Regensburg 2010 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 27: Networks: From Topology to Dynamics V (joint session of BP, DY, SOE)

DY 27.2: Talk

Thursday, March 25, 2010, 16:15–16:30, H44

Regular graph properties of the plasmodial vein network of the slime mould Physarum polycephalum — Werner Baumgarten and •Marcus Hauser — Otto-von-Guericke-Universität Magdeburg, Abteilung Biophysik, Institut für Experimentelle Physik, Universitätsplatz 2, 39106 Magdeburg, Germany

The plasmodium of the slime mould Physarum polycephalum is a single multi-nucleate giant amoeboid cell. It forms a characteristic two-dimensional vein network, where the apical end of the plasmodium extends to search for new food sources, while the dense network of tubular veins is in charge of transport of protoplasm throughout the giant cell.

A graph theoretical analysis of the vein network of the Physarum polycephalum strain HU195×HU200 reveals that the nodes have exclusively the degree 3, i.e., each node connects to exactly three veins. This means that the vein network of this slime mould forms a regular cubic graph, and hence does not show small-world properties. The intensities of the edges (the vein segments) connecting a pair of nodes differ, thus forming a weighted graph. The distributions of the lengths and areas of the veins follow exponential distributions, while their widths are distributed either log-normally or normally. Interestingly, these functional dependencies are robust during the entire evolution of the growing plasmodial vein network of Physarum polycephalum.