The nonlinear initiation of side--branching by activator-inhibitor-substrate (Turing) morphogenesis

Abstract

An understanding of the underlying mechanism of side--branching is paramount in controlling and/or therapeutically treating mammalian organs, such as lungs, kidneys, and glands. Motivated by an activator-inhibitor-substrate approach that is conjectured to dominate the initiation of side--branching in pulmonary vascular pattern, I demonstrate a distinct transverse front instability in which new fingers grow out of an oscillatory breakup dynamics at the front line, without any typical length scale. These two features are attributed to unstable peak solutions in 1D that subcritically emanate from the Turing bifurcation and that exhibit repulsive interactions. The results are based on a bifurcation analysis and numerical simulations, and provide a potential strategy toward developing a framework of side--branching also of other biological systems, such as plant roots and cellular protrusions.

7 pages, 5 figures

References in corpus (3)

• Branch Mode Selection during Early Lung Development
• Simulations demonstrate a simple network to be sufficient to control branch point selection, smooth muscle and vasculature formation during lung branching morphogenesis
• Stationary peaks in a multivariable reaction--diffusion system: Foliated snaking due to subcritical Turing instability

Cited by in corpus (4)

• Stationary peaks in a multivariable reaction--diffusion system: Foliated snaking due to subcritical Turing instability
• Instability mechanisms of repelling peak solutions in a multi-variable activator-inhibitor system
• Front propagation and global bifurcations in a multivariable reaction-diffusion model
• Emergence of rogue-like waves in a reaction-diffusion system: Stochastic output from deterministic dissipative dynamics