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Mathematical Biosciences and Engineering

2008, Volume 5, Issue 2: 277-298. doi: 10.3934/mbe.2008.5.277
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The role of feedback in the formation of morphogen territories

  • 1.
    Dalhousie University, Department of Mathematics and Statistics
  • 2.
    University of California, Irvine, Department of Developmental and Cell Biology, University of California, Irvine
  • 3.
    Center for Mathematical and Computational Biology and Department of Mathematics
  • 4.
    Center for Mathematical and Computational Biology, Department of Mathematics, University of California, Irvine, CA 92697-3875
  • Received: 01 October 2007 Accepted: 29 June 2018 Published: 01 March 2008

  • MSC : Primary: 93B07; Secondary:35K57.

  • In this paper, we consider a mathematical model for the forma- tion of spatial morphogen territories of two key morphogens: Wingless (Wg) and Decapentaplegic (DPP), involved in leg development of Drosophila. We define a gene regulatory network (GRN) that utilizes autoactivation and cross- inhibition (modeled by Hill equations) to establish and maintain stable bound- aries of gene expression. By computational analysis we find that in the presence of a general activator, neither autoactivation, nor cross-inhibition alone are suf- ficient to maintain stable sharp boundaries of morphogen production in the leg disc. The minimal requirements for a self-organizing system are a coupled system of two morphogens in which the autoactivation and cross-inhibition have Hill coefficients strictly greater than one. In addition, the GRN modeled here describes the regenerative responses to genetic manipulations of positional identity in the leg disc.

    Citation: David Iron, Adeela Syed, Heidi Theisen, Tamas Lukacsovich, Mehrangiz Naghibi, Lawrence J. Marsh, Frederic Y. M. Wan, Qing Nie. The role of feedback in the formation of morphogen territories[J]. Mathematical Biosciences and Engineering, 2008, 5(2): 277-298. doi: 10.3934/mbe.2008.5.277

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  • In this paper, we consider a mathematical model for the forma- tion of spatial morphogen territories of two key morphogens: Wingless (Wg) and Decapentaplegic (DPP), involved in leg development of Drosophila. We define a gene regulatory network (GRN) that utilizes autoactivation and cross- inhibition (modeled by Hill equations) to establish and maintain stable bound- aries of gene expression. By computational analysis we find that in the presence of a general activator, neither autoactivation, nor cross-inhibition alone are suf- ficient to maintain stable sharp boundaries of morphogen production in the leg disc. The minimal requirements for a self-organizing system are a coupled system of two morphogens in which the autoactivation and cross-inhibition have Hill coefficients strictly greater than one. In addition, the GRN modeled here describes the regenerative responses to genetic manipulations of positional identity in the leg disc.


  • This article has been cited by:

    1. A. D. Lander, Q. Nie, F. Y. M. Wan, Y.-T. Zhang, Localized Ectopic Expression of Dpp Receptors in a Drosophila Embryo, 2009, 123, 00222526, 175, 10.1111/j.1467-9590.2009.00450.x
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  • © 2008 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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