Interplay between epidermal stem cell dynamics and dermal deformation

Tissue growth is a driving force of morphological changes in living systems. Whereas the buckling instability is known to play a crutial role for initiating spatial pattern formations in such growing systems, little is known about the rationale for succeeding morphological changes beyond this instability. In mammalian skin, the dermis has many protrusions toward the epidermis, and the epidermal stem cells are typically found on the tips of these protrusions. Although the initial instability may well be explained by the buckling involving the dermis and the basal layer, which contains proliferative cells, it does not dictate the direction of these protrusions, nor the spatial patterning of epidermal stem cells. Here we introduce a particle-based model of self-replicating cells on a deformable substrate composed of the dermis and the basement membrane, and investigate the relationship between dermal deformation and epidermal stem cell pattering on it. We show that our model reproduces the formation of dermal protrusions directing from the dermis to the epidermis, and preferential epidermal stem cell distributions on the tips of the dermal protrusions, which the basic buckling mechanism fails to explain. We argue that cell-type-dependent adhesion strengths of the cells to the basement membrane are crucial factors influencing these patterns.