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. [CrossRef] [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). [CrossRef] [PubMed] [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. [CrossRef] [PubMed] [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. [CrossRef] [PubMed] [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. [CrossRef] [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. [CrossRef] [EDP Sciences] [PubMed] [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. [CrossRef] [PubMed] [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. [CrossRef] [PubMed] [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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.