# American Institute of Mathematical Sciences

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

## G1/S transition and cell population dynamics

 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.
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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