In the early stage of tooth germ development, the bud of the dental epithelium is invaginated by the underlying mesenchyme, resulting in the formation of a cap-like folded shape. This bud-to-cap transition plays a critical role in determining the steric design of the tooth. The epithelial-mesenchymal interaction within a tooth germ is essential for mediating the bud-to-cap transition. Here, we present a theoretical model to describe the autonomous process of the morphological transition, in which we introduce mechanical interactions among cells. Based on our observations, we assumed that peripheral cells of the dental epithelium bound tightly to each other to form an elastic sheet, and mesenchymal cells that covered the tooth germ would restrict its growth. By considering the time-dependent growth of cells, we were able to numerically show that the epithelium within the tooth germ buckled spontaneously, which is reminiscent of the cap-stage form. The difference in growth rates between the peripheral and interior parts of the dental epithelium, together with the steric size of the tooth germ, were determining factors for the number of invaginations. Our theoretical results provide a new hypothesis to explain the histological features of the tooth germ.
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