Skip to main content
SpringerLink
Log in

Synchronized oscillation of the segmentation clock gene in vertebrate development

  • Published:
Journal of Mathematical Biology Aims and scope Submit manuscript

Abstract

In vertebrate somitogenesis, “segmentation clock” genes (her in zebrafish, hes in mouse, and hairy in chick) show oscillation, synchronized over nearby cells through intercellular interaction. In zebrafish, neighboring cells interact by Delta-Notch signaling to realize synchronization. Under Delta-Notch, however, a cell with a high expression of the segmentation clock gene tends to suppress its expression in adjacent cells, which might produce spatial heterogeneity instead of synchronized oscillation. Here we studied the conditions under which pre-somitic mesoderm cells show synchronized oscillation of gene expression mathematically. We adopted a model that explicitly considers the kinetics of the mRNA and proteins of the segmentation clock gene and cell–cell interaction via Delta-Notch signaling. From statistical study of a model with randomly generated parameters, we revealed how the likelihood that the system generates stable synchronized oscillation depends on the rate of each reaction in the gene–protein kinetics.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Baker RE, Schnell S, Maini PK (2006) A mathematical investigation of a Clock and Wavefront model for somitogenesis. J Math Biol 52: 458–482

    Article  MATH  MathSciNet  Google Scholar 

  • Barrio M, Burrage K, Leier A, Tian T (2006) Oscillatory regulation of Hes1: Discrete stochastic delay modelling and simulation. PLoS Comput Biol 2(9): e117

    Article  Google Scholar 

  • Bessho Y, Miyoshi G, Sakata R, Kageyama R (2001) Hes7: a bHLH-type repressor gene regulated by Notch and expressed in the presomitic mesoderm. Genes Cells 6: 175–185

    Article  Google Scholar 

  • Cinquin O (2007) Repressor dimerization in the zebrafish somitogenesis clock. PLoS Comput Biol 3(2): e32

    Article  MathSciNet  Google Scholar 

  • Collier JR, Monk NA, Maini PK, Lewis JH (1996) Pattern formation by lateral inhibition with feedback: a mathematical model of delta-notch intercellular signalling. J Theor Biol 183: 429–446

    Article  Google Scholar 

  • Collier JR, Mcinerney D, Schnell S, Maini PK, Gavaghan DJ, Houston P, Stern CD (2000) A cell cycle model for somitogenesis: mathematical formulation and numerical simulation. J Theor Biol 207: 305–316

    Article  Google Scholar 

  • Cooke J, Zeeman EC (1976) A clock and wavefront model for control of the number of repeated structures during animal morphogenesis. J Theor Biol 58: 455–476

    Article  Google Scholar 

  • Dubrulle J, Pourquie O (2002) From head to tail: links between the segmentation clock and antero-posterior patterning of the embryo. Curr Opin Genet Dev 12: 519–523

    Article  Google Scholar 

  • Giudicelli F, Ozbudak EM, Wright GJ, Lewis J (2007) Setting the tempo in development: an investigation of the zebrafish somite clock mechanism. PLoS Biol 5(6): e150

    Article  Google Scholar 

  • Goldbeter A, Pourquie O (2008) Modeling the segmentation clock as a network of coupled oscillations in the Notch, Wnt and FGF signaling pathways. J Theor Biol 252: 574–585

    Article  Google Scholar 

  • Hirata H, Yoshiura S, Ohtsuka T, Bessho Y, Harada T, Yoshikawa K, Kageyama R (2002) Oscillatory expression of the bHLH factor Hes1 regulated by a negative feedback loop. Science 298: 840–843

    Article  Google Scholar 

  • Holley SA, Geisler R, Nusslein-Volhard C (2000) Control of her1 expression during zebrafish somitogenesis by a delta-dependent oscillator and an independent wave-front activity. Genes Dev 14: 1678–1690

    Google Scholar 

  • Holley SA, Julich D, Rauch GJ, Geisler R, Nusslein-Volhard C (2002) her1 and the notch pathway function within the oscillator mechanism that regulates zebrafish somitogenesis. Development 129: 1175–1183

    Google Scholar 

  • Honda H, Tanemura M, Yoshida A (1990) Estimation of neuroblast numbers in insect neurogenesis using the lateral inhibition hypothesis of cell differentiation. Development 110: 1349–1352

    Google Scholar 

  • Honda H, Tanemura M, Yoshida A (2000) Differentiation of wing epidermal scale cells in a butterfly under the lateral inhibition model—appearance of large cells in a polygonal pattern. Acta Biotheor 48: 121–136

    Article  Google Scholar 

  • Horikawa K, Ishimatsu K, Yoshimoto E, Kondo S, Takeda H (2006) Noise-resistant and synchronized oscillation of the segmentation clock. Nature 441: 719–723

    Article  Google Scholar 

  • Jaeger J, Goodwin BC (2002) Cellular oscillators in animal segmentation. In Silico Biol 2: 111–123

    Google Scholar 

  • Jiang YJ, Aerne BL, Smithers L, Haddon C, Ish-Horowicz D, Lewis J (2000) Notch signalling and the synchronization of the somite segmentation clock. Nature 408: 475–479

    Article  Google Scholar 

  • Jouve C, Palmeirim I, Henrique D, Beckers J, Gossler A, Ish-Horowicz D, Pourquie O (2000) Notch signalling is required for cyclic expression of the hairy-like gene HES1 in the presomitic mesoderm. Development 127: 1421–1429

    Google Scholar 

  • Kaern M, Menzinger M, Hunding A (2000) Segmentation and somitogenesis derived from phase dynamics in growing oscillatory media. J Theor Biol 207: 473–493

    Article  Google Scholar 

  • Kerszberg M, Wolpert L (2000) A clock and trail model for somite formation, specialization and polarization. J Theor Biol 205: 505–510

    Article  Google Scholar 

  • Kobayashi R, Tero A, Nakagaki T (2006) Mathematical model for rhythmic protoplasmic movement in the true slime mold. J Math Biol 53: 273–286

    Article  MATH  MathSciNet  Google Scholar 

  • Kuramoto Y (1984) Chemical oscillations, waves, and turbulence. Springer, Berlin

    MATH  Google Scholar 

  • Kurosawa G, Iwasa Y (2002) Saturation of enzyme kinetics in circadian clock models. J Biol Rhythms 17: 568–577

    Article  Google Scholar 

  • Lewis J (2003) Autoinhibition with transcriptional delay: a simple mechanism for the zebrafish somitogenesis oscillator. Curr Biol 13: 1398–1408

    Article  Google Scholar 

  • Mara A, Schroeder J, Chalouni C, Holley SA (2007) Priming, initiation and synchronization of the segmentation clock by deltaD and deltaC. Nat Cell Biol 9: 523–530

    Article  Google Scholar 

  • Maroto M, Dale JK, Dequeant ML, Petit AC, Pourquie O (2005) Synchronised cycling gene oscillations in presomitic mesoderm cells require cell-cell contact. Int J Dev Biol 49: 309–315

    Article  Google Scholar 

  • Masamizu Y, Ohtsuka T, Takashima Y, Nagahara H, Takenaka Y, Yoshikawa K, Okamura H, Kageyama R (2006) Real-time imaging of the somite segmentation clock: revelation of unstable oscillators in the individual presomitic mesoderm cells. Proc Natl Acad Sci USA 103: 1313–1318

    Article  Google Scholar 

  • Meinhardt H (1982) Models of biological pattern formation. Academic, New York

    Google Scholar 

  • Meinhardt H (1986) Somites in developing embryos. In: Bellairs R, Edie DA, Lash JW (eds) Nato ASI Series A, vol 118. Plenum Press, New York, pp 179–189

    Google Scholar 

  • Niwa T (1995) An introduction to the theory of differential equations and dynamical systems. Yuseisya, Tokyo

    Google Scholar 

  • Oates AC, Ho RK (2002) Hairy/E(spl)-related (Her) genes are central components of the segmentation oscillator and display redundancy with the Delta/Notch signaling pathway in the formation of anterior segmental boundaries in the zebrafish. Development 129: 2929–2946

    Google Scholar 

  • Owen MR, Sherratt JA (1998) Mathematical modelling of juxtacrine cell signalling. Math Biosci 153: 125–150

    Article  MATH  Google Scholar 

  • Ozbudak EM, Lewis J (2008) Notch signalling synchronizes the zebrafish segmentation clock but is not needed to create somite boundaries. PLoS Genet 4(2): e15

    Article  Google Scholar 

  • Palmeirim I, Henrique D, Ish-Horowicz D, Pourquie O (1997) Avian hairy gene expression identifies a molecular clock linked to vertebrate segmentation and somitogenesis. Cell 91: 639–648

    Article  Google Scholar 

  • Riedel-Kruse IH, Muller C, Oates AC (2007) Synchrony dynamics during initiation, failure, and rescue of the segmentation clock. Science 317: 1911–1915

    Article  Google Scholar 

  • Rodriguez-Gonzalez JG, Santillan M, Fowler AC, Mackey MC (2007) The segmentation clock in mice: interaction between the Wnt and Notch signalling pathways. J Theor Biol 248: 37–47

    Article  MathSciNet  Google Scholar 

  • Rudge T, Burrage K (2008) Effects of intrinsic and extrinsic noise can accelerate juxtacrine pattern formation. Bull Math Biol 70: 971–991

    Article  MATH  MathSciNet  Google Scholar 

  • Saga Y, Takeda H (2001) The making of the somite: molecular events in vertebrate segmentation. Nat Rev Genet 2: 835–845

    Article  Google Scholar 

  • Tanemura M, Honda H, Yoshida A (1991) Distribution of differentiated cells in a cell sheet under the lateral inhibition rule of differentiation. J Theor Biol 153: 287–300

    Article  Google Scholar 

  • Tiedemann HB, Schneltzer E, Zeiser S, Rubio-Aliaga I, Wurst W, Beckers J, Przemeck GKH, Hrabede Angelis M (2007) Cell-based simulation of dynamic expression patterns in the presomitic mesoderm. J Theor Biol 248: 120–129

    Article  Google Scholar 

  • Uriu K, Morishita Y, Iwasa Y (2009) Traveling wave formation in vertebrate segmentation. J Theor Biol 257: 385–396

    Article  Google Scholar 

  • Winfree AT (2000) The geometry of biological time. Springer, New York

    Google Scholar 

  • Wu Z, Yamaguchi Y (2004) Input-dependent learning rule for the memory of spatiotemporal sequences in hippocampal network with theta phase precession. Biol Cybern 90: 113–124

    Article  MATH  Google Scholar 

  • Zeiser S, Muller J, Liebscher V (2007) Modeling the Hes1 oscillator. J Comput Biol 14: 984–1000

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Biology, Faculty of Sciences, Kyushu University, Fukuoka, 812-8581, Japan

    Koichiro Uriu, Yoshihiro Morishita & Yoh Iwasa

  2. PRESTO Japan Science and Technology Agency, 4-1-8 Honcho Kawaguchi, Saitama, 332-0012, Japan

    Yoshihiro Morishita

Authors
  1. Koichiro Uriu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yoshihiro Morishita
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yoh Iwasa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Koichiro Uriu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Uriu, K., Morishita, Y. & Iwasa, Y. Synchronized oscillation of the segmentation clock gene in vertebrate development. J. Math. Biol. 61, 207–229 (2010). https://doi.org/10.1007/s00285-009-0296-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00285-009-0296-1

Keywords

Mathematics Subject Classification (2000)

Search

Navigation