Abstract
In the development of Drosophila wing disc, morphogen Dpp, which is a signaling molecule from a local region and disperses into anterior and posterior compartments, builds up a gradient with precise pattern information. Experiments have demonstrated that the key genes (brk, dad, omb and sal) and phosphorylated protein (pMad), which are activated by Dpp signaling molecules and form the gradients of the corresponding proteins of these genes, direct and control the spatial pattern of the wing disc. However, the regulatory network of these genes are in complex and nonlinear interaction with upstream regulators and downstream targets. In this paper, the mathematical model is built according to the regulatory relationships of these key genes. The stabilities of the gradients of these corresponding proteins are investigated. Furthermore, numerical simulations show that these gradients are robust with respect to some major reaction rates in this regulatory network.
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