TY - JOUR
T1 - Adding adhesion to a chemical signaling model for somite formation
AU - Armstrong, Nicola J.
AU - Painter, Kevin J.
AU - Sherratt, Jonathan A.
PY - 2009/1
Y1 - 2009/1
N2 - 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. © 2008 Society for Mathematical Biology.
AB - 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. © 2008 Society for Mathematical Biology.
KW - Cell adhesion
KW - Mathematical model
KW - Pattern formation
KW - Somitogenesis
UR - http://www.scopus.com/inward/record.url?scp=58149188099&partnerID=8YFLogxK
U2 - 10.1007/s11538-008-9350-1
DO - 10.1007/s11538-008-9350-1
M3 - Article
C2 - 18766407
SN - 0092-8240
VL - 71
SP - 1
EP - 24
JO - Bulletin of Mathematical Biology
JF - Bulletin of Mathematical Biology
IS - 1
ER -