Abstract
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.
Highlights
Several experiments suggest that epidermal stem cells tend to be found on the tips of dermal protrusions, while the transit amplifying cells occupy the rest of the dermal surface,[17,18] which we have experimentally confirmed, as shown in Fig.S1 (Supplementary Information)
In this work we introduce a mathematical model of cell division dynamics in the basal layer on a substrate composed of the basement membrane and the dermis, taking into account substrate deformability and cell type-dependent adhesion to the substrate
The dermis and the basement membrane form an elastic substrate, and the basal layer cells are attached to the basement membrane
Summary
The morphology of growing tissues is influenced by mechanical forces due to cell division, migration, and apoptosis,[1,2,3,4,5] where the buckling instability is regarded as an important pattern-forming mechanism.[6,7] Buckling is quite often observed when a growing tissue layer interacts with an elastic substrate or two growing layers with different growth rates interact with each other.[8,9,10] Many biological systems have been modeled from such a viewpoint, examples including airway epithelium,[11] intestine,[12,13,14] colonic crypt,[15] and tumor.[16] Skin provides another example of such systems, where a sheet of proliferating cells (the basal layer) is attached via the basement membrane to a soft elastic substrate (the dermis). We argue that the outward deformation of the dermis is caused by the interplay of cell-membrane adhesion and membrane elasticity, and that the epidermal stem cell distribution is determined by the difference in adhesion strength between different types of cells
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