# Mathematical model of the circadian rhythm in a population of hepatocytes

Maréchal Anastasia, Mathieu Mezache, Laurent Tournier

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Maréchal Anastasia, Mathieu Mezache, Laurent Tournier. Mathematical model of the circadian rhythm in a population of hepatocytes. Congrès des Jeunes Chercheurs, Oct 2024, Lyon, France. hal-05138317

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Submitted on 1 Jul 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Mathematical model of the circadian rhythm in a
population of hepatocytes

Anastasia Maréchal*, Mathieu Mezache*, and Laurent Tournier*

*Université Paris-Saclay, INRAE, MaIAGE, 78350, Jouy-en-Josas,
France.

The circadian clock influences behavioral and physiological processes over a period of around 24 hours. Within an organism, circadian oscillations occur at different scales. The suprachiasmatic nucleus (SCN) acts as the central clock, propagating the rhythm to peripheral clocks (tissues, organs) down to individual cells. Cellular clocks are characterized by the oscillation of key compounds, governed by a regulatory network. Recent studies such as [1] have shown that, even in the absence of a functional SCN, neighboring liver cells in mice may still exhibit synchronized oscillations, indicating some synchronization at the level of a population of cells.

Mathematical models have already been developed for the dynamics of the intracel-
lular regulatory network, centered on feedback loops based on transcription-translation
of some proteins [2] [3]. Although this type of system makes it possible to examine
the coordination of clocks of a small number of cells, it is inadequate for studying the
synchronization in an entire population.

To address this gap, an age-structured population model is constructed here to rep-
resent cells and their progression through the circadian cycle. Numerical simulations
are conducted to explore the dynamics of the model. Simulations with some parameter
sets result in a completely synchronized cell population after several cycles, while other
parameter sets lead to a desynchronized population.

References

[1] F. Sinturel, P. Gos, V. Petrenko, *et al.*, "Circadian hepatocyte clocks keep synchrony in the absence of a master pacemaker in the suprachiasmatic nucleus or other extra-hepatic clocks," *Genes & development*, vol. 35, no. 5-6, pp. 329-334, 2021.

[2] O. Diop, M. Chaves, and L. Tournier, “Qualitative analysis of mammalian circadian oscillations: cycle dynamics and robustness,” in *International Conference on Computational Methods in Systems Biology*, Springer, 2020, pp. 176–192.

[3] S. Almeida, M. Chaves, and F. Delaunay, “Transcription-based circadian mechanism controls the duration of molecular clock states in response to signaling inputs,” *Journal of theoretical biology*, vol. 484, p. 110015, 2020.