title: Oscillatory expression inEscherichia colimediated by microRNAs with transcriptional and translational time delays.
abstract: The primary objective of this study is to study oscillatory expression of gene regulatory network inEscherichia colimediated by microRNAs (sRNAs) with transcriptional and translational time delays. Motivated by the regulation of gene expression proposed by Shimoniet 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 inE.colito 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 MBet al.: Nature, 2000, 403, pp. 335-338; Lennart Hilbertet 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 ofE. coli.
authors.affiliation: Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, People's Republic of China.
authors.forename: Yuan
authors.initials: Y
authors.lastname: Zhang
authors.affiliation: Department of Mathematics, Yunnan Normal University, Kunming 650092, People's Republic of China.
authors.forename: Haihong
authors.initials: H
authors.lastname: Liu
authors.affiliation: Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, People's Republic of China. jzhou@shu.edu.cn.
authors.forename: Jin
authors.initials: J
authors.lastname: Zhou
mesh_terms: D000465:Algorithms; D001426:Bacterial Proteins / Q000235:genetics; D004926:Escherichia coli / Q000235:genetics*; D020869:Gene Expression Profiling; D015964:Gene Expression Regulation, Bacterial; D053263:Gene Regulatory Networks; D005798:Genes, Bacterial; D035683:MicroRNAs / Q000235:genetics*; D009991:Oscillometry; D014176:Protein Biosynthesis; D049490:Systems Biology; D014158:Transcription, Genetic
chemical_list: D001426:Bacterial Proteins; D035683:MicroRNAs