Skip to main content
SpringerLink
Log in

Role of Computational Modeling in Understanding Cell Cycle Oscillators

  • Protocol
Cell Cycle Oscillators

Part of the book series: Methods in Molecular Biology ((MIMB,volume 1342))

Abstract

The periodic oscillations in the activity of the cell cycle regulatory program, drives the timely activation of key cell cycle events. Interesting dynamical systems, such as oscillators, have been investigated by various theoretical and computational modeling methods. Thanks to the insights achieved by these modeling efforts we have gained considerable insights about the underlying molecular regulatory networks that can drive cell cycle oscillations. Here we review the basic features and characteristics of biological oscillators, discussing from a computational modeling point of view their specific architectures and the current knowledge about the dynamics that the life evolution selected to drive cell cycle oscillations.

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

Access this chapter

Log in via an institution
Protocol
USD 49.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Toettcher JE, Loewer A, Ostheimer GJ, Yaffe MB, Tidor B, Lahav G (2009) Distinct mechanisms act in concert to mediate cell cycle arrest. Proc Natl Acad Sci U S A 106(3):785–790. doi:10.1073/pnas.0806196106

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  2. Liu B, Bhatt D, Oltvai ZN, Greenberger JS, Bahar I (2014) Significance of p53 dynamics in regulating apoptosis in response to ionizing radiation, and polypharmacological strategies, Sci Rep 4, Article number: 6245 doi:10.1038/srep06245

  3. Ihekwaba AE, Broomhead DS, Grimley R, Benson N, White MR, Kell DB (2005) Synergistic control of oscillations in the NF-kappaB signalling pathway. Syst Biol (Stevenage) 152(3):153–160

    Article  CAS  Google Scholar 

  4. Mengel B, Hunziker A, Pedersen L, Trusina A, Jensen MH, Krishna S (2010) Modeling oscillatory control in NF-κB, p53 and Wnt signaling. Curr Opin Genet Dev 20(6):656–664. doi:10.1016/j.gde.2010.08.008

    Article  CAS  PubMed  Google Scholar 

  5. Lotka AJ (1920) Undamped oscillations derived from the law of mass action. J Am Chem Soc 42:1595–1599

    Article  CAS  Google Scholar 

  6. Prescott DM (1956) Relation between growth rate and cell division. III. Changes in nuclear volume and growth rate and prevention of cell division in Amoeba proteus resulting from cytoplasmic amputations. Exp Cell Res 11:94–98

    Article  CAS  PubMed  Google Scholar 

  7. Brooks RF, Bennett DC, Smith JA (1980) Mammalian cell cycles need two random transitions. Cell 19:493–504

    Article  CAS  PubMed  Google Scholar 

  8. Castor LN (1980) A G1 rate model accounts for cell-cycle kinetics attributed to ‘transition probability’. Nature 287:857–859

    Article  CAS  PubMed  Google Scholar 

  9. Koch AL, Schaechter M (1962) A model for statistics of the cell division process. J Gen Microbiol 29:435–454

    Article  CAS  PubMed  Google Scholar 

  10. Koch AL (1980) Does the variability of the cell cycle result from one or many chance events? Nature 286:80–82

    Article  CAS  PubMed  Google Scholar 

  11. Shields R (1977) Transition probability and the origin of variation in the cell cycle. Nature 267:704–707

    Article  CAS  PubMed  Google Scholar 

  12. Smith JA, Martin L (1973) Do cells cycle? Proc Natl Acad Sci U S A 70:1263–1267

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  13. Tyson JJ (1983) Unstable activator models for size control of the cell cycle. J Theor Biol 104:617–631

    Article  CAS  PubMed  Google Scholar 

  14. Tyson JJ, Hannsgen KB (1986) Cell growth and division: a deterministic/probabilistic model of the cell cycle. J Math Biol 23:231–246

    Article  CAS  PubMed  Google Scholar 

  15. Chen KC, Csikasz-Nagy A, Gyorffy B et al (2000) Kinetic analysis of a molecular model of the budding yeast cell cycle. Mol Biol Cell 11:369–391

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  16. Cross FR, Archambault V, Miller M et al (2002) Testing a mathematical model for the yeast cell cycle. Mol Biol Cell 13:52–70

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Chen KC, Calzone L, Csikasz-Nagy A et al (2004) Integrative analysis of cell cycle control in budding yeast. Mol Biol Cell 15:3841–3862

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  18. Queralt E, Lehane C, Novak B et al (2006) Downregulation of PP2A(Cdc55) phosphatase by separase initiates mitotic exit in budding yeast. Cell 125:719–732

    Article  CAS  PubMed  Google Scholar 

  19. Csikasz-Nagy A, Kapuy O, Gyorffy B et al (2007) Modeling the septation initiation network (SIN) in fission yeast cells. Curr Genet 51:245–255

    Article  CAS  PubMed  Google Scholar 

  20. Lygeros J, Koutroumpas K, Dimopoulos S et al (2008) Stochastic hybrid modeling of DNA replication across a complete genome. Proc Natl Acad Sci U S A 105:12295–12300

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  21. Novak B, Tyson JJ (1995) Quantitative analysis of a molecular model of mitotic control in fission yeast. J Theor Biol 173:283–305

    Article  CAS  Google Scholar 

  22. Novak B, Tyson JJ (1997) Modeling the control of DNA replication in fission yeast. Proc Natl Acad Sci U S A 94:9147–9152

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  23. Novak B, Csikasz-Nagy A, Gyorffy B et al (1998) 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  CAS  PubMed  Google Scholar 

  24. Novak B, Pataki Z, Ciliberto A et al (2001) Mathematical model of the cell division cycle of fission yeast. Chaos 11:277–286

    Article  CAS  PubMed  Google Scholar 

  25. Sveiczer A, Csikasz-Nagy A, Gyorffy B et al (2000) Modeling the fission yeast cell cycle: quantized cycle times in wee1-cdc25Delta mutant cells. Proc Natl Acad Sci U S A 97:7865–7870

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  26. Vasireddy R, Biswas S (2004) Modeling gene regulatory network in fission yeast cell cycle using hybrid petri nets. In: Neural information processing. Springer, Berlin, pp 1310–1315

    Chapter  Google Scholar 

  27. Novak B, Tyson JJ (1993) Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos. J Cell Sci 106(Pt 4):1153–1168

    CAS  PubMed  Google Scholar 

  28. Pomerening JR, Sontag ED, Ferrell JE (2003) Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2. Nat Cell Biol 5:346–351. doi:10.1038/ncb954

    Article  CAS  PubMed  Google Scholar 

  29. Sha W, Moore J, Chen K et al (2003) Hysteresis drives cell-cycle transitions in Xenopus laevis egg extracts. Proc Natl Acad Sci U S A 100:975–980

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Calzone L, Thieffry D, Tyson JJ et al (2007) Dynamical modeling of syncytial mitotic cycles in Drosophila embryos. Mol Syst Biol 3:131

    Article  PubMed  PubMed Central  Google Scholar 

  31. Ciliberto A, Tyson JJ (2000) Mathematical model for early development of the sea urchin embryo. Bull Math Biol 62:37–59

    Article  CAS  PubMed  Google Scholar 

  32. Hatzimanikatis V, Lee KH, Bailey JE (1999) A mathematical description of regulation of the G1-S transition of the mammalian cell cycle. Biotechnol Bioeng 65:631–637

    Article  CAS  PubMed  Google Scholar 

  33. Kohn KW (1998) Functional capabilities of molecular network components controlling the mammalian G1/S cell cycle phase transition. Oncogene 16:1065–1075

    Article  CAS  PubMed  Google Scholar 

  34. Novak B, Tyson JJ (2004) A model for restriction point control of the mammalian cell cycle. J Theor Biol 230:563–579

    Article  CAS  PubMed  Google Scholar 

  35. Pfeuty B, David-Pfeuty T, Kaneko K (2008) Underlying principles of cell fate determination during G1 phase of the mammalian cell cycle. Cell Cycle 7:3246–3257

    Article  CAS  PubMed  Google Scholar 

  36. Qu Z, Weiss JN, MacLellan WR (2003) Regulation of the mammalian cell cycle: a model of the G1-to-S transition. Am J Physiol Cell Physiol 284:C349–C364

    Article  CAS  PubMed  Google Scholar 

  37. Swat M, Kel A, Herzel H (2004) Bifurcation analysis of the regulatory modules of the mammalian G1/S transition. Bioinformatics 20:1506–1511

    Article  CAS  PubMed  Google Scholar 

  38. Singhania R, Sramkoski RM, Jacobberger JW, Tyson JJ (2011) A hybrid model of mammalian cell cycle regulation. PLoS Comput Biol 7(2):e1001077

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  39. Alfieri R, Barberis M, Chiaradonna F, Gaglio D, Milanesi L, Vanoni M, Klipp E, Alberghina L (2009) Towards a systems biology approach to mammalian cell cycle: modeling the entrance into S phase of quiescent fibroblasts after serum stimulation. BMC Bioinform 10(Suppl 12):S16. doi:10.1186/1471-2105-10-S12-S16

    Article  Google Scholar 

  40. Conradie R, Bruggeman FJ, Ciliberto A, Csikász-Nagy A, Novák B, Westerhoff HV, Snoep JL (2010) Restriction point control of the mammalian cell cycle via the cyclin E/Cdk2:p27 complex. FEBS J 277(2):357–367. doi:10.1111/j.1742-4658.2009.07473.x

    Article  CAS  PubMed  Google Scholar 

  41. Kapuy O, He E, Uhlmann F, Novák B (2009) Mitotic exit in mammalian cells. Mol Syst Biol 5:324. doi:10.1038/msb.2009.86

    Article  PubMed  PubMed Central  Google Scholar 

  42. Haberichter T, Mädge B, Christopher RA, Yoshioka N, Dhiman A, Miller R, Gendelman R, Aksenov SV, Khalil IG, Dowdy SF (2007) A systems biology dynamical model of mammalian G1 cell cycle progression. Mol Syst Biol 3:84. doi:10.1038/msb4100126

    Article  PubMed  PubMed Central  Google Scholar 

  43. Gérard C, Goldbeter A (2009) Temporal self-organization of the cyclin/Cdk network driving the mammalian cell cycle. Proc Natl Acad Sci U S A 106(51):21643–21648. doi:10.1073/pnas.0903827106

    Article  PubMed  PubMed Central  Google Scholar 

  44. Pfeuty B (2012) Strategic cell-cycle regulatory features that provide mammalian cells with tunable G1 length and reversible G1 arrest. PLoS One 7(4):e35291. doi:10.1371/journal.pone.0035291

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  45. Iwamoto K, Hamada H, Eguchi Y, Okamoto M (2011) Mathematical modeling of cell cycle regulation in response to DNA damage: exploring mechanisms of cell-fate determination. Biosystems 103(3):384–391. doi:10.1016/j.biosystems.2010.11.011

    Article  CAS  PubMed  Google Scholar 

  46. Davidich MI, Bornholdt S (2008) Boolean network model predicts cell cycle sequence of fission yeast. PLoS One 3(2):e1672. doi:10.1371/journal.pone.0001672

    Article  PubMed  PubMed Central  Google Scholar 

  47. Tyson JJ, Chen KC, Novák B (2001) Network dynamics and cell physiology. Nat Rev Mol Cell Biol 2:908–916. doi:10.1038/35103078

    Article  CAS  PubMed  Google Scholar 

  48. Kar S, Baumann WT, Paul MR, Tyson JJ (2009) Exploring the roles of noise in the eukaryotic cell cycle. Proc Natl Acad Sci U S A 106:6471

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  49. Tyson JJ, Chen KC, Novak B (2003) Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. Curr Opin Cell Biol 15(2):221–231. doi:10.1016/S0955-0674(03)00017-6

    Article  CAS  PubMed  Google Scholar 

  50. Csikász-Nagy A, Battogtokh D, Chen KC, Novák B, Tyson JJ (2006) Analysis of a generic model of eukaryotic cell-cycle regulation. Biophys J 90(12):4361–4379. doi:10.1529/biophysj.106.081240

    Article  PubMed  PubMed Central  Google Scholar 

  51. Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81(25):2340–2361. doi:10.1021/j100540a008

    Article  CAS  Google Scholar 

  52. Sveiczer A, Tyson JJ, Novak B (2001) A stochastic, molecular model of the fission yeast cell cycle: role of the nucleocytoplasmic ratio in cycle time regulation. Biophys Chem 92:1–15. doi:10.1016/S0301-4622(01)00183-1

    Article  CAS  PubMed  Google Scholar 

  53. Steuer R (2004) Effects of stochasticity in models of the cell cycle: from quantized cycle times to noise-induced oscillations. J Theor Biol 228:293–301. doi:10.1016/j.jtbi.2004.01.012

    Article  PubMed  Google Scholar 

  54. Mura I, Csikász-Nagy A (2008) Stochastic Petri Net extension of a yeast cell cycle model. J Theor Biol 254:859–860. doi:10.1016/j.jtbi.2008.07.019

    Article  Google Scholar 

  55. Palmisano A, Mura I, Priami C (2009) From ODEs to language-based, executable models of biological systems. In: Proceedings of the Pacific Symposium on Biocomputing 14, Kohala Coast, Hawaii, USA, pp 239–250.

    Google Scholar 

  56. Ballarini P, Mazza T, Palmisano A, Csikász-Nagy A (2009) Studying irreversible transitions in a model of cell cycle regulation. Electron Notes Theor Comput Sci 232:39–53. doi:10.1016/j.entcs.2009.02.049

    Article  Google Scholar 

  57. Csikász-Nagy A, Mura I (2010) Role of mRNA gestation and senescence in noise reduction during the cell cycle. In Silico Biol 10(1):81–88. doi:10.3233/ISB-2010-0416

    PubMed  Google Scholar 

  58. Zámborszky J, Hong CI, Csikász-Nagy A (2007) Computational analysis of mammalian cell division gated by a circadian clock: quantized cell cycles and cell size control. J Biol Rhythms 22:542–553

    Article  PubMed  Google Scholar 

  59. Fauré A, Naldi A, Chaouiya C, Thieffry D (2006) Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle. Bioinformatics 22(14):e124–e131. doi:10.1093/bioinformatics/btl210

    Article  PubMed  Google Scholar 

  60. Li F, Long T, Lu Y, Ouyang Q, Tang C (2004) The yeast cell-cycle network is robustly designed. Proc Natl Acad Sci U S A 101(14):4781–4786. doi:10.1073/pnas.0305937101

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  61. Kitano H (2002) Computational systems biology. Nature 420(6912):206–210. doi:10.1038/nature01254

    Article  CAS  PubMed  Google Scholar 

  62. Tsai TYC, Choi YS, Ma W, Pomerening JR, Tang C, Ferrell JR (2008) Robust, tunable biological oscillations from interlinked positive and negative feedback loops. Science 321(5885):126–129. doi:10.1126/science.1156951

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  63. Santos SDM, Ferrell JE (2008) Systems biology: on the cell cycle and its switches. Nature 454:288–289. doi:10.1038/454288

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  64. Simmons Kovacs LA, Orlando DA, Haase SB (2008) Transcription network and cyclin/CDKs: the yin and yang of cell cycle oscillators. Cell Cycle 7(17):2626–2629. doi:10.4161/cc.7.17.6515

    Article  PubMed  Google Scholar 

  65. Orlando DA, Lin YC, Bernard A, Wang JY, Socolar JES, Iversen ES, Hartemink AJ, Haase SB (2008) Global control of cell-cycle transcription by coupled CDK and network oscillators. Nature 453:944–947. doi:10.1038/nature06955

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  66. Simmons LA, Kovacs LA, Mayhew MB, Orlando DA, Jin Y, Li Q, Huang C, Reed SI, Mukherjee S, Haase SB (2012) Cyclin-dependent kinases are regulators and effectors of oscillations driven by a transcription factor network. Mol Cell 45(5):669–679. doi:10.1016/j.molcel.2011.12.033

    Article  Google Scholar 

  67. Sevim V, Gong X, Socolar JES (2010) Reliability of transcriptional cycles and the yeast cell-cycle oscillator. PLoS Comput Biol 6(7):e1000842. doi:10.1371/journal.pcbi.1000842

    Article  PubMed  PubMed Central  Google Scholar 

  68. Sriram K, Bernot G, Képès F (2007) A minimal mathematical model combining several regulatory cycles from the budding yeast cell cycle. IET Syst Biol 1(6):326–341. doi:10.1049/iet-syb:20070018

    Article  CAS  PubMed  Google Scholar 

  69. Elowitz MB, Leibler S (2000) A synthetic oscillatory network of transcriptional regulators. Nature 403:335–338. doi:10.1038/35002125

    Article  CAS  PubMed  Google Scholar 

  70. Goldbeter A (1991) A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. Proc Natl Acad Sci U S A 88(20):9107–9111. doi:10.1073/pnas.88.20.9107

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  71. Tyson JJ (1991) Modeling the cell division cycle: cdc2 and cyclin interactions. Proc Natl Acad Sci U S A 88(16):7328–7332. doi:10.1073/pnas.88.16.7328

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  72. Kazunari K, Samik G, Yukiko M, Hisao M, Yuki S-Y, Hiroaki K (2010) A comprehensive molecular interaction map of the budding yeast cell cycle. Mol Syst Biol 6:1. doi:10.1038/msb.2010.73

    Google Scholar 

  73. Novak B, Tyson JJ, Gyorffy B, Csikasz-Nagy A (2007) Irreversible cell-cycle transitions are due to systems-level feedback. Nat Cell Biol 9:724–728. doi:10.1038/ncb0707-724

    Article  CAS  PubMed  Google Scholar 

  74. López-Avilés S, Kapuy O, Novák B, Uhlmann F (2009) Irreversibility of mitotic exit is the consequence of systems-level feedback. Nature 459:592–595. doi:10.1038/nature07984

    Article  PubMed  PubMed Central  Google Scholar 

  75. Oikonomou C, Cross FR (2010) Frequency control of cell cycle oscillators. Curr Opin Genet Dev 20(6):605–612. doi:10.1016/j.gde.2010.08.006

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  76. Lu Y, Cross FR (2010) Periodic cyclin-Cdk activity entrains an autonomous Cdc14 release oscillator. Cell 141(2):268–279. doi:10.1016/j.cell.2010.03.021

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  77. Manzoni R, Montani F, Visintin C, Caudron F, Ciliberto A, Visintin R (2010) Oscillations in Cdc14 release and sequestration reveal a circuit underlying mitotic exit. J Cell Biol 190(2):209–222. doi:10.1083/jcb.201002026

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  78. Matsuo T, Yamaguchi S, Mitsui S, Emi A, Shimoda F, Okamura H (2003) Control mechanism of the circadian clock for timing of cell division in vivo. Science 302(5643):255–259. doi:10.1126/science.1086271

    Article  CAS  PubMed  Google Scholar 

  79. Klevecz RR, Bolen J, Forrest G, Murray DB (2003) A genomewide oscillation in transcription gates DNA replication and cell cycle. Proc Natl Acad Sci U S A 101(5):1200–1205. doi:10.1073/pnas.0306490101

    Article  Google Scholar 

  80. Mirollo RE, Strogatz SH (1990) Synchronization of pulse-coupled biological oscillators. SIAM J Appl Math 50(6):1645–1662. doi:10.1137/0150098

    Article  Google Scholar 

  81. Kanae O, Yukiko M, Akira F, Hiroaki K (2005) A comprehensive pathway map of epidermal growth factor receptor signaling. Mol Syst Biol 1:1. doi:10.1038/msb4100014

    Google Scholar 

  82. Laurence C, Amélie G, Andrei Z, François R, Emmanuel B (2008) A comprehensive modular map of molecular interactions in RB/E2F pathway. Mol Syst Biol 4:1. doi:10.1038/msb.2008.7

    Google Scholar 

  83. Malumbres M, Barbacid M (2009) Cell cycle, CDKs and cancer: a changing paradigm. Nat Rev Cancer 9:153–166. doi:10.1038/nrc2602

    Article  CAS  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Randall Division of Cell and Molecular Biophysics, King’s College London, Strand, London, SE1 1UL, UK

    Attila Csikász-Nagy

  2. Institute for Mathematical and Molecular Biomedicine, King’s College London, London, SE1 1UL, UK

    Attila Csikász-Nagy

  3. Department of Computational Biology, Research and Innovation Centre, Fondazione Edmund Mach, San Michele all’Adige, 38010, Italy

    Attila Csikász-Nagy

  4. Faculty of Engineering, EAN University, Carrera 11 No. 78 – 47, Bogotá, 11001000, Colombia

    Ivan Mura

Authors
  1. Attila Csikász-Nagy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ivan Mura
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Attila Csikász-Nagy .

Editor information

Editors and Affiliations

  1. Department of Oncology, University of Oxford, Oxford, United Kingdom

    Amanda S. Coutts

  2. Scientific writer, London, United Kingdom

    Louise Weston

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer Science+Business Media New York

About this protocol

Cite this protocol

Csikász-Nagy, A., Mura, I. (2016). Role of Computational Modeling in Understanding Cell Cycle Oscillators. In: Coutts, A., Weston, L. (eds) Cell Cycle Oscillators. Methods in Molecular Biology, vol 1342. Humana Press, New York, NY. https://doi.org/10.1007/978-1-4939-2957-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4939-2957-3_3

  • Publisher Name: Humana Press, New York, NY

  • Print ISBN: 978-1-4939-2956-6

  • Online ISBN: 978-1-4939-2957-3

  • eBook Packages: Springer Protocols

Publish with us

Policies and ethics

Search

Navigation