Modeling Hedgehog Signaling Through Flux-Saturated Mechanisms.

Hedgehog (Hh) molecules act as morphogens directing cell fate during development by activating various target genes in a concentration dependent manner. Hitherto, modeling morphogen gradient formation in multicellular systems has employed linear diffusion, which is very far from physical reality and needs to be replaced by a deeper understanding of nonlinearities. We have developed a novel mathematical approach by applying flux-limited spreading (FLS) to Hh morphogenetic actions. In the new model, the characteristic velocity of propagation of each morphogen is a new key biological parameter. Unlike in linear diffusion models, FLS modeling predicts concentration fronts and correct patterns and cellular responses over time. In addition, FLS considers not only extracellular binding partners influence, but also channels or bridges of information transfer, such as specialized filopodia or cytonemes as a mechanism of Hh transport. We detect and measure morphogen particle velocity in cytonemes in the Drosophila wing imaginal disc. Indeed, this novel approach to morphogen gradient formation can contribute to future research in the field.