Skip to main content
Log in

Modelling Cell Growth and its Modulation of the G1/S Transition

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

We present a model for the regulation of the G1/S transition by cell growth in budding yeast. The model includes a description of cell size, the extracellular nutrient concentration and a simplified model of the G1/S transition as originally reported by Chen et al. [Mol. Biol. Cell 11:369–391, 2000]. By considering cell growth proportional to cell size we show that the cell grows exponentially. In the case where cell growth is considered proportional to the concentration of a sizer protein within the cell, our model exhibits both exponential and linear cell growth for varying parameter values. The effects of varying nutrient concentration and initial cell size are considered in the context of whether progression through the cell-size checkpoint occurs. We consider our results in relation to recent experimental evidence and discuss possible experiments for testing our theoretical predictions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K., Watson, J., 1994. Molecular Biology of the Cell, 3rd edition. Garland Publishing, New York.

    Google Scholar 

  • Boye, E., Nordström, K., 2003. Coupling the cell-cycle to cell growth. EMBO Rep. 4, 757–760.

    Article  Google Scholar 

  • Brooks, R., 1996. Variability in the cell cycle and the control of proliferation. In: John, P. (Ed.), The Cell Cycle. Cambridge University Press, Cambridge, UK.

    Google Scholar 

  • Chen, K., Csikasz-Nagy, A., Gyorffy, B., Val, J., Novak, B., Tyson, J., 2000. Kinetic analysis of a molecular model of the budding yeast cell cycle. Mol. Biol. Cell 11, 369–391.

    Google Scholar 

  • Chen, K., Calzone, L., Csikasz-Nagy, A., Cross, F., Novak, B., Tyson, J., 2004. Integrative analysis of cell cycle control in budding yeast. Mol. Biol. Cell 15, 3841–3862.

    Article  Google Scholar 

  • Conlon, I., Raff, M., 1999. Size control in animal development. Cell 96, 235–244.

    Article  Google Scholar 

  • Conlon, I., Raff, M., 2003. Differences in the way a mammalian cell and yeast cells coordinate cell growth and cell-cycle progression. J. Biol. 2(7), 1–10.

    Google Scholar 

  • Cross, F., Archambault, V., Miller, M., Klovstad, M., 2002. Testing a mathematical model of the yeast cell cycle. Mol. Biol. Cell 13, 52–70.

    Article  Google Scholar 

  • David-Pfeuty, T., 1999. Potent inhibitors of cyclin-dependent kinase 2 induce nuclear accumulation of wild-type p53 and nucleolar fragmentation in human untransformed and tumour-derived cells. Oncogene 18, 7409–7422.

    Article  Google Scholar 

  • Degterev, A., Boyce, M., Yuan, J., 2003. A decade of caspases. Oncogene 22, 8543–8567.

    Article  Google Scholar 

  • Jin, Y., Yim, H., Park, J., Lee, S., 2003. Cdk2 activity is associated with depolarisation of mitochondrial membrane potential during apoptosis. Biochem. Biophys. Res. Commun. 305, 974–980.

    Article  Google Scholar 

  • Lukovic, A., Komoriya, A., Packard, B., Ucker, D.S., 2003. Caspase activity is not sufficient to execute cell death. Exp. Cell Res. 289, 384–395.

    Article  Google Scholar 

  • Nasmyth, K., 1996. At the heart of the budding yeast cycle. Trends Genet. 12, 405–412.

    Article  Google Scholar 

  • Nielsen, L., Reid, S., Greenfield, P., 1997. Cell cycle model to describe animal cell size variation and lag between cell number and biomass dynamics. Biotech. Bioeng. 56(4), 372–379.

    Article  Google Scholar 

  • Nishioka, W., Welsh, R., 1994. Susceptibility to cytotoxis t lymphoctye-induced apoptosis is a function of the proliferative status of the target. J. Exp. Med. 179, 769–774.

    Article  Google Scholar 

  • Novak, B., Csikasz-Nagy, A., Gyorffy, B., Chen, K., Tyson, J., 1998a. Mathematical model of the fission yeast cell cycle with checkpoint controls at the G1/S, G2/M and metaphase/anaphase transitions. Biophys. Chem. 72, 185–200.

    Article  Google Scholar 

  • Novak, B., Csikasz-Nagy, A., Gyorffy, B., Nasmyth, K., Tyson, J., 1998b. Model scenarios for evolution of the eukaryotic cell cycle. Phil. Trans. R. Soc. Lond. B 353, 2063–2076.

    Article  Google Scholar 

  • Novak, B., Tóth, A., Csikász-Nagy, A., Györffy, B., Tyson, J., Nasmyth, K., 1999. Finishing the cell cycle. J. Theor. Biol. 199, 223–233.

    Article  Google Scholar 

  • Nurse, P., Thuriaux, T., Nasmyth, K., 1976. Genetic control of the cell division cycle in the fission yeast S. pombe. Mol. Gen. Genet. 146, 377–386.

    Google Scholar 

  • Padmanabhan, J., Park, D., Greene, L., Shelanski, M., 1999. Role of cell cycle regulatory proteins in cerebral granule neuron apoptosis. J. Neurosci. 19, 8747–8756.

    Google Scholar 

  • Rupeš, I., 2002. Checking cell size in yeast. Trends Genet. 18(9), 479–485.

    Article  Google Scholar 

  • Tecarro, E., Obeyesekere, M., Auchmuty, G., 2003. Mathematical analysis of a 3-variable cell cycle model. Nonlinear Anal. 4(9), 87–107.

    MATH  MathSciNet  Google Scholar 

  • Tyson, J., 1999. Models of cell cycle control in eukaryotes. J. Biotech. 71, 239–244.

    Article  Google Scholar 

  • Tyson, J., Novak, B., 2001. Regulation of the eukaryotic cell cycle: Molecular antagonism, hysteresis, and irreversible transitions. J. Theor. Biol. 210, 249–263.

    Article  Google Scholar 

  • Tyson, J., Novak, B., Odell, G., Chen, K., Thron, C., 1996. Chemical kinetic theory: Understanding cell-cycle regulation. TIBS 21, 89–96.

    Google Scholar 

  • Varma, A., Morbidelli, M., Wu, H., 1999. Parametric Sensitivity in Chemical Systems. Cambridge University Press, New York.

    Google Scholar 

  • Yaglom, J., Linskens, M., Sadis, S., Rubin, D., Futcher, B., Finley, D., 1995. p34-Mediated control of cln3 cyclin degradation. Mol. Cell Biol. 15(2), 731–741.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to T. Alarcón.

Additional information

Both authors contributed equally to this article.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alarcón, T., Tindall, M.J. Modelling Cell Growth and its Modulation of the G1/S Transition. Bull. Math. Biol. 69, 197–214 (2007). https://doi.org/10.1007/s11538-006-9154-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-006-9154-0

Keywords

Navigation