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access icon free Oscillatory expression in Escherichia coli mediated by microRNAs with transcriptional and translational time delays

  • Author(s): Yuan Zhang 1, 2 1, 3 ; Haihong Liu 3 2 ; Jin Zhou 1, 2 1, 3
    • View affiliations
    • Affiliations: 1: Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, People's Republic of China ;
      2: Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, People's Republic of China ;
      3: Department of Mathematics, Yunnan Normal University, Kunming 650092, People's Republic of China
  • Source: Volume 10, Issue 6, December 2016, p. 203 – 209
    DOI:  10.1049/iet-syb.2016.0017 , Print ISSN 1751-8849, Online ISSN 1751-8857
© The Institution of Engineering and Technology
Received 21/04/2016, Accepted 14/06/2016, Revised 13/06/2016, Published 01/12/2016

The primary objective of this study is to study oscillatory expression of gene regulatory network in Escherichia coli mediated by microRNAs (sRNAs) with transcriptional and translational time delays. Motivated by the regulation of gene expression proposed by Shimoni et al. (Molecular Systems Biology, 2007), a general model of delayed gene regulatory network by sRNAs is formulated. This model can well describe many practical architectures of gene regulatory network by sRNAs, particularly when both transcriptional and translational time delays are introduced. Two functional issues on oscillatory expression of the gene regulatory network, i.e. stability and bifurcation, are investigated. Furthermore, an explicit algorithm determining the direction of Hopf bifurcation and stability of bifurcating periodic solutions is presented. It turns out that both transcriptional and translational time delays can induce gene expression in E. coli to be oscillatory even when its deterministic counterpart exhibits no oscillations. Moreover, the obtained results are in consistence with the experimental observations found in the biological literatures (Elowitz MB et al.: Nature, 2000, 403, pp. 335–338; Lennart Hilbert et al.: Mol. BioSyst, 2011, 7, pp. 2599–2607), which demonstrates that both transcriptional and translational time delays play an important role in the gene regulatory process of E. coli.

Inspec keywords: RNA; genetics; molecular biophysics; microorganisms; bifurcation

Other keywords: stability; gene regulatory network; translational time delays; oscillatory expression; Hopf bifurcation; microRNAs; transcriptional time delays; Escherichia coli

Subjects: Nonlinear dynamical systems and bifurcations; Biomolecular structure, configuration, conformation, and active sites; Macromolecular conformation (statistics and dynamics); Biomolecular interactions, charge transfer complexes

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