Stability and bifurcation of genetic regulatory networks with small RNAs and multiple delays

References

• Y. Bar-Yam, D. Harmon, and B. de Bivort, Attractors and democratic dynamics, Science 323 (2009), pp. 1016–1017. doi: 10.1126/science.1163225
   PubMed Web of Science ®Google Scholar
• J. Cao and F. Ren, Exponential stability of discrete-time genetic regulatory networks with delays, IEEE Trans. Neural Netw. 19 (2008), pp. 520–523. doi: 10.1109/TNN.2007.911748
   PubMed Web of Science ®Google Scholar
• L. Chen and K. Aihara, Stability of genetic regulatory networks with time delay, IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 49 (2002), pp. 602–608. doi: 10.1109/TCSI.2002.1001949
   Google Scholar
• M. Ghildiyal and P. Zamore, Small silencing RNAs: An expanding universe, Nat. Rev. Genet. 10 (2009), pp. 94–108. doi: 10.1038/nrg2504
   PubMed Web of Science ®Google Scholar
• S. Gottesman, Micros for microbes: Non-coding regulatory RNA in bacteria, Trends Genet. 21 (2005), pp. 399–404. doi: 10.1016/j.tig.2005.05.008
   PubMed Web of Science ®Google Scholar
• M. Lagomarsino, B. Bassetti, G. Castellani, and D. Remondini, Functional models for large-scale gene regulation networks: realism and fiction, Mol. Biosyst. 5 (2009), pp. 335–344. doi: 10.1039/b816841p
   PubMed Web of Science ®Google Scholar
• R. Lee, R. Feinbaum, and V. Ambros, The C-elegans heterochronic gene lin-4 encodes small RNAs with antisense complementarity to lin-14, Cell 75 (1993), pp. 843–854. doi: 10.1016/0092-8674(93)90529-Y
   PubMed Web of Science ®Google Scholar
• J. Lewis, Autoinhibition with transcriptional delay: A simple mechanism for the zebrafish somitogenesis oscillator, Curr. Biol. 13 (2003), pp. 1398–1408. doi: 10.1016/S0960-9822(03)00534-7
   PubMed Web of Science ®Google Scholar
• C. Li, L. Chen, and K. Aihara, Stability of genetic networks with SUM regulatory logic: Lur's systems and LMI approach, IEEE Trans. Circuits Syst. I Regul. Pap. 53 (2006), pp. 2452–2458.
   Google Scholar
• V. Kim, J. Han, and M. Siomi, Biogenesis of small RNAs in animals, Nat. Rev. Mol. Cell. Biol. 10 (2009), pp. 126–139. doi: 10.1038/nrm2632
   PubMed Web of Science ®Google Scholar
• V. Kolmanovskii and A. Myshkis, Introduction to the Theory and Applications of Functional Differential Equations, Kluwer Academic Publishers, Dordrecht, 1999.
   Google Scholar
• D. Kulasiri, L. Nguyen, S. Samarasinghe, and Z. Xie, A review of systems biology perspective on genetic regulatory networks with examples, Curr. Bioinf. 3 (2008), pp. 197–225. doi: 10.2174/157489308785909214
   Web of Science ®Google Scholar
• N.A.M. Monk, Oscillatory expression of HES1, p53, and NF-κB driven by transcriptional time delays, Curr. Biol. 13 (2003), pp. 1409–1413. doi: 10.1016/S0960-9822(03)00494-9
   Google Scholar
• F. Ren and J. Cao, Asymptotic and robust stability of genetic regulatory networks with time-varying delays, Neurocomputing 71 (2008), pp. 834–842.
   Google Scholar
• J. Shen, Z. Liu, W. Zheng, F. Xu, and L. Chen, Oscillatory dynamics in a simple gene regulatory network mediated by mall RNAs, Phys. A 388 (2009), pp. 2995–3000. doi: 10.1016/j.physa.2009.03.032
   Web of Science ®Google Scholar
• G. Wang and J. Cao, Robust exponential stability analysis for stochastic genetic networks with uncertain parameters, Commun. Nonlinear Sci. Numer. Simul. 14 (2009), pp. 3369–3378. doi: 10.1016/j.cnsns.2009.01.004
   Web of Science ®Google Scholar
• Z. Wang, H. Gao, J. Cao, and X. Liu, On delayed genetic regulatory networks with polytopic uncertainties: Robust stability analysis, IEEE Trans. Nanobiosci. 7 (2008), pp. 154–163. doi: 10.1109/TNB.2008.2000746
   PubMed Web of Science ®Google Scholar
• Y. Wang, Z. Ma, J. Shen, Z. Liu, and L. Chen, Periodic oscillation in delayed gene networks with SUM regulatory logic and small perturbations, Math. Biosci. 220 (2009), pp. 34–44. doi: 10.1016/j.mbs.2009.03.010
   PubMed Web of Science ®Google Scholar
• K. Wang, L. Wang, Z. Teng, and H. Jiang, Stability and bifurcation of genetic regulatory networks with delays, Neurocomputing 73 (2010), pp. 2882–2892. doi: 10.1016/j.neucom.2010.08.009
   Web of Science ®Google Scholar
• J. Wei and C. Yu, Hopf bifurcation analysis in a model of oscillatory gene expression with delay, Proc. Roy. Soc. Edinburgh 139A (2009), pp. 879–895. doi: 10.1017/S0308210507000091
   Google Scholar
• B. Wightman, I. Ha, and G. Ruvkun, Posttranscriptional regulation of the heterochronic gene lin-14 by lin-4 mediates temporal pattern-formation in C-elegans, Cell 75 (1993), pp. 855–862. doi: 10.1016/0092-8674(93)90530-4
   PubMed Web of Science ®Google Scholar
• F. Wu, Global and robust stability analysis of genetic regulatory networks with time-varying delays and parameter uncertainties, IEEE Trans. Biomed. Circuits Syst. 5 (2011), pp. 391–398. doi: 10.1109/TBCAS.2011.2124459
   PubMed Web of Science ®Google Scholar
• F. Wu, Stability and bifurcation of ring-structured genetic regulatory networks with time delays, IEEE Trans. Circuits Syst. I Regul. Pap. 59 (2012), pp. 1312–1320. doi: 10.1109/TCSI.2011.2173385
   Web of Science ®Google Scholar
• M. Xiao and J. Cao, Genetic oscillation deduced from Hopf bifurcation in a genetic regulatory network with delays, Math. Biosci. 215 (2008), pp. 55–63. doi: 10.1016/j.mbs.2008.05.004
   PubMed Web of Science ®Google Scholar
• P. Zamore and B. Haley, Ribo-gnome: The big world of small RNAs, Science 309 (2005), pp. 1519–1524. doi: 10.1126/science.1111444
   PubMed Web of Science ®Google Scholar
• V. Zhdanov, Kinetic models of gene expression including non-coding RNAs, Phys. Rep. 500 (2011), pp. 1–42. doi: 10.1016/j.physrep.2010.12.002
   Web of Science ®Google Scholar