Mesoscale regulatory mechanisms of branch formation generating hierarchical structure of the lung

The lung airways are characterized by long and wide proximal branches and short and thin distal branches. In this study, we investigated the emergence of this hierarchical structure through experimental observations and computational models. We focused on the branch formation in the pseudoglandular stage and examined the response of mouse lung epithelium to fibroblast growth factor 10 (FGF10) by monitoring extracellular signal-regulated kinase (ERK) activity. The ERK activity increased depending on the epithelial tissue curvature. This curvature-dependent response decreased as the development progressed. Therefore, to understand how these epithelial changes affect branching morphology, we constructed a computational model of curvature-dependent epithelial growth. We demonstrated that branch length was controlled by the curvature dependence of growth that was consistent with the experimental observations and lung morphology. However, the branching of the thin branches is suppressed in this model, which is inconsistent with the fact that thin branches in the lung are short. Thus, we introduced branch formation by apical constriction, which was shown to be regulated by Wnt signaling in our previous studies. Mathematical analysis indicated that the effect of apical constriction is cell shape-dependent, suggesting that apical constriction ameliorates the branching of thin branches. Finally, we were able to provide clarity on the hierarchical branching structure through an integrated computational model of curvature-dependent growth and cell shape regulation. We proposed that curvature-dependent growth involving FGF and Wnt-mediated cell shape regulation coordinate to control the spatial scale and frequency of branch formation.