NOLTA, IEICE
Paper

What do amoebae look before they leap?
— an efficient mechanism before
sporulation in the true slime moldPhysarum polycephalum —Hisa-Aki Tanaka 1 a) , Yuta Kondo 1 , and Hiroyuki Nei 1
1

Graduate School of Information Systems,
The University of Electro-Communications,
1-5-1 Choufugaoka, Choufu, Tokyo 182-8585, Japana)htanaka@uec.ac.jp

Received September 12, 2014; Revised December 5, 2014; Published April 1, 2015
Abstract: In this study, we investigate a moving behavior of the network which is observed
before an amoeba turns into ‘fruiting bodies’, namely it sporulates. More speciﬁcally, weobserve how Physarum polycephalum behaves after a severe environmental change; exposure tocertain strong light. Through systematic, controlled experiments (in constant dark condition,
26◦ C) we obtained four evidences, suggesting an eﬃcient mechanism of the network’s moving
by which Physarum polycephalum makes the sporulation more eﬀective, which is considered to
be important for its survival. Our ﬁnding adds a new knowledge to the biological aspect of
network science.
Key Words: spatio-temporal pattern, true slime mold, sporulation, network science

1. Introduction
A network formation from cellular level has been recently investigated in an amoeboid organism; thetrue slime mold (Physarum polycephalum). To elucidate a hidden mechanism and functioning of its
network formation, studies have been successively conducted in ‘maze solving’ [1], minimumrisk pathﬁnding [2], anticipation of periodic events [3], and searching for a solution to the traveling salesman
problem [4]. All these studies use an aggregate of plasmodium for Physarum polycephalum (Physarum,in short); an amoeboid organism stably maintained in a dynamic fan-like network structure (Fig. 1(a))
when the environment is suitable for its survival. In contrast to these studies, here we focus on anotherfacet of Physarum, i.e., a moving behavior of the network in the process when the amoeba is going toturn into ‘fruiting bodies’ (Fig. 1(b)), namely it sporulates. More precisely, we observe how Physarum
behaves in certain controlled environments before it sporulates after a severe environmental change;
exposure to certain strong light. To the authors’ knowledge, this sort of study has never been reported,
although we empirically know fruiting bodies are often formed in a relatively dry place, for example
on rotten trees or on the trunks of trees.

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Nonlinear Theory and Its Applications, IEICE, vol. 6, no. 2, pp. 275–284c
IEICE2015

DOI: 10.1588/nolta.6.275

Fig. 1. Life cycle of Physarum. (a) Plasmodium; a single cell giant amoeba.
(b) Fruiting body containing spores. (c) Sclerotia obtained from plasmodium
after dehydration.

This paper is organized as follows. In Section 2 we describe systematic, controlled experiments toinvestigate how the environment (i.e., humidity) aﬀects a spatial pattern of fruiting bodies formations.
Then, in Section 3 we show resulting four observations on the moving behavior of the network which
Physarum exhibits before sporulation. Implications and insights from these observations are discussed
in Section 4.

2. Methods
In all experiments, we used the plasmodium of the true slime mold Physarum polycephalum (sporulated and cloned in Ueda-Nakagaki Lab, in Hokkaido Univ.), which is regenerated from the sclerotia(Fig. 1(c)). It was cultured with oat ﬂakes for at least about a few days after regeneration fromsclerotia in the dark. Before experiments, the plasmodium was allowed to move and extend on a plain
agar plate (1%) in a trough at 26◦ C for 12 hours.

2.1 Experiment A: climbing and gathering behavior
Two kinds of materials (i.e., the amoebae) were prepared before experiments. One is the amoeba
which has been exposed to the strong light; three ﬂuorescent lights (27 W, FPL27EX-N, Panasonic)
from distance of ten centimeters for 6 hours. The other one was kept in a constant dark condition
at 26◦ C as described above. It is noted that this ﬂuorescent light has enough power at around 360
nm wavelength which is known to be one of eﬀective action spectra for sporulation [5], and thetemperature of the amoeba was carefully maintained at around 26◦ C during this exposure.
Then, certain amount of amoeba was cut out and put on the center of a glass plate with a wet
paper ﬁlter on it, and this glass plate was put steady in the cylindrical glass container (height 12 cm,
diameter 9 cm) as shown in Fig. 2. This container has a glass lid on the top, and there is an invisibly
small gap between the container and its lid. The average humidity in the container is around 90%
RH. All experiments were carried out under a static condition; 26◦ C, 50% RH, constant dark in an
incubator (Type KCL2000A, Eyela Co.). The behaviour of amoebae was continuously monitored by
a CCD camera (Fig. 2) under infrared lights with 945 nm wavelength which is known not to cause
any eﬀect on Physarum.

276

Fig. 2.

Fig. 3.
setup.

Experiment A setup.

Experiment B setup. (a) Setup in the incubator. (b) Detail of theFig. 4. Thin plastic container used in experiment B. (a) Detail of the container; plasmodium and agar gel on the left end, small vent holes on the rightend. (b) Local humidity measured inside the container. (Note, in this particular picture a larger agar band was put in the container.)

2.2 Experiment B: spatial distribution of fruiting bodies
To observe a moving behavior of the amoebae in a spatially sloped humidity condition, experiment B
was carried out. The experiment setup is essentially the same to the one of experiment A, but only
the glass container (Fig. 2) was replaced with a thin plastic container; sterile petri plate AW2000,
EIKEN Co., size: 14 cm × 10 cm × 1.5 cm (shown in Figs. 3 and 4).
In experiment A, the amoebae were allowed to freely move along the two dimensional surface inside277

the glass container (Fig. 2). In contrast, here in experiment B the amoebae were conﬁned in a thinplastic container (shown in Figs. 3 and 4), and the moving behavior of the amoebae is expected totake place in the two dimensional bottom of the container. (In fact, this expectation was veriﬁed inall (more than one hundred) trials shown in Section 3.2.) In addition, the local humidity inside thecontainer is easily controlled and measured (Fig. 4(b)), which is diﬃcult for the case of experiment A.
The mechanism by which the local humidity was spatially sloped in the thin container, is explained
as follows. As shown in Fig. 4(a), initially an agar gel band (14 cm × 2 cm × 0.6 cm) was cut out andput on the left end in the container. The container has 19 small vent holes on the right end; 2 mmdiameter, 5 mm distance with each other, and the container was set in a constant humidity in the
incubator. As the result, after a short transient, a spatially sloped local humidity; higher humidity
on the left and lower one on the right, was formed. This local humidity was precisely measured (asshown in Fig. 4(b)) by a humidity transducer (TA503-RGS, Toplas Engineering Co.). It is noted that
this spatially sloped local humidity was stably maintained during each trial.
Under the above static humidity pattern, the cultured and prepared amoebae of 0.01 g and foods(oat ﬂakes, 0.1 g) (see Section 2.1 for detail) were uniformly put on the agar gel band. The behaviourof amoebae was continuously monitored by a CCD camera as in experiment A.

3. Results
All results obtained from experiments A and B are shown in Table I.

3.1 Experiment A: climbing and gathering behavior
By analyzing the video records obtained in experiment A (Section 2.1), the following patterns (i) and(ii) are observed. For verifying each pattern multiple trials were carried out (as shown in Table I)
under the mentioned static condition in experiment A.
(i) With probability 87.5% (i.e., 7 out of 8 trials), the amoebae exposed to the strong light crawled upward and gathered at the upper part of the container before they form their fruiting bodies, (Fig. 5(a)).
In contrast, if the amoebae were not exposed to the strong light, they swept uniformly inside the conTable I. Statistics of experiments A and B, that examined fruiting bodyformations respectively.

ExperimentLight exposure time [min]Humidity [% RH]#(Trials)#(Sporulation)

A
360
50
11
8

A
None
50
10
0

A
360
Sealed18
8A
None
Sealed
10
0

B
360
90
25
25

B
None
90
16
1

B
360
50
25
24

B
None
50
18
0

Fig. 5. Fruiting bodies of Physarum formed in (a) the container with a smallloophole on the top, and in (b) the completely sealed container. White loops
indicate the regions where fruiting bodies are formed.

278

B
360
30
33
26

B
None
30
18
0

Fig. 6. Measured local humidity. (a) Two dimensional static pattern of local
humidity. Numbers indicate the local humidity at each point. (b) Local humidity distributions in one dimension; data sets ×, +, and ×+ are respectively
obtained under 90, 50, and 30% RH humidity in the incubator.

tainer and did not show any particular ‘climbing’ or ‘gathering’ behaviour.
(ii) In contrast to (i), if the gap of the container is completely sealed, the amoebae exposed tostrong light did not show any particular ‘climbing’ and ‘gathering’ behaviour before their sporulation(Fig. 5(b)). Instead, they formed fruiting bodies almost uniformly in the container for each trial.

3.2 Experiment B: spatial distribution of fruiting bodies
Figure 6 shows the measured local humidity inside the thin plastic container for experiment B. For
this measurement, only an agar gel band (14 × 2 × 0.6 cm) was put on the left end in the container;
the amoebae was not put in the container at this stage. A static, spatially sloped humidity patternis obtained as shown in Fig. 6(a), for instance, for 30% RH humidity condition in the incubator. As
we see in Fig. 6(a), two dimensional spatial patterns can be reduced to one dimentional distributions,since the local humidity is almost constant along the vertical axis for any given L. Hence, we measured
a reduced one dimensional distributions of the local humidity respectively for cases of 90, 50, and 30%
RH humidity in the incubator as shown in Fig. 6(b), after we have checked that the two dimensional
local humidity pattern is uniformly sloped (as shown in Fig. 6(a)) in each case. These three local
humidity distributions show a clear linear characteristics in the range of 2 ≤ L ≤ 14 cm as shown in
Fig. 6(b).
Figure 7(a) shows a typical spatial pattern of fruiting bodies formation in this experiment B. As
shown in Fig. 7(a), a ﬁne 0.5 × 0.5 cm mesh is introduced, and for each 0.5 × 0.5 cm small square
the following quantiﬁcation procedure is applied for counting fruiting bodies; if no fruiting body exist
it gives 0, if the area of fruiting bodies image occupies less than 30% it gives 1, if the area occupies
less than 60% larger than 30% it gives 2, if the area occupies less than 90% larger than 60% it gives
3, and if the area occupies larger than 90% it gives 4. This procedure was automatically done by animage processing software. Note that this procedure is reliable since fruiting bodies can be densely
formed but still separated with each other.
Figures 7(b), (c), and (d) respectively show the two dimensional histogram for multiple instances ofsporulation (shown in Table I) for the case of 90, 50, and 30% RH humidity in the incubator, which
is obtained through the above quantiﬁcation procedure. Figures 8(a), (b), and (c) show one dimensional spatial distributions of fruiting bodies respectively reduced from two dimensional histograms
Figs. 7(b), (c), and (d). The reduction to one dimensional distributions is made simply by summingup the elements in the two dimensional histogram for each L (i.e., the horizontal axis of the twodimensional histogram, 0 < L < 14 cm) and then by normalizing the total of the elements to unity.
Note that this reduction is reasonable since the values of the elements for a given L are not widely
spread over L (the vertical axis) as observed in Figs. 7(b), (c), and (d).
From the above two dimensional histograms (Fig. 7) and one dimensional distributions of fruiting
bodies (Fig. 8) the following observations are obtained.
(iii) If the amoeba exposed to strong light was put in a thin, ﬂat square container in which the local
humidity was almost spatially uniform between 95% RH and 90% RH, fruiting bodies were uniformly279

Fig. 7. Spatial pattern of fruiting bodies formation for three diﬀerent local
humidity patterns. (a) A typical formation pattern of fruiting bodies. (b), (c),(d) Two dimensional histograms of fruiting bodies distribution over multiple
instances; (b) sums 25 instances for the case of 90% RH humidity in the incubator, (c) 24 instances for the case of 50% RH humidity in the incubator, and(d) 26 instances for the case of 30% RH humidity in the incubator.

distributed in the container.
(iv) In contrast to (iii), if the local humidity was spatially sloped between 95% RH and 50% RH (or
30% RH), most fruiting bodies were formed in a range of the local humidity between around 75% RH
and 95% RH.
Finally, we investigate a time evolution of the network of the plasmodium. Figure 9 shows a typicaltime evolution of a network for the normal plasmodium (not exposed to strong light). As is observed inFig. 9 the network was always connected to the wet agar gel band on the left end and the plasmodium
stayed around the gel band, although its network was constantly transforming. In contrast to thenormal plasmodium, Fig. 10 shows a typical time evolution of a network for the plasmodium exposedto the strong light. Initially, the network was connected to the agar gel (as in the snapshots 1, 2,
3, 4, and 5 of Fig. 10). Then, right before the sporulation (the snapshot 8) the network was rapidly
extended (the snapshot 6). Eventually, the connection to the gel band was lost (the snapshot 7) andthe fruiting bodies were formed in a relatively dry area. It is reasonable to assume this observed
network dynamics explains how the spatial pattern in the observation (iii) is realized.

4. Discussion and conclusions
It is known that Physarum in the normal condition (not exposed to the strong light) prefers wet
environments (i.e., hygrotaxis). Actually, part of the observations (i) and (ii) in Section 3.1, and theobservation in Fig. 9 seem consistent to this fact, i.e., the amoebae not exposed to the strong lightalways stayed around the wet places. In contrast, the amoebae exposed to the strong light clearlylost this characteristic and eventually left from the wet places, as observed in (i), (ii) in Section 3.1,
and in Fig. 10. Now, the following questions naturally arise.
(a) Do the amoebae ‘intentionally’ search for a relatively dry place and head for there, right before
their sporulation? Or, do they merely lose their hygrotaxis before their sporulation? And,(b) how does the surrounding environment aﬀect a spatial pattern of fruiting bodies formation?
One possible, decent answer to the question (a) might be to attribute the sporulation of fruiting280

Fig. 8. Comparison of one dimensional spatial distributions of fruiting bodies. Graphs show one dimensional distributions of fruiting bodies over multiple
instances. (Note that these distributions are the probability distribution functions, and the uniform distribution gives the value of 1/14  0.0714 which isshown in Figs. 8(a), (b), and (c).) Data sets × indicate the associated local
humidity patterns respectively shown in Fig. 6(b). (a) Distribution for thecase of 90% RH in Fig. 6(b). (b) Distribution for the case of 50% RH in
Fig. 6(b). (c) Distribution for the case of 30% RH in Fig. 6(b). (d) Comparison of distribution (a) and distribution (b). (e) Comparison of distribution (b)and distribution (c).

bodies to a putative ‘threshold detector’ incorporated in the organism, which makes Physarum sporulate if a certain local humidity is sensed. Nevertheless, only such a ‘threshold detector’ does notclearly explain our observations in this study, because the network is not disconnected and goes backand forth until the sporulation (as shown in Fig. 10).
Although the question (a) seems diﬃcult to be answered at this stage, the observation (iii) in
Section 3.2 gives an answer to the question (b). Namely, only certain spatially sloped local humidity
condition in Section 3.2 is enough for Physarum to concentrate their fruiting bodies in a particularrange with moderate humidity from 75% RH to 95% RH.
One interpretation of the above answer in a real environment is as follows. After sporulation,
Physarum has to leap over the air as spores to increase the chance of survival. From this fact, theobservations (i), (ii), (iii), and (iv) suggest the following reasonable tactics of Physarum optimizing
the eﬃciency of sporulation. For instance in experiment A, after Physarum senses the local humidity
in the container, it concentrates its fruiting bodies around the gap, and this increases the chance ofsurvival after the sporulation. Similarly, in experiment B Physarum decreases the risk of death due
to dryness before sporulation, and at the same time it increases the chance of survival as spores after281

Fig. 9. Time evolution of a network for the normal plasmodium. Snapshots
are taken every 2 hours. In the snapshots 2, 3, 4, 5, 6, and 7, red areas indicate
the new additions to the previous snapshot obtained by an image processing
software, showing a newly swept area by the plasmodium network. Note thatthin red lines on the right in the snapshots 4 and 7 are due to a temporalmoisture and they are nothing to do with the plasmodium.

sporulation by forming fruiting bodies at a relatively dry place, i.e., by climbing up to a relatively
higher place in the real environment of woods, without using information from the sun light during thenight. To obtain a deeper understanding of the network behavior, further experiments and analysis
are required. For instance, in experiment B, a diﬀerent size of the container or diﬀerent local humidity
patterns are worth for investigating to see how the distribution of fruiting bodies formation is altered.

Acknowledgments
We thank Profs. A. Tero and T. Saigusa, and Profs. T. Nakagaki, T. Ueda, and R. Kobayashi for
helpful comments and discussions over the years. H. T. thanks W. H. Auden for his encouragement [6].

282Fig. 10. Time evolution of a network for the plasmodium exposed to thestrong light. Snapshots are taken every 2 hours. In the snapshots 2, 3, 4,
5, 6, and 7, red areas indicate the new additions to the previous snapshot
obtained by an image processing software, showing a newly swept area by theplasmodium network. In the snapshot 8, fruiting bodies are formed.

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