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Arnold tongue entrainment reveals dynamical principles of the embryonic segmentation clock

View ORCID ProfilePaul Gerald Layague Sanchez, Victoria Mochulska, View ORCID ProfileChristian Mauffette Denis, View ORCID ProfileGregor Mönke, Takehito Tomita, Nobuko Tsuchida-Straeten, Yvonne Petersen, View ORCID ProfileKatharina F. Sonnen, View ORCID ProfilePaul François, View ORCID ProfileAlexander Aulehla
doi: https://doi.org/10.1101/2021.10.20.465101
Paul Gerald Layague Sanchez
aEuropean Molecular Biology Laboratory (EMBL), Developmental Biology Unit, Meyerhofstraße 1, 69117 Heidelberg, Germany
dDepartment of Genetics and Evolution, University of Geneva, 1205 Geneva, Switzerland
hCollaboration for joint PhD degree between EMBL and Heidelberg University, Faculty of Biosciences, 69120 Heidelberg, Germany
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Victoria Mochulska
bMcGill University, H3A 2T8 Montréal, Canada
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Christian Mauffette Denis
bMcGill University, H3A 2T8 Montréal, Canada
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Gregor Mönke
aEuropean Molecular Biology Laboratory (EMBL), Developmental Biology Unit, Meyerhofstraße 1, 69117 Heidelberg, Germany
eErnst Strüngmann Institute for Neuroscience, 60528 Frankfurt am Main, Germany
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Takehito Tomita
aEuropean Molecular Biology Laboratory (EMBL), Developmental Biology Unit, Meyerhofstraße 1, 69117 Heidelberg, Germany
hCollaboration for joint PhD degree between EMBL and Heidelberg University, Faculty of Biosciences, 69120 Heidelberg, Germany
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Nobuko Tsuchida-Straeten
aEuropean Molecular Biology Laboratory (EMBL), Developmental Biology Unit, Meyerhofstraße 1, 69117 Heidelberg, Germany
fUniversitätsklinikum Heidelberg, 69120 Heidelberg, Germany
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Yvonne Petersen
cEuropean Molecular Biology Laboratory (EMBL), Transgenic Service, Meyerhofstraße 1, 69117 Heidelberg, Germany
fUniversitätsklinikum Heidelberg, 69120 Heidelberg, Germany
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Katharina F. Sonnen
aEuropean Molecular Biology Laboratory (EMBL), Developmental Biology Unit, Meyerhofstraße 1, 69117 Heidelberg, Germany
gHubrecht Institute 3584 CT Utrecht, The Netherlands
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Paul François
bMcGill University, H3A 2T8 Montréal, Canada
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  • For correspondence: paul.francois2@mcgill.ca aulehla@embl.de
Alexander Aulehla
aEuropean Molecular Biology Laboratory (EMBL), Developmental Biology Unit, Meyerhofstraße 1, 69117 Heidelberg, Germany
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  • For correspondence: paul.francois2@mcgill.ca aulehla@embl.de
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Abstract

Living systems exhibit an unmatched complexity, due to countless, entangled interactions across scales. Here we aim to understand a complex system, i.e. segmentation timing in mouse embryos, without a reference to these detailed interactions. To this end, we develop a coarse-grained approach, in which theory guides the experimental identification of the segmentation clock entrainment responses.

We demonstrate period- and phase-locking of the segmentation clock across a wide range of entrainment parameters, including higher-order coupling. These quantifications allow to derive the phase response curve (PRC) and Arnold tongues of the segmentation clock, revealing its essential dynamical properties. Our results indicate that the somite segmentation clock has characteristics reminiscent of a highly non-linear oscillator close to an infinite period bifurcation and suggests the presence of long-term feedbacks.

Combined, this coarse-grained theoretical-experimental approach reveals how we can derive simple, essential features of a highly complex dynamical system, providing precise experimental control over the pace and rhythm of the somite segmentation clock.

Competing Interest Statement

The authors have declared no competing interest.

Footnotes

  • This version of the manuscript has been revised based on the peer review at 'Review Commons'; see detailed point by point response provided as separate file.

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY 4.0 International license.
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Posted April 30, 2022.
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Arnold tongue entrainment reveals dynamical principles of the embryonic segmentation clock
Paul Gerald Layague Sanchez, Victoria Mochulska, Christian Mauffette Denis, Gregor Mönke, Takehito Tomita, Nobuko Tsuchida-Straeten, Yvonne Petersen, Katharina F. Sonnen, Paul François, Alexander Aulehla
bioRxiv 2021.10.20.465101; doi: https://doi.org/10.1101/2021.10.20.465101
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Arnold tongue entrainment reveals dynamical principles of the embryonic segmentation clock
Paul Gerald Layague Sanchez, Victoria Mochulska, Christian Mauffette Denis, Gregor Mönke, Takehito Tomita, Nobuko Tsuchida-Straeten, Yvonne Petersen, Katharina F. Sonnen, Paul François, Alexander Aulehla
bioRxiv 2021.10.20.465101; doi: https://doi.org/10.1101/2021.10.20.465101

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