Theory of branching morphogenesis via local interactions and global cues

Branching morphogenesis governs the formation of many organs such as lung, kidney, and the neurovascular system. Many studies have recently explored system-specific molecular and cellular regulatory mechanisms underlying single branching events. However, how large-scale tree structure arises from local interactions remains unclear. In particular, the respective role of stochasticity, self-organizing rules, and global cues such as guidance or repulsion in allowing for robust tissue growth is often poorly defined. Here, we develop a theoretical framework to describe a stochastic and self-organized branching process in the presence of external guidance, based on branching and annihilating random walks in an external potential. Using a continuum model for the angular alignment of branch segments with an external field, we quantitatively predict signatures of external guidance vs. local rules, such as angle distributions and the area invaded by the branched networks. We compare our theoretical results with experimental data on innervation of the zebrafish caudal fin and find good quantitative agreement. Our model provides a generic framework to explore directed tissue growth at different scales ranging from neuronal branching to epithelial branching such as in sprouting angiogenesis.