| Abstract | Dorsal Ventral patterning in drosophila helps determine the boundary between amnioserosa and the dorsal ectoderm. The major morphogen involved is a heterodimer comprising Short gastrulation (Sog) and Twisted gastrulation (Tsg). These proteins are secreted into the perivitteline space, react together and diffuse. The metaloprotease Tolloid (Tld) inactivates Sog when it is bound to Dpp/Scw. In the early blastoderm, Dpp levels are moderate throughout the dorsal ectoderm and pMad, a downstream component, is broadly distributed. Later the maximum pMad concentration increases and localizes at the dorsal midline. Wang and Ferguson suggested that positive feedback might be involved in the contraction and this was demonstrated by computational analysis of a detailed reaction-diffusion model using both a surface binding protein (SBP) and endocytosis. We have extended this model to study how stochastic fluctuations effect the boundary formation. We created three stochastic models: a single cell model, a spatial model, and a downstream network model using a modified Gillepsie algorithm. In the single cell model we found bistability only with endocytosis and SBP. In this model we additionally found that endocytosis reduces the maximal coefficient of variation in BMPs. In the spatial model we found that positive feedback allows for the amniosersa to contract and creates a sharper boundary. We also found contraction in the spatial model with and without endocytosis, however without endocytosis there was a larger variation in the threshold position. In our final model we analyzed the downstream network that creates the positive feedback loop. We found that as we decrease the strength of the positive feedback, the level of compartment differentiation decreases. With the stronger positive feedback we also found the noise in pMad is amplified compared to the upstream level and the differences of noise among compartments are large. In conclusion the single cell model, spatial model, and downstream network model showed that the stochastic fluctuations effect both the location and the strength of the contraction in the boundary between the amnioserosa and dorsal ectoderm. |
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