Last modified: 2014-03-28

#### Abstract

*Physarum polycephalum* is a unicellular, multinucleate slime mold in the Mycetozoa group that exhibits remarkable capabilities, including the ability to construct efficient networks when foraging food [1].

The Physarum cell grows, as long as nutrition is abundant. When nutrition is limited, Physarum forms a network of interconnected veins; the veins are gel-like tubes in which the cytoplasm flows. It has been experimentally observed that, with two food sources, Physarum's tubular network often retracts to the shortest path between the food sources.

Tero, Kobayashi and Nakagaki [2] proposed a model for the dynamics of the Physarum, which in the computer simulations converged to the shortest path on any initial network. We analytically prove that, under this model, the mass of the mold has to eventually converge to the shortest path in the initial network between the two food sources, independently of the structure of the initial network or of the initial mass distribution.

This presentation is based on the work in [3,4] and is supported by the Italian Flagship Initiative "InterOmics" (PB.P05).

**References**

[1] Toshiyuki Nakagaki, Hiroyasu Yamada, Agota Toth: Maze-solving by an amoeboid organism. Nature 407:470 (2000)

[2] Atsushi Tero, Ryo Kobayashi, Toshiyuki Nakagaki: A mathematical model for adaptive transport network in path finding by true slime mold. Journal of Theoretical Biology 244: 553-564 (2007)[3] Vincenzo Bonifaci, Kurt Mehlhorn, Girish Varma: Physarum can compute shortest paths. Journal of Theoretical Biology 309: 121-133 (2012)

[4] Vincenzo Bonifaci: Physarum can compute shortest paths: A short proof. Information Processing Letters 113(1-2): 4-7 (2013)