Circadian Clocks pp 335-357 | Cite as

# Mathematical Modeling in Chronobiology

## Abstract

Circadian clocks are autonomous oscillators entrained by external *Zeitgebers* such as light–dark and temperature cycles. On the cellular level, rhythms are generated by negative transcriptional feedback loops. In mammals, the suprachiasmatic nucleus (SCN) in the anterior part of the hypothalamus plays the role of the central circadian pacemaker. Coupling between individual neurons in the SCN leads to precise self-sustained oscillations even in the absence of external signals. These neuronal rhythms orchestrate the phasing of circadian oscillations in peripheral organs. Altogether, the mammalian circadian system can be regarded as a network of coupled oscillators. In order to understand the dynamic complexity of these rhythms, mathematical models successfully complement experimental investigations. Here we discuss basic ideas of modeling on three different levels (1) rhythm generation in single cells by delayed negative feedbacks, (2) synchronization of cells via external stimuli or cell–cell coupling, and (3) optimization of chronotherapy.

## Keywords

Bifurcations Entrainment Modelling Oscillations Synchronization## Notes

### Acknowledgments

The authors thank Jana Hinners and Anna Erzberger for their contributions to numerical simulations, Adrian E. Granada, Michael Mackey, and Francis Levi for fruitful discussions, and DFG (SFB 618, InKomBio) and BMBF (ColoNet, Circage FKZ 0315899) for financial support.

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