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Bifurcations and Dynamics of the Rb-E2F Pathway Involving miR449

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  • 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
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    References listed on IDEAS

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    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.
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