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

OBJECTIVE: The Delta-Notch signaling pathway induces fine-grained patterns of differentiation from initially homogeneous progenitor cells in many biological contexts, including Drosophila bristle formation, where mathematical modeling reportedly suggests the importance of production rate of the components of this signaling pathway. In contrast, the epithelial differentiation of bile ducts in the developing liver is unique in that it occurs around the portal vein cells, which express extremely high amounts of Delta ligands and act as a disturbance for the amount of Delta ligands in the field by affecting the expression levels of downstream target genes in the cells nearby. In the present study, we mathematically examined the dynamics of the Delta-Notch signaling pathway components in disturbance-driven biliary differentiation, using the model for fine-grained patterns of differentiation. RESULTS: 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. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s13104-021-05656-y.