Theory of branching morphogenesis by local interactions and global guidance

Abstract

Branching morphogenesis governs the formation of many organs such as lung, kidney, and the neurovascular system. Many studies have explored system-specific molecular and cellular regulatory mechanisms, as well as self-organizing rules underlying branching morphogenesis. However, in addition to local cues, branched tissue growth can also be influenced by global guidance. Here, we develop a theoretical framework for a stochastic self-organized branching process in the presence of external cues. Combining analytical theory with numerical simulations, we predict differential signatures of global vs. local regulatory mechanisms on the branching pattern, such as angle distributions, domain size, and space-filling efficiency. We find that branch alignment follows a generic scaling law determined by the strength of global guidance, while local interactions influence the tissue density but not its overall territory. Finally, using zebrafish innervation as a model system, we test these key features of the model experimentally. Our work thus provides quantitative predictions to disentangle the role of different types of cues in shaping branched structures across scales.

Dynamic Instability of Dendrite Tips Generates the Highly Branched Morphologies of Sensory Neurons

“…Other important aspects of dendrite morphology, such as branch diameters (Liao et al 2021) and the three-dimensionality of class IV cells (Han et al 2012), have not been included in the model. Moreover, the model does not take into account the guidance of class IV dendrites by external cues such as the cuticular epithelium (Parrish et al, 2009; Uçar et al, 2021) and other neurons (Grueber et al, 2002), though theoretical tools have recently been developed to incorporate these cues (Parrish et al, 2009; Uçar et al, 2021). Finally, the internal branches in our model are completely immobile, whereas we have observed internal branch movements with respect to the substrate.…”

Spatiotemporal dynamics of self-organized branching in pancreas-derived organoids

“…While each organ might possess a specific set of mechanisms for branching morphogenesis, both at the molecular and at the physical level 19,32 , minimal biophysical models using simple local rules have been shown to recapitulate important structural properties such as size or network topology, across a range of organs, established through self-organization 20,33 .…”

Dynamic instability of dendrite tips generates the highly branched morphologies of sensory neurons

“…Other important aspects of dendrite morphology, such as branch diameters ( 46 ) and the three-dimensionality of class IV cells ( 18 ), have not been included in the model. Moreover, the model does not take into account the guidance of class IV dendrites by external cues such as the cuticular epithelium ( 14 , 52 ) and other neurons ( 39 ), although theoretical tools have recently been developed to incorporate these cues ( 14 , 52 ). Last, the internal branches in our model are completely immobile, whereas we have observed internal branch movements with respect to the substrate.…”