Deterministic versus stochastic models for circadian rhythms

Journal of Biological Physics

Volumn 28, Issue 4, 2002, Pages 637-653

  Gonze, D ^a   Halloy, J ^a   Goldbeter, A ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

Circadian rhythms; Molecular noise; Robustness; Stochastic simulations

Indexed keywords

MESSENGER RNA; NUCLEAR PROTEIN;

CIRCADIAN RHYTHM; CONFERENCE PAPER; CONTROLLED STUDY; DECOMPOSITION; DROSOPHILA; GENETIC ANALYSIS; INTERMETHOD COMPARISON; NEUROSPORA; NONHUMAN; OSCILLATION; PRIORITY JOURNAL; SIMULATION; STOCHASTIC MODEL;

NEUROSPORA;

EID: 0036957459     PISSN: 00920606     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021286607354     Document Type: Conference Paper

References (28)

1. Moore-Ede, M.C., Sulzman, F.M. and Fuller, C.A.: The Clocks that Time Us. Physiology of the Circadian Timing System, Harvard Univ. Press, Cambridge, MA, 1982.
2. Edmunds, L.N. Jr.: Cellular and Molecular Bases of Biological Clocks. Models and Mechanisms for Circadian Timekeeping, Springer, New York, 1988.
3. Dunlap, J.C.: Molecular Bases for Circadian Clocks, Cell 96 (1999), 271-290.
4. Young, M.W.: Life's 24-hour Clock: Molecular Control of Circadian Rhythms in Animal Cells, Trends Biochem. Sci. 25 (2000), 601-606.
5. Williams, J.A. and Sehgal A.: Molecular Components of the Circadian System in Drosophila, Annu. Rev. Physiol. 63 (2001), 729-755.
6. Young, M.W. and Kay, S.A.: Time Zones: A Comparative Genetics of Circadian Clocks, Nature Rev. Genetics 2 (2001), 702-715.
7. Reppert, S.M. and Weaver D.R.: Molecular Analysis of Mammalian Circadian Rhythms, Annu. Rev. Physiol. 63 (2001), 647-676.
8. Hardin, P.E., Hall, J.C. and Rosbash, M.: Feedback of the Drosophila Period Gene Product on Circadian Cycling of its Messenger RNA Levels, Nature 343 (1990), 536-540.
9. Goldbeter, A.: A Model for Circadian Oscillations in the Drosophila Period Protein (PER), Proc. R. Soc. Lond. B 261 (1995), 319-324.
10. Goldbeter, A.: Biochemical Oscillations and Cellular Rhythms. The Molecular Bases of Periodic and Chaotic Behaviour, Cambridge Univ. Press, Cambridge, UK, 1996.
11. Leloup, J.-C. and Goldbeter, A.: A Model for Circadian Rhythms in Drosophila Incorporating the Formation of a Complex between the PER and TIM Proteins, J. Biol. Rhythms 13 (1998), 70-87.
12. Leloup, J.-C., Gonze, D. and Goldbeter, A.: Limit Cycle Models for Circadian Rhythms Based on Transcriptional Regulation in Drosophila and Neurospora, J. Biol. Rhythms 14 (1999), 433- 448.
13. Leloup, J.-C. and Goldbeter, A.: Modeling the Molecular Regulatory Mechanism of Circadian Rhythms in Drosophila, BioEssays 22 (2000), 84-93.
14. Ueda, H.R., Hagiwara, M. and Kitano, H.: Robust Oscillations within the Interlocked Feedback Model of Drosophila Circadian Rhythm, J. Theor. Biol. 210 (2001), 401-406.
15. Smolen, P., Baxter, D.A. and Byrne, J.H.: Modeling Circadian Oscillations with Interlocking Positive and Negative Feedback Loops, J. Neurosci. 21 (2001), 6644-6656.
16. Gillespie, D.T.: A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions, J. Comput. Phys. 22 (1976), 403-434.
17. Gillespie, D.T.: Exact Stochastic Simulation of Coupled Chemical Reactions, J. Phys. Chem. 81 (1977), 2340-2361.
18. Nicolis, G. and Prigogine, L: Self-Organization in Nonequilibrium Systems, Wiley, New York, 1977.
19. Morton-Firth, C.J. and Bray, D.: Predicting Temporal Fluctuations in an Intracellular Signalling Pathway, J. Theor. Biol. 192 (1998), 117-128.
20. Baras, F., Pearson, J.E. and Malek Mansour, M.: Microscopic Simulation of Chemical Oscillations in Homogeneous Systems, J. Chem. Phys. 93 (1990), 5747-5750.
21. Baras, F.: Stochastic Analysis of Limit Cycle Behaviour, In: L. Schimansky-Geier and T. Poeschel (eds.), Stochastic Dynamics, Lecture Notes in Physics (LNP484), Springer-Verlag, Berlin, 1997, pp. 167-178.
22. McAdams, H.H. and Arkin, A.: Stochastic Mechanisms in Gene Expression, Proc. Natl. Acad. Sci. USA 94 (1997), 814-819.
23. Arkin, A., Ross, J. and McAdams, H.H.: Stochastic Kinetic Analysis of Developmental Pathway Bifurcation in Phage λ-Infected Escherichia coli Cells, Genetics 149 (1998), 1633-1648.
24. Gonze, D., Halloy, J. and Goldbeter, A.: Robustness of Circadian Rhythms with Respect to Molecular Noise, Proc. Natl. Acad. Sci. USA 99 (2002), 673-678.
25. Barkai, N. and Leibler, S.: Circadian Clocks Limited by Noise, Nature 403 (2000), 267-268.
26. von Hippel, P.H. and Berg, O.G.: Facilitated Target Location in Biological Systems, J. Biol. Chem. 264 (1989), 675-678.
27. Kraus, M., Lais, P. and Wolf, B.: Structured Biological Modelling: A Method for the Analysis and Simulation of Biological Systems Applied to Oscillatory Intracellular Calcium Waves, BioSystems 27 (1992), 145-169.
28. Gonze, D., Halloy, J., Leloup, J.C. and Goldbeter, A.: Stochastic models for circadian rhythms: effect of molecular noise on periodic and chaotic behavior. C.R. Biologies (2003), in press.