Abstract
Circadian endogenous clocks of eukaryotic organisms are an established and rapidly developing research field. To investigate and simulate in an effective model the effect of external stimuli on such clocks and their components we developed a software framework for download and simulation. The application is useful to understand the different involved effects in a mathematical simple and effective model. This concerns the effects of Zeitgebers, feedback loops and further modifying components. We start from a known mathematical oscillator model, which is based on experimental molecular findings. This is extended with an effective framework that includes the impact of external stimuli on the circadian oscillations including high dose pharmacological treatment. In particular, the external stimuli framework defines a systematic procedure by input-output-interfaces to couple different oscillators. The framework is validated by providing phase response curves and ranges of entrainment. Furthermore, Aschoffs rule is computationally investigated. It is shown how the external stimuli framework can be used to study biological effects like points of singularity or oscillators integrating different signals at once. The mathematical framework and formalism is generic and allows to study in general the effect of external stimuli on oscillators and other biological processes. For an easy replication of each numerical experiment presented in this work and an easy implementation of the framework the corresponding Mathematica files are fully made available. They can be downloaded at the following link: https://www.biozentrum.uni-wuerzburg.de/bioinfo/computing/circadian/.
Highlights
Circadian endogenous clocks of eukaryotic organisms are an established and rapidly developing research field
As nicely summarized in1, circadian clocks have the following well defined properties: (1) they entrain to Zeitgeber cycles with a limited range of entrainment, (2) they can follow phase shifts of Zeitgeber cycles, but they need a certain number of transient cycles until they have established their previous phase to the Zeitgeber cycle, (3) they can be phase-shifted by light-pulses in a time-dependent manner that is characterized in a phase-response curve, (4) they free-run under constant conditions with a species-specific period, which is light-dependent
Our aim is to start from a known mathematical oscillator model based on experimental findings and extend it to an effective modeling framework for the circadian clock that includes the impact of external stimuli
Summary
Circadian endogenous clocks of eukaryotic organisms are an established and rapidly developing research field. When comparing for example the mouse circadian clock with the fruit fly circadian clock, which are standard models for mammalian and insect clocks, the following differences become evident: (1) The mouse (Mus musculus) clock has a narrower range of entrainment and it needs longer to follow phase-shifts of the Zeitgeber cycle than the fruit fly (Drosophila melanogaster) clock. This suggests that it is less plastic and less light-sensitive. Experiment Synchronization to external Zeitgeber Restart of the endogenous clock Entrainment to different external periods Stimulus of constant intensity (Aschoff ’s rule) Phase-response curves Synchronization of peripheral clocks by the SCN Points of singularity
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