The role of mathematical models of signaling networks is showcased by examples from Drosophila development. Three models of consecutive stages in dorsoventral patterning are presented. We begin with a compartmental model of intracellular reactions that generates a gradient of nuclear-localized Dorsal, exhibiting constant shape and dynamic amplitude. A simple thermodynamic model of equilibrium binding explains how a spatially uniform transcription factor, Zelda, can act in combination with a graded factor, Dorsal, to cooperatively regulate gene expression borders. Finally, we formulate a dynamic and stochastic model that predicts spatiotemporal patterns of Sog expression based on known patterns of its transcription factor, Dorsal. The future of coupling multifarious models across multiple temporal and spatial scales is discussed.
Keywords: Compartmental model; Dorsoventral patterning; Drosophila; Gene expression; Master equation; Multiscale modeling; Stochastic modeling and simulation.
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