Glycoprotein-mediated phase repartition

This model is inspired from the Wg (Zecca et al., 1996) and Decapentaplegic (Dpp; Nellen et al., 1996) morphogen gradients in the Drosophila wing-disc, but could also apply to other gradients, such as the Sonic Hedgehog (Shh) gradient in the developing neural tube (Briscoe et al., 2001). Dally (Tsuda et al., 1999; abbreviated Dll) and Dally-like (Khare and Baumgartner, 2000, Baeg et al., 2001; abbreviated Dlp) are cell-surface heparan sulfate proteoglycans, tethered to the membrane by a GPI anchor (ie, glypicans), which have been shown to influence both Dpp and Wg signalling. In the Drosophila wing disc, Wg and Dpp cannot diffuse into clones deficient for both Dll and Dlp, or into clones deficient for heparan-sulfate synthesis (Belenkaya et al., 2004, Han et al., 2005); it has been proposed that Dll acts as a Wg co-receptor, while Dlp mediates Wg movement across cells (Baeg et al., 2001), but Dll seems to also have a role in mediating inter-cellular movement (Han et al., 2005). Importantly, Dlp can be released into the extracellular matrix by the secreted protein Notum (Kreuger et al., 2004), and Dll-Notum interactions have been shown to be essential for wing-disc patterning (Han et al., 2005), suggesting that Dll could also be released by Notum. Notum is mainly expressed in the region of high Wg signalling, and can itself be released into the extracellular matrix (Gerlitz and Basler, 2002, Giráldez et al., 2002). Notum would not be taken into account in a model for Dpp gradient establishment (see below for a further discussion of Notum as regards the Wg and Dpp gradients).

In the model proposed here, and illustrated in Figure 1 Dll and Dlp are considered as a single entity (noted as $d$ in the equations detailed in Appendix A.4), which binds to the morphogen $m$. Two populations are considered, one in the extracellular matrix (EM), and one on the cell membrane (mem); cell membrane-attached $d$ molecules are relased into the extracellular matrix by Notum ($n$). The crucial hypothesis of the model is that the morphogen equilibrates between the extracellular matrix and membrane phases, following the repartition of $d$. Extracellular morphogen is injected at the left boundary, and Notum synthesized (and considered to be immediately secreted) over the first 10$\mu m$. Both free and bound receptor populations are taken into account, with a fixed rate of receptor synthesis, and unregulated degradation.

In order for the model to be compatible with the experimental data showing the absence of diffusion of morphogen into clones deficient for Dll and Dlp, only the EM morphogen and Notum are considered to diffuse.

Figure 1: (A) Distribution of Wg, Dpp, Dll/Dlp, and Notum in a Drosophila third instar wing disc. (B) Glycoprotein phase-repartition model for Wg signaling.