An Extended Mathematical Model for Anterior-Posterior Patterning of Drosophila Wing Discs

Patterning and growth of Drosophila wing discs are controlled by the Decapentaplegic (Dpp) signaling pathways. It is very interesting to investigate mechanisms by which the highly asymmetric patterns of Thickveins (Tkv) and Phosphorylated Mothers Against Dpp (pMad) are established in Drosophila wing discs. In this work, we improved and extended a previous mathematical model which theoretically provided a comprehensive view of the formation of Tkv gradients. In particular, a decreasing Hill function is introduced to remove a model parameter constraint. Moreover, we attempt to further extend the model by incorporating Division abnormally delayed (Dally) which has been believed to play an important role in stabilizing Dpp signaling and patterning. It turns out that theoretical results by our extended model match key experimental observations quite well.