An effective model of endogenous clocks and external stimuli determining circadian rhythms
Tim Breitenbach, Charlotte Helfrich-Förster, Thomas Dandekar
Investigating circadian endogenous clocks of organisms by experiments is an established research field. This work intends to contribute to the theoretical understanding how external stimuli affect the circadian rhythms of animals, more specific of flies and mice. For this purpose we extend a known mathematical oscillator model, which is based on experimental molecular findings with an effective framework that includes the impact of external stimuli on the circadian oscillations. Our framework is able to simulate the following experimental results that differ in flies and mice: (1) the limits of range of entrainment, (2) the amplitudes of phase response curves, (3) period changes and arrhythmic behavior under constant light.Furthermore, the model is suited to simulate the coupling of different oscillators such as central and peripheral clocks as well as the input of further external stimuli to the peripheral clocks like food intake in mice. With a similar idea the issue of singularity points of circadian clocks is modeled and related to different model approaches. For an easy confirmability of each numerical experiment presented in this work there are corresponding Mathematica files available. They can be downloaded below and are named according to the subsection where the file is related to. The files are commented and are set such that they generate the corresponding figure in the paper.
Files are used to reproduce the figures of the paper "An effective model of endogenous clocks and external stimuli determining circadian rhythms" by Tim Breitenbach, Charlotte Helfrich-Föster and Thomas Dandekar. The code examples are executed with Mathematica. The computations are conveniently done on a desktop PC with 4 GB RAM and a four core CPU at 2.4 GHz for each core with a version of Wolfram Mathematica of the number 10.1.0.0. Files for the numerical experiments in the corresponding part of the paper
Phase_shifts_by_a_strong_stimulus_fly_entrainment.nb Phase_shifts_by_a_strong_stimulus_mRNA_knockdown.nb Phase_shifts_by_a_strong_stimulus_transcription_inhibition.nb Phase_shifts_by_a_strong_stimulus_translation_entrainment.nb Phase_shifts_by_a_strong_stimulus_translation_inhibition.nb
All the scripts can be downloaded directly with the links.