Berlin 2018 – wissenschaftliches Programm

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BP: Fachverband Biologische Physik

BP 10: Postersession II

BP 10.54: Poster

Montag, 12. März 2018, 17:30–19:30, Poster C

Limitations of Murray's law in a dynamic network — •Noah Ziethen, Felix Bäuerle, Nico Schramma, and Karen Alim — Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany

The morphology of biological networks is often regarded as the result of optimization under a given demand. Optimization for minimal dissipation under cost for the maintenance of a tubular network leads to a relation between the radii of tubes meeting at a network node, denoted Murray's law. So far, the theoretical prediction of Murray's law has been found to agree surprisingly well with what seems to be any kind of vascular networks ranging from plants and animals. Contrary to the uni-directional flows in vascular networks the slime mould Physarum polycephalum exhibits oscillatory shuttle flow, providing an excellent test case to investigate the limitations and underpinnings of Murray's law.

Here, we image and analyze the dynamic network morphology of P. polycephalum over time. Quantification of Murray's law does not yield accordance with the theoretical predictions. A widely spread distribution of branching ratios was observed in which the mean value did not agree with Murray's law. Nevertheless, a decreasing trend of the branching ratio was observed. The time evolution of the decrease correlated with the phenomenon of pruning. The relation between the local branching ratio and the different regions of the slime mould showed a slightly different distributions in branching ratios for pruning and non-pruning regions.