Juan & Du, Lin & Yang, Hui, 2016. "Stochastic resonance in a genetic toggle model with harmonic excitation and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 91-100.
    5. Huang, Chengdai & Cao, Jinde & Xiao, Min, 2016. "Hybrid control on bifurcation for a delayed fractional gene regulatory network," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 19-29.
    6. Zang, Hong & Zhang, Tonghua & Zhang, Yanduo, 2015. "Bifurcation analysis of a mathematical model for genetic regulatory network with time delays," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 204-226.
    7. Jinying Tan & Ruangang Pan & Lei Qiao & Xiufen Zou & Zishu Pan, 2012. "Modeling and Dynamical Analysis of Virus-Triggered Innate Immune Signaling Pathways," PLOS ONE, Public Library of Science, vol. 7(10), pages 1-15, October.
    8. Wu, Juan & Xu, Yong & Ma, Shaojuan, 2019. "Realizing the transformation of logic gates in a genetic toggle system under Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 171-179.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:complx:1409865. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.