American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Tailored finite point method for the interface problem
  • NHM Home
  • This Issue
  • Next Article
    A uniformly second order numerical method for the one-dimensional discrete-ordinate transport equation and its diffusion limit with interface
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 and Heterogeneous Media, 2009, 4 (1) : 67-90. doi: 10.3934/nhm.2009.4.67
[1]

Orit Lavi, Doron Ginsberg, Yoram Louzoun. Regulation of modular Cyclin and CDK feedback loops by an E2F transcription oscillator in the mammalian cell cycle. Mathematical Biosciences & Engineering, 2011, 8 (2) : 445-461. doi: 10.3934/mbe.2011.8.445
[2]

Ricardo Borges, Àngel Calsina, Sílvia Cuadrado. Equilibria of a cyclin structured cell population model. Discrete and Continuous Dynamical Systems - B, 2009, 11 (3) : 613-627. doi: 10.3934/dcdsb.2009.11.613
[3]

Frédérique Billy, Jean Clairambault, Franck Delaunay, Céline Feillet, Natalia Robert. Age-structured cell population model to study the influence of growth factors on cell cycle dynamics. Mathematical Biosciences & Engineering, 2013, 10 (1) : 1-17. doi: 10.3934/mbe.2013.10.1
[4]

Ali Ashher Zaidi, Bruce Van Brunt, Graeme Charles Wake. A model for asymmetrical cell division. Mathematical Biosciences & Engineering, 2015, 12 (3) : 491-501. doi: 10.3934/mbe.2015.12.491
[5]

Qi Wang, Lifang Huang, Kunwen Wen, Jianshe Yu. The mean and noise of stochastic gene transcription with cell division. Mathematical Biosciences & Engineering, 2018, 15 (5) : 1255-1270. doi: 10.3934/mbe.2018058
[6]

Paolo Ubezio. Unraveling the complexity of cell cycle effects of anticancer drugs in cell populations. Discrete and Continuous Dynamical Systems - B, 2004, 4 (1) : 323-335. doi: 10.3934/dcdsb.2004.4.323
[7]

Janet Dyson, Rosanna Villella-Bressan, G. F. Webb. The evolution of a tumor cord cell population. Communications on Pure and Applied Analysis, 2004, 3 (3) : 331-352. doi: 10.3934/cpaa.2004.3.331
[8]

Cristina Anton, Alan Yong. Stochastic dynamics and survival analysis of a cell population model with random perturbations. Mathematical Biosciences & Engineering, 2018, 15 (5) : 1077-1098. doi: 10.3934/mbe.2018048
[9]

Tomas Alarcon, Philipp Getto, Anna Marciniak-Czochra, Maria dM Vivanco. A model for stem cell population dynamics with regulated maturation delay. Conference Publications, 2011, 2011 (Special) : 32-43. doi: 10.3934/proc.2011.2011.32
[10]

Yu-Hsien Chang, Guo-Chin Jau. The behavior of the solution for a mathematical model for analysis of the cell cycle. Communications on Pure and Applied Analysis, 2006, 5 (4) : 779-792. doi: 10.3934/cpaa.2006.5.779
[11]

Katarzyna Pichór, Ryszard Rudnicki. Applications of stochastic semigroups to cell cycle models. Discrete and Continuous Dynamical Systems - B, 2019, 24 (5) : 2365-2381. doi: 10.3934/dcdsb.2019099
[12]

Mostafa Adimy, Laurent Pujo-Menjouet. Asymptotic behavior of a singular transport equation modelling cell division. Discrete and Continuous Dynamical Systems - B, 2003, 3 (3) : 439-456. doi: 10.3934/dcdsb.2003.3.439
[13]

Shinji Nakaoka, Hisashi Inaba. Demographic modeling of transient amplifying cell population growth. Mathematical Biosciences & Engineering, 2014, 11 (2) : 363-384. doi: 10.3934/mbe.2014.11.363
[14]

A. Chauviere, L. Preziosi, T. Hillen. Modeling the motion of a cell population in the extracellular matrix. Conference Publications, 2007, 2007 (Special) : 250-259. doi: 10.3934/proc.2007.2007.250
[15]

Gheorghe Craciun, Baltazar Aguda, Avner Friedman. Mathematical Analysis Of A Modular Network Coordinating The Cell Cycle And Apoptosis. Mathematical Biosciences & Engineering, 2005, 2 (3) : 473-485. doi: 10.3934/mbe.2005.2.473
[16]

Richard L Buckalew. Cell cycle clustering and quorum sensing in a response / signaling mediated feedback model. Discrete and Continuous Dynamical Systems - B, 2014, 19 (4) : 867-881. doi: 10.3934/dcdsb.2014.19.867
[17]

David S. Ross, Christina Battista, Antonio Cabal, Khamir Mehta. Dynamics of bone cell signaling and PTH treatments of osteoporosis. Discrete and Continuous Dynamical Systems - B, 2012, 17 (6) : 2185-2200. doi: 10.3934/dcdsb.2012.17.2185
[18]

Yuchi Qiu, Weitao Chen, Qing Nie. Stochastic dynamics of cell lineage in tissue homeostasis. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 3971-3994. doi: 10.3934/dcdsb.2018339
[19]

Yangjin Kim, Hans G. Othmer. Hybrid models of cell and tissue dynamics in tumor growth. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1141-1156. doi: 10.3934/mbe.2015.12.1141
[20]

Huiyan Zhu, Xingfu Zou. Dynamics of a HIV-1 Infection model with cell-mediated immune response and intracellular delay. Discrete and Continuous Dynamical Systems - B, 2009, 12 (2) : 511-524. doi: 10.3934/dcdsb.2009.12.511

2021 Impact Factor: 1.41

Tools

Metrics

  • PDF downloads (87)
  • HTML views (0)
  • Cited by (1)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy