Branching geometry induced by lung self-regulated growth.

Branching morphogenesis is a widely spread phenomenon in nature. In organogenesis, it results from the inhomogeneous growth of the epithelial sheet, leading to its repeated branching into surrounding mesoderm. Lung morphogenesis is an emblematic example of tree-like organogenesis common to most mammals. The core signalling network is well identified, notably the Fgf10/Shh couple, required to initiate and maintain branching. In a previous study, we showed that the restriction by SHH of Fgf10 expression domain to distal mesenchyme spontaneously induces differential epithelial proliferation leading to branching. A simple Laplacian model qualitatively reproduced FGF10 dynamics in the mesenchyme and the spontaneous self-avoiding branching morphogenesis. However, early lung geometry has several striking features that remain to be addressed. In this paper, we investigate, through simulations and data analysis, if the FGF10-diffusion scenario accounts for the following aspects of lung morphology: size dispersion, asymmetry of branching events, and distal epithelium-mesothelium equilibrium. We report that they emerge spontaneously in the model, and that most of the underlying mechanisms can be understood as dynamical interactions between gradients and shape. This suggests that specific regulation may not be required for the emergence of these striking geometrical features.