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Experimental models for Murray's law

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Title: Experimental models for Murray's law
Authors: Akita, Dai Browse this author
Kunita, Itsuki Browse this author
Fricker, Mark D. Browse this author
Kuroda, Shigeru Browse this author →ORCID
Sato, Katsuhiko Browse this author →KAKEN DB
Nakagaki, Toshiyuki Browse this author →KAKEN DB
Keywords: slime mold
transport network
scaling law
energy minimization
Issue Date: 18-Jan-2017
Publisher: IOP Publishing
Journal Title: Journal of Physics D : Applied Physics
Volume: 50
Issue: 2
Start Page: 024001
Publisher DOI: 10.1088/1361-6463/50/2/024001
Abstract: Transport networks are ubiquitous in multicellular organisms and include leaf veins, fungal mycelia and blood vessels. While transport of materials and signals through the network plays a crucial role in maintaining the living system, the transport capacity of the network can best be understood in terms of hydrodynamics. We report here that plasmodium from the large, single-celled amoeboid Physarum was able to construct a hydrodynamically optimized veinnetwork when evacuating biomass from confined arenas of various shapes through a narrow exit. Increasingly thick veins developed towards the exit, and the network spanned the arena via repetitive bifurcations to give a branching tree. The Hausdorff distance from all parts of the plasmodium to the vein network was kept low, whilst the hydrodynamic conductivity from distal parts of the network to the exit was equivalent, irrespective of the arena shape. This combination of spatial patterning and differential vein thickening served to evacuate biomass at an equivalent rate across the entire arena. The scaling relationship at the vein branches was determined experimentally to be 2.53-3.29, consistent with predictions from Murray's law. Furthermore, we show that mathematical models for self-organised, adaptive transport in Physarum simulate the experimental network organisation well if the scaling coefficient of the current-reinforcement rule is set to 3. In simulations, this resulted in rapid development of an optimal network that minimised the combined volume and frictional energy in comparison with other scaling coefficients. This would predict that the boundary shear forces within each vein are constant throughout the network, and would be consistent with a feedback mechanism based on a sensing a threshold shear at the vein wall.
Type: article (author version)
Appears in Collections:電子科学研究所 (Research Institute for Electronic Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 中垣 俊之

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