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An Analysis of Overall Network Architecture Reveals an Infinite-period Bifurcation Underlying Oscillation Arrest in the Segmentation Clock

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 exerts spatiotemporal control of the somitic patterning has required a combination of experimental and mathematical modeling strategies. Significant progress has been made for the zebrafish clockwork. However, due to its complexity, the clockwork of the amniote segmentation regulatory network has not been fully elucidated. Here, we address the question of how oscillations are arrested in the amniote segmentation clock. We do this by constructing a minimal model of the regulatory network, which privileges architectural information over molecular details. With a suitable choice of parameters, our model is able to reproduce the oscillatory behavior of the Wnt, Notch and FGF signaling pathways in presomitic mesoderm (PSM) cells. By introducing positional information via a single Wnt3a gradient, we show that oscillations are arrested following an infinite-period bifurcation. Notably: the oscillations increase their amplitude as cells approach the anterior PSM and remain in an upregulated state when arrested; the transition from the oscillatory regime to the upregulated state exhibits hysteresis; and opposing Fgf8 and RA gradients along the PSM naturally arise in our simulations. We hypothesize that the interaction between a limit 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 observed segmentation patterning. Our results agree with previously unexplained experimental observations and suggest a simple plausible mechanism for spatiotemporal control of somitogenesis 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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References

Références

Aulehla, A., Pourquié, O.. Signaling gradients during paraxial mesoderm development. Cold Spring Harb. Perspect. Biol., 2 (2010), a000869. CrossRefGoogle ScholarPubMed
Aulehla, A., Wehrle, C., Brand-Saberi, B., Kemler, R., Gossler, A., Kanzler, B., Herrman, B. G.. Wnt3a plays a major role in the segmentation clock controlling somitogenesis. Dev. Cell., 4 (2003), 395-406. CrossRefGoogle Scholar
Aulehla, A., Wiegrabe, W., Baubet, V., Wahl, M. B., Deng, X., Taketo, M., Lewandoski, M., Pourquié, O.. A β-catenin gradient links the clock and wavefront systems in mouse embryo segmentation. Nat. Cell. Biol., 10 (2008), 186-193. CrossRefGoogle ScholarPubMed
Campanelli, M., Gedeon, T.. Somitogenesis clock-wave initiation requires differential decay and multiple binding sites for clock protein. PLoS Comp. Biol., 6 (2010), e1000728. CrossRefGoogle ScholarPubMed
M. Campanelli. Multicellular mathematical models of somitogenesis. PhD thesis Montana State University (2009), ISBN 9781109317299.
Christ, B., Ordahl, C. P.. Early stages of chick somite development. Anat. Embryol., 191 (1995), 381-396. CrossRefGoogle ScholarPubMed
Cinquin, O.. Understanding the somitogenesis clock: what’s missing ? Mech. Dev., 124 (2007), 501-517. CrossRefGoogle Scholar
Cooke, J., Zeeman, E. C.. A clock and wavefront model for control of the number of repeated structures during animal morphogenesis. J. Theor. Biol., 58 (1976), 455-476. CrossRefGoogle ScholarPubMed
Dequéant, M. L., Glynn, E., Gaudenz, K., Wahl, M., Chen, J., Mushegian, A., Pourquié, O.. A complex oscillating network of signaling genes underlies the mouse segmentation clock. Science, 314 (2006), 1595-1598. CrossRefGoogle Scholar
Dequéant, M. L., Pourquié, O.. Segmental patterning of the vertebrate embryonic axis. Nat. Rev. Gen., 9 (2008), 370-382. CrossRefGoogle ScholarPubMed
Diez del Corral, R., Olivera-Martínez, I., Goriely, A., Gale, E., Maden, M., Storey, K.. Opposing FGF and retinoid pathways control ventral neural pattern, neuronal differentiation, and segmentation during body axis extension. Neuron, 40 (2003), 65-79. CrossRefGoogle ScholarPubMed
Dubrulle, J., Pourquié, O.. Coupling segmentation to axis formation. Dev., 131 (2004), 5783-5793. CrossRefGoogle ScholarPubMed
Dubrulle, J., Pourquié, O.. fgf8 mRNA decay establishes a gradient that couples axial elongation to patterning in the vertebrate embryo. Nature, 427 (2004), 419-422. CrossRefGoogle ScholarPubMed
B. Ermentrout. Simulating, analyzing, and animating dynamical systems: a guide to XPPAUT for researchers and students. 1st Ed. Society for Industrial Mathematics. Philadelphia (2002).
Gibb, S., Maroto, M., Dale, J. K.. The segmentation clock mechanism moves up a notch. Trends Cell Biol., 20 (2010), 593-600. CrossRefGoogle ScholarPubMed
Gibb, S., Zagorska, A., Melton, K., Tenin, G., Vacca, I., Trainor, P., Maroto, M., Dale, J. K.. Interfering with Wnt signalling alters the periodicity of the segmentation clock. Dev. Biol., 330 (2009), 21-31. CrossRefGoogle ScholarPubMed
Giudicelli, F., Özbudak, E. M., Wright, G. J., Lewis, J.. Setting the tempo in development: An investigation of the zebrafish somite clock mechanism. PLoS Biol., 5 (2007), 1309-1323. CrossRefGoogle ScholarPubMed
Goldbeter, A., Gonze, D., Pourquié, O.. Sharp developmental thresholds defined through bistability by antagonistic gradients of retinoic acid and FGF signaling. Dev. Dyn., 236 (2007), 1495-1508. CrossRefGoogle ScholarPubMed
Goldbeter, A., Pourquié, O.. Modeling the segmentation clock as a network of coupled oscillations in the Notch, Wnt and FGF signaling pathways. J. Theor. Biol., 252 (2008), 574-585. CrossRefGoogle ScholarPubMed
Gomez, C., Özbudak, E. M., Wunderlich, J., Baumann, D., Lewis, J., Pourquié, O.. Control of segment number in vertebrate embryos. Nat. Lett., 454 (2008), 335-339. CrossRefGoogle ScholarPubMed
Ishikawa, A., Kitajima, S., Takahashi, Y., Kokub, H., Kanno, J., Inoue, T., Saga, Y.. Mouse Nkd2, a Wnt antagonist, exhibits oscillatory gene expression in the PSM under the control of Notch signaling. Mech. Dev., 121 (2004), 1443-1453. CrossRefGoogle Scholar
Jensen, P. B., Pedersen, L., Krishna, S., Jensen, M. H.. A Wnt oscillator model for somitogenesis. Biophys. J., 98 (2010), 943-950. CrossRefGoogle ScholarPubMed
Lewis, J.. Autoinhibition with transcriptional delay: a simple mechanism for the zebrafish somitogenesis oscillator. Curr. Biol., 13 (2003), 1398-1408. CrossRefGoogle Scholar
Palmeirim, I., Henrique, D., Ish-Horowicz, D., Pourquié, O.. Avian hairy gene expression identifies a molecular clock linked to vertebrate segmentation and somitogenesis. Cell, 91 (1997), 639-648. CrossRefGoogle ScholarPubMed
Rida, P. C. G., Le Minh, N., Jiang, Y. J.. A Notch feeling of somite segmentation and beyond. Dev. Biol., 265 (2004), 2-22. CrossRefGoogle ScholarPubMed
Rodríguez-González, J. G., Santillán, M., Fowler, A. C., Mackey, M. C.. The segmentation clock in mice: interaction between the Wnt and Notch signalling pathways. J. Theor. Biol., 248 (2007), 37-47. CrossRefGoogle Scholar
Saga, Y., Takeda, H.. The making of the somite: Molecular events in vertebrate segmentation. Nat. Rev. Gen., 2 (2001), 835-845. CrossRefGoogle ScholarPubMed
Santillán, M., Mackey, M. C.. A proposed mechanism for the interaction of the segmentation clock and the determination front in somitogenesis. PLoS ONE, 3 (2008), e1561. CrossRefGoogle Scholar
Wahl, M. B., Deng, C., Lewandoski, M., Pourquié, O.. FGF signaling acts upstream of the NOTCH and WNT signaling pathways to control segmentation clock oscillations in mouse somitogenesis. Dev., 134 (2007), 4033-4041. CrossRefGoogle Scholar
Yasuhiko, Y., Haraguchi, S., Kitajima, S., Takahashi, Y., Kanno, J., Saga, Y.. Tbx6-mediated notch signaling controls somite-specific mesp2 expression. Proc. Natl. Acad. Sci. USA, 103 (2006), 3651-6. CrossRefGoogle Scholar