title: Tuning the phase of circadian entrainment.
abstract: The circadian clock coordinates daily physiological, metabolic and behavioural rhythms. These endogenous oscillations are synchronized with external cues ('zeitgebers'), such as daily light and temperature cycles. When the circadian clock is entrained by a zeitgeber, the phase difference ψ between the phase of a clock-controlled rhythm and the phase of the zeitgeber is of fundamental importance for the fitness of the organism. The phase of entrainment ψ depends on the mismatch between the intrinsic period τ and the zeitgeber period T and on the ratio of the zeitgeber strength to oscillator amplitude. Motivated by the intriguing complexity of empirical data and by our own experiments on temperature entrainment of mouse suprachiasmatic nucleus (SCN) slices, we present a theory on how clock and zeitgeber properties determine the phase of entrainment. The wide applicability of the theory is demonstrated using mathematical models of different complexity as well as by experimental data. Predictions of the theory are confirmed by published data on Neurospora crassa strains for different period mismatches τ - T and varying photoperiods. We apply a novel regression technique to analyse entrainment of SCN slices by temperature cycles. We find that mathematical models can explain not only the stable asymptotic phase of entrainment, but also transient phase dynamics. Our theory provides the potential to explore seasonal variations of circadian rhythms, jet lag and shift work in forthcoming studies.
authors.affiliation: Institute for Theoretical Biology, Charité Universitätsmedizin Berlin, Berlin, Germany grigory.bordyugov@hu-berlin.de.
authors.forename: Grigory
authors.initials: G
authors.lastname: Bordyugov
authors.affiliation: Laboratory of Chronobiology, Charité Universitätsmedizin Berlin, Berlin, Germany.
authors.forename: Ute
authors.initials: U
authors.lastname: Abraham
authors.affiliation: Department of Systems Biology, Harvard Medical School, Boston, MA, USA.
authors.forename: Adrian
authors.initials: A
authors.lastname: Granada
authors.affiliation: Institute for Theoretical Biology, Charité Universitätsmedizin Berlin, Berlin, Germany.
authors.forename: Pia
authors.initials: P
authors.lastname: Rose
authors.affiliation: Department of B-Cell Immunology, Deutsches Krebsforschungszentrum, Heidelberg, Germany.
authors.forename: Katharina
authors.initials: K
authors.lastname: Imkeller
authors.affiliation: Laboratory of Chronobiology, Charité Universitätsmedizin Berlin, Berlin, Germany.
authors.forename: Achim
authors.initials: A
authors.lastname: Kramer
authors.affiliation: Institute for Theoretical Biology, Humboldt Universität zu Berlin, Berlin, Germany.
authors.forename: Hanspeter
authors.initials: H
authors.lastname: Herzel
mesh_terms: D000818:Animals; D057906:Circadian Clocks / Q000502:physiology*; D051379:Mice; D008954:Models, Biological; D009492:Neurospora crassa / Q000502:physiology*; D017440:Photoperiod; D013493:Suprachiasmatic Nucleus / Q000502:physiology*
keywords: chronotype; circadian clock; entrainment phase; mathematical model