Planar differential growth rates determine the position of folds in complex epithelia

Folding is a fundamental process shaping epithelial sheets into 3D architectures of organs. Initial positioning of folds is the foundation for the emergence of correct tissue morphology. Mechanisms forming individual folds have been studied, yet the precise positioning of the folds in complex, multi-folded epithelia is an open question. We present a model of morphogenesis, encompassing local differential growth, and tissue mechanics to investigate tissue fold positioning. We use Drosophila melanogaster wing imaginal disc as our model system, and show that there is spatial and temporal heterogeneity in its planar growth rates. This planar differential growth is the main driver for positioning the folds. Increased stiffness of the apical layer and confinement by the basement membrane drive fold formation. These influence fold positions to a lesser degree. The model successfully predicts the emergent morphology of wingless spade mutant in vivo, via perturbations solely on planar differential growth rates in silico.