Discussion

We have detailed two mechanisms for the creation of a morphogen gradient, which do not share restrictions of mechanisms which have been previously studied:

• Separation of the morphogen into an extracellular phase, from which it cannot directly interact with receptors, and a cell-membrane phase; the corresponding mathematical model does not require any degradation scheme of receptor-morphogen complexes, and can accommodate biochemical parameters over a very wide range of values. Values which show correlation when interesting gradients are formed are the relative rates of morphogen degradation and phase equilibration, as well as rates related to the relative levels of extracellular matrix and cell-membrane concentrations. These are good candidates for experimental observation and manipulation.
• Oligomerization of the morphogen into a compound which does not interact with receptors, as could be the case for Sonic Hedgehog.

Both these mechanisms create in effect a dynamic sub-population of morphogen that travels unhindered by receptor interaction, allowing the morphogen gradient not to die off too quickly or saturate receptors. Tracking of the membrane diffusion of single molecules is feasible (as shown for example by Murakoshi et al., 2004); extending these experiments to extracellular diffusion would allow one to assess whether sets of individual paths indeed reflect the sort of diffusion which underlies these new models.

The phase repartition model is compatible with both observations that proteoglycans are indispensable for Dpp and Wg diffusion, and that cell membrane-tethered diffusion would be too slow to account for the observed speed of gradient establishment (Lander et al., 2002). Its absence of requirement for receptor-mediated morphogen degradation is also in line with the lack of requirement of the receptors Fz and Fz2 to establish a Wg gradient (Han et al., 2005).

It has only recently been discovered that Dlp's GPI anchor can be cleaved, releasing it into the extracellular matrix. Since Notum is synthesized only in a region of high Wg signaling, it has been proposed that this localized expression has a role in promoting morphogen diffusion to regions of less intense signaling. However, our model makes the counter-intuitive suggestion that this may not be the case. This is in line with experiments showing that misexpression of Notum in the dorsal compartment of a Drosophila wing disc has symmetrical effects on the dorsal and ventral compartments (Giráldez et al., 2002), and with the fact that Dpp has been show to also require Dll and Dlp for its diffusion (Belenkaya et al., 2004). If Notum (and the EM and membrane fractions of Dll and Dlp) had a strongly non-homogenous distribution along the dorso-ventral axis, one would expect interference with Dpp signalling, which takes place in a gradient orthogonal to that of Wg (Figure 1).

Semi-quantitative imaging of the membrane-associated and free, extracellular sub-populations would provide crucial data to test models with. In particular, to accomodate experimental data showing that morphogen diffusion does not occur over clones deficient in Dll and Dlp (Belenkaya et al., 2004, Han et al., 2005), the phase repartition model makes the important assumption that extracellular Dlp has a negligible diffusion rate.

Even though parameter sets were identified which allow Shh-like oligomerization to give rise to suitable gradients, this did not happen as readily as for the phase repartition model. This could very well have to do with the fact that glycoproteins also seem to be essential to the establishment of a Shh gradient (Han et al., 2004), and that the two phenomena need to be taken into account together.