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Maze-solving by an amoeboid organism


The plasmodium of the slime mould Physarum polycephalum is a large amoeba-like cell consisting of a dendritic network of tube-like structures (pseudopodia). It changes its shape as it crawls over a plain agar gel and, if food is placed at two different points, it will put out pseudopodia that connect the two food sources. Here we show that this simple organism has the ability to find the minimum-length solution between two points in a labyrinth.


We took a growing tip of an appropriate size from a large plasmodium in a 25 × 35 cm culture trough and divided it into small pieces. We then positioned these in a maze created by cutting a plastic film and placing it on an agar surface. The plasmodial pieces spread and coalesced to form a single organism that filled the maze (Fig. 1a), avoiding the dry surface of the plastic film. At the start and end points of the maze, we placed 0.5 × 1 × 2 cm agar blocks containing nutrient (0.1 mg g−1 of ground oat flakes). There were four possible routes (α1, α2, β1, β2) between the start and end points (Fig. 1a).

Figure 1: Maze-solving by Physarum polycephalum.
figure 1

a, Structure of the organism before finding the shortest path. Blue lines indicate the shortest paths between two agar blocks containing nutrients: α1 (41 ± 1 mm); α2 (33 ± 1 mm); β1 (44 ± 1 mm); andβ 2 (45 ± 1 mm). b, Four hours after the setting of the agar blocks (AG), the dead ends of the plasmodium shrink and the pseudopodia explore all possible connections. c, Four hours later, the shortest path has been selected. Plasmodium wet weight, 90 ± 10 mg. Yellow, plasmodium; black, ‘walls’ of the maze; scale bar, 1 cm. d, Path selection. Numbers indicate the frequency with which each pathway was selected. ‘None’, no pseudopodia (tubes) were put out. See Supplementary Information for an animated version of a–c .

The plasmodium pseudopodia reaching dead ends in the labyrinth shrank (Fig. 1b), resulting in the formation of a single thick pseudopodium spanning the minimum length between the nutrient-containing agar blocks (Fig. 1c). The exact position and length of the pseudopodium was different in each experiment, but the path through α2 — which was about 22% shorter than that through α1 — was always selected (Fig. 1d). About the same number of tubes formed through β1 and β2 as the difference (about 2%) in their path lengths is lost in the meandering of the tube trajectory and is within experimental error.

The addition of food leads to a local increase in the plasmodium's contraction frequency, initiating waves propagating towards regions of lower frequency1,2,3,4,5, in accordance with the theory of phase dynamics6. The plasmodial tube is reinforced or decays when it lies parallel or perpendicular, respectively, to the direction of local periodic contraction7; the final tube, following the wave propagation, will therefore link food sites by the shortest path.

To maximize its foraging efficiency, and therefore its chances of survival, the plasmodium changes its shape in the maze to form one thick tube covering the shortest distance between the food sources. This remarkable process of cellular computation implies that cellular materials can show a primitive intelligence8,9,10.


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Correspondence to Toshiyuki Nakagaki.

Supplementary information

Contraction waves in the plasmodium extending in a maze just after the food supply was added. Waves were visualized by monitoring the accompanying rhythmic changes in the thickness of the plasmodium utilizing video image analysis (see Ueda et al. Exp. Cell Res. 162, 486-494; 1986). Red, green and blue correspond to an increase, no change and a decrease in the plasmodium thickness compared to the state 30 s earlier, respectively. Colour bar represents a cycle of the pattern variations. In the early stages after the food is supplied, as the plasmodium 'solves' the maze, the contraction waves increase in size and decrease in number, often propagating to and from the food-sites. (MOV 2600 kb)

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Nakagaki, T., Yamada, H. & Tóth, Á. Maze-solving by an amoeboid organism. Nature 407, 470 (2000).

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