On biological flow networks: Antagonism between hydrodynamic and metabolic stimuli as driver of topological transitions.

A plethora of computational models have been developed in recent decades to account for the morphogenesis of complex biological fluid networks, such as capillary beds. Contemporary adaptation models are based on optimization schemes where networks react and adapt toward given flow patterns. Doing so, a system reduces dissipation and network volume, thereby altering its final form. Yet, recent numeric studies on network morphogenesis, incorporating uptake of metabolites by the embedding tissue, have indicated the conventional approach to be insufficient. Here, we systematically study a hybrid-model which combines the network adaptation schemes intended to generate space-filling perfusion as well as optimal filtration of metabolites. As a result, we find hydrodynamic stimuli (wall-shear stress) and filtration based stimuli (uptake of metabolites) to be antagonistic as hydrodynamically optimized systems have suboptimal uptake qualities and vice versa. We show that a switch between different optimization regimes is typically accompanied with a complex transition between topologically redundant meshes and spanning trees. Depending on the metabolite demand and uptake capabilities of the adaptating networks, we are further able to demonstrate the existence of nullity re-entrant behavior and the development of compromised phenotypes such as dangling non-perfused vessels and bottlenecks. Author summaryBiological flow networks, such as capillaries, do not grow fully developed and matured in their final and functional form. Instead they grow a rudimentary network which self-organizes bit by bit in the context of their surrounding tissue, perfusion and other stimuli. Interestingly, it has been repeatedly shown that this development is mechano-transductional in nature, coupling complex bio-chemical signaling to mechanical cues such as wall-shear stress. In accordance with previous studies we propose a minimal hybrid model that takes into account stimuli in the form of the actual metabolite uptake of the surrounding tissue and the conventional wall-shear stress approach, and incorporate these into the metabolic cost function scheme. We present a numeric evaluation of our model, displaying the antagonistic interplay of uptake and shear stress driven morphogenesis as well as the topological ramifications and frustrated network formations, i.e. dangling branches, bottlenecks and re-entrant behavior in terms of redundancy transitions.