Robustness of positional specification by the Hedgehog morphogen gradient

Spatial gradients of Hedgehog signalling play a central role in many patterning events during animal development, regulating cell fate determination and tissue growth in a variety of tissues and developmental stages. Experimental evidence suggests that many of the proteins responsible for regulating Hedgehog signalling and transport are themselves targets of Hedgehog signalling, leading to multiple levels of feedback within the system. We use mathematical modelling to analyse how these overlapping feedbacks combine to regulate patterning and potentially enhance robustness in the Drosophila wing imaginal disc. Our results predict that the regulation of Hedgehog transport and stability by glypicans, as well as multiple overlapping feedbacks in the Hedgehog response network, can combine to enhance the robustness of positional specification against variability in Hedgehog levels. We also discuss potential trade-offs between robustness and additional features of the Hedgehog gradient, such as signalling range and size regulation.