Homeotic compartment curvature and tension control spatiotemporal folding dynamics.

Shape is a conspicuous and fundamental property of biological systems entailing the function of organs and tissues. While much emphasis has been put on how tissue tension and mechanical properties drive shape changes, whether and how a given tissue geometry influences subsequent morphogenesis remains poorly characterized. Here, we explored how curvature, a key descriptor of tissue geometry, impinges on the dynamics of epithelial tissue invagination. We found that the morphogenesis of the fold separating the adult Drosophila head and thorax segments is driven by the invagination of the Deformed (Dfd) homeotic compartment. Dfd controls invagination by modulating actomyosin organization and in-plane epithelial tension via the Tollo and Dystroglycan receptors. By experimentally introducing curvature heterogeneity within the homeotic compartment, we established that a curved tissue geometry converts the Dfd-dependent in-plane tension into an inward force driving folding. Accordingly, the interplay between in-plane tension and tissue curvature quantitatively explains the spatiotemporal folding dynamics. Collectively, our work highlights how genetic patterning and tissue geometry provide a simple design principle driving folding morphogenesis during development.