Homeostatic balance in the intestinal epithelium relies on a fast cellular turnover, which is coordinated by an intricate interplay between biochemical signalling, mechanical forces and organ geometry. We review recent modelling approaches that have been developed to understand different facets of this remarkable homeostatic equilibrium. Existing models offer different, albeit complementary, perspectives on the problem. First, biomechanical models aim to explain the local and global mechanical stresses driving cell renewal as well as tissue shape maintenance. Second, compartmental models provide insights into the conditions necessary to keep a constant flow of cells with well-defined ratios of cell types, and how perturbations can lead to an unbalance of relative compartment sizes. A third family of models address, at the cellular level, the nature and regulation of stem fate choices that are necessary to fuel cellular turnover. We also review how these different approaches are starting to be integrated together across scales, to provide quantitative predictions and new conceptual frameworks to think about the dynamics of cell renewal in complex tissues.
Keywords: Cell migration; Intestinal homeostasis; Stem cell fate; Stochastic process; Theoretical modelling; Tissue mechanics.
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