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

Original Article


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.


Cell cycle Cln3 Yeast Cell growth 


  1. 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
  2. Boye, E., Nordström, K., 2003. Coupling the cell-cycle to cell growth. EMBO Rep. 4, 757–760.CrossRefGoogle Scholar
  3. 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
  4. 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
  5. 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.CrossRefGoogle Scholar
  6. Conlon, I., Raff, M., 1999. Size control in animal development. Cell 96, 235–244.CrossRefGoogle Scholar
  7. 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
  8. Cross, F., Archambault, V., Miller, M., Klovstad, M., 2002. Testing a mathematical model of the yeast cell cycle. Mol. Biol. Cell 13, 52–70.CrossRefGoogle Scholar
  9. 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.CrossRefGoogle Scholar
  10. Degterev, A., Boyce, M., Yuan, J., 2003. A decade of caspases. Oncogene 22, 8543–8567.CrossRefGoogle Scholar
  11. 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.CrossRefGoogle Scholar
  12. 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.CrossRefGoogle Scholar
  13. Nasmyth, K., 1996. At the heart of the budding yeast cycle. Trends Genet. 12, 405–412.CrossRefGoogle Scholar
  14. 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.CrossRefGoogle Scholar
  15. 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.CrossRefGoogle Scholar
  16. 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.CrossRefGoogle Scholar
  17. 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.CrossRefGoogle Scholar
  18. Novak, B., Tóth, A., Csikász-Nagy, A., Györffy, B., Tyson, J., Nasmyth, K., 1999. Finishing the cell cycle. J. Theor. Biol. 199, 223–233.CrossRefGoogle Scholar
  19. 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
  20. 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
  21. Rupeš, I., 2002. Checking cell size in yeast. Trends Genet. 18(9), 479–485.CrossRefGoogle Scholar
  22. Tecarro, E., Obeyesekere, M., Auchmuty, G., 2003. Mathematical analysis of a 3-variable cell cycle model. Nonlinear Anal. 4(9), 87–107.MATHMathSciNetGoogle Scholar
  23. Tyson, J., 1999. Models of cell cycle control in eukaryotes. J. Biotech. 71, 239–244.CrossRefGoogle Scholar
  24. Tyson, J., Novak, B., 2001. Regulation of the eukaryotic cell cycle: Molecular antagonism, hysteresis, and irreversible transitions. J. Theor. Biol. 210, 249–263.CrossRefGoogle Scholar
  25. Tyson, J., Novak, B., Odell, G., Chen, K., Thron, C., 1996. Chemical kinetic theory: Understanding cell-cycle regulation. TIBS 21, 89–96.Google Scholar
  26. Varma, A., Morbidelli, M., Wu, H., 1999. Parametric Sensitivity in Chemical Systems. Cambridge University Press, New York.Google Scholar
  27. 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

Copyright information

© Society for Mathematical Biology 2006

Authors and Affiliations

  1. 1.Bioinformatics Unit, Department of Computer ScienceUniversity College LondonLondonUK
  2. 2.Mathematical InstituteUniversity of OxfordOxfordUK

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