Colon crypts, a single sheet of epithelia cells, consist of a periodic pattern of stem cells, transit-amplifying cells, and terminally differentiated cells that constantly renew and turnover. Experimental evidence suggests that Wnt signaling promotes and regulates stem cell division, differentiation, and possible cell migrations while intestinal BMP signaling inhibits stem cell self-renewal and repression in crypt formation. As more molecular details on Wnt and BMP in crypts are being discovered, little is still known about how complex interactions among Wnt, BMP, and different types of cells, and surrounding environments may lead to de novo formation of multiple crypts or how such interactions affect regeneration and stability of 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.