Models of growth, patterning and stem cell dynamics in epithelial tissues
Edouard Hannezo, Institut Curie, Paris, France.

An essential property of living tissues is a permanent cell turnover due to cell division and cell death, which has important effects on their mechanical response. Since cells often grow and divide in a constrained environment, cellular divisions and apoptosis induce internal stresses in tissues that influence deeply their morphologies. Conversely, there is a mechanical feedback on cellular growth, differentiation, and organ development. We study theoretically the shapes of a dividing epithelial monolayer of cells lying on top of a planar elastic stroma. The pressure created by cell division provokes a so-called buckling instability at a finite wavelength leading to the formation of periodic arrays of villi and crypts. Moreover, we wish to understand the interplay between mechanics and stem cell dynamics. We provide a theoretical framework for the homeostasis of stem-cell containing epithelial tissues, using mechanical equations which describe the size of the tissue and kinetic equations which describe the interconversions of the cell populations. We show that several features, such as the evolution of stem cell fractions during intestinal development, the shape of a developing intestinal wall, as well as the increase of the proliferative compartment in cancer initiation can be studied and understood from generic modeling which does not rely on a particular regulatory mechanism. Finally, inspired by recent experiments, we propose a model where cell division rates are regulated by the mechanical stresses in the epithelial sheet. We show that pressure-controlled growth can, in addition to the previous features, also explain with few parameters the formation of stem cell compartments as well as the morphologies observed when a colonic crypt becomes cancerous. We also discuss optimal strategies of wound healing, in connection with experiments on the cornea. Finally, we derive an analytic model based on the interplay between stresses generated by stem cell division and differentiated cell migration, that generically give rise to a patterning instability and well defined stem cell compartments.

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