From Signals to Patterns: Space, Time, and Mathematics in Developmental Biology

We now have a wealth of information about the molecular signals that act on cells in embryos, but how do the control systems based on these signals generate pattern and govern the timing of developmental events? Here, I discuss four examples to show how mathematical modeling and quantitative experimentation can give some useful answers. The examples concern the Bicoid gradient in the early Drosophila embryo, the dorsoventral patterning of a frog embryo by bone morphogenetic protein signals, the auxin-mediated patterning of plant meristems, and the Notch-dependent somite segmentation clock.

[1]  W. Bialek,et al.  Stability and Nuclear Dynamics of the Bicoid Morphogen Gradient , 2007, Cell.

[2]  Olivier Pourquié,et al.  Segmental patterning of the vertebrate embryonic axis , 2008, Nature Reviews Genetics.

[3]  Ingmar H Riedel-Kruse,et al.  Synchrony Dynamics During Initiation, Failure, and Rescue of the Segmentation Clock , 2007, Science.

[4]  E. Meyerowitz,et al.  Patterns of Auxin Transport and Gene Expression during Primordium Development Revealed by Live Imaging of the Arabidopsis Inflorescence Meristem , 2005, Current Biology.

[5]  C. Kimmel,et al.  Two linked hairy/Enhancer of split-related zebrafish genes, her1 and her7, function together to refine alternating somite boundaries. , 2002, Development.

[6]  Julian Lewis,et al.  Setting the Tempo in Development: An Investigation of the Zebrafish Somite Clock Mechanism , 2007, PLoS biology.

[7]  Julian Lewis,et al.  Notch Signalling Synchronizes the Zebrafish Segmentation Clock but Is Not Needed To Create Somite Boundaries , 2007, PLoS genetics.

[8]  N. Barkai,et al.  Robustness of the BMP morphogen gradient in Drosophila embryonic patterning , 2022 .

[9]  Olivier Pourquié,et al.  fgf8 mRNA decay establishes a gradient that couples axial elongation to patterning in the vertebrate embryo , 2004, Nature.

[10]  W. Bialek,et al.  Diffusion and scaling during early embryonic pattern formation. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[11]  W. Bialek,et al.  Probing the Limits to Positional Information , 2007, Cell.

[12]  Pierre Barbier de Reuille,et al.  Computer simulations reveal novel properties of the cell-cell signaling network at the shoot apex in /Arabidopsis , 2005 .

[13]  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.

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

[15]  P. Prusinkiewicz,et al.  A plausible model of phyllotaxis , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[16]  Jie Chen,et al.  A Complex Oscillating Network of Signaling Genes Underlies the Mouse Segmentation Clock , 2006, Science.

[17]  Lewis Wolpert,et al.  Principles of Development , 1997 .

[18]  H. Meinhardt,et al.  Pattern formation by local self-activation and lateral inhibition. , 2000, BioEssays : news and reviews in molecular, cellular and developmental biology.

[19]  E. Robertis,et al.  Regulation of ADMP and BMP2/4/7 at Opposite Embryonic Poles Generates a Self-Regulating Morphogenetic Field , 2005, Cell.

[20]  Winfried Wiegraebe,et al.  A β-catenin gradient links the clock and wavefront systems in mouse embryo segmentation , 2008, Nature Cell Biology.

[21]  Scott A Holley,et al.  The genetics and embryology of zebrafish metamerism , 2007, Developmental dynamics : an official publication of the American Association of Anatomists.

[22]  Przemyslaw Prusinkiewicz,et al.  Towards the systems biology of auxin-transport-mediated patterning. , 2007, Trends in plant science.

[23]  Julian Lewis Autoinhibition with Transcriptional Delay A Simple Mechanism for the Zebrafish Somitogenesis Oscillator , 2003, Current Biology.

[24]  C. Kimmel,et al.  Stages of embryonic development of the zebrafish , 1995, Developmental dynamics : an official publication of the American Association of Anatomists.

[25]  E. Mjolsness,et al.  An auxin-driven polarized transport model for phyllotaxis , 2006, Proceedings of the National Academy of Sciences of the United States of America.

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

[27]  David Ish-Horowicz,et al.  Notch signalling and the synchronization of the somite segmentation clock , 2000, Nature.

[28]  H. Spemann Embryonic development and induction , 1938 .

[29]  Shigeru Kondo,et al.  Noise-resistant and synchronized oscillation of the segmentation clock , 2006, Nature.

[30]  J. Cooke,et al.  Scale of body pattern adjusts to available cell number in amphibian embryos , 1981, Nature.

[31]  Andrew C Oates,et al.  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 , 2002 .

[32]  Ertugrul M. Ozbudak,et al.  The vertebrate segmentation clock: the tip of the iceberg. , 2008, Current opinion in genetics & development.

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

[34]  Ryoichiro Kageyama,et al.  Periodic repression by the bHLH factor Hes7 is an essential mechanism for the somite segmentation clock. , 2003, Genes & development.

[35]  G. Jürgens,et al.  Local, Efflux-Dependent Auxin Gradients as a Common Module for Plant Organ Formation , 2003, Cell.

[36]  Onn Brandman,et al.  Feedback Loops Shape Cellular Signals in Space and Time , 2008, Science.

[37]  M. Bennett,et al.  Regulation of phyllotaxis by polar auxin transport , 2003, Nature.

[38]  N. Barkai,et al.  Scaling of the BMP activation gradient in Xenopus embryos , 2008, Nature.