Math. Model. Nat. Phenom.
Volume 7, Number 6, 2012Biological oscillations
|Page(s)||107 - 125|
|Published online||12 December 2012|
Modeling Biological Rhythms in Cell Populations
1 Université de Lyon, CNRS UMR 5208,
Université Lyon 1, Institut Camille Jordan 43 blvd. du 11 novembre 1918,
2 INRIA project-team DRACULA, INRIA-antenne Lyon-La Doua, Batiment CEI-1 66 Boulevard Niels Bohr, 69603 Villeurbanne cedex France
⋆ Corresponding author. E-mail: firstname.lastname@example.org
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.
Mathematics Subject Classification: 92B / 92C / 35L / 34E / 34N
Key words: biological rhythms / circadian clock / cell cycle / chronotherapy / delay differential equation / age-structured equations
© EDP Sciences, 2012
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