A Multicellular Model of Intestinal Crypt Buckling and Fission

Abstract

Crypt fission is an in vivo tissue deformation process that is involved in both intestinal homeostasis and colorectal tumourigenesis. Despite its importance, the mechanics underlying crypt fission are currently poorly understood. Recent experimental development of organoids, organ-like buds cultured from crypt stem cells in vitro, has shown promise in shedding light on crypt fission. Drawing inspiration from observations of organoid growth and fission in vivo, we develop a computational model of a deformable epithelial tissue layer. Results from in silico experiments show the stiffness of cells and the proportions of cell subpopulations affect the nature of deformation in the epithelial layer. In particular, we find that increasing the proportion of stiffer cells in the layer increases the likelihood of crypt fission occurring. This is in agreement with and helps explain recent experimental work.

Mathematical Models of Organoid Cultures

“…One advantage of these types of models is that they allow the agents to make decisions according to a set of rules and provide realistic heterogeneous patterns, which can be valuable in the study of organoid phenotypes. However, they require significant computation power as compared with aggregate or equation-based models; for instance, the model generated by Langlands et al (2016) and modified by Almet et al (2018) required approximately 13 min of CPU time for 100 simulated hours. Additionally, they demand coding skills to generate a customized simulation code or the use of dedicated software frameworks such as CHASTE or CGAL.…”

“…(A) A 3D model of intestinal organoids developed to investigate the distribution of cell populations and growth patterns provoked by Wnt and Notch signaling dynamics (Buske et al, 2012; Thalheim et al, 2018). (B) A 2D model of the cross section of a confluent intestinal epithelial layer, designed to study the biomechanical interactions between cells to produce crypt fission (Langlands et al, 2016; Almet et al, 2018). (C) Representation of a simulated optic-cup organoid (Okuda et al, 2018a).…”

“…Different proliferation properties of the two cell populations were not modeled. The model was recently extended by Almet et al (2018) to further explore the biomechanical properties involved in intestinal organoid crypt fission. Instead of defining Paneth and stem cells, they distinguished between soft cells (i.e.…”

Mathematical model for simulation of morphological changes associated to crypt fission in the colon

“…The biomechanism governing the abnormal crypt fission origin has not been completely understood, see [2,19,40]. In fact, some works link this origin to the APC mutations in the proliferative cells and to the activation of Wnt signaling, both responsible for an upward enlargement of the proliferation region, as discussed in [8,59,61,63,73], and considered in our model.…”

“…The activation of Wnt signaling and the transcription factors regulate cell proliferation and differentiation, leading to the expansion of stem cells and/or to the block of cell differentiation. Further researches, see [2] and [40], relate the biomechanism for fission to a heterogeneous distribution of stem and Paneth-like cells at the crypt base, that differ for their stiffness and adhesion at the crypt base. This situation leads to an overproduction of stem cells, and becomes responsible for normal crypt fission starting in the middle of the crypt base and for a buckling when it begins over the crypt base.…”