The mechanism of sudden stripe formation during dorso-ventral patterning in Drosophila.

The front and back (ventral and dorsal part respectively) of arthropods and chordates are defined by a highly conserved mechanism during early embryonic development [De Robertis and Kuroda in Annu. Rev. Cell Dev. Biol. 20, 285-308 (2004)]. An important feature is the sudden formation of a narrow midline peak of signaling. Mathematical models have helped to improve our understanding of the underlying mechanism [Eldar et al. in Nature 419(6904), 304-308 (2002); Mizutani in Dev. Cell 8(6), 915-924 (2005); Shimmi et al. in Cell 120(6), 873-886, (2005)]. In particular, the most recent model shows that diffusion and receptor-dependent degradation of the morphogen together with protease-mediated cleavage of a carrier protein for the morphogen are sufficient for the sudden generation of a sharp midline peak [Mizutani in Dev. Cell 8(6), 915-924 (2005)]. How these processes give rise to the observed pattern and how sensitive the model is to changes in parameter values has, however, not been resolved by this numerical study. By analysing the model in detail, we find that the sudden formation of a signaling peak is the consequence of the inversion of the gradient of the morphogen-carrier complex in the dorsal domain. As a consequence ligand is suddenly transported into rather than out of the midline, and a midline peak forms. We further show that a two-component carrier complex, consisting of Sog and Tsg, is required for abrupt peak formation. We derive quantitative conditions for the time and concentration at which the peak forms. We identify the receptor concentration, the ligand production and degradation rates, and the carrier production, diffusion, and cleavage rates as parameters to which the model is sensitive. Numerical studies confirm our analysis.