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Mathematical analysis of a generalised p53-Mdm2 protein gene expression model

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  • Piotrowska, Monika J.
  • Bartłomiejczyk, Agnieszka
  • Bodnar, Marek

Abstract

We propose the generalisation of the p53-Mdm2 protein gene expression model introduced by Monk (2003). We investigate the stability of a unique positive steady state and formulate conditions which guarantee the occurrence of the Hopf bifurcation. We show that oscillatory behaviour can be caused not only by time lag in protein transcription process, but also can be present in the model without time delay. Moreover, we investigate the stability of new born periodic solutions. Theoretical results are illustrated by numerical simulations and interpreted from the biological point of view.

Suggested Citation

  • Piotrowska, Monika J. & Bartłomiejczyk, Agnieszka & Bodnar, Marek, 2018. "Mathematical analysis of a generalised p53-Mdm2 protein gene expression model," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 26-44.
    • Handle: RePEc:eee:apmaco:v:328:y:2018:i:c:p:26-44
    DOI: 10.1016/j.amc.2018.01.014
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    References listed on IDEAS

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    1. Bert Vogelstein & David Lane & Arnold J. Levine, 2000. "Surfing the p53 network," Nature, Nature, vol. 408(6810), pages 307-310, November.
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