Modelling Biological Clocks with Bio-PEPA: Stochasticity and Robustness for the Neurospora crassa Circadian Network

  • Ozgur E. Akman
  • Federica Ciocchetta
  • Andrea Degasperi
  • Maria Luisa Guerriero
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5688)

Abstract

Circadian clocks are biochemical networks, present in nearly all living organisms, whose function is to regulate the expression of specific mRNAs and proteins to synchronise rhythms of metabolism, physiology and behaviour to the 24 hour day/night cycle. Because of their experimental tractability and biological significance, circadian clocks have been the subject of a number of computational modelling studies.

In this study we focus on the simple circadian clock of the fungus Neurospora crassa. We use the Bio-PEPA process algebra to develop both a stochastic and a deterministic model of the system. The light on/off mechanism responsible for entrainment to the day/night cycle is expressed using discrete time-dependent events in Bio-PEPA.

In order to validate our model, we compare it against the results of previous work which demonstrated that the deterministic model is in agreement with experimental data. Here we investigate the effect of stochasticity on the robustness of the clock’s function in biological timing. In particular, we focus on the variations in the phase and amplitude of oscillations in circadian proteins with respect to different factors such as the presence/absence of a positive feedback loop, and the presence/absence of light. The time-dependent sensitivity of the model with respect to some key kinetic parameters is also investigated.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dunlap, J.P., Loros, J.L., DeCoursey, P.J.: Chronobiology: Biological Timekeeping. Sinauer, Sunderland (2003)Google Scholar
  2. 2.
    Young, M., Kay, S.: Time zones: a comparative genetics of circadian clocks. Nat. Rev. Genet. 2(9), 702–715 (2001)CrossRefPubMedGoogle Scholar
  3. 3.
    Tyson, J., Hong, C., Thron, C., Novak, B.: A simple model of circadian rhythms based on dimerization and proteolysis of PER and TIM. J. Biophys. 77, 2411–2417 (1999)CrossRefGoogle Scholar
  4. 4.
    Ueda, H., Hagiwara, M., Kitano, H.: Robust oscillations within the interlocked feedback model of Drosophila circadian rhythm. J. Theor. Biol. 210, 401–406 (2001)CrossRefPubMedGoogle Scholar
  5. 5.
    Locke, J., Kozma-Bognar, L., Gould, P., Fehér, B., Kevei, E., Nagy, F., Turner, M., Hall, A., Millar, A.: Experimental validation of a predicted feedback loop in the multi-oscillator clock of Arabidopsis thaliana. Mol. Sys. Biol. 2, 59 (2006)Google Scholar
  6. 6.
    Zeilinger, M., Farré, E., Taylor, S., Kay, S., Doyle, F.: A novel computational model of the circadian clock in Arabidopsis that incorporates PRR7 and PRR9. Mol. Sys. Biol. 2(60) (2006)Google Scholar
  7. 7.
    Leloup, J., Goldbeter, A.: Toward a detailed computational model for the mammalian circadian clock. Proc. Natl. Acad. Sci. USA 100, 7051–7056 (2003)CrossRefPubMedPubMedCentralGoogle Scholar
  8. 8.
    Forger, D., Peskin, C.: Model based conjectures on mammalian clock controversies. Theor. Biol. 230(4), 533–539 (2004)CrossRefGoogle Scholar
  9. 9.
    Loros, J., Dunlap, J.: Genetic and molecular analysis of circadian rhythms in Neurospora. Annu. Rev. Physiol. 63, 757–794 (2001)CrossRefPubMedGoogle Scholar
  10. 10.
    Leloup, J., Gonze, D., Goldbeter, A.: Limit cycle models for circadian rhythms based on transcriptional regulation in Drosophila and Neurospora. J. Biol. Rhythms 14(6), 433–448 (1999)CrossRefPubMedGoogle Scholar
  11. 11.
    Francois, P.: A model for the Neurospora circadian clock. Biophys. J. 88(4), 2369–2383 (2005)CrossRefPubMedPubMedCentralGoogle Scholar
  12. 12.
    Ruoff, P., Loros, J., Dunlap, J.: The relationship between FRQ-protein stability and temperature compensation in the Neurospora circadian clock. Proc. Natl. Acad. Sci. USA 102(49), 17681–17686 (2005)CrossRefPubMedPubMedCentralGoogle Scholar
  13. 13.
    Akman, O., Locke, J., Tang, S., Carré, I., Millar, A., Rand, D.: Isoform switching facilitates period control in the Neurospora crassa circadian clock. Mol. Sys. Biol. 4, 64 (2008)Google Scholar
  14. 14.
    Hong, C., Jolma, I., Loros, J., Dunlap, J., Ruoff, P.: Simulating dark expressions and interactions of frq and wc-1 in the Neurospora circadian clock. Biophys. J. 94(4), 1221–1232 (2008)CrossRefPubMedGoogle Scholar
  15. 15.
    Gonze, D., Halloy, J., Goldbeter, A.: Robustness of circadian rhythms with respect to molecular noise. Proc. Natl. Acad. Sci. USA 99(2), 673–678 (2002)CrossRefPubMedPubMedCentralGoogle Scholar
  16. 16.
    Smolen, P., Baxter, D., Byrne, J.: Reduced models of the circadian oscillators in Neurospora crassa and Drosophila melanogaster illustrate mechanistic similarities. OMICS 7(4), 337–354 (2003)CrossRefPubMedGoogle Scholar
  17. 17.
    McAdams, H., Arkin, A.: Stochastic mechanisms in gene expression. Proc. Natl. Acad. Sci. USA 94(3), 814–819 (1997)CrossRefPubMedPubMedCentralGoogle Scholar
  18. 18.
    Akman, O., Rand, D., Brown, P., Millar, A.: Robustness from flexibility in the fungal circadian clock (submitted, 2009)Google Scholar
  19. 19.
    Ciocchetta, F., Hillston, J.: Bio-PEPA: a Framework for the Modelling and Analysis of Biological Systems. Theoretical Computer Science (to appear, 2009)Google Scholar
  20. 20.
    Ciocchetta, F., Hillston, J.: Bio-PEPA: an extension of the process algebra PEPA for biochemical networks. In: Proc. of FBTC 2007. ENTCS, vol. 194, pp. 103–117 (2008)Google Scholar
  21. 21.
    Vitalini, M., de Paula, R., Park, W., Bell-Pedersen, D.: The rhythms of life: circadian output pathways in Neurospora. J. Biol. Rhythms 21(6), 432–444 (2006)CrossRefPubMedGoogle Scholar
  22. 22.
    Merrow, M., Boesl, C., Ricken, J., Messerschmitt, M., Goedel, M., Roenneberg, T.: Entrainment of the Neurospora circadian clock. Chronobiol. Int. 23(1-2), 71–78 (2006)CrossRefPubMedGoogle Scholar
  23. 23.
    Merrow, M., Franchi, L., Dragovic, Z., Gorl, M., Johnson, J., Brunner, M., Macino, G., Roenneberg, T.: Circadian regulation of the light input pathway in Neurospora crassa. EMBO J. 20(3), 307–315 (2001)CrossRefPubMedPubMedCentralGoogle Scholar
  24. 24.
    Froehlich, A., Loros, J., Dunlap, J.: Rhythmic binding of a WHITE COLLAR-containing complex to the frequency promoter is inhibited by FREQUENCY. Proc. Natl. Acad. Sci. USA 100(10), 5914–5919 (2003)CrossRefPubMedPubMedCentralGoogle Scholar
  25. 25.
    Cheng, P., Yang, Y., Liu, Y.: Interlocked feedback loops contribute to the robustness of the Neurospora circadian clock. Proc. Natl. Acad. Sci. USA 98(13), 7408–7413 (2001)CrossRefPubMedPubMedCentralGoogle Scholar
  26. 26.
    Ciocchetta, F.: Bio-PEPA with events. Transactions on Computational Systems Biology (to appear, 2009)Google Scholar
  27. 27.
    Bio-PEPA Home Page, http://www.biopepa.org/
  28. 28.
  29. 29.
    Gillespie, D.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)CrossRefGoogle Scholar
  30. 30.
  31. 31.
    Gibson, M., Bruck, J.: Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels. The Journal of Chemical Physics 104, 1876–1889 (2000)CrossRefGoogle Scholar
  32. 32.
    Schafmeier, T., Káldi, K., Diernfellner, A., Mohr, C., Brunner, M.: Phosphorylation-dependent maturation of Neurospora circadian clock protein from a nuclear repressor toward a cytoplasmic activator. Cell 20(3), 297–306 (2006)Google Scholar
  33. 33.
    Heinrich, R., Schuster, S.: The Regulation of Cellular Systems. Chapman and Hall, Boca Raton (1996)CrossRefGoogle Scholar
  34. 34.
    Degasperi, A., Gilmore, S.: Sensitivity Analysis of Stochastic Models of Bistable Biochemical Reactions. In: Bernardo, M., Degano, P., Zavattaro, G. (eds.) SFM 2008. LNCS, vol. 5016, pp. 1–20. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  35. 35.
    Cao, Y., Petzold, L.: Accuracy limitations and the measurements of errors in the stochastic simulation of chemically reacting systems. J. Comput. Phys. 212(1), 6–24 (2006)CrossRefGoogle Scholar
  36. 36.
    Rao, C.V., Arkin, A.P.: Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm. J. Chem. Phys. 118(11), 4999–5010 (2003)CrossRefGoogle Scholar
  37. 37.
    Bundschuh, R., Hayot, F., Jayaprakash, C.: Fluctuations and Slow Variables in Genetic Networks. Biophys. J. 84, 1606–1615 (2003)CrossRefPubMedPubMedCentralGoogle Scholar
  38. 38.
    Cao, Y., Gillespie, D., Petzold, L.: Accelerated Stochastic Simulation of the Stiff Enzyme-Substrate Reaction. Journal of Chemical Physics 123, 144917–144929 (2005)CrossRefPubMedGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Ozgur E. Akman
    • 1
  • Federica Ciocchetta
    • 2
  • Andrea Degasperi
    • 3
  • Maria Luisa Guerriero
    • 4
  1. 1.Centre for Systems Biology at EdinburghThe University of EdinburghEdinburghScotland, UK
  2. 2.The Microsoft ResearchUniversity of Trento Centre for Computational and Systems BiologyTrentoItaly
  3. 3.Laboratory for Foundations of Computer ScienceThe University of EdinburghEdinburghScotland, UK
  4. 4.Department of Computing ScienceThe University of GlasgowGlasgowScotland, UK

Personalised recommendations