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Modeling Biological Rhythms in Cell Populations

Published online by Cambridge University Press:  12 December 2012

R. El Cheikh ,
T. Lepoutre  and
S. Bernard
R. El Cheikh
Affiliation:
Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France INRIA project-team DRACULA, INRIA-antenne Lyon-La Doua, Batiment CEI-1 66 Boulevard Niels Bohr, 69603 Villeurbanne cedex France
T. Lepoutre
Affiliation:
Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France INRIA project-team DRACULA, INRIA-antenne Lyon-La Doua, Batiment CEI-1 66 Boulevard Niels Bohr, 69603 Villeurbanne cedex France
S. Bernard*
Affiliation:
Université de Lyon, CNRS UMR 5208, Université Lyon 1, Institut Camille Jordan 43 blvd. du 11 novembre 1918, F-69622 Villeurbanne cedex, France INRIA project-team DRACULA, INRIA-antenne Lyon-La Doua, Batiment CEI-1 66 Boulevard Niels Bohr, 69603 Villeurbanne cedex France
*
⋆ Corresponding author. E-mail: bernard@math.univ-lyon1.fr
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Abstract

Biological rhythms occur at different levels in the organism. In single cells, the cell division cycle shows rhythmicity in the way its molecular regulators, the cyclin dependant kinases (CDKs), modulate their activity periodically to ensure a healthy progression. In tissues, cell proliferation is driven by the circadian clock, which modulates the progression through the cell cycle along the day. The circadian clock shows endogenous rhythmicity through a robust network of transcription-translation feedback loops that create sustained oscillations. Rhythmicity is preserved in cell populations by the coordination of the clocks among cells, through rhythmic synchronization signals. Here we discuss mechanisms for generating rhythmic activities in cell populations by reviewing some of the mathematical models that deal with them. We discuss the implication of biological rhythms for tissue growth and the possible application to chronomodulated cancer treatments.

Keywords

biological rhythmscircadian clockcell cyclechronotherapydelay differential equationage-structured equations
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 6: Biological oscillations , 2012 , pp. 107 - 125
Copyright
© EDP Sciences, 2012

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