Positive And Negative Feedback Loops Coupled By Common Transcription Activator And Repressor
Languages of publication
Dynamical systems consisting of two interlocked loops with negative and positive feedback have been studied using the linear analysis of stability and numerical solutions. Conditions for saddle-node bifurcation were formulated in a general form. Conditions for Hopf bifurcations were found in a few symmetrical cases. Auto-oscillations, when they exist, are generated by the negative feedback repressive loop. This loop determines the frequency and amplitude of oscillations. The positive feedback loop of activation slightly modifies the oscillations. Oscillations are possible when the difference between Hilll’s coefficients of the repression and activation is sufficiently high. The highly cooperative activation loop with a fast turnover slows down or even makes the oscillations impossible. The system under consideration can constitute a component of epigenetic or enzymatic regulation network.
1 - 3 - 2015
13 - 3 - 2015
- 1. References: Alon U. (2007) Network motifs: theory and experimental approaches. Nature Reviews Genetics 8, 450-461. [WoS][Crossref]
- 2. Dunlap J.C. (1999) Molecular bases for circadian clocks, Cell 96, 271-290
- 3. Feng D., Lazar M.A. (2012) Clocks, metabolism, and the epigenome, Mol. Cell 47, 158-167. [WoS]
- 4. Goodwin B.C. (1966) Oscillatory behavior in enzymatic control processes. Advances in Enzyme Regulation 3, 425-438
- 5. Hogg W.S.(2005) Essential Microbiology, Wiley, Chichester.
- 6. Invernizzi S., T reu G. (1991) Quantitative analysis of the Hopf bifurcation in the Goodwin n-dimensional metabolic control system, J. Math. Biol. 29, 733-742. [Crossref]
- 7. Jolma I.W., Laerum O.D., Lillo C., Ruoff P. (2010) Circadian oscillators in eukaryotes. WIREs Systems Biology and Medicine 2, 533-549 [WoS][Crossref]
- 8. Majercak J., Wen-Feng Chen, Edery I. (2004), Splicing of the period gene 3’- terminal intron is regulated by light, circadian clock factors, and phospholipase C, Mol. Cell Biol. 24, 3359-3372. [Crossref]
- 9. Müller S., Hofbauer J., Endler L., F lamm C ., Widder S., S chuster P . (2006) A generalized model of the repressilator. J. Math. Biol. 53, 905-937 [Crossref]
- 10. Nayfeh A.H., Balachndran B. (1995), Applied Nonlinear Dynamics, Wiley, New York.
- 11. Niehrs Ch., Pollet N. (1999), Synexpression groups in eukaryotes, Nature 402, 483-487.
- 12. Oster H. (2010), Circadian clocks and metabolism, chpt. 5, in: Albrecht U. (ed.) The Circadian Clock, Springer, New York.
- 13. Ripperger J.A, Brown S.A. (2010) Transcriptional regulation of circadian clocks, chpt. 2, in: Albrecht U. (ed.) The Circadian Clock, Springer, New York.
- 14. Saithong T., Painter H.J., Millar A.J. (2010), The contribution of the interlocking loops and extensive nonlinearity to the properties of circadian clock models. PLoS ONE 5 (11) e13867, doi: 101371. [WoS]
- 15. Sielewiesiuk J., Łopaciuk A. (2012) Regulation of gene expression by Goodwin’s loop with many genes. Annales Universitatis Mariae Curie-Skłodowska, sectio AAA Physica 67, 31-45.
- 16. Steiger D . K öster T . ( 2011), Spotlight on post-transcriptional control in the circadian system. Cell Mol. Life Sci. 68, 71-83.[Crossref][WoS]
Publication order reference