Oscillatory expression in Escherichia coli mediated by microRNAs with transcriptional and translational time delays.

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.