Bulletin of Mathematical Biology

, Volume 59, Issue 3, pp 517–532 | Cite as

Hierarchically coupled ultradian oscillators generating robust circadian rhythms

  • Rafael A. Barrio
  • Limei Zhang
  • Philip K. Maini


Ensembles of mutually coupled ultradian cellular oscillators have been proposed by a number of authors to explain the generation of circadian rhythms in mammals. Most mathematical models using many coupled oscillators predict that the output period should vary as the square root of the number of participating units, thus being inconsistent with the well-established experimental result that ablation of substantial parts of the suprachiasmatic nuclei (SCN), the main circadian pacemaker in mammals, does not eliminate the overt circadian functions, which show no changes in the phases or periods of the rhythms. From these observations, we have developed a theoretical model that exhibits the robustness of the circadian clock to changes in the number of cells in the SCN, and that is readily adaptable to include the successful features of other known models of circadian regulation, such as the phase response curves and light resetting of the phase.


Circadian Rhythm Circadian Clock Couple Oscillator Suprachiasmatic Nucleus Circadian Oscillation 
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Copyright information

© Society for Mathematical Biology 1997

Authors and Affiliations

  • Rafael A. Barrio
    • 1
  • Limei Zhang
    • 2
  • Philip K. Maini
    • 3
  1. 1.Instftuto de FísicaUNAMMéxicoMexico
  2. 2.Departmeneto de Fisiología, Facultad de MedicinaUNAMMéxicoMexico
  3. 3.Centre for Mathematical Biology, Mathematical InstituteUniversity of OxfordOxfordUK

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