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Adding Adhesion to a Chemical Signaling Model for Somite Formation

Bulletin of Mathematical Biology volume 71, pages 1–24 (2009)Cite this article

Abstract

Somites are condensations of mesodermal cells that form along the two sides of the neural tube during early vertebrate development. They are one of the first instances of a periodic pattern, and give rise to repeated structures such as the vertebrae. A number of theories for the mechanisms underpinning somite formation have been proposed. For example, in the “clock and wavefront” model (Cooke and Zeeman in J. Theor. Biol. 58:455–476, 1976), a cellular oscillator coupled to a determination wave progressing along the anterior-posterior axis serves to group cells into a presumptive somite. More recently, a chemical signaling model has been developed and analyzed by Maini and coworkers (Collier et al. in J. Theor. Biol. 207:305–316, 2000; Schnell et al. in C. R. Biol. 325:179–189, 2002; McInerney et al. in Math. Med. Biol. 21:85–113, 2004), with equations for two chemical regulators with entrained dynamics. One of the chemicals is identified as a somitic factor, which is assumed to translate into a pattern of cellular aggregations via its effect on cell–cell adhesion. Here, the authors propose an extension to this model that includes an explicit equation for an adhesive cell population. They represent cell adhesion via an integral over the sensing region of the cell, based on a model developed previously for adhesion driven cell sorting (Armstrong et al. in J. Theor. Biol. 243:98–113, 2006). The expanded model is able to reproduce the observed pattern of cellular aggregates, but only under certain parameter restrictions. This provides a fuller understanding of the conditions required for the chemical model to be applicable. Moreover, a further extension of the model to include separate subpopulations of cells is able to reproduce the observed differentiation of the somite into separate anterior and posterior halves.

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Affiliations

  1. Department of Mathematics and the Maxwell Institute for Mathematical Sciences, School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK

    Nicola J. Armstrong, Kevin J. Painter & Jonathan A. Sherratt

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  1. Nicola J. Armstrong
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  2. Kevin J. Painter
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  3. Jonathan A. Sherratt
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Corresponding author

Correspondence to Kevin J. Painter.

Additional information

N.J. Armstrong was supported by a Doctoral Training Account Studentship from EPSRC. K.J. Painter and J.A. Sherratt were supported in part by Integrative Cancer Biology Program Grant CA113004 from the US National Institute of Health and in part by BBSRC grant BB/D019621/1 for the Centre for Systems Biology at Edinburgh.

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Armstrong, N.J., Painter, K.J. & Sherratt, J.A. Adding Adhesion to a Chemical Signaling Model for Somite Formation. Bull. Math. Biol. 71, 1–24 (2009). https://doi.org/10.1007/s11538-008-9350-1

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  • DOI: https://doi.org/10.1007/s11538-008-9350-1

Keywords

  • Somitogenesis
  • Cell adhesion
  • Mathematical model
  • Pattern formation