The role of feedback in the formation of morphogen territories

Pages: 277 - 298, Volume 5, Issue 2, April 2008

doi:10.3934/mbe.2008.5.277       Abstract        Full Text (557.0K)       Related Articles

David Iron - Dalhousie University, Department of Mathematics and Statistics, Canada (email)
Adeela Syed - University of California, Irvine, Department of Developmental and Cell Biology, University of California, Irvine, United States (email)
Heidi Theisen - University of California, Irvine, Department of Developmental and Cell Biology, University of California, Irvine, United States (email)
Tamas Lukacsovich - University of California, Irvine, Department of Developmental and Cell Biology, University of California, Irvine, United States (email)
Mehrangiz Naghibi - Dalhousie University, Department of Mathematics and Statistics, Canada (email)
Lawrence J. Marsh - University of California, Irvine, Department of Developmental and Cell Biology, University of California, Irvine, United States (email)
Frederic Y. M. Wan - Center for Mathematical and Computational Biology and Department of Mathematics, United States (email)
Qing Nie - Center for Mathematical and Computational Biology, Department of Mathematics, University of California, Irvine, CA 92697-3875, United States (email)

Abstract: 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:  pattern formation, gene regulatory network, dynamical systems, partial differential equations.
Mathematics Subject Classification:  Primary: 93B07; Secondary:35K57.

Received: October 2007;      Accepted: January 2008;      Published: March 2008.