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A central question in biology is how secreted morphogens act to induce different cellular responses within a group of cells in a concentration-dependent manner. Modeling morphogenetic output in multicellular systems has so far employed linear diffusion, which is the normal type of diffusion associated with Brownian processes. However, there is evidence that at least some morphogens, such as Hedgehog (Hh) molecules, may not freely diffuse. Moreover, the mathematical analysis of such models necessarily implies unrealistic instantaneous spreading of morphogen molecules, which are derived from the assumptions of Brownian motion in its continuous formulation. A strict mathematical model considering Fick's diffusion law predicts morphogen exposure of the whole tissue at the same time. Such a strict model thus does not describe true biological patterns, even if similar and attractive patterns appear as results of applying such simple model. To eliminate non-biological behaviors from diffusion models we introduce flux-limited spreading (FLS), which implies a restricted velocity for morphogen propagation and a nonlinear mechanism of transport. Using FLS and focusing on intercellular Hh-Gli signaling, we model a morphogen gradient and highlight the propagation velocity of morphogen particles as a new key biological parameter. This model is then applied to the formation and action of the Sonic Hh (Shh) gradient in the vertebrate embryonic neural tube using our experimental data on Hh spreading in heterologous systems together with published data. Unlike linear diffusion models, FLS modeling predicts concentration fronts and the evolution of gradient dynamics and responses over time. In addition to spreading restrictions by extracellular binding partners, we suggest that the constraints imposed by direct bridges of information transfer such as nanotubes or cytonemes underlie FLS. Indeed, we detect and measure morphogen particle velocity in such cell extensions in different syst

Hedgehog can signal both at a short and long-range, and acts as a morphogen during development in various systems. We studied the mechanisms of Hh release and spread using the Drosophila wing imaginal disc as a model system for polarized epithelium. We analyzed the cooperative role of the glypican Dally, the extracellular factor Shifted (Shf, also known as DmWif), and the Immunoglobulin-like (Ig-like) and Fibronectin III (FNNIII) domain-containing transmembrane proteins, Interference hedgehog (Ihog) and its related protein Brother of Ihog (Boi), in the stability, release and spread of Hh. We show that Dally and Boi are required to prevent apical dispersion of Hh; they also aid Hh recycling for its release along the basolateral part of the epithelium to form a long-range gradient. Shf/DmWif on the other hand facilitates Hh movement restrained by Ihog, Boi and Dally, establishing equilibrium between membrane attachment and release of Hh. Furthermore, this protein complex is part of thin filopodia-like structures or cytonemes, suggesting that the interaction between Dally, Ihog, Boi and Shf/DmWif is required for cytoneme-mediated Hh distribution during gradient formation. © 2013 Elsevier Inc.

Hedgehog (Hh) moves from the producing cells to regulate the growth and development of distant cells in a variety of tissues. Here, we have investigated the mechanism of Hh release from the producing cells to form a morphogenetic gradient in the Drosophila wing imaginal disk epithelium. We describe that Hh reaches both apical and basolateral plasma membranes, but the apical Hh is subsequently internalized in the producing cells and routed to the basolateral surface, where Hh is released to form a longrange gradient. Functional analysis of the 12-transmembrane protein Dispatched, the glypican Dally-like (Dlp) protein, and the Iglike and FNNIII domains of protein Interference Hh (Ihog) revealed that Dispatched could be involved in the regulation of vesicular trafficking necessary for basolateral release of Hh, Dlp, and Ihog. We also show that Dlp is needed in Hh-producing cells to allow for Hh release and that Ihog, which has been previously described as an Hh coreceptor, anchors Hh to the basolateral part of the disk epithelium.