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Abstracts
The paper presents a simple analysis of a long Goodwin’s loop containing many genes. The genes form a closed series. The rate of transcription of any gene is up or down regulated by theprotein product of the preceding gene. We describe the loop with a system of ordinary differential equations of order s. Oscillatory solutions of the system are possible at the odd number of repressions and any number of inductions if the product of all Hill’s coefficients, related to both repressions and inductions, is larger than: [...]
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Year
Volume
Issue
Pages
33-45
Physical description
Dates
published
1 - 01 - 2012
online
15 - 05 - 2013
Contributors
author
- Biophysics Department, Institute of Physics, Maria Curie-Skłodowska University pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, sielewiesiuk@poczta.umcs.lublin.pl
author
- Biophysics Department, Institute of Physics, Maria Curie-Skłodowska University pl. M. Curie-Skłodowskiej 1, 20-031 Lublin
References
- [1] Goodwin, B. C., Oscillatory behavior in enzymatic control processes, Advances in EnzymeRegulation 3 (1965), 425-438.
- [2] Goodwin, B. C., An entrainment model for timed enzyme synthesis in bacteria, Nature 209 (1966), 479-481.
- [3] Invernizzi, S., Treu, G., Quantitative analysis of the Hopf bifurcation in the Goodwin n-dimensional metabolic control system, J. Math. Biol. 29 (1991), 733-742. [Crossref]
- [4] Müller, S., Hofbauer, J., Endler, L., Flamm, Ch., Widder, S., Schuster, P., A generalized model of the repressilator, J. Math. Biol. 53 (2006), 905-937. [Crossref]
- [5] Purcell, O., Savery, N. J., Grierson, C. S., di Bernardo, M., A comparative analysis of synthetic genetic oscillators, J. R. Soc. Interface, doi:10.1098/rsif.2010.0183, Published online. [Crossref]
- [6] Smith, H., Oscillations and multiple steady states in a cyclic gene model with repression, J.Math. Biol. 25 (1987), 169-190.[Crossref]
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_v10246-012-0013-6