How coupling determines the entrainment of circadian clocks

Abstract

Autonomous circadian clocks drive daily rhythms in physiology and behaviour. A network of coupled neurons, the suprachiasmatic nucleus (SCN), serves as a robust self-sustained circadian pacemaker. Synchronization of this timer to the environmental light-dark cycle is crucial for an organism’s fitness. In a recent theoretical and experimental study it was shown that coupling governs the entrainment range of circadian clocks. We apply the theory of coupled oscillators to analyse how diffusive and mean-field coupling affects the entrainment range of interacting cells. Mean-field coupling leads to amplitude expansion of weak oscillators and, as a result, reduces the entrainment range. We also show that coupling determines the rigidity of the synchronized SCN network, i.e. the relaxation rates upon perturbation. Our simulations and analytical calculations using generic oscillator models help to elucidate how coupling determines the entrainment of the SCN. Our theoretical framework helps to interpret experimental data.

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References

  1. 1.

    T. Roenneberg, S. Daan, M. Merrow, J. Biol. Rhythms 18, 183 (2003)

    Article  Google Scholar 

  2. 2.

    C. Huygens, Horologium oscillatorium, English translation: The pendulum clock (Iowa State University Press, Ames, 1986, 1673)

  3. 3.

    Y. Kuramoto, Chemical oscillations, waves, and turbulence (Courier Dover Publications, 2003)

  4. 4.

    V.S. Anishchenko, V. Astakhov, A. Neiman, T. Vadivasova, L. Schimansky-Geier, Nonlinear Dynamics of Chaotic and Stochastic Systems: Tutorial and Modern Developments (Springer-Verlag, New York, LLC, 2007)

  5. 5.

    A. Balanov, N. Janson, D. Postnov, O. Sosnovtseva, Synchronization: From Simple to Complex (Springer-Verlag, New York, 2009)

  6. 6.

    H. Ukai, H.R. Ueda, Ann. Rev. Physiol. 72, 579 (2010)

    Article  Google Scholar 

  7. 7.

    D.K. Welsh, D.E. Logothetis, M. Meister, S.M. Reppert, Neuron 14, 697 (1995)

    Article  Google Scholar 

  8. 8.

    E.D. Herzog, S.J. Aton, R. Numano, Y. Sakaki, H. Tei, J. Biol. Rhythms 19, 35 (2004)

    Article  Google Scholar 

  9. 9.

    A.C. Liu et al., Cell 129, 605 (2007)

    Article  Google Scholar 

  10. 10.

    S.J. Aton, E.D. Herzog, Neuron 48, 531 (2005)

    Article  Google Scholar 

  11. 11.

    D.K. Welsh, J.S. Takahashi, S.A. Kay, Ann. Rev. Physiol. 72, 551 (2010)

    Article  Google Scholar 

  12. 12.

    M. Comas, D.G.M. Beersma, K. Spoelstra, S. Daan, J. Biol. Rhythms 21, 362 (2006)

    Article  Google Scholar 

  13. 13.

    H.D. Piggins, M.C. Antle, B. Rusak, J. Neurosci. 15, 5612 (1995)

    Google Scholar 

  14. 14.

    C. Pittendrigh, S. Daan, J. Comp. Physiol. A 106, 291 (1976)

    Article  Google Scholar 

  15. 15.

    J. Aschoff, H. Pohl, Naturwissenschaften 65, 80 (1978)

    ADS  Article  Google Scholar 

  16. 16.

    J. Vilaplana, T. Cambras, A. Campuzano, A. Díez-Noguera, Chronobiol. Int. 14, 9 (1997)

    Article  Google Scholar 

  17. 17.

    K. Yagita, H. Okamura, FEBS Lett. 465, 79 (2000)

    Article  Google Scholar 

  18. 18.

    E.D. Buhr, S.H. Yoo, J.S. Takahashi, Science 330, 379 (2010)

    ADS  Article  Google Scholar 

  19. 19.

    U. Abraham, A.E. Granada, P.O. Westermark, M. Heine, A. Kramer, H. Herzel, Mol. Syst. Biol. 6, 438 (2010)

    Article  Google Scholar 

  20. 20.

    A. Winfree, The geometry of biological time (Springer-Verlag, New York, 1980)

  21. 21.

    R.E. Kronauer, C.A. Czeisler, S.F. Pilato, M.C. Moore-Ede, E.D. Weitzman, Am. J. Physiol. 242, R3 (1982)

    Google Scholar 

  22. 22.

    L. Glass, M.M. Mackey, From Clocks to Chaos: The Rhythms of Life (Princeton University Press, 1988)

  23. 23.

    J.C. Leloup, A. Goldbeter, Proc. Natl. Acad. Sci. U.S.A. 100, 7051 (2003)

    ADS  Article  Google Scholar 

  24. 24.

    D.B. Forger, C.S. Peskin, Proc. Natl. Acad. Sci. U.S.A. 100, 14806 (2003)

    ADS  Article  Google Scholar 

  25. 25.

    S. Becker-Weimann, J. Wolf, H. Herzel, A. Kramer, Biophys. J. 87, 3023 (2004)

    ADS  Article  Google Scholar 

  26. 26.

    A.E. Granada, H. Herzel, PLoS One 4, e7057 (2009)

  27. 27.

    S. Yamaguchi, H. Isejima, T. Matsuo, R. Okura, K. Yagita, M. Kobayashi, H. Okamura, Science 302, 1408 (2003)

    ADS  Article  Google Scholar 

  28. 28.

    P.O. Westermark, D.K. Welsh, H. Okamura, H. Herzel, PLoS Comput. Biol. 5, e1000580 (2009)

  29. 29.

    C.S. Pittendrigh, W.T. Kyner, T. Takamura, J. Biol. Rhythms 6, 299 (1991)

    Article  Google Scholar 

  30. 30.

    M.H. Vitaterna, C.H. Ko, A.M. Chang, E.D. Buhr, E.M. Fruechte, A. Schook, M.P. Antoch, F.W. Turek, J.S. Takahashi, Proc. Natl. Acad. Sci. U.S.A. 103, 9327 (2006)

    ADS  Article  Google Scholar 

  31. 31.

    S.A. Brown, D. Kunz, A. Dumas, P.O. Westermark, K. Vanselow, A. Tilmann-Wahnschaffe, H. Herzel, A. Kramer, Proc. Natl. Acad. Sci. U.S.A. 105, 1602 (2008)

    ADS  Article  Google Scholar 

  32. 32.

    H.T. van der Leest, J.H.T. Rohling, S. Michel, J.H. Meijer, PLoS One 4, e4976 (2009)

  33. 33.

    W. Ebeling, H. Herzel, W. Richert, L. Schimansky-Geier, Z. Angew. Math. Mech. 66, 141 (1986)

    MathSciNet  MATH  Article  Google Scholar 

  34. 34.

    R. Wever, J. Theor. Biol. 36, 119 (1972)

    Article  Google Scholar 

  35. 35.

    M.D. Schwartz, C. Wotus, T. Liu, W.O. Friesen, J. Borjigin, G.A. Oda, H.O. de la Iglesia, Proc. Natl. Acad. Sci. U.S.A. 106, 17540 (2009)

    ADS  Article  Google Scholar 

  36. 36.

    A.E. Granada, T. Cambras, A. Díez-Noguera, H. Herzel, Interface Focus 1, 153 (2011)

    Article  Google Scholar 

  37. 37.

    K. Bar-Eli, J. Phys. Chem. 88, 3616 (1984)

    Article  Google Scholar 

  38. 38.

    D. Aronson, G. Ermentrout, N. Kopell, Physica D 41, 403 (1990)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  39. 39.

    G. Asher, U. Schibler, Cell Metabol. 13, 125 (2011)

    Article  Google Scholar 

  40. 40.

    J.S. O’Neill, E.S. Maywood, J.E. Chesham, J.S. Takahashi, M.H. Hastings, Science 320, 949 (2008)

    ADS  Article  Google Scholar 

  41. 41.

    A. Granada, R.M. Hennig, B. Ronacher, A. Kramer, H. Herzel, Methods Enzymol. 454, 1 (2009)

    Article  Google Scholar 

  42. 42.

    A. Pikovsky, O. Popovych, Y. Maistrenko, Phys. Rev. Lett. 87, 044102 (2001)

    ADS  Article  Google Scholar 

  43. 43.

    E. Doedel, R. Paffenroth, A. Champneys, T. Fairgrieve, Y. Kuznetsov, B. Oldeman, B. Sandstede, X. Wang, AUTO2000: Continuation and bifurcation software for ordinary differential equations (with HOMCONT), Technical report, Concordia University, 2002

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Correspondence to G. Bordyugov.

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Bordyugov, G., Granada, A.E. & Herzel, H. How coupling determines the entrainment of circadian clocks. Eur. Phys. J. B 82, 227 (2011). https://doi.org/10.1140/epjb/e2011-20337-1

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Keywords

  • Coupling Strength
  • Circadian Clock
  • Couple Oscillator
  • Limit Cycle Oscillator
  • Bifurcation Line