917
Views
109
CrossRef citations to date
0
Altmetric
Original Articles

Delayed coupling theory of vertebrate segmentation

, , , , &
Pages 55-66 | Received 06 Aug 2008, Published online: 07 Sep 2010

References

  • Aulehla , A , Wehrle , C , Brand‐Saberi , B , Kemler , R , Gossler , A , Kanzler , B and Herrmann , BG . 2003 . “Wnt3a plays a major role in the segmentation clock controlling somitogenesis.” . Dev. Cell , 4 : 395 – 406 .
  • Aulehla , A , Wiegraebe , W , Baubet , V , Wahl , MB , Deng , C , Taketo , M , Lewandoski , M and Pourquié, , O . 2008 . “A β‐catenin gradient links the clock and wavefront systems in mouse embryo segmentation.” . Nat. Cell Biol. , 10 : 186 – 193 .
  • Bernard , S , Čajavec , B , Pujo‐Menjouet , L , Mackey , MC and Herzel , H . 2006 . “Modelling transcriptional feedback loops: the role of Gro/TLE1 in Hes1 oscillations.” . Philos. Trans. R. Soc. London, Ser. A , 364 : 1155 – 1170 .
  • Beta , C and Mikhailov , AS . 2004 . “Controlling spatiotemporal chaos in oscillatory reaction‐diffusion systems by time‐delay autosynchronization.” . Physica D , 199 : 173 – 184 .
  • Bulman , MP , Kusumi , K , Frayling , TM , McKeown , C , Garrett , C , Lander , ES , Krumlauf , R , Hattersley , AT , Ellard , S and Turnpenny , PD . 2000 . “Mutations in the human Delta homologue DLL3, cause axial skeletal defects in spondylocostal dysostosis.” . Nat. Genet. , 24 : 438 – 441 .
  • Casagrande , V , Togashi , Y and Mikhailov , AS . 2007 . “Molecular synchronization waves in arrays of allosterically regulated enzymes.” . Phys. Rev. Lett. , 99 : 048301
  • Chipman , AD and Akam , M . 2008 . “The segmentation cascade in the centipede Strigamia maritima: involvement of the Notch pathway and pair‐rule gene homologues.” . Dev. Biol. , 319 : 160 – 169 .
  • Cinquin , O . 2003 . “Is the somitogenesis clock really cell‐autonomous? A coupled‐oscillator model of segmentation.” . J. Theor. Biol. , 224 : 459 – 468 .
  • Cinquin , O . 2007 . “Repressor dimerization in the zebrafish somitogenesis clock.” . PLOS Comput. Biol. , 3 : e32
  • Cooke , J and 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 .
  • Cross , MC and Hohenberg , PC . 1993 . “Pattern formation outside of equilibrium.” . Rev. Mod. Phys. , 65 : 851 – 1112 .
  • Damens , WGM . 2007 . “Evolutionary conservation and divergence of the segmentation process in arthropods.” . Dev. Dyn. , 236 : 1379 – 1391 .
  • Dubrulle , J and Pourquié, , O . 2004 . “fgf8 mRNA decay establishes a gradient that couples axial elongation to patterning in the vertebrate embryo.” . Nature London , 427 : 419 – 422 .
  • Dubrulle , J , McGrew , MJ and Pourquié, , O . 2001 . “Fgf signaling controls somite boundary position and regulates segmentation clock control of spatiotemporal Hox gene activation.” . Cell , 106 : 219 – 232 .
  • Earl , MG and Strogatz , SH . 2003 . “Synchronization in oscillator networks with delayed coupling: A stability criterion.” . Phys. Rev. E , 67 : 036204
  • Elmasri , H , Liedtke , D , Lücking , G , Volff , JN , Gessler , M and Winkler , C . 2004 . “her7 and hey1, but not lunatic fringe show dynamic expression during somitogenesis in medaka Oryzias latipes.” . Gene Expr. Patterns , 4 : 553 – 559 .
  • See EPAPS Document No. E‐HJFOA5–3‐004901 for supplemental material. This document can be reached through a direct link in the online article's HTML reference section or via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html).
  • Feng , P and Navaratna , M . 2007 . “Modeling periodic oscillations during somitogenesis.” . Math. Biosci. Eng. , 4 : 661 – 673 .
  • Franz , AL , Roy , R , Shaw , LB and Schwartz , IB . 2008 . “Effect of multiple time delays on intensity fluctuation dynamics in fiber ring lasers.” . Phys. Rev. E , 78 : 016208
  • Gajewski , M , Elmasri , H , Girschick , M , Sieger , D and Winkler , C . 2006 . “Comparative analysis of her genes during fish somitogenesis suggests a mouse/chick‐like mode of oscillation in medaka.” . Dev. Genes Evol. , 216 : 315 – 332 .
  • Giudicelli , F , Özbudak , EM , Wright , GJ and Lewis , J . 2007 . “Setting the tempo in development: an investigation of the zebrafish somite clock mechanism.” . PLoS Biol. , 5 : 1309 – 1323 .
  • Goldbeter , A , Gonze , D and Pourquié, , O . 2007 . “Sharp developmental thresholds defined through bistability by antagonistic gradients of retinoic acid and FGF signaling.” . Dev. Dyn. , 236 : 1495 – 1508 .
  • Goldbeter , A and Pourquié, , 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 .
  • Gomez , C , Özbudak , EM , Wunderlich , J , Baumann , D , Lewis , J and Pourquié, , O . 2008 . “Control of segment number in vertebrate embryos.” . Nature London , 454 : 335 – 339 .
  • Hassard , B and Wan , YH . 1978 . “Bifurcation formulae derived from center manifold theory.” . J. Math. Anal. Appl. , 63 : 297 – 312 .
  • Heuss , SF , Ndiaye‐Lobry , D , Six, , EM , Israël , A and Logeat , F . 2008 . “The intracellular region of Notch ligands Dl11 and Dl13 regulates their trafficking and signaling activity.” . Proc. Natl. Acad. Sci. U.S.A. , 105 : 11212 – 11217 .
  • Hirata , H , Yoshiura , S , Ohtsuka , T , Bessho , Y , Harada , T , Yoshikawa , K and Kageyama , R . 2002 . “Oscillatory expression of the bHLH factor Hes1 regulated by a negative feedback loop.” . Science , 298 : 840 – 843 .
  • Holley , SA . 2007 . “The genetics and embryology of zebrafish metamerism.” . Dev. Dyn. , 236 : 1422 – 1449 .
  • Holley , SA , Geisler , R and Nüsslein‐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 .
  • Holley , SA , Jülich , D , Rauch , GJ , Geisler , R and Nüsslein‐Volhard , C . 2002 . “her1 and the notch pathway function within the oscillator mechanism that regulates zebrafish somitogenesis.” . Development , 129 : 1175 – 1183 .
  • Horikawa , K , Ishimatsu , K , Yoshimoto , E , Kondo , S and Takeda , H . 2006 . “Noise‐resistant and synchronized oscillation of the segmentation clock.” . Nature London , 441 : 719 – 723 .
  • Itoh , M . 2003 . “Mind bomb is a ubiquitin ligase that is essential for efficient activation of Notch signaling by Delta.” . Dev. Cell , 4 : 67 – 82 .
  • Jaeger , J and Goodwin , BC . 2001 . “A cellular oscillator model for periodic pattern formation.” . J. Theor. Biol. , 213 : 171 – 181 .
  • Jensen , MH , Sneppen , K and Tiana , G . 2003 . “Sustained oscillations and time delays in gene expression of protein Hes1.” . FEBS Lett. , 541 : 176 – 177 .
  • Jiang , Y‐J , Aerne , BL , Smithers , L , Haddon , C , Ish‐Horowicz , D and Lewis , J . 2000 . “Notch signaling and the synchronization of the somite segmentation clock.” . Nature London , 408 : 475 – 479 .
  • Jülich , D . 2005 . “beamter/deltaC and the role of Notch ligands in the zebrafish somite segmentation, hindbrain neurogenesis and hypochord differentiation.” . Dev. Biol. , 286 : 391 – 404 .
  • Kaern , M , Menziger , M and Hunding , A . 2000 . “Segmentation and somitogenesis derived from phase dynamics in growing oscillatory media.” . J. Theor. Biol. , 207 : 473 – 493 .
  • Kim , M , Bertram , M , Pollman , M , von Oertzen , A , Mikhailov , AS , Rotermund , HH and Ertl , G . 2001 . “Controlling chemical turbulence by global delayed feedback: pattern formation in catalytic CO oxidation on Pt(110).” . Science , 292 : 1357 – 1360 .
  • Kuramoto , Y . 1984 . Chemical Oscillations, Waves and Turbulence , Berlin : Springer .
  • Leier , A , Marquez‐Lago , TT , Burrage , K and Burrage , P . 2008 . “Modeling intrinsic noise and delays in chemical kinetics of coupled autoregulated oscillating cells.” . Int. J. Multiscale Comp. Eng. , 6 : 77 – 86 .
  • Lewis , J . 2003 . “Autoinhibition with transcriptional delay: a simple mechanism for the zebrafish somitogenesis oscillator.” . Curr. Biol. , 13 : 1398 – 1408 .
  • MacDonald , N . 1989 . Biological Delay Systems , Cambridge : Cambridge University Press .
  • Manrubia , SC , Mikhailov , AS and Zanette , DH . 2004 . Emergence of Dynamical Order , 1st ed. , Singapore : World Scientific .
  • Mara , A , Schroeder , J , Chalouni , C and Holley , SA . 2007 . “Priming, initiation and synchronization of the segmentation clock by deltaD and deltaC.” . Nat. Cell Biol. , 9 : 523 – 530 .
  • Masamizu , Y , Ohtsuka , T , Takashima , Y , Nagahara , H , Takenaka , Y , Yoshikawa , K , Okamura , H and Kageyama , R . 2006 . “Real‐time imaging of the segmentation clock: revelation of unstable oscillators in the individual presomitic mesoderm cells.” . Proc. Natl. Acad. Sci. U.S.A. , 103 : 1313 – 1318 .
  • Mazzitello , KI , Arizmendi , CM and Hentschel , HGE . 2008 . “Converting genetic network oscillations into somite spatial patterns.” . Phys. Rev. E , 78 : 021906
  • Momiji , H and Monk , NAM . 2008 . “Dissecting the dynamics of the Hes1 genetic oscillator.” . J. Theor. Biol. , 254 : 784 – 798 .
  • Monk , NAM . 2003 . “Oscillatory expression of Hes1, p53, and NF‐κB driven by transcriptional time delays.” . Curr. Biol. , 13 : 1409 – 1413 .
  • Niebur , E , Schuster , HG and Kammen , DM . 1991 . “Collective frequencies and metastability in networks of limit‐cycle oscillators with time delay.” . Phys. Rev. Lett. , 67 : 2753 – 2756 .
  • Nishii , J , Uno , Y and Suzuki , R . 1994 . “Mathematical models for the swimming pattern of a lamprey. I. Analysis of collective oscillators with time‐delayed interaction and multiple coupling.” . Biol. Cybern. , 72 : 1 – 9 .
  • Oates , AC and Ho , RK . 2002 . “Hairy/Espl‐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 .
  • Oates , AC , Mueller , C and Ho , RK . 2005 . “Cooperative function of deltaC and her7 in anterior segment formation.” . Dev. Biol. , 280 : 133 – 149 .
  • Özbudak , EM and Lewis , J . 2008 . “Notch signalling synchronizes the zebrafish segmentation clock but is not needed to create somite boundaries.” . PLoS Genet. , 4 (2) : e15
  • Palmeirim , I , Henrique , D , Ish‐Horowicz , D and Pourquié, , O . 1997 . “Avian hairy gene expression identifies a molecular clock linked to vertebrate segmentation and somitogenesis.” . Cell , 91 : 639 – 648 .
  • Pascoal , S , Carvalho , CR , Rodriguez‐León , J , Delfini, , M‐C , Duprez , D , Thorsteinsdóttir , S and Palmeirim , I . 2007 . “A molecular clock operates during chick autopod proximal‐distal outgrowth.” . J. Mol. Biol. , 368 : 303 – 309 .
  • Riedel‐Kruse , IH , Müller , C and Oates , AC . 2007 . “Synchrony dynamics during initiation, failure and rescue of the segmentation clock.” . Science , 317 : 1911 – 1915 .
  • Rodríguez‐González , JG , Santillán , M , Fowler , AC and Mackey , MC . 2007 . “The segmentation clock in mice: interaction between the Wnt and Notch signalling pathways.” . J. Theor. Biol. , 248 : 37 – 47 .
  • Santillán , M and Mackey , MC . 2008 . “A proposed mechanism for the interaction of the segmentation clock and the determination front in somitogenesis.” . PLoS ONE , 3 : e1561
  • Sawada , A , Shinya , M , Jiang , Y‐J , Kawakami , A , Kuroiwa , A and Takeda , H . 2001 . “Fgf/MAPK signalling is a crucial positional cue in somite boundary formation.” . Development , 128 : 4873 – 4880 .
  • Schröter , C , Herrgen , L , Cardona , A , Brouhard , GJ , Feldman , B and Oates , AC . 2008 . “Dynamics of zebrafish somitogenesis.” . Dev. Dyn. , 237 : 545 – 553 .
  • Schuster , HG and Wagner , P . 1989 . “Mutual entrainment of two limit cycle oscillators with time delayed coupling.” . Prog. Theor. Phys. , 81 : 939 – 945 .
  • Tam , PP . 1981 . “The control of somitogenesis in mouse embryos.” . J. Embryol. Exp. Morphol. , 65 : 103 – 128 .
  • Tiana , G , Krishna , S , Pigolotti , S , Jensen , MH and Sneppen , K . 2007 . “Oscillations and temporal signalling in cells.” . Phys. Biol. , 4 : R1 – R17 .
  • Tiedemann , HB , Schneltzer , E , Zeiser , S , Rubio‐Aliaga , I , Wurst , W , Beckers , J , Przemeck , GKH and Hrabé de Angelis, , M . 2007 . “Cell‐based simulation of dynamic expression patterns in the presomitic mesoderm.” . J. Theor. Biol. , 248 : 120 – 129 .
  • Verdugo , A and Rand , R . 2008 . “Hopf bifurcation in a DDE model of gene expression.” . Commun. Nonlinear Sci. Numer. Simul. , 13 : 235 – 242 .
  • Wahl , MB , Deng , C , Lewandoski , M and Pourquié, , O . 2007 . “FGF signaling acts upstream of the NOTCH and WNT signaling pathways to control segmentation clock oscillations in mouse somitogenesis.” . Development , 134 : 4033 – 4041 .
  • Wolpert , L , Smith , J , Jessell , T , Lawrence , P , Robertson , E and Meyerowitz , E . 2006 . Principles of Development, , 3rd ed. , Oxford : Oxford University Press .
  • Wünsche, , H‐J . 2005 . “Synchronization of delay‐coupled oscillators: a study of semiconductor lasers.” . Phys. Rev. Lett. , 94 : 163901
  • Yeung , MKS and Strogatz , SH . 1999 . “Time delay in the Kuramoto model of coupled oscillators.” . Phys. Rev. Lett. , 82 : 648 – 651 .
  • Zhang , L , Kendrick , C , Jülich , D and Holley , SA . 2008 . “Cell cycle progression is required for zebrafish somite morphogenesis but not segmentation clock function.” . Development , 135 : 2065 – 2070 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.