Free Access
Issue
Math. Model. Nat. Phenom.
Volume 7, Number 6, 2012
Biological oscillations
Page(s) 126 - 166
DOI https://doi.org/10.1051/mmnp/20127607
Published online 20 December 2012
  1. A.W. Murray, M.W. Kirschner. Cyclin synthesis drives the early embryonic cell cycle. Nature 339 (1989), 275–280. [CrossRef] [PubMed] [Google Scholar]
  2. A. Murray, T. Hunt. The Cell Cycle : An Introduction. W.H. Freeman and Company (1993), New York. [Google Scholar]
  3. M.A. Félix, J.C. Labbé, M. Dorée, T. Hunt, E. Karsenti. Triggering of cyclin degradation in interphase extracts of amphibian eggs by cdc2 kinase. Nature 346 (1990), 379–382. [CrossRef] [PubMed] [Google Scholar]
  4. J.J. Tyson. Modeling the cell division cycle : cdc2 and cyclin interactions. Proc. Natl. Acad. Sci. USA 88 (1991), 7328–7332. [CrossRef] [Google Scholar]
  5. A. Goldbeter. A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. Proc. Natl. Acad. Sci. USA 88 (1991), 9107–9111. [CrossRef] [Google Scholar]
  6. B. Novak, J.J. Tyson. Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos. J. Cell. Sci. 106 (1993), 1153–1168. [PubMed] [Google Scholar]
  7. J.E. Jr Ferrell, E.M. Machleder. The biochemical basis of an all-or-none cell fate switch in Xenopus oocytes. Science 280 (1998), 895–898. [CrossRef] [PubMed] [Google Scholar]
  8. J.R. Pomerening, E.D. Sontag, J.E. Jr Ferrell. Building a cell cycle oscillator : hysteresis and bistability in the activation of Cdc2. Nat. Cell. Biol. 5 (2003), 346–351. [CrossRef] [PubMed] [Google Scholar]
  9. W. Sha, J. Moore, K. Chen, A.D. Lassaleta, C.-S. Yi, J.J. Tyson, J.C. Sible. Hysteresis drives cell-cycle transitions in Xenopus laevis egg extracts. Proc. Natl. Acad. Sci. USA 100 (2003), 975–980. [CrossRef] [Google Scholar]
  10. B. Novak, J.J. Tyson. Modeling the control of DNA replication in fission yeast. Proc. Natl. Acad. Sci. USA 94 (1997), 9147–9152. [CrossRef] [Google Scholar]
  11. K.C. Chen, L. Calzone, A. Csikasz-Nagy, F.R. Cross, B. Novak, J.J. Tyson. Integrative analysis of cell cycle control in budding yeast. Mol. Biol. Cell. 15 (2004), 3841–3862. [CrossRef] [PubMed] [Google Scholar]
  12. D. Barik, W.T. Baumann, M.R. Paul, B. Novak, J.J. Tyson. A model of yeast cell-cycle regulation based on multisite phosphorylation. Mol. Syst. Biol. 6 (2010), 405. [CrossRef] [PubMed] [Google Scholar]
  13. D.O. Morgan. Principles of Cdk regulation. Nature 374 (1995), 131–134. [CrossRef] [PubMed] [Google Scholar]
  14. D.O. Morgan. The Cell Cycle : Principles of Control. Oxford Univ Press, UK, (2006). [Google Scholar]
  15. Z. Qu, J.N. Weiss, W.R. MacLellan. Regulation of the mammalian cell cycle : a model of the G1-to-S transition. Am. J. Physiol. Cell. Physiol. 284 (2003), 349–364. [CrossRef] [Google Scholar]
  16. M. Swat, A. Kel, H. Herzel. Bifurcation analysis of the regulatory modules of the mammalian G1/S transition. Bioinformatics 20 (2004), 1506–1511. [CrossRef] [PubMed] [Google Scholar]
  17. B. Pfeuty, T. David-Pfeuty, K. Kaneko. Underlying principles of cell fate determination during G1 phase of the mammalian cell cycle. Cell Cycle 7 (2008), 3246–3257. [CrossRef] [PubMed] [Google Scholar]
  18. B. Novak, J.J. Tyson. A model for restriction point control of the mammalian cell cycle. J. Theor. Biol. 230 (2004), 563–579. [CrossRef] [PubMed] [Google Scholar]
  19. E. He, O. Kapuy, R.A. Oliveira, F. Uhlmann, J.J. Tyson, B. Novak. System-level feedbacks make the anaphase switch irreversible. Proc. Natl. Acad. Sci. USA 108 (2011), 10016–10021. [CrossRef] [Google Scholar]
  20. C. Gérard, A. Goldbeter. Temporal self-organization of the cyclin/Cdk network driving the mammalian cell cycle. Proc. Natl. Acad. Sci. USA 106 (2009), 21643–21648. [Google Scholar]
  21. C. Gérard, A. Goldbeter. A skeleton model for the network of cyclin-dependent kinases driving the mammalian cell cycle. Interface Focus 1 (2011), 24–35. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  22. C. Gérard, D. Gonze, A. Goldbeter. Effect of positive feedback loops on the robustness of oscillations in the network of cyclin-dependent kinases driving the mammalian cell cycle. FEBS J. 279 (2012), 3411–3431. [CrossRef] [PubMed] [Google Scholar]
  23. A. Chauhan, S. Lorenzen, H. Herzel, S. Bernard. Regulation of mammalian cell cycle progression in the regenerating liver. J. Theor. Biol. 283 (2011), 103–112. [CrossRef] [PubMed] [Google Scholar]
  24. C. Gérard, A. Goldbeter. Entrainment of the mammalian cell cycle by the circadian clock : Modeling two coupled cellular rhythms. PLoS Comput. Biol. 8(5) : e1002516, (2012). [Google Scholar]
  25. E. Filipski, V.M. King, X.M. Li, T.G. Granda, M.C. Mormont, X. Liu, B. Claustrat, M.H. Hastings, F. Lévi. Host circadian clock as a control point in tumor progression. J. Natl. Cancer Inst. 94 (2002), 690–697. [Google Scholar]
  26. L. Fu, C.C. Lee. The circadian clock : pacemaker and tumour suppressor. Nature 3 (2003), 350–361. [Google Scholar]
  27. J.S. Pendergast, M. Yeom, B.A. Reyes, Y. Ohmiya, S. Yamazaki. Disconnected circadian and cell cycles in a tumor- driven cell line. Commun. Integr. Biol. 3 (2010), 536–539. [CrossRef] [PubMed] [Google Scholar]
  28. L.A. Segel. On the validity of the steady state assumption of enzyme kinetics. Bull. Math. Biol. 50 (1988), 579–593. [MathSciNet] [PubMed] [Google Scholar]
  29. J.A. Borghans, R.J. de Boer, L.A. Segel. Extending the quasi-steady state approximation by changing variables. Bull. Math. Biol. 58 (1996), 43–63. [CrossRef] [PubMed] [Google Scholar]
  30. A. Ciliberto, F. Capuani, J.J. Tyson. Modeling networks of coupled enzymatic reactions using the total quasi-steady state approximation. PLoS Comput. Biol. 3 :e45, (2007). [CrossRef] [PubMed] [Google Scholar]
  31. W. Zachariae, K. Nasmyth. Whose end is destruction : cell division and the anaphase-promoting complex. Genes Dev. 13 (1999), 2039–2058. [Google Scholar]
  32. E.R. Kramer, N. Scheuringer, A.V. Podtelejnikov, M. Mann, J.M. Peters. Mitotic regulation of the APC activator proteins CDC20 and CDH1. Mol. Biol. Cell. 11 (2000), 1555–1569. [CrossRef] [PubMed] [Google Scholar]
  33. I. Hoffmann, P.R. Clarke, M.J. Marcote, E. Karsenti, G. Draetta. Phosphorylation and activation of human cdc25-C by cdc2-cyclin B and its involvement in the self-amplification of MPF at mitosis. EMBO J. 12 (1993), 53–63. [PubMed] [Google Scholar]
  34. M. Sabouri-Ghomi, A. Ciliberto, S. Kar, B. Novak, J.J. Tyson. Antagonism and bistability in protein interaction networks. J. Theor. Biol. 250 (2008), 209–218. [CrossRef] [PubMed] [Google Scholar]
  35. A. Goldbeter, D.E. Jr Koshland. An amplified sensitivity arising from covalent modification in biological systems. Proc. Natl. Acad. Sci. USA 78 (1981), 6840–6844. [Google Scholar]
  36. H. Matsushime, D.E. Quelle, S.A. Shurtleff, M. Shibuya, C.J. Sherr, J.-Y. Kato. D-type cyclin-dependent kinase activity in mammalian cells. Mol. Cell. Biol. 14 (1994), 2066–2076. [PubMed] [Google Scholar]
  37. A. Goldbeter, C. Gérard, J.-C. Leloup. Biologie des systèmes et rythmes cellulaires. Médecine/Sciences 26 (2010), 49–56. [Google Scholar]
  38. A. Goldbeter, C. Gérard, J.-C. Leloup, D. Gonze, G. Dupont. Systems biology of cellular rhythms. FEBS Lett. 586 (2012), 2955–2965. [CrossRef] [PubMed] [Google Scholar]
  39. C. Gérard, A. Goldbeter. From simple to complex patterns of oscillatory behavior in a model for the mammalian cell cycle containing multiple oscillatory circuits. Chaos 20 (2010), 045109. [Google Scholar]
  40. S. Mittnacht. Control of pRB phosphorylation. Curr. Opin. Genet. Dev. 8 (1998), 21–27. [CrossRef] [PubMed] [Google Scholar]
  41. J.W. Harbour, D.C. Dean. The Rb/E2F pathway : expanding roles and emerging paradigms. Genes Dev. 14 (2000), 2393–2409. [CrossRef] [PubMed] [Google Scholar]
  42. J.-H. Dannenberg, A. van Rossum, L. Schuijff, H. te Riele. Ablation of the Retinoblastoma gene family deregulates G1 control causing immortalization and increased cell turnover under growth-restricting conditions. Genes Dev. 14 (2000), 3051–3064. [CrossRef] [PubMed] [Google Scholar]
  43. J. Sage, G.J. Mulligan, L.D. Attardi, A. Miller, S. Chen, B. Williams, E. Theodorou, T. Jacks. Targeted disruption of the three Rb-related genes leads to loss of G1 control and immortalization. Genes Dev. 14 (2000), 3037–3050. [CrossRef] [PubMed] [Google Scholar]
  44. J.R. Pomerening, S.Y. Kim, J.E. Jr Ferrell. Systems-level dissection of the cell-cycle oscillator : bypassing positive feedback produces damped oscillations. Cell 122 (2005), 565–578. [CrossRef] [PubMed] [Google Scholar]
  45. D. Gonze, M. Hafner. Positive feedbacks contribute to the robustness of the cell cycle with respect to molecular noise. Adv. in theory of control, signals. LNCIS 407, (2010) pp. 283–295 (Lévine J & Müllhaupt, eds), Springer-Verlag Berlin Heidelberg, Germany. [Google Scholar]
  46. C. Gérard, A. Goldbeter. From quiescence to proliferation : Cdk oscillations drive the mammalian cell cycle. Front. Physiol. 3 (2012), 413. [PubMed] [Google Scholar]
  47. A. Altinok, D. Gonze, F. Lévi, A. Goldbeter. An automaton model for the cell cycle. Interface Focus 1 (2011), 36–47. [Google Scholar]
  48. A. Altinok, F. Lévi, A. Goldbeter. A cell cycle automaton model for probing circadian patterns of anticancer drug delivery. Adv. Drug Deliv. Rev. 59 (2007), 1036–1053. [CrossRef] [PubMed] [Google Scholar]
  49. A.T. Winfree. Discontinuities and singularities in the timing of nuclear division. In : Cell Cycle Clocks. L.N. Edmunds Jr, ed. Marcel Dekker, New York and Basel, (1984) pp. 63–80. [Google Scholar]
  50. L.N. Jr. Edmunds. Cellular and Molecular Bases of Biological Clocks. Models and Mechanisms for Circadian Time- keeping. Springer, New York (1988). [Google Scholar]
  51. A.T. Winfree. The Geometry of Biological Time. Springer, New York (Reprinted as Springer Study Edition, 1990, Springer, Berlin, 1980). [Google Scholar]
  52. J.-C. Leloup, A. Goldbeter. A molecular explanation for the long-term suppression of circadian rhythms by a single light pulse. Am. J. Physiol. Reg. Integr. Comp. Physiol. 280 (2001), R1206-R1212. [Google Scholar]
  53. D. Gonze, A. Goldbeter. A model for a network of phosphorylation-dephosphorylation cycles displaying the dynamics of dominoes and clocks. J Theor Biol 210 (2001), 167–186. (See erratum : J. Theor. Biol. 212 (2001), 565. [CrossRef] [PubMed] [Google Scholar]
  54. I. Conlon, M. Raff. Differences in the way a mammalian cell and yeast cells coordinate cell growth and cell-cycle progression. J. Biol. 2 (2003), 7. [CrossRef] [PubMed] [Google Scholar]

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