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Modélisation du dialogue hôte-microbiote au voisinage de l’épithélium de l'intestin distal

Abstract : Human health and physiology relie both on human cells activity and on intestinal microbiota activity, as well as on their interactions. In Mammals, the intestinal epithelium is very densely folded, and the smallest fold is called the intestinal crypt. It is also the simplest unit of the host-microbiota crosstalk. The size of a crypt, which is made of approximately 700 cells, and the detailed knowledge that we have of its functionning are amenable to build a detailed mathematical model. We constructed an individual-based model of epithelial cells interacting with chemicals produced by the microbiota which diffuse in the crypt lumen. This model is formalised as a piecewise determinist Markov process. It accounts for: local interactions due to cell contact (among which are mechanical interactions); cell proliferation, differenciation and extrusion which are regulated spatially or by chemicals concentrations; chemicals diffusing and reacting with cells. We demonstrate the convergence of the stochastic individual-based model to a deterministic model under the assumption of large population. A second limit model is obtained formally when the size of cells goes to 0. We aim at obtaining deterministic limit model because they can be simulated much faster, and can be used to improve understanding of the stochastic model or can be coupled with a model of the whole colon. The three models are implemented, convergence of models is shown numerically, and simulations of the individual-based model are analysed to show that qualitative behaviour of the crypt is reproduced.
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https://tel.archives-ouvertes.fr/tel-03145857
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Submitted on : Thursday, February 18, 2021 - 4:21:27 PM
Last modification on : Wednesday, January 19, 2022 - 4:58:35 PM
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  • HAL Id : tel-03145857, version 1

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Léo Darrigade. Modélisation du dialogue hôte-microbiote au voisinage de l’épithélium de l'intestin distal. Probabilités [math.PR]. Université Paris-Saclay, 2020. Français. ⟨NNT : 2020UPASM008⟩. ⟨tel-03145857⟩

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