Dynamical analysis of the regulatory network defining the dorsal-ventral boundary of the Drosophila wing imaginal disc

The larval development of the Drosophila melanogaster wings is organized by the protein Wingless, which is secreted by cells adjacent to the dorsal-ventral (DV) boundary. Two signaling processes acting between the second and early third instars and between the mid- and late third instar control the expression of Wingless in these boundary cells. Here, we integrate both signaling processes into a logical multivalued model encompassing four cells, i.e., a boundary and a flanking cell at each side of the boundary. Computer simulations of this model enable a qualitative reproduction of the main wild-type and mutant phenotypes described in the experimental literature. During the first signaling process, Notch becomes activated by the first signaling process in an Apterous-dependent manner. In silico perturbation experiments show that this early activation of Notch is unstable in the absence of Apterous. However, during the second signaling process, the Notch pattern becomes consolidated, and thus independent of Apterous, through activation of the paracrine positive feedback circuit of Wingless. Consequently, we propose that appropriate delays for Apterous inactivation and Wingless induction by Notch are crucial to maintain the wild-type expression at the dorsal-ventral boundary. Finally, another mutant simulation shows that cut expression might be shifted to late larval stages because of a potential interference with the early signaling process.