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.
Key wordsHedgehog gradient Mathematical modeling Cytonemes and vesicles in Hh Flux-saturated mechanism Dispersion
The paper has been partially supported by Junta de Andalucía Project FQM 954. IG was supported by Fundamental Biology (BFU2011-25987) and Consolider (CDS 2007-00008) program grants from the Spanish Ministry of Economy and Commutativity (MINECO), by Marie Curie FP7- Integration Network (ITN 238186) grant and by an institutional grant to Centro de Biología Molecular “Severo Ochoa” from the Fundación Areces. J.C., O.S., and J.S. were supported in part by Spanish MINECO, project MTM2011-23384 and FEDER funds. JC is also partially supported by La Caixa “Collaborative Mathematical Research’’ programme and a Juan de la Cierva grant of the spanish MEC.
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