The morphology of a typical developing biological transportation network, the vein network of the plasmodium of the myxomycete Physarum polycephalum is analyzed during its free extension. The network forms a classical, regular graph, and has exclusively nodes of degree 3. This contrasts to most real-world transportation networks which show small-world or scale-free properties. The complexity of the vein network arises from the weighting of the lengths, widths, and areas of the vein segments. The lengths and areas follow exponential distributions, while the widths are distributed log-normally. These functional dependencies are robust during the entire evolution of the network, even though the exponents change with time due to the coarsening of the vein network.

The plasmodium of the slime mould Physarum polycephalum forms a transportation network of veins, in which protoplasm is transported due to peristaltic pumping. This network forms a planar, weighted, undirected graph that, for the first time, can be extracted automatically from photographs or movies. Thus, data from real transportation networks have now become available for the investigation of network properties. We determine the local drag of the vein segments and use these data to calculate the transport efficiency. We unravel which veins form the backbone of the transportation network by using a centrality measure from graph theory. The principal vein segments lie on relatively ample cycles of veins, and the most important segments are those that belong simultaneously to two of these principal cycles. Each principal cycle contains a series of smaller cycles of veins of lower transport efficiency, thus reflecting the hierarchical and self-similar structure of the transportation network. Finally, we calculate accessibility maps that show how easily different nodes of the network may be reached from a given reference node.

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3143 10The giant unicellular slime mould Physarum polycephalum forms an

The acellular slime mould Physarum polycephalum forms giant plasmodia that consist of an apical zone, which is succeeded by a vast network of veins where protoplasm is periodically transported back and forth. The apical zone is formed by a dense layer of viscoelastic cell material, whose leading edge is characterized by the development of undulations, which are called fingers. The dynamics of finger formation and evolution was studied. The front is characterized by alternating events of front advancement and stagnation, which are reflected in the development of the fingers. Therefore, the dynamics of the front was divided into two distinct, periodically alternating regimes. The dispersion relations, i.e., the growth rates of fingers of different wavelengths, observed in these two regimes were found to be symmetric, except for the sign of the growth rates. Furthermore, finger splitting occurred once the fingers reached a critical curvature. Our findings are discussed in terms of the intracellular dynamics of this slime mould.