Computational Models of Cell Cycle Transitions

  • Rosa Hernansaiz-Ballesteros
  • Kirsten Jenkins
  • Attila Csikász-Nagy
Part of the Methods in Molecular Biology book series (MIMB, volume 1819)


The cell cycle is one of the best understood cellular processes in biology. Many of the key interactions occurring throughout the cell cycle have already been identified. This feature makes the system ideally suited for modelers who can use all the available interaction knowledge to build a systems level model of the underlying molecular regulatory network. This model can serve to identify gaps in our knowledge and to test theoretical assumptions or constrain the space of possible solutions. The cell cycle is a repetitive chain of events that goes through several checkpoints. Thus, the cell cycle can be studied under the perspective of an oscillator with checkpoints built into it, or as a series of switch-like transitions that goes from one state to another, converging on a closed loop. We shall discuss that latter position and present a framework for building and analyzing differential equation models of switch-like behavior. We shall then apply and review diverse models for each of the cell cycle transitions and discuss how multiple switches are combined in the cell cycle to create fast and robust transitions.

Key words

Cell cycle Mathematical modeling Biological switches Bistability Systems biology 



R.H.B is supported by Microsoft Research through its PhD Scholarship Programme and K.J. is supported by the EPSRC Centre for Doctoral Training in Cross-Disciplinary Approaches to Non-Equilibrium Systems (CANES, EP/L015854/1).


  1. 1.
    Donnell MO, Langston L, Stillman B, Donnell MO, Langston L, Bell SP, Kaguni JM, Pfeiffer V, Lingner J, Cotmore SF, Tattersall P, Zielke N, Edgar BA, Melvin L (2013) Principles and concepts of DNA replication. Cold Spring Harb Perspect Biol 5:1–14CrossRefGoogle Scholar
  2. 2.
    McAdams HH, Shapiro L (2003) A bacterial cell-cycle regulatory network operating in time and space. Science (80) 301(5641):1874–1877CrossRefGoogle Scholar
  3. 3.
    Ausmees N, Jacobs-Wagner C (2003) Spatial and temporal control of differentiation and cell cycle progression in Caulobacter crescentus. Annu Rev Microbiol 57(1):225–247CrossRefGoogle Scholar
  4. 6.
    Kelman LM, Kelman Z (2014) Archaeal DNA replication. Annu Rev Genet 48:71–97CrossRefGoogle Scholar
  5. 7.
    Csikász-Nagy A, Palmisano A, Zámborszky J (2011) Molecular network dynamics of cell cycle control: transitions to start and finish. Methods Mol Biol 761:277–291CrossRefGoogle Scholar
  6. 8.
    Alberts B, Johnson A, Lewis J, Morgan D, Raff M, Roberts K (2015) Molecular biology of the cell, 6th edn. Garland Science, New YorkGoogle Scholar
  7. 9.
    Hartwell LH, Mortimer RK, Culotti J, Culotti M (1973) Genetic control of the cell division cycle in yeast: V. Genetic analysis of cdc mutants. Genetics 74(2):267–286PubMedPubMedCentralGoogle Scholar
  8. 10.
    Nurse P (1975) Genetic control of cell size at cell division in yeast. Nature 256:547–551CrossRefGoogle Scholar
  9. 11.
    Evans T, Rosenthal ET, Youngblom J, Distel D, Hunt T (1983) Cyclin: a protein specified by maternal mRNA in sea urchin eggs that is destroyed at each cleavage division. Cell 33(2):389–396CrossRefGoogle Scholar
  10. 12.
    Tyson JJ, Novak B (2001) Regulation of the eukaryotic cell cycle: molecular antagonism, hysteresis, and irreversible transitions. J Theor Biol 210(2):249–263CrossRefGoogle Scholar
  11. 13.
    Santos SDM, Ferrell JE (2008) Systems biology: on the cell cycle and its switches. Nature 454(7202):288–289CrossRefGoogle Scholar
  12. 16.
    Musacchio A, Ciliberto A (2012) The spindle-assembly checkpoint and the beauty of self-destruction. Nat Struct Mol Biol 19(11):1059–1061CrossRefGoogle Scholar
  13. 19.
    Tyson JJ (1999) Models of cell cycle control in eukaryotes. J Biotechnol 71(1):239–244CrossRefGoogle Scholar
  14. 22.
    Kitano H, Funahashi A, Matsuoka Y, Oda K (2005) Using process diagrams for the graphical representation of biological networks. Nat Biotechnol 23(8):961–966CrossRefGoogle Scholar
  15. 23.
    Alon U (2007) Network motifs: theory and experimental approaches. Nat Rev Genet 8(6):450–461CrossRefGoogle Scholar
  16. 29.
    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 15:221–231CrossRefGoogle Scholar
  17. 30.
    Novák B, Tyson JJ (2008) Design principles of biochemical oscillators. Nat Rev Mol Cell Biol 9(12):981–991CrossRefGoogle Scholar
  18. 31.
    Goldbeter A (1991) A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. Proc Natl Acad Sci 88(20):9107–9111CrossRefGoogle Scholar
  19. 32.
    Griffith JS (1968) Mathematics of cellular control processes II. Positive feedback to one gene. J Theor Biol 20(2):209–216CrossRefGoogle Scholar
  20. 35.
    Brandman O, Ferrell JE, Li R, Meyer T (2005) Interlinked fast and slow positive feedback loops drive reliable cell decisions. Science (80) 310(5747):496–498CrossRefGoogle Scholar
  21. 36.
    Ferrell JE (2008) Feedback regulation of opposing enzymes generates robust, all-or-none bistable responses. Curr Biol 18(6):R244–R245CrossRefGoogle Scholar
  22. 37.
    Angeli D, Ferrell JE, Sontag ED (2004) Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems. Proc Natl Acad Sci 101(7):1822–1827CrossRefGoogle Scholar
  23. 38.
    Novak B, Tyson JJ, Gyorffy B, Csikasz-Nagy A (2007) Irreversible cell-cycle transitions are due to systems-level feedback. Nat Cell Biol 9(7):724–728CrossRefGoogle Scholar
  24. 39.
    Goldenfeld N, Kadanoff LP (1999) Simple lessons from complexity. Science (80) 284(5411):87–89CrossRefGoogle Scholar
  25. 44.
    Wang R-S, Saadatpour A, Albert R (2012) Boolean modeling in systems biology: an overview of methodology and applications. Phys Biol 9(5):55001CrossRefGoogle Scholar
  26. 47.
    Barik D, Baumann WT, Paul MR, Novak B, Tyson JJ (2010) A model of yeast cell-cycle regulation based on multisite phosphorylation. Mol Syst Biol 6(1):405PubMedPubMedCentralGoogle Scholar
  27. 48.
    Goldbeter A, Koshland DE (1981) An amplified sensitivity arising from covalent modification in biological systems. Proc Natl Acad Sci 78(11):6840–6844CrossRefGoogle Scholar
  28. 49.
    Rudorf S, Thommen M, Rodnina MV, Lipowsky R (2014) Deducing the kinetics of protein synthesis in vivo from the transition rates measured in vitro. PLoS Comput Biol 10(10):e1003909CrossRefGoogle Scholar
  29. 50.
    Davidi D, Noor E, Liebermeister W, Bar-Even A, Flamholz A, Tummler K, Barenholz U, Goldenfeld M, Shlomi T, Milo R (2016) Global characterization of in vivo enzyme catalytic rates and their correspondence to in vitro kcat measurements. Proc Natl Acad Sci 113(12):3401–3406CrossRefGoogle Scholar
  30. 51.
    Kuznetsov Y (2013) Elements of applied bifurcation theory. Springer, New YorkGoogle Scholar
  31. 52.
    Hoops S, Sahle S, Gauges R, Lee C, Pahle J, Simus N, Singhal M, Xu L, Mendes P, Kummer U (2006) COPASI—a complex pathway simulator. Bioinformatics 22(24):3067–3074CrossRefGoogle Scholar
  32. 53.
    Zwolak JW, Tyson JJ, Watson LT (2005) Parameter estimation for a mathematical model of the cell cycle in frog eggs. J Comput Biol 12(1):48–63CrossRefGoogle Scholar
  33. 54.
    Panning TD, Watson LT, Allen NA, Chen KC, Shaffer CA, Tyson JJ (2008) Deterministic parallel global parameter estimation for a model of the budding yeast cell cycle. J Glob Optim 40(4):719–738CrossRefGoogle Scholar
  34. 55.
    Tsai TY-C, Choi YS, Ma W, Pomerening JR, Tang C, Ferrell JE (2008) Robust, tunable biological oscillations from interlinked positive and negative feedback loops. Science (80) 321(5885):126–129CrossRefGoogle Scholar
  35. 56.
    Csikász-Nagy A (2009) Computational systems biology of the cell cycle. Brief Bioinform 10(4):424–434CrossRefGoogle Scholar
  36. 57.
    Ferrell JE, Tsai TY-C, Yang Q (2011) Modeling the cell cycle: why do certain circuits oscillate? Cell 144(6):874–885CrossRefGoogle Scholar
  37. 58.
    Skotheim JM, Di Talia S, Siggia ED, Cross FR (2008) Positive feedback of G1 cyclins ensures coherent cell cycle entry. Nature 454(7202):291–296CrossRefGoogle Scholar
  38. 59.
    Bloom J, Cross FR (2007) Multiple levels of cyclin specificity in cell-cycle control. Nat Rev Mol Cell Biol 8(2):149–160CrossRefGoogle Scholar
  39. 60.
    Nash P, Tang X, Orlicky S, Chen Q, Gertler FB, Mendenhall MD, Sicheri F, Pawson T, Tyers M (2001) Multisite phosphorylation of a CDK inhibitor sets a threshold for the onset of DNA replication. Nature 414(6863):514–521CrossRefGoogle Scholar
  40. 61.
    Ferrell JE (2002) Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability. Curr Opin Cell Biol 14(2):140–148CrossRefGoogle Scholar
  41. 64.
    Barberis M, Klipp E (2007) Insights into the network controlling the G1/S transition in budding yeast. Genome Inform 18:85–99PubMedGoogle Scholar
  42. 66.
    Schmoller KM, Turner JJ, Kõivomägi M, Skotheim JM (2015) Dilution of the cell cycle inhibitor Whi5 controls budding-yeast cell size. Nature 526(7572):268–272CrossRefGoogle Scholar
  43. 68.
    Wagner MV, Smolka MB, de Bruin RAM, Zhou H, Wittenberg C, Dowdy SF (Jan. 2009) Whi5 regulation by site specific CDK-phosphorylation in Saccharomyces cerevisiae. PLoS One 4(1):e4300CrossRefGoogle Scholar
  44. 69.
    Liu X et al (2015) Reliable cell cycle commitment in budding yeast is ensured by signal integration. Elife 4:1–19Google Scholar
  45. 70.
    Charvin G, Oikonomou C, Siggia ED, Cross FR (2010) Origin of irreversibility of cell cycle start in budding yeast. PLoS Biol 8(1):e1000284CrossRefGoogle Scholar
  46. 71.
    Garí E, Volpe T, Wang H, Gallego C, Futcher B, Aldea M (2001) Whi3 binds the mRNA of the G1 cyclin CLN3 to modulate cell fate in budding yeast. Genes Dev 15(21):2803–2808PubMedPubMedCentralGoogle Scholar
  47. 73.
    Nash RS, Volpe T, Futcher B (2001) Isolation and characterization of WHI3, a size-control gene of Saccharomyces cerevisiae. Genetics 157(4):1469–1480PubMedPubMedCentralGoogle Scholar
  48. 74.
    Mizunuma M, Tsubakiyama R, Ogawa T, Shitamukai A, Kobayashi Y, Inai T, Kume K, Hirata D (2013) Ras/cAMP-dependent protein kinase (PKA) regulates multiple aspects of cellular events by phosphorylating the Whi3 cell cycle regulator in budding yeast. J Biol Chem 288(15):10558–10566CrossRefGoogle Scholar
  49. 75.
    Vergés E, Colomina N, Garí E, Gallego C, Aldea M (2007) Cyclin Cln3 is retained at the ER and released by the J chaperone Ydj1 in late G1 to trigger cell cycle entry. Mol Cell 26(5):649–662CrossRefGoogle Scholar
  50. 76.
    Ferrezuelo F, Colomina N, Palmisano A, Garí E, Gallego C, Csikász-Nagy A, Aldea M (2012) The critical size is set at a single-cell level by growth rate to attain homeostasis and adaptation. Nat Commun 3:1012CrossRefGoogle Scholar
  51. 77.
    Adames NR, Schuck PL, Chen KC, Murali TM, Tyson JJ, Peccoud J (2015) Experimental testing of a new integrated model of the budding yeast Start transition. Mol Biol Cell 26(22):3966–3984CrossRefGoogle Scholar
  52. 78.
    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):4361–4379CrossRefGoogle Scholar
  53. 79.
    Domingo-Sananes MR, Kapuy O, Hunt T, Novak B (2011) Switches and latches: a biochemical tug-of-war between the kinases and phosphatases that control mitosis. Philos Trans R Soc B 366(1584):3584–3594CrossRefGoogle Scholar
  54. 80.
    O’Farrell PH (2001) Triggering the all-or-nothing switch into mitosis. Trends Cell Biol 11(12):512–519CrossRefGoogle Scholar
  55. 83.
    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(4):1153–1168PubMedGoogle Scholar
  56. 84.
    Araujo AR, Gelens L, Sheriff RSM, Santos SDM (2016) Positive feedback keeps duration of mitosis temporally insulated from upstream cell-cycle events. Mol Cell 64(2):362–375CrossRefGoogle Scholar
  57. 85.
    Krasinska L, Domingo-Sananes MR, Kapuy O, Parisis N, Harker B, Moorhead G, Rossignol M, Novak B, Fisher D (2011) Protein phosphatase 2A controls the order and dynamics of cell-cycle transitions. Mol Cell 44(3):437–450CrossRefGoogle Scholar
  58. 86.
    Mochida S, Maslen SL, Skehel M, Hunt T (2010) Greatwall phosphorylates an inhibitor of protein phosphatase 2A that is essential for mitosis. Science (80) 330(6011):1670–1673CrossRefGoogle Scholar
  59. 87.
    Gérard C, Tyson JJ, Coudreuse D, Novák B (2015) Cell cycle control by a minimal Cdk network. PLoS Comput Biol 11(2):e1004056CrossRefGoogle Scholar
  60. 88.
    Cardelli L, Csikász-Nagy A (2012) The cell cycle switch computes approximate majority. Sci Rep 2:656CrossRefGoogle Scholar
  61. 89.
    Cardelli L (2014) Morphisms of reaction networks that couple structure to function. BMC Syst Biol 8(1):84CrossRefGoogle Scholar
  62. 90.
    López-Avilés S, Kapuy O, Novák B, Uhlmann F (2009) Irreversibility of mitotic exit is the consequence of systems-level feedback. Nature 459(7246):592–595CrossRefGoogle Scholar
  63. 91.
    Simonetta M, Manzoni R, Mosca R, Mapelli M, Massimiliano L, Vink M, Novak B, Musacchio A, Ciliberto A (2009) The influence of catalysis on mad2 activation dynamics. PLoS Biol 7(1):e1000010CrossRefGoogle Scholar
  64. 92.
    Holt LJ, Krutchinsky AN, Morgan DO (2008) Positive feedback sharpens the anaphase switch. Nature 454(7202):353–357CrossRefGoogle Scholar
  65. 93.
    Romanel A, Jensen LJ, Cardelli L, Csikász-Nagy A (2012) Transcriptional regulation is a major controller of cell cycle transition dynamics. PLoS One 7(1):e29716CrossRefGoogle Scholar
  66. 94.
    Fisher D, Krasinska L, Coudreuse D, Novák B (2012) Phosphorylation network dynamics in the control of cell cycle transitions. J Cell Sci 125(Pt 20):4703–4711CrossRefGoogle Scholar
  67. 95.
    Cardelli L, Hernansaiz-Ballesteros RD, Dalchau N, Csikász-Nagy A (2017) Efficient Switches in Biology and Computer Science. PLoS Comput Biol 13(1):e1005100. CrossRefPubMedPubMedCentralGoogle Scholar
  68. 96.
    Angluin D, Aspnes J, Eisenstat D (2008) A simple population protocol for fast robust approximate majority. Distrib Comput 21(2):87–102CrossRefGoogle Scholar
  69. 97.
    Cardelli L, Csikász-Nagy A, Dalchau N, Tribastone M, Tschaikowski M (2016) Noise reduction in complex biological switches. Sci Rep 6:20214CrossRefGoogle Scholar
  70. 98.
    Kitano H (2007) A robustness-based approach to systems-oriented drug design. Nat Rev Drug Discov 5(3):202–210CrossRefGoogle Scholar
  71. 99.
    Kaizu K, Ghosh S, Matsuoka Y, Moriya H, Shimizu-Yoshida Y, Kitano H (2010) A comprehensive molecular interaction map of the budding yeast cell cycle. Mol Syst Biol 6(1):415PubMedPubMedCentralGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Rosa Hernansaiz-Ballesteros
    • 1
  • Kirsten Jenkins
    • 1
  • Attila Csikász-Nagy
    • 1
    • 2
  1. 1.Randall Division of Cell and Molecular Biophysics and Institute for Mathematical and Molecular BiomedicineKing’s College LondonLondonUK
  2. 2.Faculty of Information Technology and BionicsPázmány Péter Catholic UniversityBudapestHungary

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