Segmentation-clock synchronization in circular-lattice networks of embryonic presomitic-mesoderm cells

Jesús Pantoja-Hernández; Moisés Santillán; Jesús Pantoja-Hernández; Moisés Santillán

doi:10.3934/math.2021344

AIMS Mathematics

2021, Volume 6, Issue 6: 5817-5836. doi: 10.3934/math.2021344

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Segmentation-clock synchronization in circular-lattice networks of embryonic presomitic-mesoderm cells

Centro de Investigación y de Estudios Avanzados del IPN, Unidad Monterrey, Vía del Conocimiento 201, Parque PIIT, 66628 Apodaca NL, MÉXICO

Received: 02 October 2020 Accepted: 27 February 2021 Published: 26 March 2021
MSC : 37N25, 92B25

Somitogenesis is the process by means of which a tissue known as presomitic mesoderm (PSM) is segmented in blocks of cells, called somites, along the anterior-posterior axis of the developing embryo in segmented animals. In vertebrates, somites give rise to axial skeleton, cartilage, tendons, skeletal muscle, and dermis. Somite formation occurs periodically, and this periodicity is driven by a genetic oscillator that operates within PSM cells and is known as the segmentation clock. The correct synchronization of the segmentation clock among PSM cells is essential for somitogenesis to develop normally. When synchronization is disrupted, somites form irregularly and, in consequence, the tissues that originate from them show clear malformations. In this work, based in a model for zebrafish segmentation clock, we investigate by means of a mathematical modeling approach, how PSM-cell synchronization is affected by factors like: the size of PSM-cell networks, the amount of cell-to-cell interactions per PSM cell, the strength of these interactions, and the inherent variability among PSM cells. Interestingly we found that very small PSM-cell networks are unable to synchronize. Moreover, the effect of decreasing the strength of interactions among PSM cells is corrected by increasing the network connectivity-level, and a moderated level of variability among cells can have a positive effect on synchronization, specially in large networks.
- somitogenesis,
- presomitic mesoderm,
- synchronization,
- delay differential equations,
- circular lattice
Citation: Jesús Pantoja-Hernández, Moisés Santillán. Segmentation-clock synchronization in circular-lattice networks of embryonic presomitic-mesoderm cells[J]. AIMS Mathematics, 2021, 6(6): 5817-5836. doi: 10.3934/math.2021344

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Abstract

Somitogenesis is the process by means of which a tissue known as presomitic mesoderm (PSM) is segmented in blocks of cells, called somites, along the anterior-posterior axis of the developing embryo in segmented animals. In vertebrates, somites give rise to axial skeleton, cartilage, tendons, skeletal muscle, and dermis. Somite formation occurs periodically, and this periodicity is driven by a genetic oscillator that operates within PSM cells and is known as the segmentation clock. The correct synchronization of the segmentation clock among PSM cells is essential for somitogenesis to develop normally. When synchronization is disrupted, somites form irregularly and, in consequence, the tissues that originate from them show clear malformations. In this work, based in a model for zebrafish segmentation clock, we investigate by means of a mathematical modeling approach, how PSM-cell synchronization is affected by factors like: the size of PSM-cell networks, the amount of cell-to-cell interactions per PSM cell, the strength of these interactions, and the inherent variability among PSM cells. Interestingly we found that very small PSM-cell networks are unable to synchronize. Moreover, the effect of decreasing the strength of interactions among PSM cells is corrected by increasing the network connectivity-level, and a moderated level of variability among cells can have a positive effect on synchronization, specially in large networks.

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