Stochastic models for circadian rhythms: Effect of molecular noise on periodic and chaotic behaviour

Comptes Rendus - Biologies

Volumn 326, Issue 2, 2003, Pages 189-203

  Gonze, Didier ^a   Halloy, José ^a   Leloup, Jean Christophe ^a   Goldbeter, Albert ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

Chaos; Circadian rhythms; Molecular noise; Robustness; Stochastic simulations

Indexed keywords

MESSENGER RNA; REGULATOR PROTEIN;

CIRCADIAN RHYTHM; MOLECULAR ANALYSIS;

AUTOREGULATION; CIRCADIAN RHYTHM; COMPLEX FORMATION; COMPUTER PREDICTION; COMPUTER SIMULATION; CONTROLLED STUDY; DARKNESS; DROSOPHILA; GENE EXPRESSION REGULATION; GENE REPRESSION; LIGHT DARK CYCLE; MATHEMATICAL COMPUTING; MOLECULE; NOISE; NONHUMAN; OSCILLATION; REVIEW; STEADY STATE; STOCHASTIC MODEL;

EID: 0012599475     PISSN: 16310691     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1631-0691(03)00016-7     Document Type: Review

References (32)

1. M.C. Moore-Ede, F.M. Sulzman, C.A. Fuller, The Clocks that Time Us. Physiology of the Circadian Timing System, Harvard University Press, Cambridge, MA, USA, 1982.
2. L.N. Edmunds, Cellular and Molecular Bases of Biological Clocks. Models and Mechanisms for Circadian Timekeeping, Springer, New York, 1988.
3. J.C. Dunlap, Molecular bases for circadian clocks, Cell 96 (1999) 271-290.
4. M.W. Young, Life's 24-hour clock: molecular control of circadian rhythms in animal cells, Trends Biochem. Sci. 25 (2000) 601-606.
5. J.A. Williams, A. Sehgal, Molecular components of the circadian system in Drosophila, Annu. Rev. Physiol. 63 (2001) 729-755.
6. M.W. Young, S.A. Kay, Time zones: a comparative genetics of circadian clocks, Nature Rev. Genet. 2 (2001) 702-715.
7. S.M. Reppert, D.R. Weaver, Molecular analysis of mammalian circadian rhythms, Annu. Rev. Physiol. 63 (2001) 647-676.
8. P.E. Hardin, J.C. Hall, M. Rosbash, Feedback of the Drosophila period gene product on circadian cycling of its messenger RNA levels, Nature 343 (1990) 536-540.
9. A. Goldbeter, A model for circadian oscillations in the Drosophila period protein (PER), Proc. R. Soc. Lond. B 261 (1995) 319-324.
10. A. Goldbeter, Biochemical Oscillations and Cellular Rhythms. The Molecular Bases of Periodic and Chaotic Behaviour, Cambridge University Press, Cambridge, UK, 1996.
11. J.-C. Leloup, A. Goldbeter, 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. J.-C. Leloup, D. Gonze, A. Goldbeter, Limit cycle models for circadian rhythms based on transcriptional regulation in Drosophila and Neurospora, J. Biol. Rhythms 14 (1999) 433-448.
13. J.-C. Leloup, A. Goldbeter, Modeling the molecular regulatory mechanism of circadian rhythms in Drosophila, BioEssays 22 (2000) 84-93.
14. H.R. Ueda, M. Hagiwara, H. Kitano, Robust oscillations within the interlocked feedback model of Drosophila circadian rhythm, J. Theor. Biol. 210 (2001) 401-406.
15. P. Smolen, D.A. Baxter, J.H. Byrne, Modeling circadian oscillations with interlocking positive and negative feedback loops, J. Neurosci. 21 (2001) 6644-6656.
16. N. Barkai, S. Leibler, Circadian clocks limited by noise, Nature 403 (2000) 267-268.
17. D. Gonze, J. Halloy, A. Goldbeter, Robustness of circadian rhythms with respect to molecular noise, Proc. Natl Acad. Sci. USA 99 (2002) 673-678.
18. D.T. Gillespie, A general method for numerically simulating the stochastic time evolution of coupled chemical reactions, J. Comput. Phys. 22 (1976) 403-434.
19. D.T. Gillespie, Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem. 81 (1977) 2340-2361.
20. D. Gonze, J. Halloy, A. Goldbeter, Deterministic versus stochastic models for circadian rhythms, J. Biol. Phys. 28 (2002) 637-653.
21. J.-C. Leloup, A. Goldbeter, Chaos and birhythmicity in a model for circadian oscillations of the PER and TIM proteins in Drosophila, J. Theor. Biol. 198 (1999) 445-459.
22. G. Nicolis, I. Prigogine, Self-Organization in Nonequilibrium Systems, Wiley, New York, 1977.
23. C.J. Morton-Firth, D. Bray, Predicting temporal fluctuations in an intracellular signalling pathway, J. Theor. Biol. 192 (1998) 117-128.
24. F. Baras, J.E. Pearson, M. Malek Mansour, Microscopic simulation of chemical oscillations in homogeneous systems, J. Chem. Phys. 93 (1990) 5747-5750.
25. F. Baras, Stochastic analysis of limit cycle behaviour, in: L. Schimansky-Geier, T. Poeschel (Eds.), Stochastic Dynamics, Lecture Notes in Physics (LNP484), Springer-Verlag, Berlin, 1997, pp. 167-178.
26. H.H. McAdams, A. Arkin, Stochastic mechanisms in gene expression, Proc. Natl. Acad. Sci. USA 94 (1997) 814-819.
27. A. Arkin, J. Ross, H.H. McAdams, Stochastic kinetic analysis of developmental pathway bifurcation in phage λ-infected Escherichia coli cells, Genetics 149 (1998) 1633-1648.
28. D. Gonze, J. Halloy, P. Gaspard, Biochemical clocks and molecular noise, theoretical study of robustness factor, J. Chem. Phys. 116 (2002) 10997-11010.
29. P.H. von Hippel, O.G. Berg, Facilitated target location in biological systems, J. Biol. Chem. 264 (1989) 675-678.
30. P. Peeters, G. Nicolis, Intrinsic fuctuations in chaotic dynamics, Physica A 188 (1992) 426-435.
31. P. Geysermans, F. Baras, Particle simulation of chemical chaos, J. Chem. Phys. 105 (1996) 1402-1408.
32. E.J. Doedel, AUTO, A program for automatic bifurcation analysis of autonomous systems, Congr. Num. 30 (1981) 265-284.