Network design algorithm of a slime mold

[The slime mold Physarum polycephalum] “can find the shortest path through a maze (15–17) or connect different arrays of food sources in an efficient manner with low total length… yet short average minimum distance… between pairs of food sources… with a high degree of fault tolerance… to accidental disconnection (11, 18, 19)”

This paper provide a model of the slime mold’s network construction algorithm.

“When [Physarum] grows on a nutrient-rich substratum, it covers the surface as a coherent layer (like a pancake). If nutrition becomes limited, it forms fenestrae and finally transforms into a network of interconnected veins that enclose the entire cytoplasmic volume (see the figure). Each vein is a gel-like tube covered by a cell membrane and contains a core of fluid cytoplasm. By rhythmic contraction of its cytoskeleton, cytoplasm is continually pumped through these veins, and this continuous mixing seems to be the reason why all nuclei proceed synchronously through the cell division cycle. The network architecture is highly dynamic. Veins change in thickness, they may form and vanish again, and the plasmodium as a whole can crawl over its substratum, moving over centimeters in a couple of hours. Plasmodia usually do not dissociate. If food sources are spatially separated, such as oat flakes scattered over a wet surface, the plasmodial veins attempt to connect these food sources along the shortest possible pathways, even finding optimized paths through a maze (2). How this optimization is performed in terms of molecular mechanisms remains a challenging question.”

[The model is] “based on feedback loops between the thickness of each tube and internal protoplasmic flow (18–22) in which high rates of streaming stimulate an increase in tube diameter, whereas tubes tend to decline at low flow rates (23). The initial shape of a plasmodium is represented by a randomly meshed lattice with a relatively fine spacing … The edges represent plasmodial tubes in which protoplasm flows, and nodes are junctions between tubes.”

(commentary)

Atsushi Tero, Seiji Takagi, Tetsu Saigusa, Kentaro Ito, Dan P. Bebber, Mark D. Fricker, Kenji Yumiki, Ryo Kobayashi, and Toshiyuki Nakagaki. Rules for Biologically Inspired Adaptive Network Design. Science 327 (5964), 439. (22 January 2010)

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