Background. The regulation of bone morphogenetic protein (BMP) signaling by extracellular BMP binding proteins is of great importance in development and in disease progression. BMP signaling is essential during embryogenesis and wing development in Drosophila melanogaster, but because the signaling pathway components are all conserved, observations in Drosophila may provide insight into how BMP signaling is modulated in vertebrate development. In this work, mathematical analysis was used to uncover key regulation mechanisms of BMP signaling, design new experiments, address questions of function, and to analyze biological robustness.

Principal findings. BMP patterning of the Drosophila embryo and pupal wings is a complex process of secretion, transport, signaling, and gene control. The BMP heterodimer Dpp/Scw is transported from its broad region of production to a narrow region of signaling by a heterodimer inhibitor (Sog/Tsg). Once localized, Dpp/Scw binds to the BMP receptors and forms a heterotetrameric-signaling complex, which ultimately defines the spatial pattern of gene expression in a concentration dependent manner. The key steps of BMP regulation can be decomposed into three interacting modules: (i) ligand and inhibitor dimerization, (ii) extracellular transport, and (iii) signaling/genetic feedback. Module (i) demonstrates that heterodimer formation enhances the robustness of the system by making the output patterns insensitive to changes in the gene copy number for most of the patterning components. Module (ii) demonstrates that redistribution of BMP signaling molecules requires a balance of inhibitor binding and protease cleavage that leads to a net flux and subsequent accumulation of ligands towards to dorsal midline. Interestingly, while inhibitor transport of Dpp/Scw is effective at restricting the region of BMP signaling, additional factors are necessary to dynamically refine the signal in the embryo. To further study BMP-mediated patterning a 3D finite element model of the blastoderm embryo and an image analysis program were developed. The 3D model reproduces many of the BMP signaling patterns observed in embryos with ectopic gene expression of BMP genes only when positive feedback of a co-receptor is included in the patterning mechanism. The 3D model was also used to determine a mechanism of scale-invariance for anterior/posterior embryonic patterning.

Conclusions. Mechanistic models of embryo development enhance our ability to formulate experiments, predict the function of novel factors, understand non-intuitive results such as robustness, and better understand the balance of processes that lead to patterns of gene expression.