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The Cell Cycle is a Limit Cycle*

Published online by Cambridge University Press:  20 December 2012

C. Gérard  and
A. Goldbeter
C. Gérard
Affiliation:
Unité de Chronobiologie théorique, Faculté des Sciences, Université Libre de Bruxelles (ULB) Campus Plaine, CP 231, B-1050 Brussels, Belgium On leave at the Department of Biochemistry, University of Oxford, Oxford, UK
A. Goldbeter*
Affiliation:
Unité de Chronobiologie théorique, Faculté des Sciences, Université Libre de Bruxelles (ULB) Campus Plaine, CP 231, B-1050 Brussels, Belgium
*
⋆ Corresponding author. E-mail: [email protected]
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Abstract

Progression along the successive phases of the mammalian cell cycle is driven by anetwork of cyclin-dependent kinases (Cdks). This network is regulated by a variety ofnegative and positive feedback loops. We previously proposed a detailed, 39-variable modelfor the Cdk network and showed that it is capable of temporal self-organization in theform of sustained oscillations, which correspond to the repetitive, transient, sequentialactivation of the cyclin- Cdk complexes that govern the successive phases of the cellcycle [Gérard and Goldbeter (2009) Proc Natl Acad Sci 106, 21643-8]. Here we compare thedynamical behavior of three models of different complexity for the Cdk network driving themammalian cell cycle. The first is the detailed model that counts 39 variables and isbased on Michaelis-Menten kinetics for the enzymatic steps. From this detailed model, webuild a version based only on mass-action kinetics, which counts 80 variables. In thisversion we do not need to assume that enzymes are present in much smaller amounts thattheir substrates, which is not necessarily the case in the cell cycle. We show that thesetwo versions of the model for the Cdk network yield similar results. In particular theypredict sustained oscillations of the limit cycle type. We show that the model for the Cdknetwork can be reduced to a version containing only 5 variables, which is more amenable tostochastic simulations. This skeleton version retains the dynamic properties of the morecomplex versions of the model for the Cdk network in regard to Cdk oscillations. Theregulatory wiring of the Cdk network therefore governs its dynamic behavior, regardless ofthe degree of molecular detail. We discuss the relative advantages of each version of themodel, all of which support the view that the mammalian cell cycle behaves as a limitcycle oscillator.

Keywords

cell cyclemodelCdk networkoscillationscellular rhythm
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 6: Biological oscillations , 2012 , pp. 126 - 166
Copyright
© EDP Sciences, 2012

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Footnotes

*

Note to the reader: due to technical reasons, the PDF version published on January 28, 2013 should replace the previous version.

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