Mathematical Modeling and Experimental Verification of the Proneural Wave

Spatio-temporal pattern formation during development is regulated by interactions of multiple signaling pathways. To understand complex signaling networks, we used the Drosophila visual system as a model because neural differentiation progresses in a spatiotemporally ordered manner. During the development of the visual system, a wave of differentiation, called the proneural wave, sweeps across the brain surface and determines the timing of differentiation of neuroepithelial cells into neuroblasts, which are neural stem cells in Drosophila. Propagation of the proneural wave is regulated through a combination of signaling pathways, including the Notch, EGF, and JAK/STAT. We combined mathematical modeling with in vivo experiments, the results of which revealed that Notch-mediated lateral inhibition and EGF-mediated reaction diffusion determine the speed of progression of the proneural wave. We reported that JAK/STAT signaling has a noise-canceling function to assure robust neuroblast differentiation. Furthermore, we introduced a continuation method from spatially discretized models while conserving the cell size and lattice. This mathematical method enables us to introduce information from spatially discrete to spatially continuous models, rendering it suitable for applications in both experimental and mathematical analyses. Our interdisciplinary studies have revealed new functions of signaling pathways that have previously been difficult to address by conventional biological experiments.