Chaos and birhythmicity in a model for circadian oscillations of the PER and TIM proteins in Drosophila

Journal of Theoretical Biology

Volumn 198, Issue 3, 1999, Pages 445-459

  Leloup, Jean Christophe ^a   Goldbeter, Albert ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

PROTEIN;

ARTICLE; CIRCADIAN RHYTHM; DROSOPHILA; GENE EXPRESSION REGULATION; MODEL; NEGATIVE FEEDBACK; NONHUMAN; OSCILLATION; PRIORITY JOURNAL;

EID: 0033532569     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1999.0924     Document Type: Article

References (37)

1. Allada, R., White, N. E., So, W. V., Hall, J. C., & Rosbash, M. (1998). A mutant Drosophila homolog of mammalian clock disrupts circadian rhythms and transcription of period and timeless. Cell 93, 791-804.
2. Baylies, M. K., Weiner, L., Vosshall, L. B., Saez, L. & Young, M. W. (1993). Genetic, molecular, and cellular studies of the per locus and its products in Drosophila melanogaster. In: Molecular Genetics of Biological Rhythms (Young, M. W., eds) pp. 123-153. New York: M. Dekker.
3. Borghans, J. A. M., Dupont, G. & Goldbeter, A. (1997). Complex intracellular calcium oscillations. A theoretical exploration of possible mechanisms. Biophys. Chem. 66, 25-41.
4. Crosthwaite, S. K., Dunlap, J. C. & Loros, J. L. (1997). Neurospora wc-1 and wc-2: Transcription, photoresponses, and the origins of circadian rhythmicity. Science 276, 763-769.
5. Darlington, T. K., Wager-Smith, K., Ceriani, M. F., Staknis, D., Gekakis, N., Steeves, T. D. L., Weitz, C. J., Takahashi, J. S. & Kay, S. A. (1998). Closing the circadian loop: Clock-induced transcription of its own inhibitors per and tim. Science 280, 1599-1603.
6. Decroly, O. & Goldbeter, A. (1982). Birhythmicity, chaos, and other patterns of temporal self-organization in a multiply regulated biochemical system. Proc. Nat. Acad. Sci. U.S.A. 79, 6917-6921.
7. Doedel, E. J. (1981). Auto: A program for the automatic bifurcation analysis of autonomous systems. Congr. Num. 30, 265-284.
8. Dunlap, J. C. (1996). Genetics and molecular analysis of circadian rhythms. Annu. Rev. Genet. 30, 579-601.
9. Edery, I., Zwiebel, L. J., Dembinska, M. E. & Rosbash, M. (1994). Temporal phosphorylation of the Drosophila period protein. Proc. Nat. Acad. Sci. U.S.A. 91, 2260-2264.
10. Goldbeter, A. (1995). A model for circadian oscillations in the Drosophila period (PER) protein. Proc. R. Soc. Lond. B 261, 319-324.
11. Goldbeter, A. (1996). Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour. Cambridge: Cambridge University Press.
12. Gonze, D., Leloup, J.-C. & Goldbeter, A. (1999). Theoretical models for circadian oscillations in Neurospora and Drosophila. C. R. Acad. Sci. (Paris) III (in press).
13. Goodwin, B. C. (1965). Oscillatory behavior in enzymatic control processes. Adv. Enzyme Regul. 3, 425-438.
14. Hall, J. C. (1995). Tripping along the trail to the molecular mechanisms of biological clocks. Trends Neurosci. 18, 230-240.
15. Hall, J. C. & Rosbash, M. (1987). Genes and biological rhythms. Trends Genet. 3, 185-191.
16. 2+ oscillations. Bull. Math. Biol. 61, 507-530.
17. Hunter-Ensor, M., Ousley, A. & Sehgal, A. (1996). Regulation of the Drosophila protein timeless suggests a mechanism for resetting the circadian clock by light. Cell 84, 677-685.
18. Koike, N., Hida, A., Numano, R., Hirose, M., Sakaki, Y. & Tei, H. (1998). Identification of the mammalian homologues of the Drosophila timeless gene, Timeless 1. FEBS Lett. 441, 427-431.
19. Konopka, R. J. & Benzer, S. (1971). Clock mutants of Drosophila melanogaster. Proc. Nat. Acad. Sci. U.S.A. 68, 2112-2116.
20. Kloss, B., Price, J. L., Saez, L., Blau, J., Rothenfluh, A., Wesley, C. S. & Young, M. W. (1998). The Drosophila clock gene double-time encodes a protein closely related to human casein kinase Iε. Cell 94, 97-107.
21. Lakin-Thomas, P. L., Brody, S. & Cote, G. C. (1991). Amplitude model for the effects of mutations and temperature on period and phase resetting of the Neurospora circadian oscillator. J. Biol. Rhythms 6, 281-297.
22. Lee, C., Parikh, V., Itsukaichi, T., Bae, K. & Edery, I. (1996). Resetting the Drosophila clock by photic regulation of PER and a PER-TIM complex. Science 271, 1740-1744.
23. Leloup, J.-C. & Goldbeter, A. (1998). A model for circadian rhythms in Drosophila incorporating the formation of a complex between the Per and Tim proteins. J. Biol. Rhythms 13, 70-87.
24. Myers, M. P., Wager-Smith, K., Rothenfluh-Hilfiker, A. & Young, M. W. (1996). Light-induced degradation of timeless and entrainment of the Drosophila circadian clock. Science 271, 1736-1740.
25. Pittendrigh, C. S. (1960). Circadian rhythms and the circadian organization of living systems. Cold Spring Harb. Symp. Quant. Biol. 25, 159-182.
26. Price, J. L., Blau, J., Rothenfluh, A., Abodeely, M., Kloss, B. & Young, M. W. (1998). Double-time is a new Drosophila clock gene that regulates period protein accumulation. Cell 94, 83-95.
27. Romond, P.-C., Rustici, M., Gonze, D. & Goldbeter, A. (1999). Alternating oscillations and chaos in a model of two coupled biochemical oscillators driving successive phases of the cell cycle. Ann. N. Y. Acad. Sci. (in press).
28. Rosbash, M. (1995). Molecular control of circadian rhythms. Curr. Opin. Genet. 5, 662-668.
29. Ruoff, P., Mohsenzadeh, S. & Rensing, L. (1996). Circadian rhythms and protein turnover: The effect of temperature on the period lengths of clock mutants simulated by the Goodwin oscillator. Naturwissenschaften 83, 514-517.
30. Rutila, J. E., Suri, V., Le, M., So, W. V., Rosbash, M. & Hall, J. C. (1998). Cycle is a second bHLH-PAS clock protein essential for circadian rhythmicity and transcription of Drosophila period and timeless. Cell 93, 805-814.
31. Sehgal, A., Price, J. L., Man, B. & Young, M. W. (1994). Loss of circadian behavioral rhythms and per RNA oscillations in the Drosophila mutant timeless. Science 263, 1603-1606.
32. Shearman, L. P., Zylka, M. J., Weaver, D. R., Kolakowski, L. F. Jr. & Reppert, S. M. (1997). Two period homologs: Circadian expression and photic regulation in the suprachiasmatic nuclei. Neuron 19, 1261-1269.
33. Tei, H., Okamura, H., Shigeyoshi, Y., Fukuhara, C., Ozawa, R., Hirose, M. & Sakaki, Y. (1997). Circadian oscillation of a mammalian homologue of the Drosophila period gene. Nature 389, 512-516.
34. Vosshall, L. B., Price, J. L., Sehgal, A., Saez, L. & Young, M. W. (1994). Block in nuclear localization of period protein by a second clock mutation, timeless. Science 263, 1606-1609.
35. Yu, Q., Jacquier, A. C., Citri, Y., Hamblen, M., Hall, J. C. & Rosbash, M. (1987). Molecular mapping of point mutations in the period gene that stop or speed up biological clocks in Drosophila melanogaster. Proc. Nat. Acad. Sci. U.S.A. 84, 784-788.
36. Zeng, H., Qian, Z., Myers, M. P. & Rosbash, M. (1996). A light-entrainment mechanism for the Drosophila circadian clock. Nature 380, 129-135.
37. Zylka, M. J., Shearman, L. P., Levine, J. D., Jin, X., Weaver, D. R. & Reppert, S. M. (1998). Molecular analysis of mammalian timeless. Neuron 21, 1115-1122.