Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-24T13:58:04.020Z Has data issue: false hasContentIssue false
  • English
  • Français

The Cell Cycle is a Limit Cycle*

Published online by Cambridge University Press:  20 December 2012

C. Gérard  and
A. Goldbeter
C. Gérard
Affiliation:
Unité de Chronobiologie théorique, Faculté des Sciences, Université Libre de Bruxelles (ULB) Campus Plaine, CP 231, B-1050 Brussels, Belgium On leave at the Department of Biochemistry, University of Oxford, Oxford, UK
A. Goldbeter*
Affiliation:
Unité de Chronobiologie théorique, Faculté des Sciences, Université Libre de Bruxelles (ULB) Campus Plaine, CP 231, B-1050 Brussels, Belgium
*
⋆ Corresponding author. E-mail: [email protected]
Get access

Abstract

Progression along the successive phases of the mammalian cell cycle is driven by anetwork of cyclin-dependent kinases (Cdks). This network is regulated by a variety ofnegative and positive feedback loops. We previously proposed a detailed, 39-variable modelfor the Cdk network and showed that it is capable of temporal self-organization in theform of sustained oscillations, which correspond to the repetitive, transient, sequentialactivation of the cyclin- Cdk complexes that govern the successive phases of the cellcycle [Gérard and Goldbeter (2009) Proc Natl Acad Sci 106, 21643-8]. Here we compare thedynamical behavior of three models of different complexity for the Cdk network driving themammalian cell cycle. The first is the detailed model that counts 39 variables and isbased on Michaelis-Menten kinetics for the enzymatic steps. From this detailed model, webuild a version based only on mass-action kinetics, which counts 80 variables. In thisversion we do not need to assume that enzymes are present in much smaller amounts thattheir substrates, which is not necessarily the case in the cell cycle. We show that thesetwo versions of the model for the Cdk network yield similar results. In particular theypredict sustained oscillations of the limit cycle type. We show that the model for the Cdknetwork can be reduced to a version containing only 5 variables, which is more amenable tostochastic simulations. This skeleton version retains the dynamic properties of the morecomplex versions of the model for the Cdk network in regard to Cdk oscillations. Theregulatory wiring of the Cdk network therefore governs its dynamic behavior, regardless ofthe degree of molecular detail. We discuss the relative advantages of each version of themodel, all of which support the view that the mammalian cell cycle behaves as a limitcycle oscillator.

Keywords

cell cyclemodelCdk networkoscillationscellular rhythm
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 6: Biological oscillations , 2012 , pp. 126 - 166
Copyright
© EDP Sciences, 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

Note to the reader: due to technical reasons, the PDF version published on January 28, 2013 should replace the previous version.

References

Références

Murray, A.W., Kirschner, M.W.. Cyclin synthesis drives the early embryonic cell cycle. Nature 339 (1989), 275–280. CrossRefGoogle Scholar
A. Murray, T. Hunt. The Cell Cycle : An Introduction. W.H. Freeman and Company (1993), New York.
Félix, M.A., Labbé, J.C., Dorée, M., Hunt, T., Karsenti, E.. Triggering of cyclin degradation in interphase extracts of amphibian eggs by cdc2 kinase. Nature 346 (1990), 379–382. CrossRefGoogle ScholarPubMed
Tyson, J.J.. Modeling the cell division cycle : cdc2 and cyclin interactions. Proc. Natl. Acad. Sci. USA 88 (1991), 7328–7332. CrossRefGoogle Scholar
Goldbeter, A.. A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. Proc. Natl. Acad. Sci. USA 88 (1991), 9107–9111. CrossRefGoogle ScholarPubMed
Novak, B., Tyson, J.J.. Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos. J. Cell. Sci. 106 (1993), 1153–1168. Google ScholarPubMed
Ferrell, J.E. Jr, Machleder, E.M.. The biochemical basis of an all-or-none cell fate switch in Xenopus oocytes. Science 280 (1998), 895–898. CrossRefGoogle Scholar
Pomerening, J.R., Sontag, E.D., Ferrell, J.E. Jr. Building a cell cycle oscillator : hysteresis and bistability in the activation of Cdc2. Nat. Cell. Biol. 5 (2003), 346–351. CrossRefGoogle ScholarPubMed
Sha, W., Moore, J., Chen, K., Lassaleta, A.D., Yi, C.-S., Tyson, J.J., Sible, J.C.. Hysteresis drives cell-cycle transitions in Xenopus laevis egg extracts. Proc. Natl. Acad. Sci. USA 100 (2003), 975–980. CrossRefGoogle ScholarPubMed
Novak, B., Tyson, J.J.. Modeling the control of DNA replication in fission yeast. Proc. Natl. Acad. Sci. USA 94 (1997), 9147–9152. CrossRefGoogle ScholarPubMed
Chen, K.C., Calzone, L., Csikasz-Nagy, A., Cross, F.R., Novak, B., Tyson, J.J.. Integrative analysis of cell cycle control in budding yeast. Mol. Biol. Cell. 15 (2004), 3841–3862. CrossRefGoogle Scholar
Barik, D., Baumann, W.T., Paul, M.R., Novak, B., Tyson, J.J.. A model of yeast cell-cycle regulation based on multisite phosphorylation. Mol. Syst. Biol. 6 (2010), 405. CrossRefGoogle ScholarPubMed
Morgan, D.O.. Principles of Cdk regulation. Nature 374 (1995), 131–134. CrossRefGoogle ScholarPubMed
D.O. Morgan. The Cell Cycle : Principles of Control. Oxford Univ Press, UK, (2006).
Qu, Z., Weiss, J.N., MacLellan, W.R.. Regulation of the mammalian cell cycle : a model of the G1-to-S transition. Am. J. Physiol. Cell. Physiol. 284 (2003), 349–364. CrossRefGoogle ScholarPubMed
Swat, M., Kel, A., Herzel, H.. Bifurcation analysis of the regulatory modules of the mammalian G1/S transition. Bioinformatics 20 (2004), 1506–1511. CrossRefGoogle ScholarPubMed
Pfeuty, B., David-Pfeuty, T., Kaneko, K.. Underlying principles of cell fate determination during G1 phase of the mammalian cell cycle. Cell Cycle 7 (2008), 3246–3257. CrossRefGoogle ScholarPubMed
Novak, B., Tyson, J.J.. A model for restriction point control of the mammalian cell cycle. J. Theor. Biol. 230 (2004), 563–579. CrossRefGoogle ScholarPubMed
He, E., Kapuy, O., Oliveira, R.A., Uhlmann, F., Tyson, J.J., Novak, B.. System-level feedbacks make the anaphase switch irreversible. Proc. Natl. Acad. Sci. USA 108 (2011), 10016–10021. CrossRefGoogle Scholar
Gérard, C., Goldbeter, A.. Temporal self-organization of the cyclin/Cdk network driving the mammalian cell cycle. Proc. Natl. Acad. Sci. USA 106 (2009), 21643–21648. CrossRefGoogle ScholarPubMed
Gérard, C., Goldbeter, A.. A skeleton model for the network of cyclin-dependent kinases driving the mammalian cell cycle. Interface Focus 1 (2011), 24–35. CrossRefGoogle Scholar
Gérard, C., Gonze, D., Goldbeter, A.. 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. CrossRefGoogle Scholar
Chauhan, A., Lorenzen, S., Herzel, H., Bernard, S.. Regulation of mammalian cell cycle progression in the regenerating liver. J. Theor. Biol. 283 (2011), 103–112. CrossRefGoogle ScholarPubMed
Gérard, C., Goldbeter, A.. Entrainment of the mammalian cell cycle by the circadian clock : Modeling two coupled cellular rhythms. PLoS Comput. Biol. 8(5) : e1002516, (2012). CrossRefGoogle ScholarPubMed
Filipski, E., King, V.M., Li, X.M., Granda, T.G., Mormont, M.C., Liu, X., Claustrat, B., Hastings, M.H., Lévi, F.. Host circadian clock as a control point in tumor progression. J. Natl. Cancer Inst. 94 (2002), 690–697. CrossRefGoogle ScholarPubMed
Fu, L., Lee, C.C.. The circadian clock : pacemaker and tumour suppressor. Nature 3 (2003), 350–361. Google ScholarPubMed
Pendergast, J.S., Yeom, M., Reyes, B.A., Ohmiya, Y., Yamazaki, S.. Disconnected circadian and cell cycles in a tumor- driven cell line. Commun. Integr. Biol. 3 (2010), 536–539. CrossRefGoogle Scholar
Segel, L.A.. On the validity of the steady state assumption of enzyme kinetics. Bull. Math. Biol. 50 (1988), 579–593. CrossRefGoogle ScholarPubMed
Borghans, J.A., de Boer, R.J., Segel, L.A.. Extending the quasi-steady state approximation by changing variables. Bull. Math. Biol. 58 (1996), 43–63. CrossRefGoogle ScholarPubMed
Ciliberto, A., Capuani, F., Tyson, J.J.. Modeling networks of coupled enzymatic reactions using the total quasi-steady state approximation. PLoS Comput. Biol. 3 :e45, (2007). CrossRefGoogle ScholarPubMed
Zachariae, W., Nasmyth, K.. Whose end is destruction : cell division and the anaphase-promoting complex. Genes Dev. 13 (1999), 2039–2058. CrossRefGoogle ScholarPubMed
Kramer, E.R., Scheuringer, N., Podtelejnikov, A.V., Mann, M., Peters, J.M.. Mitotic regulation of the APC activator proteins CDC20 and CDH1. Mol. Biol. Cell. 11 (2000), 1555–1569. CrossRefGoogle ScholarPubMed
Hoffmann, I., Clarke, P.R., Marcote, M.J., Karsenti, E., Draetta, G.. 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. Google ScholarPubMed
Sabouri-Ghomi, M., Ciliberto, A., Kar, S., Novak, B., Tyson, J.J.. Antagonism and bistability in protein interaction networks. J. Theor. Biol. 250 (2008), 209–218. CrossRefGoogle ScholarPubMed
Goldbeter, A., Koshland, D.E. Jr. An amplified sensitivity arising from covalent modification in biological systems. Proc. Natl. Acad. Sci. USA 78 (1981), 6840–6844. CrossRefGoogle Scholar
Matsushime, H., Quelle, D.E., Shurtleff, S.A., Shibuya, M., Sherr, C.J., Kato, J.-Y.. D-type cyclin-dependent kinase activity in mammalian cells. Mol. Cell. Biol. 14 (1994), 2066–2076. CrossRefGoogle Scholar
Goldbeter, A., Gérard, C., Leloup, J.-C.. Biologie des systèmes et rythmes cellulaires. Médecine/Sciences 26 (2010), 49–56. CrossRefGoogle Scholar
Goldbeter, A., Gérard, C., Leloup, J.-C., Gonze, D., Dupont, G.. Systems biology of cellular rhythms. FEBS Lett. 586 (2012), 2955–2965. CrossRefGoogle ScholarPubMed
Gérard, C., Goldbeter, A.. From simple to complex patterns of oscillatory behavior in a model for the mammalian cell cycle containing multiple oscillatory circuits. Chaos 20 (2010), 045109. CrossRefGoogle Scholar
Mittnacht, S.. Control of pRB phosphorylation. Curr. Opin. Genet. Dev. 8 (1998), 21–27. CrossRefGoogle Scholar
Harbour, J.W., Dean, D.C.. The Rb/E2F pathway : expanding roles and emerging paradigms. Genes Dev. 14 (2000), 2393–2409. CrossRefGoogle ScholarPubMed
Dannenberg, J.-H., van Rossum, A., Schuijff, L., te Riele, H.. 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. CrossRefGoogle ScholarPubMed
Sage, J., Mulligan, G.J., Attardi, L.D., Miller, A., Chen, S., Williams, B., Theodorou, E., Jacks, T.. Targeted disruption of the three Rb-related genes leads to loss of G1 control and immortalization. Genes Dev. 14 (2000), 3037–3050. CrossRefGoogle ScholarPubMed
Pomerening, J.R., Kim, S.Y., Ferrell, J.E. Jr. Systems-level dissection of the cell-cycle oscillator : bypassing positive feedback produces damped oscillations. Cell 122 (2005), 565–578. CrossRefGoogle ScholarPubMed
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.
Gérard, C., Goldbeter, A.. From quiescence to proliferation : Cdk oscillations drive the mammalian cell cycle. Front. Physiol. 3 (2012), 413. CrossRefGoogle ScholarPubMed
Altinok, A., Gonze, D., Lévi, F., Goldbeter, A.. An automaton model for the cell cycle. Interface Focus 1 (2011), 36–47. CrossRefGoogle Scholar
Altinok, A., Lévi, F., Goldbeter, A.. A cell cycle automaton model for probing circadian patterns of anticancer drug delivery. Adv. Drug Deliv. Rev. 59 (2007), 1036–1053. CrossRefGoogle ScholarPubMed
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.
L.N. Jr. Edmunds. Cellular and Molecular Bases of Biological Clocks. Models and Mechanisms for Circadian Time- keeping. Springer, New York (1988).
A.T. Winfree. The Geometry of Biological Time. Springer, New York (Reprinted as Springer Study Edition, 1990, Springer, Berlin, 1980).
Leloup, J.-C., Goldbeter, A.. 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 ScholarPubMed
Gonze, D., Goldbeter, A.. 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. CrossRefGoogle ScholarPubMed
Conlon, I., Raff, M.. Differences in the way a mammalian cell and yeast cells coordinate cell growth and cell-cycle progression. J. Biol. 2 (2003), 7. CrossRefGoogle Scholar