The formation of the Thickveins (Tkv) gradient in Drosophila wing discs: A theoretical study

The development of the wing imaginal disc (wing disc) is commonly adopted for the studies of patterning and growth which are two fundamental problems in developmental biology. Decapentaplegic (Dpp) signaling regulates several aspects of wing development, such as the anterior (A)-posterior (P) patterning, cellular growth rate, and cell adhesion. The distribution and activity of Dpp signaling are controlled in part by the expression level of its major type I receptor, Thickveins (Tkv). In this paper, we focus on theoretically investigating mechanisms by which the highly asymmetric pattern of Tkv is established in Drosophila wing discs. To the end, a mathematical model of Hh signaling and Dpp signaling is proposed and validated by comparisons with experimental observations. Our model provides a comprehensive view of the formation of Tkv gradients in wing discs. We found that engrailed (En), Hedgehog (Hh) signaling, and Dpp signaling cooperate to establish the asymmetric gradients of Tkv and pMad in the wing disc. Moreover, our model suggests a Brinker-mediated mechanism of Dpp-dependent repression of Tkv. Based on this mechanism, a couple of predicted experimental observations have been provided for further lab confirmation.