Epithelial tissue folding pattern in confined geometry

The primordium of the exoskeleton of an insect is epithelial tissue with characteristic patterns of folds. As the insect develops from larva to pupa, the spreading of these folds produces the three-dimensional shape of the exoskeleton of the insect. It is known that the three-dimensional exoskeleton shape has already been encoded in characteristic patterns of folds in the primordium; however, a description of how the epithelial tissue forms with the characteristic patterns of folds remains elusive. The present paper suggests a possible mechanism for the formation of the folding pattern. During the primordium development, because of the epithelial tissue is surrounded by other tissues, cell proliferation proceeds within a confined geometry. To elucidate the mechanics of the folding of the epithelial tissue in the confined geometry, we employ a three-dimensional vertex model that expresses tissue deformations based on cell mechanical behaviors and apply the model to examine the effects of cell divisions and the confined geometry on epithelial folding. Our simulation results suggest that the orientation of the axis of cell division is sufficient to cause different folding patterns in silico and that the restraint of out-of-plane deformation due to the confined geometry determines the interspacing of the folds.