American Institute of Mathematical Sciences

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2008, 5(2): 277-298. doi: 10.3934/mbe.2008.5.277

The role of feedback in the formation of morphogen territories

David Iron 1, , Adeela Syed 2, , Heidi Theisen 2, , Tamas Lukacsovich 2, , Mehrangiz Naghibi 1, , Lawrence J. Marsh 2, , Frederic Y. M. Wan 3, and  Qing Nie 4,

1. 

Dalhousie University, Department of Mathematics and Statistics, Canada, Canada
2. 

University of California, Irvine, Department of Developmental and Cell Biology, University of California, Irvine, United States, United States, United States, United States
3. 

Center for Mathematical and Computational Biology and Department of Mathematics, United States
4. 

Center for Mathematical and Computational Biology, Department of Mathematics, University of California, Irvine, CA 92697-3875

Received  October 2007 Revised  January 2008 Published  March 2008

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.
Keywords: gene regulatory network, pattern formation, partial differential equations., dynamical systems.
Mathematics Subject Classification: Primary: 93B07; Secondary:35K5.
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. Mathematical Biosciences & Engineering, 2008, 5 (2) : 277-298. doi: 10.3934/mbe.2008.5.277
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