Skip to main content
SpringerLink
Log in

A Coupled Oscillatory Model Mimicking Avian Circadian Regulatory Systems

  • Published:
Journal of Biological Physics Aims and scope Submit manuscript

Abstract

Much evidence indicates that the pineal gland and thesuprachiasmatic nucleus (SCN) are the primary pacemakers in the housesparrow, Passer domesticus. The interactions between the pineal andSCN predicted by the neuroendocrine loop model indicates that uncouplingwould cause the two oscillators to damp out in constant darkness. Basedupon the original neuroendocrine loop model, a mathematical frameworkof the house sparrow circadian regulatory organization that incorporatesdamping and co-inhibitory coupling has been formulated. The proposedmodel clearly indicates that two coupled oscillators must be 180°out of the phase for sustaining oscillations. From damping coefficients,which can be determined from experimental data, other parameters suchas external stimuli (interaction coefficient) and characteristicfrequencies can then be computed. Based upon earlier studies and simulations,we conclude that the sparrow pineal gland dampens more rapidly than does theSCN, suggesting that the SCN are probably more important in sparrowsthan previously thought. The model also provides the explanations ofendogenous circadian period (tau) alteration. Finally, we extend this modelto other avian and to mammalian circadian systems. We suggest that avianand mammalian circadian systems may differ in damping coefficients ofpineal glands and the degree of SCN dominance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cassone, V.M. and Menaker, M.: Is the avian circadian system a neuroendocrine loop?, J. Exp. Zool. 232 (1984), 529-549.

    Google Scholar 

  2. Gaston, S. and Menaker, M.: Pineal function: the biological clock in sparrows?, Science 160 (1968), 1125-1127.

    Google Scholar 

  3. Binkley, S., Kluth, E. and Menaker, M.: Pineal function in sparrows: circadian rhythms and body temperature, Science 197 (1971), 1181-83.

    Google Scholar 

  4. Zimmerman, N.M. and Menaker, M.: Neural connections of sparrow pineal: role in circadian control of activity, Science 190 (1975), 477-479.

    Google Scholar 

  5. Zimmerman, N.M. and Menaker, M.: The pineal gland, a pacemaker within the circadian system of the house sparrow, Proc. natn. Acad. Sci. U.S.A. 76 (1979), 999-1003.

    Google Scholar 

  6. Murakami, N., Nakamura, H., Nishi, R., Marumoto, N. and Nasu, T.: Comparsion of circadian oscillation of melatonin release in pineal cells of house sparrow, pigeon and Japanese quail using cell perfusion system, Brain Res. 651 (1994), 209-214.

    Google Scholar 

  7. Takahashi, J.S., Hamm. H. and Menaker, M.: Circadian rhythms of melatonin release from individual superfused chicken pineal glands in vitro, Proc. natn. Acad. Sci. U.S.A. 77 (1980), 2319-2322.

    Google Scholar 

  8. Zatz, M.: Light and norepinephrine similarly prevent damping of the melatonin rhythm in cultured chick pineal cells: regulation of coupling between the pacemaker and overt rhythm, J. Biol. Rhythm 6(2) (1991), 137-148.

    Google Scholar 

  9. Cassone, V.M. and Menaker, M.: Sympathetic regulation of the chicken pineal rhythms, Brain Res. 289 (1983), 129-135.

    Google Scholar 

  10. Turek, F.W., McMillan, J.P. and Menaker, M.: Melatonin: effects on circadian locomotor rhythm in sparrows, Science 194 (1976), 1441-1443.

    Google Scholar 

  11. Ebihara, S. and Kawamura, K.: The role of pineal organ and the suprachiasmatic nucleus in the control of circadian locomotor rhythms in the Java sparrow (Padda oryzivora), J. Comp. Physiol. A. 141 (1981), 207-214.

    Google Scholar 

  12. Heigl, S. and Gwinner, E.: Synchronization of circadian rhythms of house sparrows by oral melatonin: effects of changing period, J. Biol. Rhythms Sep. 10(3) (1995), 225-233.

    Google Scholar 

  13. Lu, J. and Cassone, V.M.: Daily melatonin administration synchronizes circadian pattern of brain metabolism and behavior in pinealectomized house sparrow (Passer domesticus), J. Comp. Physiol. A. 173 (1993), 775-782.

    Google Scholar 

  14. Cassone, V.M. and Moore, R.Y.: Retinohypothalamic projection and suprachiasmatic nucleus of the house sparrow (Passer domesticus), J. Comp. Neurol. 266 (1987), 171-182.

    Google Scholar 

  15. Takahashi, J.S. and Menaker, M.: Role of the suprachiasmatic nucleus in the circadian system of the house sparrow, J. Neurosci. 2 (1982), 815-828.

    Google Scholar 

  16. Cassone, V.M., Forsyth, A.M. and Woodlee, G.M.: Hypothalamic regulation of circadian noradrenergic input to the chick pineal gland, J. Comp. Physiol. A. 167 (1990), 187-192.

    Google Scholar 

  17. Cassone, V.M.: Circadian variation of [14C]2-deoxyglucose uptake within the suprachiasmatic nucleus of the house sparrow (Passer domesticus), Brain Res. 459 (1988), 178-182.

    Google Scholar 

  18. Lu, J. and Cassone, V.M: Pineal regulation of 2-[14C]deoxyglucose uptake and 2-[125I]iodomelatonin binding in visual system of house sparrow (Passer domesticus), J. Comp. Physiol. A. 173 (1993), 765-774.

    Google Scholar 

  19. Juss, T.V.S., Davis, I.R., Kollett, B.K. and Mason, R.: Circadian rhythm in neuronal discharge activity in the quail lateral hypothalamic retinoreceipent nucleus (LHRN) recording in vitro, J. Physiol. 475 (1994), 132.

    Google Scholar 

  20. Menaker, M. and Zimmerman, N.: Role of the pineal in the circadian system of birds, Am. Zool. 16 (1976), 45-55.

    Google Scholar 

  21. Gwinner, E.: Effects of pinealectomy on circadian locomotor activity rhythms in European Starling (Sturnus vulgaris), J. Comp. Physiol. A. 126 (1978), 123-129.

    Google Scholar 

  22. Gwinner, E.: Melatonin in the circadian system of birds: model of internal resonance, in T. Hiroshige and K. Homa (eds.), Circadian Clocks and Ecology, Hokkaido Press, Sapporo, 1989, pp. 127-153.

    Google Scholar 

  23. Fulford, G., Forrester, P. and Jones, A.: Modelling with Differential and Difference Equations, Cambridge University Press, Cambridge, 1997.

    Google Scholar 

  24. Arrowsmith, D.K. and Place, C.M.: Ordinary Differential Equations, Chapman & Hall, London, 1982.

    Google Scholar 

  25. Nicolis, G.: Introduction to Nonlinear Science, Cambridge University Press, Cambridge, 1995.

    Google Scholar 

  26. Verhust, F.: Nonlinear Differential Equations and Dynamic Systems (2nd ed.), Springer, Berlin, 1996.

    Google Scholar 

  27. Cassone, V.M. and Brooks, D.S.: Sites of melatonin action in the sparrow brain (Passer domesticus), J. Exp. Zool. 260(3) (1991), 302-309.

    Google Scholar 

  28. Cassone, V.M., Lane, R.F. and Menaker, M.: Melatonin-induced increases in serotonin concentration in specific regions of the chicken brain, Neuroendocrinol. 266 (1986), 171-182.

    Google Scholar 

  29. Cassone, V.M.: Melatonin: time in a bottle', Oxford Review of Reproductive Biology 12 (1990), 319-367.

    Google Scholar 

  30. Takahashi, J.S., Murakami, N., Nikaido, S.S., Pratt, B.L. and Robertson, L.M.: The avian pineal, a vertebrate model system of circadian oscillator: cellular regulation of circadian rhythms by light, second messengers, and macromolecular synthesis, Recent Prog. in Hormone Res. 45 (1989), 279-351.

    Google Scholar 

  31. Halanay, A.: Differential Equations: Stability, Oscillations, Time Lags, Academic Press, New York and London, 1966.

    Google Scholar 

  32. Wiener, J.: Generalized Solutions of Functional Differential Equations, World Scientific, Singapore, 1993.

    Google Scholar 

  33. Diekmann, O., van Gils, S.A., Verduyn Lunel, S.M. and Walther, H.-O.: Delay Equations: Functional-, Complex-, and Nonlinear Analysis, Springer-Verlag, New York, Berlin, 1995.

    Google Scholar 

  34. Gopalsamy, K., Grove, E.A. and Ladas, G.: Neural delay differential equations with variable delays, in: A.R. Aftabizadeh (ed.), Differential Equations and Applications, Ohio University Press, Athens, 1988, pp. 343-347.

    Google Scholar 

  35. French, A.P.: Vibration and Waves, W.W Norton Company. Inc., New York, 1968.

    Google Scholar 

  36. Gaston, S.: The influence of the pineal organ on the circadian activity rhythm in birds, in: M. Menaker (ed.), Biochronmetry, National Academy of Sciences, Washington, D.C., 1971.

    Google Scholar 

  37. Eskin, A.: Some properties of the system controlling the circadian activity of sparrows, in: M. Menaker (ed.), Biochronmetry, National Academy of Sciences, Washington, D.C., 1971.

    Google Scholar 

  38. Pavlidis, T.: Populations of interacting oscillators and circadian rhythms, J. Theor. Biol. 22 (1969), 418-436.

    Google Scholar 

  39. Enright, J.T.: Temporal precision in circadian systems: a reliable neuronal clock from unreliable components, Science 209 (1980), 1542-1545.

    Google Scholar 

  40. Wever, R.A.: Mathematical models of circadian one-and multi-oscillator systems, in: G.A. Carpenter (ed.), Some Mathematical Questions in Biology Circadian Rhythms, The American Mathematical Society, Providence, Rhode Island, 1987, pp. 205-65.

    Google Scholar 

  41. Daan, S. and Beersma, D.: Circadian gating of human-wake cycles, in: M.C. Moore-Ede and C.A. Czeisler (eds.), Mathematical Models of the Circadian Sleep-Wake Cycle, Raven Press, New York, 1984, pp. 129-159.

    Google Scholar 

  42. Winfree, A.T.: The Timing of Biological Clock, Freeman, New York, 1987.

    Google Scholar 

  43. Winfree, A.T.: The Geometry of Biological Time, Springer-Verlag, Berlin, New York, 1990.

    Google Scholar 

  44. Carpender, G.A. and Grossberg, S.: A neural theory of circadian rhythms: the gated pacemaker, Biol. Cybernetics 48 (1983), 35-59.

    Google Scholar 

  45. Forger, D.B., Jewett, M.E. and Kronauer, R.E.: A simpler model of the human circadian pacemaker, Biol. Rhythms 14(6) (1999), 532-537.

    Google Scholar 

  46. Gander, P.H., Kronauer, R.E., Czeisler, C.A. and Moore-Ede, M.C.: Simulating the action of zeitgebers on a coupled two-oscillator model of the human circadian syste, J. Am. Physiol. 247 (1984), R418-R426.

    Google Scholar 

  47. Richie, C.G. and Womack, B.F.: A Mathematical Model For The Biological Clock of Passer Domesticus, Technical Report No. 28, University of Texas, 1966.

  48. Enright, J.T.: Mutual excitation of damped oscillators and self-sustainment of circadian rhythms, in: M.C. Moore-Ede and C.A. Czeisler (eds.), Mathematical Models of the Circadian Sleep-Wake Cycle, Raven Press, New York, 1984, pp. 1-17.

    Google Scholar 

  49. Hoffmann, K.: Splitting of the circadian rhythm as a function of light intensity, in: M. Menaker (ed.), Biochronometry, National Academy of Sciences, 1971, pp. 134-151.

  50. Meijer, J.H., Daan, S., Overkamp, J.F. and Hermann, P.M.: The two-oscillator circadian system of tree shrew (Turpaia belangeri) and its response to light pulse, J. Biol. Rhythms 5 (1990), 1-16.

    Google Scholar 

  51. Pickard, G.E., Turek, F.W. and Sollars, R.J.: Light intensity and splitting in the golden hamster, Physiol. & Behav. 54 (1993), 1-5.

    Google Scholar 

  52. Underwood, H. and Siopes J.T.: Circadian organization in the Japanese quail, J. Exp. Zool. 232 (1984), 557-566.

    Google Scholar 

  53. MacBride, S.E.: Pineal biochemical rhythms of the chicken (Gallus domesticus): light cycles and locomotor activity correlates, Ph.D. Thesis, University of Pittsburgh, Pittsburgh, PA, 1973.

    Google Scholar 

  54. Ebihara, S., Uchiyama, K. and Oshima, I.: Circadian organization in the pigeon, role of the pineal organ and eye, J. Comp. Physiol. 154 (1984), 59-69.

    Google Scholar 

  55. Murakami, N., Takamure, M., Takahashi, K., Utunomiya, K., Kurda, H. and Etoh, T.: Longterm cultured neurons from rat suprachiasmatic nucleus retain the capacity for circadian oscillation of vasopressin release, Brain Res. 545 (1991), 347-350.

    Google Scholar 

  56. Simpson, S.M. and Follett, B.K.: Pineal and hypothalamic pacemakers: their role in regulating circadian rhythmicity in Japanese quail, J. Comp. Physiol. A. 144 (1981), 381-389.

    Google Scholar 

  57. Klein, C.D. and Moore, R.Y.: Pineal N-acetyltransferse and hydroxyindole-Omethyltransferase: control by the retinohypothalamic tract and the suprachiasmatic nucleus, Brain Res. 174 (1979), 245-262.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Biosystems Modelling, Department of Industrial Engineering, Texas A&M University, College Station, TX, 77843-3131, U.S.A

    Hsin-i Wu

  2. Department of Neurology, Beth Israel Deaconess Medical Center and Harvard Medical School, Boston, MA, 02115, U.S.A

    Jun Lu

  3. Department of Biology, University of New Mexico, Albuquerque, NM, 87131-1091, U.S.A

    Bai-Lian Li

Authors
  1. Hsin-i Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bai-Lian Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, Hi., Lu, J. & Li, BL. A Coupled Oscillatory Model Mimicking Avian Circadian Regulatory Systems. Journal of Biological Physics 26, 261–272 (2000). https://doi.org/10.1023/A:1010378224387

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1010378224387

Search

Navigation