Transitions in the model of epithelial patterning.

We analyze pattern formation in the model of cell communication in Drosophila egg development. The model describes the regulatory network formed by the epidermal growth factor receptor (EGFR) and its ligands. The network is activated by the oocyte-derived input that is modulated by feedback loops within the follicular epithelium. We analyze these dynamics within the framework of a recently proposed mathematical model of EGFR signaling (Shvartsman et al. [2002] Development 129:2577-2589). The emphasis is on the large-amplitude solutions of the model that can be correlated with the experimentally observed patterns of protein and gene expression. Our analysis of transitions between the major classes of patterns in the model can be used to interpret the experimentally observed phenotypic transitions in eggshell morphology in Drosophila melanogaster. The existence of complex patterns in the model can be used to account for complex eggshell morphologies in related fly species.