### Abstract

A striking example of coupling between growth and form occurs during the segmentation of the vertebrate embryo. During segmentation, pairs of segments, one on either side of the anterior-posterior axis, bud off from the presomitic mesoderm (PSM) at regular intervals in time. In the clock and wavefront model, a multicellular oscillator regulates the time at which the next pair of segments form whilst a wavefront regulates their spatial location. In most mathematical models of segmentation, it is assumed that cells in the PSM are oscillators that have a constant natural frequency. Based on recent experimental findings, here we propose a model in which the natural oscillation frequency of each PSM cell is a function of its position in the cell cycle. Given adequate oscillator coupling and that cells in the PSM are randomly distributed in the cell cycle, we find that the emergent oscillator frequency is a weighted average of the constituent oscillator frequencies with the weightings dependent on the fraction of cells in a given cell cycle state. Here, we show that such a model can allow for coupling between pattern formation and growth rate in PSM tissue.

Original language | English |
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Journal | Journal of Theoretical Biology |

Early online date | 20 May 2019 |

DOIs | |

Publication status | E-pub ahead of print - 20 May 2019 |

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### Keywords

- Cell cycle
- Clock and wavefront model
- Coupled oscillator
- NICD
- Presomitic mesoderm
- Somitogenesis clock

### Cite this

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**Cell cycle regulation of oscillations yields coupling of growth and form in a computational model of the presomitic mesoderm.** / Murray, P. J. (Lead / Corresponding author); Carrieri, F. A.; Dale, J. K.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Cell cycle regulation of oscillations yields coupling of growth and form in a computational model of the presomitic mesoderm

AU - Murray, P. J.

AU - Carrieri, F. A.

AU - Dale, J. K.

PY - 2019/5/20

Y1 - 2019/5/20

N2 - A striking example of coupling between growth and form occurs during the segmentation of the vertebrate embryo. During segmentation, pairs of segments, one on either side of the anterior-posterior axis, bud off from the presomitic mesoderm (PSM) at regular intervals in time. In the clock and wavefront model, a multicellular oscillator regulates the time at which the next pair of segments form whilst a wavefront regulates their spatial location. In most mathematical models of segmentation, it is assumed that cells in the PSM are oscillators that have a constant natural frequency. Based on recent experimental findings, here we propose a model in which the natural oscillation frequency of each PSM cell is a function of its position in the cell cycle. Given adequate oscillator coupling and that cells in the PSM are randomly distributed in the cell cycle, we find that the emergent oscillator frequency is a weighted average of the constituent oscillator frequencies with the weightings dependent on the fraction of cells in a given cell cycle state. Here, we show that such a model can allow for coupling between pattern formation and growth rate in PSM tissue.

AB - A striking example of coupling between growth and form occurs during the segmentation of the vertebrate embryo. During segmentation, pairs of segments, one on either side of the anterior-posterior axis, bud off from the presomitic mesoderm (PSM) at regular intervals in time. In the clock and wavefront model, a multicellular oscillator regulates the time at which the next pair of segments form whilst a wavefront regulates their spatial location. In most mathematical models of segmentation, it is assumed that cells in the PSM are oscillators that have a constant natural frequency. Based on recent experimental findings, here we propose a model in which the natural oscillation frequency of each PSM cell is a function of its position in the cell cycle. Given adequate oscillator coupling and that cells in the PSM are randomly distributed in the cell cycle, we find that the emergent oscillator frequency is a weighted average of the constituent oscillator frequencies with the weightings dependent on the fraction of cells in a given cell cycle state. Here, we show that such a model can allow for coupling between pattern formation and growth rate in PSM tissue.

KW - Cell cycle

KW - Clock and wavefront model

KW - Coupled oscillator

KW - NICD

KW - Presomitic mesoderm

KW - Somitogenesis clock

UR - http://www.scopus.com/inward/record.url?scp=85066483373&partnerID=8YFLogxK

U2 - 10.1016/j.jtbi.2019.05.006

DO - 10.1016/j.jtbi.2019.05.006

M3 - Article

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

SN - 0022-5193

ER -