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A simple model of genetic oscillations through regulated degradation

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  • Bottani, Samuel
  • Grammaticos, Basile

Abstract

We present a simple model which aims at the description of the dynamics of cellular regulation through genetic circuits involving a feedback loop between a regulatory factor and a target that specifically triggers degradation of this regulator. In particular we study the possibility for this simple model to reproduce stable oscillations which have been recently observed experimentally. Our model takes the form of a time-delayed differential system and is inspired by the core circuit for the stress resistance p53 system. Depending on the protein degradation rates and the value of the delay we show that it is possible, in the presence of stress, to switch from a stable steady state to one of persistent oscillations (which die out when the stress disappears).

Suggested Citation

  • Bottani, Samuel & Grammaticos, Basile, 2008. "A simple model of genetic oscillations through regulated degradation," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1468-1482.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:5:p:1468-1482
    DOI: 10.1016/j.chaos.2008.03.010
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    1. Drew Endy & Roger Brent, 2001. "Modelling cellular behaviour," Nature, Nature, vol. 409(6818), pages 391-395, January.
    2. Adimy, Mostafa & Crauste, Fabien & Halanay, Andrei & Neamţu, Mihaela & Opriş, Dumitru, 2006. "Stability of limit cycles in a pluripotent stem cell dynamics model," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 1091-1107.
    3. Albert Goldbeter, 2002. "Computational approaches to cellular rhythms," Nature, Nature, vol. 420(6912), pages 238-245, November.
    4. Ygal Haupt & Ruth Maya & Anat Kazaz & Moshe Oren, 1997. "Mdm2 promotes the rapid degradation of p53," Nature, Nature, vol. 387(6630), pages 296-299, May.
    5. Michael B. Elowitz & Stanislas Leibler, 2000. "A synthetic oscillatory network of transcriptional regulators," Nature, Nature, vol. 403(6767), pages 335-338, January.
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    Cited by:

    1. Bottani, Samuel & Grammaticos, Basil, 2012. "Stochastic and deterministic simulations of a delayed genetic oscillation model: Investigating the validity of reductions," Chaos, Solitons & Fractals, Elsevier, vol. 45(5), pages 588-602.
    2. Zhdanov, Vladimir P., 2012. "Periodic perturbation of genetic oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 45(5), pages 577-587.

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