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March  2009, 4(1): 67-90. doi: 10.3934/nhm.2009.4.67

G1/S transition and cell population dynamics

Fadia Bekkal-Brikci 1, , Giovanna Chiorino 2, and  Khalid Boushaba 3,

1. 

Institut de Recherche pour le Développement, 32 avenue Henri Varagnat 93143 Bondy Cedex
2. 

Laboratory of Cancer Pharmacogenomics, Fondo Edo Tempia, via Malta 3, 13900 Biella, Italy
3. 

Iowa State University, Department of Mathematics, 482 Carver Hall Ames, IA 50011

Received  February 2008 Revised  November 2008 Published  February 2009

In this paper we present a model connecting the state of molecular components during the cell cycle at the individual level to the population dynamic. The complexes Cyclin E/CDK2 are good markers of the cell state in its cycle. In this paper we focus on the first transition phase of the cell cycle ($S-G_{2}-M$) where the complexe Cyclin E/CDK2 has a key role in this transition. We give a simple system of differential equations to represent the dynamic of the Cyclin E/CDK2 amount during the cell cycle, and couple it with a cell population dynamic in such way our cell population model is structured by cell age and the amount of Cyclin E/CDK2 with two compartments: cells in the G1 phase and cells in the remainder of the cell cycle ($S-G_{2}-M$). A cell transits from the G1 phase to the S phase when Cyclin E/CDK2 reaches a threshold, which allow us to take into account the variability in the timing of G1/S transition. Then the cell passes through $S-G_{2}-M$ phases and divides with the assumption of unequal division among daughter cells of the final Cyclin E/CDK2 amount. The existence and the asymptotic behavior of the solution of the model is analyzed.
Keywords: semi group., cell population dynamics, Cyclin E/CDK2, G$_{1}/S$ transition, unequal cell division, cell cycle.
Mathematics Subject Classification: 92D25, 92C40, 58K5.
Citation: Fadia Bekkal-Brikci, Giovanna Chiorino, Khalid Boushaba. G1/S transition and cell population dynamics. Networks & Heterogeneous Media, 2009, 4 (1) : 67-90. doi: 10.3934/nhm.2009.4.67
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