Computational approaches to cellular rhythms

Nature

Volumn 420, Issue 6912, 2002, Pages 238-245

  Goldbeter, Albert ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

CELLS; COMPUTER SIMULATION; FEEDBACK; GENES; MATHEMATICAL MODELS; METABOLISM;

INTRACELLULAR COMMUNICATION;

RANDOM PROCESSES;

BIOLOGY; METABOLISM; OSCILLATION;

CALCIUM TRANSPORT; CELL ACTIVITY; CELL COMMUNICATION; CIRCADIAN RHYTHM; COMPUTER SIMULATION; FEEDBACK SYSTEM; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MOLECULAR DYNAMICS; MOLECULAR MECHANICS; NONHUMAN; OSCILLATION; PRIORITY JOURNAL; REVIEW;

ANIMALS; CALCIUM; CALCIUM SIGNALING; CELL PHYSIOLOGY; CIRCADIAN RHYTHM; COMPUTER SIMULATION; FEEDBACK, BIOCHEMICAL; MODELS, BIOLOGICAL; PERIODICITY;

EID: 0037079015     PISSN: 00280836     EISSN: None     Source Type: Journal    
DOI: 10.1038/nature01259     Document Type: Review

References (89)

1. Fessard, A. Propriétés Rythmiques de la Matière Vivante (Hermann, Paris, 1936).
2. Winfree, A. T. The Geometry of Biological Time 2nd edn (Springer, New York, 2001).
3. Goldbeter, A. Biochemical Oscillations and Cellular Rhythms. The Molecular Bases of Periodic and Chaotic Behaviour (Cambridge Univ. Press, Cambridge, 1996).
4. Volterra, V. Fluctuations in the abundance of a species considered mathematically. Nature 118, 558-560 (1926).
5. Hodgkin, A. L. & Huxley, A. F. A quantitative description of membrane currents and its application to conduction and excitation in nerve. J. Physiol. (Land.) 117, 500-544 (1952).
6. Koch, C. & Segev, I. (eds) Methods in Neuronal Modeling. From Synapses to Networks 2nd Edn (MIT Press, Cambridge, MA. 1998).
7. Keener, J. P. & Sneyd, J. Mathematical Physiology (Springer, New York, 1998).
8. Noble, D. Modeling the heart - From genes to cells to the whole organ, Science 295, 1678-1682 (2002).
9. Nicolis, G. & Prigogine, I. Self-Organization in Nonequilibrium Systems. From Dissipative Structures to Order through Fluctuations (Wiley, New York, 1977).
10. Thomas, R. & d'Ari, R. Biological Feedback (CRC Press, Boca Raton, FL, 1990).
11. Ferrell, J. E. Jr Self-perpetuating states in signal transduction: Positive feedback, double-negative feedback and bistability. Curr. Opin. Cell Biol. 14, 140-148 (2002).
12. Doedel, E. J. AUTO: A program for the automatic bifurcation analysis of autonomous systems. Cong. Numer. 30, 265-284 (1981). (Available at http://ftp.cs.concordia.ca/pub/doedel/auto/.)
13. Hess, B. & Boiteux, A. Oscillatory phenomena in biochemistry. Annu. Rev. Biochem. 40, 237-258 (1971).
14. Goldbeter, A. & Caplan, S. R. Oscillatory enzymes. Annu. Rev. Biophys. Bioeng. 5, 449-476 (1976).
15. Berridge, M. J. Elementary and global aspects of calcium signalling. J. Physiol. (Lond.) 499, 291-306 (1997).
16. Meyer, T. & Stryer, L. Molecular model for receptor-stimulated calcium spiking. Proc. Natl. Acad. Sci. USA 85, 5051-5055 (1988).
17. 2+ oscillations and for their frequency encoding through protein phosphorylation. Proc Natl. Acad. Sci. USA 87, 1461-1465 (1990).
18. 2+ concentration. Proc. Natl. Acad. Sci. USA 89, 9895-9899 (1992).
19. 2+ release. Biophys. J. 67, 2191-2204 (1994).
20. Sneyd, J., Charles, A. C. & Sanderson, M. J. A model for the propagation of intercellular calcium waves. Am. J. Physiol. 266, C293-C302 (1994).
21. Dupont, G. et al. Mechanism of receptor-oriented intercellular calcium wave propagation in hepatocytes. FASEB J. 14, 279-289 (2000).
22. Schuster, S., Marhl, M. & Höfer, T. Modelling of simple and complex calcium oscillations. From single-cell responses to intercellular signalling. Eur. J. Biochem. 269, 1333-1355 (2002).
23. Swillens, S., Dupont, G., Combettes, L. & Champeil, P. From calcium blips to calcium puffs: Theoretical analysis of the requirements for interchannel communication. Proc. Natl. Acad. Sci. USA 96, 13750-13755 (1999).
24. Spitzer, N. C., Lautermilch, N. J., Smith, R. D. & Gomez,T. M. Coding of neuronal differentiation by calcium transients. Bio Essays 22, 811-817 (2000).
25. 2+ oscillations. Science 279, 227-230 (1998).
26. 2+ spikes. Nature 418, 93-96 (2002).
27. Dormann, D., Kim, J. Y., Devreotes, P. N. & Weijer, C. J. cAMP receptor affinity controls wave dynamics, geometry and morphogenesis in Dictyostelium. J. Cell Sci. 114, 2513-2523 (2001).
28. Martiel, J. L. & Goldbeter, A. A model based on receptor desensitization for cyclic AMP signaling in Dictyostelium cells. Biophys J. 52, 807-829 (1987).
29. Tang, Y. & Othmer, H. G. Excitation, oscillations and wave propagation in a G-protein-based model of signal transduction in Dictyostelium discoideum. Phil. Trans. R. Soc. Lond. B 349, 179-195 (1995).
30. Palsson, E. & Cox, E. C. Origin and evolution of circular waves and spirals in Dictyostelium discoideum territories. Proc. Natl. Acad. Sci. USA 93, 1151-1155 (1996).
31. Lauzeral, J., Halloy, J. & Goldbeter, A. Desynchronization of cells on the developmental path triggers the formation of spiral waves of cAMP during Dictyostelium aggregation. Proc. Natl. Acad. Sci. USA 94, 9153-9158 (1997).
32. Bretschneider, T., Siegert, F. & Weijer, C. J. Three-dimensional scroll waves of cAMP could direct cell movement and gene expression in Dictyostelium slugs. Proc Natl. Acad. Sci USA 92, 4387-4391 (1995).
33. Chadwick, D. J. & Goode, J. A. (eds) Mechanisms and Biological Significance of Pulsatite Hormone Secretion (Novartis Found. Symp. 227) (Wiley, Chichester, 2000).
34. Knobil, E. Patterns of horntone signals and hormone action. New Engl. J. Med. 305, 1582-1583 (1981).
35. Belchetz, P. E., Plant, T. M., Nakai, Y., Keogh, E. J. & Knobil, E. Hypophysial responses to continuous and intermittent delivery of hypothalamic gonadotropin-releasing hormone. Science 202, 631-633 (1978).
36. Hindmarsh, P. C., Stanhope, R., Preece, M. A. & Brook, C. G. D. Frequency of administration of growth hormone - An important factor in determining growth response to exogenous growth hormone. Horm. Res. 33(Suppl. 4), 83-89 (1990).
37. Tornheim, K. Are metabolic oscillations responsible for normal oscillatory insulin secretion? Diabetes 46, 1375-1380 (1997).
38. Li, Y. X. & Goldbeter, A. Frequency specificity in intercellular communication: The influence of patterns of periodic signalling on target cell responsiveness. Biophys. 155, 125-145 (1989).
39. Goldbeter, A., Dupont, G. & Halloy, J. The frequency encoding of pulsatility. Novartis Found. Symp. 227, 19-36 (2000).
40. Wagner, C., Caplan, S. R. & Tannenbaum, G. S. Genesis of the ultradian rhythm of GH secretion: A new model unifying experimental observations in rats. Am. J. Physiol. 275, E 1046-E1054 (1998).
41. Maki, L. W. & Keizer, J. Mathematical analysis of a proposed mechanism for oscillatory insulin secretion in perifused HIT-15 cells. Bull. Math. Biol. 57, 569-591 (1995).
42. Dunlap, J. C. Molecular bases for circadian clocks. Cell 96, 271-290 (1999).
43. Young, M. W. & Kay, S. A. Time zones: A comparative genetics of circadian clocks. Nature Rev. Genet. 2, 702-715 (2001).
44. Reppert, S. M. & Weaver, D. R. Coordination of circadian timing in mammals. Nature 418, 935-941 (2002).
45. Hardin, P. E., Hall, J. C. & Rosbash, M. Feedback of the Drosophila period gene product on circadian cycling of its messenger RNA levels. Nature 343, 536-540 (1990).
46. Kronauer, R. E., Forger, D. B. & Jewett, M. E. Quantifying human circadian pacemaker response to brief, extended, and repeated light stimuli over the phototopic range. Biol. Rhythms 14, 500-515 (1999).
47. Gonze, D., Roussel, M. & Goldbeter, A. A model for the enhancement of fitness in cyanobacteria based on resonance of a circadian oscillator with the external light-dark cycle. J. Theor. Biol. 214, 577-597 (2002).
48. Goodwin, B. C. Oscillatory behavior in enzymatic control processes. Adv. Enzyme Regal. 3, 425-438(1965).
49. Ruoff, P., Vinsjevik, M., Monnerjahn, C. & Rensing, L. The Goodwin model: Simulating the effect of light pulses on the circadian sporulation rhythm of Neurospora crassa. J. Theor. Biol. 209, 29-42 (2001).
50. Goldbeter, A. A model for circadian oscillations in the Drosophila period protein (PER). Proc. R. Soc. Lond. B261, 319-324 (1995).
51. Leloup, J. C. & 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, 70-87 (1998).
52. Tyson, J. J., Hong, C. I., Thron, C. D. & Novak, B. A simple model of circadian rhythms based on dimerization and proteolysis of PER and TIM. Biophys. J. 77, 2411-2417 (1999).
53. Glossop, N. R., Lyons, L. C. & Hardin, P. E. interlocked feedback loops within the Drosophila circadian oscillator. Science 286, 766-768 (1999).
54. Shearman, L. P. et al. Interacting molecular loops in the mammalian circadian clock. Science 288, 1013-1019 (2000).
55. Preitner, N. et al. The orphan nuclear receptor REV-ERBα controls circadian transcription within the positive limb of the mammalian circadian oscillator. Cell 110, 251-260 (2002).
56. Ueda, H. R, Hagiwara, M. & Kitano, H. Robust oscillations within the interlocked feedback model of Drosophila circadian rhythm. J. Theor. Biol. 210, 401-406 (2001).
57. Smolen, P., Baxter, D. A. & Byrne, J. H. Modeling circadian oscillations with interlocking positive and negative feedback loops. J. Neurosci. 21, 6644-6656 (2001).
58. Leloup, J. C. & Goldbeter, A. Towards a detailed computational model for the mammalian circadian clock. Proc. Natl. Acad. Sci. USA (submitted).
59. Richardson, G. S. & Malin, H. V. Circadian rhythm sleep disorders: Pathophysiology and treatment. J. Clin. Neurophysiol. 13, 17-31 (1996).
60. Toh, K. L. et al. An hPer2 phosphorylation site mutation in familial advanced sleep phase syndrome. Science 291, 1040-1043 (2001).
61. Ebisawa, T. et al. Association of structural polymorphisms in the human period3 gene with delayed sleep phase syndrome. EMBO Rep. 2, 342-346 (2001).
62. Leloup, J. C. & Goldbeter, A. A molecular explanation for the long-term suppression of circadian rhythms by a single light pulse. Am. J. Physiol. Regul. Integr. Comp. Physiol. 280, R1206-R1212 (2001).
63. Barkai, N. & Leibler, S. Circadian clocks limited by noise. Nature 403, 267-268 (2000).
64. Gonze, D., Halloy, J. & Goldbeter, A. Robustness of circadian rhythms with respect to molecular noise. Proc. Natl. Acad. Sci. USA 99, 673-678 (2002).
65. Vilar, J. M., Kueh, H. Y., Barkai, N. & Leibler, S. Mechanisms of noise-resistance in genetic oscillators. Proc. Natl. Acad. Sci. USA 99, 5988-5992 (2002).
66. Goldbeter, A. et al. From simple to complex oscillatory behavior in metabolic and genetic control networks. Chaos 11, 247-260 (2001).
67. Rinzel, J. A formal classification of bursting mechanisms in excitable systems. Lect. Notes Biomath. 71, 267-281 (1987).
68. Olsen, L. F. & Degn, H. Chaos in biological systems. Q. Rev. Biophys. 18, 165-225 (1985).
69. Glass, L. & Mackey, M.C. From Clocks to Chaos: The Rhythms of Life (Princeton Univ. Press, Princeton, 1988).
70. 2+ oscillations in a new model for non-excitable cells. Cell Calcium 17, 225-232 (1995).
71. Kummer, U. et al. Switching from simple to complex oscillations in calcium signaling. Biophys. J. 79, 1188-1195 (2000).
72. Goldbeter, A. A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. Proc Natl. Acad. Sci. USA 88, 9107-9111 (1991).
73. Novak, B. & Tyson, J. J. Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos. J. Cell Sci. 106, 1153-1168 (1993).
74. Tyson, J. J. & Novak, B. Regulation of the eukaryotic cell cycle: Molecular antagonism, hysteresis, and irreversible transitions. J. Theor. Biol. 210, 249-263.
75. Tyson, J. J., Chen, K. & Novak, B. Network dynamics and cell physiology. Nature Rev. Mol. Cell Biol. 2, 908-916 (2001).
76. Elowitz, M. B. & Leibler, S. A synthetic oscillatory network of transcriptional regulators. Nature 403, 335-338 (2000).
77. Gardner, T. S., Cantor, C. R. & Collins, J. J. Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339-342 (2000).
78. Lev Bar-Or, R. et al. Generation of oscillations by the p53-Mdm2 feedback loop: A theoretical and experimental study. Proc Natl. Acad. Sci. USA 97, 11250-11255 (2000).
79. Maroto, M. & Pourquié, O. A molecular clock involved in somite segmentation. Curr. Top. Dev. Biol. 51, 221-248 (2001).
80. Jacquer, M., Renault, G., Lallet, S., de Mey, J. & Goldbeter, A. Oscillatory nucleocytoplasmic shuttling of the general stress response transcriptional activator Msn2 in Saccharomyces cerevisiae. Nature (submitted).
81. Boiteux, A., Goldbeter, A. & Hess, B. Control of oscillating glycolysis of yeast by stochastic, periodic, and steady source of substrate: A model and experimental study. Proc. Natl. Acad. Sci. USA 72, 3829-3833 (1975).
82. Termonia, Y. & Ross, J. Oscillations and control features in glycolysis: Numerical analysis of a comprehensive model. Proc. Natl. Acad. Sci. USA 78, 2952-2956 (1981).
83. Hynne, F., Dano, S. & Sorensen, P. G. Full-scale model of glycolysis in Saccharomyces cerevisiae. Biophys. Chem. 94, 121-163 (2001).
84. Reijenga, K. A., Westerhoff, H. V., Kholodenko, B. N. & Snoep, J. L. Control analysis for autonomously oscillating biochemical networks. Biophys. J. 82, 99-108 (2002).
85. Hartwell, L. H., Hopfield, J. J., Leibler, S. & Murray, A. W. From molecular to modular cell biology. Nature 402 (Suppl.), C47-C52 (1999).
86. Koshland, D. E. Jr The era of pathway quantification. Science 280, 852-853 (1998).
87. Petty, H. R. Neutrophil oscillations: Temporal and spatiotemporal aspects of cell behavior. Immunol. Res. 23, 85-94 (2001).
88. Nielsen, K., Sorensen, P. G. & Hynne, F. Chaos in glycolysis. J. Theor. Biol. 186, 303-306 (1997).
89. Honma, S. et al. Dec1 and Dec2 are regulators of the mammalian molecular clock. Nature 419, 841-844 (2002).