Mathematical analysis of the effect of portal vein cells on biliary epithelial cell differentiation through the Delta-Notch signaling pathway.

A portal vein cell induced a high Notch signal in its neighboring cells, which corresponded to epithelial differentiation, depending on the production rates of Delta ligands and Notch receptors. In addition, this epithelial differentiation tended to occur in conditions where fine-grained patterning was reported to be lacking. These results highlighted the potential importance of the stability towards homogeneity determined by the production rates in Delta ligands and Notch receptors, in a disturbance-dependent epithelial differentiation.