The third instar Drosophila wing disc has provided examples of molecules forming morphogen gradients (reviewed by Cadigan, 2002). Whether the transport of morphogens relies on passive extracellular diffusion has been a source of intense debate (see for example Kerszberg and Wolpert, 1998, Kruse et al., 2004, Lander et al., 2002), but recent experimental data has dealt a new hand by greatly clarifying the role of extracellular proteoglycans in the establishment of morphogen gradients (Baeg et al., 2004, Belenkaya et al., 2004, Han et al., 2004,2005); mathematical models are yet to be developed to take this role into account.
It was first observed by Kerszberg and Wolpert (1998), and confirmed by Lander et al. (2002), that a simple system of morphogen diffusion and receptor binding will generally create a traveling wave of receptor saturation and not a stable gradient of bound receptor. It has been shown that this problem can be alleviated by hypothesizing a mechanism of ligand-receptor complex degradation and slow association constants (Lander et al., 2002), the possibility of signaling for internalized complexes (Lander et al., 2002), similar to the ligand-triggered, but ligand-free, receptor dimers of Kerszberg and Wolpert (1998), or self-enhanced ligand degradation (Eldar et al., 2003). We propose here two other simple mechanisms for suitably-shaped morphogen gradients to arise, one based on morphogen oligomerization, and one based on the role of extracellular glycoproteins. The latter model illustrates what the role of extracellular glycoproteins could be, and also provides a specific insight into the establishment of the Wingless (Wg) gradient, one of the morphogens identified in the Drosophila wing disc.