Abstract

Circadian rhythms are biological rhythms with a period close to 24h. They become entrained to the Earth's solar day via different periodic cues, so-called zeitgebers. The entrainment of circadian rhythms to a single zeitgeber was investigated in many mathematical clock models of different levels of complexity, ranging from the Poincaré oscillator and the Goodwin model to biologically more detailed models of multiple transcriptional translational feedback loops. However, circadian rhythms are exposed to multiple coexisting zeitgebers in nature. Therefore, we study synergistic effects of two coexisting zeitgebers on different components of the circadian clock. We investigate the induction of period genes by light together with modulations of nuclear receptor activities by drugs and metabolism. Our results show that the entrainment of a circadian rhythm to two coexisting zeitgebers depends strongly on the phase difference between the two zeitgebers. Synergistic interactions of zeitgebers can strengthen diurnal rhythms to reduce detrimental effects of shift-work and jet lag. Medical treatment strategies which aim for stable circadian rhythms should consider interactions of multiple zeitgebers.

Highlights

  • The synchronisation of external rhythms (“zeitgebers”) with endogenous circadian clocks is a central topic in chronobiology (Aschoff and Pohl, 1978)

  • Zeitgeber signals with period T interact with intrinsic rhythms characterised by their free running periods τ

  • On the single cell level intercellular coupling (Tokuda et al, 2018) and cell intrinsic rhythms can interact rhythmically with components of the circadian clock. This is evident for the cell cycle (Feillet et al, 2014; Droin et al, 2019; Almeida et al, 2020a; Battaglin et al, 2021), metabolic (Woller et al, 2016) and redox rhythms (Del Olmo, 2021)

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Summary

Introduction

1.1 Entrainment of Circadian RhythmsThe synchronisation of external rhythms (“zeitgebers”) with endogenous circadian clocks is a central topic in chronobiology (Aschoff and Pohl, 1978). Zeitgeber signals with period T (on Earth typically 24 h) interact with intrinsic rhythms characterised by their free running periods τ. The intrinsic period τ adapts to the zeitgeber period T, a phenomenon referred to as entrainment. The inner rhythm adapts a stable phase relationship with respect to the Zeitgeber known as phase of entrainment ψ. It is this phase of entrainment that allows synchronisation of rhythmic physiological processes (Rensing and Ruoff, 2002; Dunlap et al, 2004; Yan et al, 2008) to rhythmic environments (light, temperature, nutrition). We analyse mathematical models of the mammalian circadian clock of intermediate complexity with at least five clock genes allowing modulations of different feedback loops

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