A cellular oscillator model for periodic pattern formation.

In this paper, we present a model for pattern formation in developing organisms that is based on cellular oscillators (CO). An oscillatory process within cells serves as a developmental clock whose period is tightly regulated by cell autonomous or non-autonomous mechanisms. A spatial pattern is generated as a result of an initial temporal ordering of the cell oscillators freezing into spatial order as the clocks slow down and stop at different times or phases in their cycles. We apply a CO model to vertebrate somitogenesis and show that we can reproduce the dynamics of periodic gene expression patterns observed in the pre-somitic mesoderm. We also show how varying somite lengths can be generated with the CO model. We then discuss the model in view of experimental evidence and its relevance to other instances of biological pattern formation, showing its versatility as a pattern generator.

[1]  N. Patel,et al.  Expression of engrailed during segmentation in grasshopper and crayfish. , 1989, Development.

[2]  V. French,et al.  Disruption of segmentation in a short germ insect embryo. I. The location of abnormalities induced by heat shock. , 1986, Journal of embryology and experimental morphology.

[3]  V. French,et al.  Disruption of segmentation in a short germ insect embryo. II. The structure of segmental abnormalities induced by heat shock. , 1986, Journal of embryology and experimental morphology.

[4]  F Radtke,et al.  Oscillating expression of c-Hey2 in the presomitic mesoderm suggests that the segmentation clock may use combinatorial signaling through multiple interacting bHLH factors. , 2000, Developmental biology.

[5]  B. Edgar,et al.  Developmental Control of Cell Cycle Regulators: A Fly's Perspective , 1996, Science.

[6]  J. Dunlap.  Molecular Bases for Circadian Clocks , 1999, Cell.

[7]  Scott F. Gilbert,et al.  Embryology : constructing the organism , 1997 .

[8]  Mark A. J. Chaplain,et al.  On Growth and Form: Spatio-temporal Pattern Formation in Biology , 2000 .

[9]  D. SUMMERBELL,et al.  Positional Information in Chick Limb Morphogenesis , 1973, Nature.

[10]  P K Maini,et al.  Clock and induction model for somitogenesis , 2000, Developmental dynamics : an official publication of the American Association of Anatomists.

[11]  A chemical flow system mimics waves of gene expression during segmentation. , 2000, Biophysical chemistry.

[12]  D. Duboule,et al.  Control of colinearity in AbdB genes of the mouse HoxD complex. , 1998, Molecular cell.

[13]  C. Muratov.  Synchronization, chaos, and the breakdown of collective domain oscillations in reaction-diffusion systems , 1996, patt-sol/9608005.

[14]  P. Calow,et al.  Invertebrates: a new synthesis. , 1988 .

[15]  R. Keynes,et al.  Mechanisms of vertebrate segmentation. , 1988, Development.

[16]  D. Weisblat,et al.  Segmental expression of an engrailed-class gene during early development and neurogenesis in an annelid. , 1991, Development.

[17]  D. Lloyd,et al.  THE OCCURRENCE AND FUNCTIONS OF ULTRADIAN RHYTHMS , 1991, Biological reviews of the Cambridge Philosophical Society.

[18]  A. Goldbeter,et al.  Biochemical Oscillations And Cellular Rhythms: Contents , 1996 .

[19]  A. Turing.  The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[20]  E. C. Zeeman,et al.  A clock and wavefront model for control of the number of repeated structures during animal morphogenesis. , 1976, Journal of theoretical biology.

[21]  O. Pourquié,et al.  Avian hairy Gene Expression Identifies a Molecular Clock Linked to Vertebrate Segmentation and Somitogenesis , 1997, Cell.

[22]  O. Pourquié,et al.  A clock-work somite. , 2000, BioEssays : news and reviews in molecular, cellular and developmental biology.

[23]  D. A. Ede,et al.  Somites in Developing Embryos , 1986, NATO ASI Series.

[24]  Nigel A. Brown,et al.  Waves of mouse Lunatic fringe expression, in four-hour cycles at two-hour intervals, precede somite boundary formation , 1998, Current Biology.

[25]  L Wolpert,et al.  A clock and trail model for somite formation, specialization and polarization. , 2000, Journal of theoretical biology.

[26]  B. Goodwin,et al.  A phase-shift model for the spatial and temporal organization of developing systems. , 1969, Journal of theoretical biology.

[27]  C. Stern,et al.  Clocked gene expression in somite formation. , 1998, BioEssays : news and reviews in molecular, cellular and developmental biology.

[28]  Mads Kærn,et al.  Segmentation and somitogenesis derived from phase dynamics in growing oscillatory media. , 2000, Journal of theoretical biology.

[29]  Marcos González-Gaitán,et al.  Gradient Formation of the TGF-β Homolog Dpp , 2000, Cell.

[30]  J. E. Mee.  Pattern formation in fragmented eggs of the short germ insect Schistocerca gregaria , 1986, Roux's archives of developmental biology.

[31]  J. Cooke,et al.  Control of somite number during morphogenesis of a vertebrate, Xenopus laevis , 1975, Nature.

[32]  H. Meinhardt.  Models of biological pattern formation , 1982 .

[33]  D. Johnson,et al.  Cyclins and cell cycle checkpoints. , 1999, Annual review of pharmacology and toxicology.

[34]  A. Fritz,et al.  Zebrafish Mesp family genes, mesp-a and mesp-b are segmentally expressed in the presomitic mesoderm, and Mesp-b confers the anterior identity to the developing somites. , 2000, Development.

[35]  R. Keynes,et al.  Periodic segmental anomalies induced by heat shock in the chick embryo are associated with the cell cycle. , 1989, Development.

[36]  Olivier Pourquié,et al.  The lunatic Fringe gene is a target of the molecular clock linked to somite segmentation in avian embryos , 1998, Current Biology.

[37]  O. Pourquié,et al.  Notch signalling is required for cyclic expression of the hairy-like gene HES1 in the presomitic mesoderm. , 2000, Development.

[38]  J. Gurdon,et al.  Activin has direct long-range signalling activity and can form a concentration gradient by diffusion , 1997, Current Biology.

[39]  P K Maini,et al.  A cell cycle model for somitogenesis: mathematical formulation and numerical simulation. , 2000, Journal of theoretical biology.

[40]  Hans Meinhardt,et al.  Models of Segmentation , 1986 .

[41]  Cyrille Alexandre,et al.  The progeny of wingless-expressing cells deliver the signal at a distance in Drosophila embryos , 2000, Current Biology.

[42]  E. Rosenthal,et al.  Selective translation of mRNA controls the pattern of protein synthesis during early development of the surf clam, Spisula solidissima , 1980, Cell.

[43]  Brian C. Goodwin,et al.  Analytical physiology of cells and developing organisms , 1976 .