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An Analysis of Overall Network Architecture Reveals anInfinite-period Bifurcation Underlying Oscillation Arrest in the SegmentationClock

Published online by Cambridge University Press:  12 December 2012

E. Zavala  and
M. Santillán
E. Zavala
Affiliation:
Centro de Investigación y de Estudios Avanzados del IPN, Depto. de Biomedicina Molecular. Av. Instituto Politécnico Nacional 2508, Col. San Pedro Zacatenco, CP 07360 México DF, México
M. Santillán*
Affiliation:
Centro de Investigación y de Estudios Avanzados del IPN, Unidad Monterrey. Vía del Conocimiento 201, Parque PIIT, CP 66600 Apodaca NL, México Centre for Applied Mathematics in Bioscience and Medicine. 3655 Promenade Sir William Osler McIntyre Medical Building, Room 1123A, Montreal, QC H3G 1Y6, Canada
*
⋆ Corresponding author. E-mail: msantillan@cinvestav.mx
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Abstract

Unveiling the mechanisms through which the somitogenesis regulatory network exertsspatiotemporal control of the somitic patterning has required a combination ofexperimental and mathematical modeling strategies. Significant progress has been made forthe zebrafish clockwork. However, due to its complexity, the clockwork of the amniotesegmentation regulatory network has not been fully elucidated. Here, we address thequestion of how oscillations are arrested in the amniote segmentation clock. We do this byconstructing a minimal model of the regulatory network, which privileges architecturalinformation over molecular details. With a suitable choice of parameters, our model isable to reproduce the oscillatory behavior of the Wnt, Notch and FGF signaling pathways inpresomitic mesoderm (PSM) cells. By introducing positional information via a single Wnt3agradient, we show that oscillations are arrested following an infinite-period bifurcation.Notably: the oscillations increase their amplitude as cells approach the anterior PSM andremain in an upregulated state when arrested; the transition from the oscillatory regimeto the upregulated state exhibits hysteresis; and opposing Fgf8 and RA gradients along thePSM naturally arise in our simulations. We hypothesize that the interaction between alimit cycle (originated by the Notch delayed-negative feedback loop) and a bistable switch(originated by the Wnt-Notch positive cross-regulation) is responsible for the observedsegmentation patterning. Our results agree with previously unexplained experimentalobservations and suggest a simple plausible mechanism for spatiotemporal control ofsomitogenesis in amniotes.

Keywords

somitogenesisvertebrate embryodelay differential equationsbistabilitySNICSNIPER bifurcation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 7 , Issue 6: Biological oscillations , 2012 , pp. 95 - 106
Copyright
© EDP Sciences, 2012

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