The role of feedback in the formation of morphogen territories - David Iron; Adeela Syed; Heidi Theisen; Tamas Lukacsovich; Mehrangiz Naghibi; Lawrence J. Marsh; Frederic Y. M. Wan; Qing Nie (Mathematical Biosciences and Engineering)
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. Wedefine 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 presenceof a general activator, neither autoactivation, nor cross-inhibition alone are suf-ficient to maintain stable sharp boundaries of morphogen production in the legdisc. The minimal requirements for a self-organizing system are a coupledsystem of two morphogens in which the autoactivation and cross-inhibitionhave Hill coefficients strictly greater than one. In addition, the GRN modeledhere describes the regenerative responses to genetic manipulations of positionalidentity in the leg disc.