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A Spatio-Temporal Model of Notch Signalling in the Zebrafish Segmentation Clock: Conditions for Synchronised Oscillatory Dynamics

Author

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  • Alan J Terry
  • Marc Sturrock
  • J Kim Dale
  • Miguel Maroto
  • Mark A J Chaplain

Abstract

In the vertebrate embryo, tissue blocks called somites are laid down in head-to-tail succession, a process known as somitogenesis. Research into somitogenesis has been both experimental and mathematical. For zebrafish, there is experimental evidence for oscillatory gene expression in cells in the presomitic mesoderm (PSM) as well as evidence that Notch signalling synchronises the oscillations in neighbouring PSM cells. A biological mechanism has previously been proposed to explain these phenomena. Here we have converted this mechanism into a mathematical model of partial differential equations in which the nuclear and cytoplasmic diffusion of protein and mRNA molecules is explictly considered. By performing simulations, we have found ranges of values for the model parameters (such as diffusion and degradation rates) that yield oscillatory dynamics within PSM cells and that enable Notch signalling to synchronise the oscillations in two touching cells. Our model contains a Hill coefficient that measures the co-operativity between two proteins (Her1, Her7) and three genes (her1, her7, deltaC) which they inhibit. This coefficient appears to be bounded below by the requirement for oscillations in individual cells and bounded above by the requirement for synchronisation. Consistent with experimental data and a previous spatially non-explicit mathematical model, we have found that signalling can increase the average level of Her1 protein. Biological pattern formation would be impossible without a certain robustness to variety in cell shape and size; our results possess such robustness. Our spatially-explicit modelling approach, together with new imaging technologies that can measure intracellular protein diffusion rates, is likely to yield significant new insight into somitogenesis and other biological processes.

Suggested Citation

  • Alan J Terry & Marc Sturrock & J Kim Dale & Miguel Maroto & Mark A J Chaplain, 2011. "A Spatio-Temporal Model of Notch Signalling in the Zebrafish Segmentation Clock: Conditions for Synchronised Oscillatory Dynamics," PLOS ONE, Public Library of Science, vol. 6(2), pages 1-18, February.
  • Handle: RePEc:plo:pone00:0016980
    DOI: 10.1371/journal.pone.0016980
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    References listed on IDEAS

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    1. Yun-Jin Jiang & Birgit L. Aerne & Lucy Smithers & Catherine Haddon & David Ish-Horowicz & Julian Lewis, 2000. "Notch signalling and the synchronization of the somite segmentation clock," Nature, Nature, vol. 408(6811), pages 475-479, November.
    2. Olivier Cinquin, 2007. "Repressor Dimerization in the Zebrafish Somitogenesis Clock," PLOS Computational Biology, Public Library of Science, vol. 3(2), pages 1-11, February.
    3. Ertuğrul M Özbudak & Julian Lewis, 2008. "Notch Signalling Synchronizes the Zebrafish Segmentation Clock but Is Not Needed To Create Somite Boundaries," PLOS Genetics, Public Library of Science, vol. 4(2), pages 1-11, February.
    4. Céline Gomez & Ertuğrul M. Özbudak & Joshua Wunderlich & Diana Baumann & Julian Lewis & Olivier Pourquié, 2008. "Control of segment number in vertebrate embryos," Nature, Nature, vol. 454(7202), pages 335-339, July.
    5. Kazuki Horikawa & Kana Ishimatsu & Eiichi Yoshimoto & Shigeru Kondo & Hiroyuki Takeda, 2006. "Noise-resistant and synchronized oscillation of the segmentation clock," Nature, Nature, vol. 441(7094), pages 719-723, June.
    6. François Giudicelli & Ertuğrul M Özbudak & Gavin J Wright & Julian Lewis, 2007. "Setting the Tempo in Development: An Investigation of the Zebrafish Somite Clock Mechanism," PLOS Biology, Public Library of Science, vol. 5(6), pages 1-15, May.
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