A reaction–diffusion mechanism influences cell lineage progression as a basis for formation, regeneration, and stability of intestinal crypts

We present a mathematical model that contains Wnt and BMP, a cell lineage, and their feedback regulations to study formation, regeneration, and stability of multiple crypts. The computational explorations and linear stability analysis of the model suggest a reaction–diffusion mechanism, which exhibits a short-range activation of Wnt plus a long-range inhibition with modulation of BMP signals in a growing tissue of cell lineage, can account for spontaneous formation of multiple crypts with the spatial and temporal pattern observed in experiments. Through this mechanism, the model can recapitulate some distinctive and important experimental findings such as crypt regeneration and crypt multiplication. BMP is important in maintaining stability of crypts and loss of BMP usually leads to crypt multiplication with a fingering pattern.The study provides a mechanism for de novo formation of multiple intestinal crypts and demonstrates a synergetic role of Wnt and BMP in regeneration and stability of intestinal crypts. The proposed model presents a robust framework for studying spatial and temporal dynamics of cell lineages in growing tissues driven by multiple signaling molecules.The colonic crypt, a basic functional unit of the intestine, is made up of a single sheet of columnar epithelial cells, which form finger-like invaginations into the underlying connective tissue of lamina propria [1]. A human colon that consists of millions of crypts undergoes continual self-renewal and the intestinal epithelium is completely renewed within 3–5？days in humans [2]. Evidence has pointed to the location of the stem-cell population at the base of the crypt, within the stem-cell niche, formed by the stem cells themselves and mesenchymal cells that surround the crypt base [3]. Stem cells are thought to feed a spatial compartment above the crypt base where most cell proliferation occurs. This part of crypt is thought to house the transit-amplifying (TA) cells that may be committed to one o