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An age-and-cyclin-structured cell population model for healthy and tumoral tissues

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Abstract

We present a nonlinear model of the dynamics of a cell population divided into proliferative and quiescent compartments. The proliferative phase represents the complete cell cycle (G 1−S−G 2−M) of a population committed to divide at its end. The model is structured by the time spent by a cell in the proliferative phase, and by the amount of Cyclin D/(CDK4 or 6) complexes. Cells can transit from one compartment to the other, following transition rules which differ according to the tissue state: healthy or tumoral. The asymptotic behaviour of solutions of the nonlinear model is analysed in two cases, exhibiting tissue homeostasis or tumour exponential growth. The model is simulated and its analytic predictions are confirmed numerically.

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Authors and Affiliations

  1. Projet BANG, UR Rocquencourt, Institut de Recherche en Informatique et en Automatique, BP 105, Le Chesnay Cedex, 78150, France

    Fadia Bekkal Brikci, Jean Clairambault & Benoît Perthame

  2. Institute for Theoretical Medicine, Clinical Pharmacology Department EA3736, Faculty of Medecine RTH Laennec, University Lyon 1, Paradin st, 69376, Lyon Cedex 08, France

    Benjamin Ribba

Authors
  1. Fadia Bekkal Brikci
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  2. Jean Clairambault
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  3. Benjamin Ribba
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  4. Benoît Perthame
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Correspondence to Jean Clairambault.

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Bekkal Brikci, F., Clairambault, J., Ribba, B. et al. An age-and-cyclin-structured cell population model for healthy and tumoral tissues. J. Math. Biol. 57, 91–110 (2008). https://doi.org/10.1007/s00285-007-0147-x

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  • DOI: https://doi.org/10.1007/s00285-007-0147-x

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