| Pattern formation in developing organisms can be regulated at a variety of levels, from gene sequence to anatomy. At this level of complexity, mechanistic models of development become essential for integrating data, guiding future experiments, and predicting the effects of genetic and physical perturbations. However, the formulation and analysis of quantitative models of development are limited by high levels of uncertainty in experimental measurements and a large number of both known and unknown system components. At the same time, an expanding arsenal of experimental tools can constrain models and directly test their predictions, making the modeling efforts not only necessary, but feasible. Using a number of problems in Drosophila development, we first discuss how models can be used to test the feasibility of proposed patterning mechanisms and characterize their systems-level properties.; In Chapter 2, we introduce the epidermal growth factor receptor (EGFR) patterning system and analyze a model of EGFR patterning in Drosophila embryonic development. This model is based on genetic and biochemical information regarding ligand/receptor interactions. Argos, a diffusible inhibitor of the system, acts by sequestering the EGFR ligand Spitz. We use computational modeling to show that this biochemically-determined mechanism of Argos action can explain available genetic data for EGFR/Spitz/Argos interactions in vivo. The goal of our modeling effort is to predict the currently undetectable concentration gradients of Spitz and Argos. However, such prediction requires quantitative estimates of the model parameters. In particular, due to the ligand sequestration mechanism, the spatial distribution of Argos cannot be inferred from a model based on the current literature data, and thus remains an open question. To begin to answer this question, in Chapter 3 we study two opposing simplifications to the model, one in which the spatial distribution of Argos is perfectly localized, and the other in which Argos is completely diffuse. We find that both models can explain the literature data of wild type and argos null mutant embryos. We show that analysis of two additional genetic backgrounds can differentiate between the two models, and propose the analogous experiments. We stand in favor of the localized Argos model based on a simple cost-benefit argument.; Finally, in Chapter 4, we analyze data from fluorescent in situ hybridization experiments to quantify the effect of EGFR signaling in both wild type embryos and embryos that overexpress an activator of the system. Using these and previously published literature data as inputs to our model, we estimate the values of the model parameters. This allows us to characterize the spatial distributions of the previously unknown concentration profiles of Spitz and Argos. We find that Spitz is a short-ranged ligand, acting over a distance of only ∼3 cell diameters, and that the concentration of Argos in this system must exceed that of Spitz to ensure correct patterning. |
