Elsevier

Biophysical Chemistry

Volume 107, Issue 1, 1 January 2004, Pages 1-5
Biophysical Chemistry

Smart network solutions in an amoeboid organism

https://doi.org/10.1016/S0301-4622(03)00189-3Get rights and content

Abstract

We present evidence that the giant amoeboid organism, the true slime mold, constructs a network appropriate for maximizing nutrient uptake. The body of the plasmodium of Physarum polycephalum contains a network of tubular elements by means of which nutrients and chemical signals circulate through the organism. When food pellets were presented at different points on the plasmodium it accumulated at each pellet with a few tubes connecting the plasmodial concentrations. The geometry of the network depended on the positions of the food sources. Statistical analysis showed that the network geometry met the multiple requirements of a smart network: short total length of tubes, close connections among all the branches (a small number of transit food-sites between any two food-sites) and tolerance of accidental disconnection of the tubes. These findings indicate that the plasmodium can achieve a better solution to the problem of network configuration than is provided by the shortest connection of Steiner's minimum tree.

Introduction

The body of the plasmodium of Physarum polycephalum contains a network of tubular elements by means of which nutrients and chemical signals circulate through the organism in an effective manner [1], [2], [3]. Circulation is based on streaming through a complicated network of tubular channels. Thus, the geometry of the channel network is related to the exchange of chemicals within the organism. Since the tubes disassemble and reassemble within a period of a few hours in response to external conditions, this organism is very useful for studying the function and dynamics of natural adaptive networks.

When food sources were presented to a starved plasmodium that was spread over the entire agar surface as shown in Fig. 2a1 (the yellow shape corresponds to the organism), it concentrated at each food source. Almost the entire plasmodium accumulated at the food sources and covered each of them in order to absorb nutrient. Only a few thick tubes remained connecting the quasi-separated components of the plasmodium (see for example Fig. 2a3). Since the driving force for transportation is the difference of hydrostatic pressure along the tube, hydrodynamic theory implies that thick short tubes are in principle the most effective for transportation. By forming such a pattern, the organism derives the maximum of nutrient in the minimum of time. Hence this strategy is rather smart; it implies that the plasmodium can solve a complex problem. In order to investigate how this is done we studied the shape and properties of the tube networks formed in response to several different arrangements of food sources, distributed as shown in Fig. 1.

Section snippets

Organism and culture

The plasmodium of Physarum polycephalum was used. The sclerotia, which is a resting stage in the life cycle, formed on a filter paper (5×20 cm2) were soaked in water once and put on the plain agar gel (1%) in a trough (35×25 cm2). After 10 h, the plasmodium regenerated from the sclerotia and extended over the agar gel. The frontal part of the plasmodium was cut into many pieces (0.5×0.5 cm2), which were served for experiments.

Preparation of required shapes of the plasmodium, as the initial conditions prior to the application of food-sources

For the configuration of three food-sources as shown in Fig. 1a, a

Results

Fig. 2a–d reproduce some plasmodial tube networks we observed in response to food sources located at the vertices of an equilateral triangle. At the outset the plasmodium formed a fairly uniform circular sheet of tubes over the surface of the wet agar (a1:0 h). After the food sources had been present for a while most of the tubes had disappeared and a network of fine tubes took their place (a2:6 h). Later there remained only a few thick tubes connecting all three major components of the

Discussion

How does the organism obtain the smart solution? Two empirical rules describing changes in body shape are known: (1) tube of open ends are likely to disappear in the first step and (2) when two or more tubes connect the same two food sources, the longer tubes tend to disappear [3]. These changes in the tubular structure of the plasmodium are closely related to the spatio-temporal dynamics of cellular rhythms [1]. Shuttle streaming of protoplasm, which is driven by hydrostatic pressure induced

Conclusions

The Physarum plasmodium can construct an efficient transportation network which meets the multiple requirements of short length of network and low degree of separation between food sources, as well as tolerance of accidental disconnection at random position. The plasmodium can achieve a better network configuration than that based on the shortest connection of Steiner's minimum tree, which is impressive considering that it is very hard for humans even to deduce Steiner's connections for just a

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