Demographic Fluctuations and Inherent Time Scales in a Genetic Circuit

  • Hildegard Meyer-Ortmanns
  • Darka Labavić
Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)


We review results on a genetic circuit made out of a self-activating species A that activates its own repressor B in a negative feedback loop. We consider this motif in three descriptions: a deterministic coarse-grained one from the start, its stochastic pendant, and a stochastic version with an improved time resolution. We study the conditions under which we can derive the deterministic coarse-grained from the stochastic time-resolved version. As it can be shown from the time-resolved version, the regular oscillations which are found in a number of realizations of this motif, fade away for slow binding rates of the transcription factors to the promoter regions of the genes. Results of our Gillespie simulations match well with mean-field predictions if the averaging over states accounts for the inherent time scales. The occurrence of quasi-cycles in the stochastic descriptions raises the question as to which oscillations in natural systems are of mere demographic origin.


Genetic circuits Quasi-cycles Coarse-graining 



We would like to thank our collaborators A. Garai (UC San Diego), W. Janke and H. Nagel (University of Leipzig) as well as B. Waclaw (University of Edinburgh) for their contributions to different parts of the work.


  1. 1.
    Martiel J, Goldbeter A (1987) A model on receptor desensitization for cyclic AMP signaling in dictyostelium cells. Biophys J 52:807–828 CrossRefGoogle Scholar
  2. 2.
    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 106:1153–1168 Google Scholar
  3. 3.
    Pomerening JR, Kim SY, Ferrell JE Jr. (2005) Systems-level dissection of the cell-cycle oscillator: bypassing positive feedback produces damped oscillations. Cell 122:565–578 CrossRefGoogle Scholar
  4. 4.
    Tyson JJ (1991) Modeling the cell division cycle: cdc2 and cyclin interactions. Proc Natl Acad Sci USA 88:7328–7332 ADSCrossRefGoogle Scholar
  5. 5.
    Qiao L, Nachbar RB, Kevrekidis IG, Shvartsman SY (2007) Bistability and oscillations in the Huang-Ferrell model of MAPK signaling. PLoS Comput Biol 3:1819–1826 MathSciNetCrossRefGoogle Scholar
  6. 6.
    Vilar JMG, Kueh HY, Barkai N, Leibler S (2002) Mechanisms of noise-resistance in genetic oscillators. Proc Natl Acad Sci USA 99:5988–5992 ADSCrossRefGoogle Scholar
  7. 7.
    Ingolia NT, Murray AW (2004) The ups and downs of modeling the cell cycle. Curr Biol 14:R771–R777 CrossRefGoogle Scholar
  8. 8.
    Krishna S, Semsey S, Jensen M (2009) Frustrated bistability as a means to engineer oscillations in biological systems. Phys Biol 6:036009. 8pp ADSCrossRefGoogle Scholar
  9. 9.
    Garai A, Waclaw B, Nagel H, Meyer-Ortmanns H (2012) Stochastic description of a bistable frustrated unit. J Stat Mech 2012:P01009 (28 pp) CrossRefGoogle Scholar
  10. 10.
    Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81:2340–2361 CrossRefGoogle Scholar
  11. 11.
    Van Kampen NG (2005) Stochastic processes in physics and chemistry. North-Holland, Amsterdam Google Scholar
  12. 12.
    Kaluza P, Meyer-Ortmanns H (2010) On the role of frustration in exciatble systems. Chaos 20:043111 (11 pp) ADSCrossRefGoogle Scholar
  13. 13.
    Labavić D, Nagel H, Janke W, Meyer-Ortmanns H (2012) Coarse-grained modeling of genetic circuits as a function of the inherent time scales. arXiv:1209.0581v1
  14. 14.
    Butler T, Goldenfeld N (2009) Robust ecological pattern formation induced by demographic noise. Phys Rev E 80:030902(R) (4 pp) ADSGoogle Scholar
  15. 15.
    Butler T, Goldenfeld N (2011) Fluctuation-driven Turing patterns. Phys Rev E 84:011112 (12 pp) ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.School of Engineering and ScienceJacobs UniversityBremenGermany

Personalised recommendations