Robust multiple-fate morphogen gradients are essential for embryo development. In this talk, I introduce the approaches of quantitative analysis in the study of the robustness of morphogen gradients. First, I will serval mathematical models of morphogen gradient (such as Dpp in Drosophila wing imaginal disc) formation. The models are established basic on different assumptions on the mechanisms for the transportation of morphogens. Second, I will show recent results on the theoretical studies for mechanisms to form robust morphogen gradients. Two mechanisms are highlighted:
Mechanism 1. Substantial (reversible) binding of slowly turned over morphogen molecules with membrane-bound non-receptors with the resulting non-signling (morphogen) complexes degrading at a sufficiently rapid rate.
Mechanism 2. Fast binding of rapidly turned over free morphogen molecules with non-receptors so that the non-signaling complexes downstream through a "bucket brigade" process.