Autonomous epithelial folding induced by an intracellular mechano-polarity feedback loop

Epithelial tissues form folded structures during embryonic development and organogenesis. Whereas substantial efforts have been devoted to identifying mechanical and biochemical mechanisms that induce folding, whether and how their interplay synergistically shapes epithelial folds remains poorly understood. Here we propose a mechano-biochemical model for dorsal fold formation in the early Drosophila embryo, an epithelial folding event induced by shifts of cell polarity. Based on experimentally observed apical domain homeostasis, we couple cell mechanics to polarity and find that mechanical changes following the initial polarity shifts alter cell geometry, which in turn influences the reaction-diffusion of polarity proteins, thus forming a feedback loop between cell mechanics and polarity. This model can induce spontaneous fold formation in silico, recapitulate polarity and shape changes observed in vivo, and confer robustness to tissue shape change against small fluctuations in mechanics and polarity. These findings reveal emergent properties of a developing epithelium under control of intracellular mechano-polarity coupling. Author summary Epithelial cells perform a myriad of vital physiological functions that depend on proper cell shape and patterned protein distribution within the cells, known as the cell polarity. Both cell shape and cell polarity have been extensively studied, yet a theoretical link between them remains lacking. We construct a model that integrates mechanical forces, cell shape, and intracellular protein distribution into a feedback loop and find that epithelial tissue folding can occur spontaneously by a local trigger of cell polarity change, which resembles dorsal fold formation in the early Drosophila embryo. In particular, the proposed feedback loop ensures a constant folded shape despite variable physical and chemical conditions, which suggests a mechanism that endows epithelial cells with robust shape formation in a noisy environment. Our work demonstrates that intracellular mechano-polarity feedback plays a fundamental role in shaping and maintaining epithelial morphology.