Relation between learning process and morphology of transport tube network in plasmodium of Physarum polycephalum

To study the state of the learning memory in the plasmodium, we focused on the network of transport tubes that form over the goal block. Figure 6 and Figure 7 show the typical results of network formation on the goal blocks after crossing control and Quinine bridges, respectively. In the control experiments, the branching network (tree) was formed, and there was little day-to-day change in the network morphology (Figures 6A–D). On the contrary, in the Quinine experiments, the network morphology changed from a tree structure to a mesh structure over the course of days (Figures 7A–D).

These typical images of the networks were obtained from the final states of the network formation process, which lasts from the covering stage to the end of the observation of the day (Supplementary Movie S3 for control experiment and Supplementary Movie S4 for Quinine experiment). To quantify the process of network formation, the orientation angles of transport tubes were examined. Figures 6E–H and Figures 7E–H show the time course of the orientation angles. For example, in Figures 6E, G, H (control, Day 1, 3, and 4), and Figure 7E (Quinine, Day 1), the orientation angles of tubes were always approximately parallel (approximately 10–30 o ) to a direction denoted by arrows in Figures 6A, 7B, which is the direction of the plasmodium advancing during network formation. This characterizes the tree network. Meanwhile, in Figures 7F–H (Quinine, Day 2–4), the orientation angles were initially only parallel, but later, vertical angles (about 70–80 o ) were added to the end. This final state characterizes the mesh network. This correspondence between orientation angle and network formation was later used to automatically determine the classification of network shapes for a large number of samples.

The angle data from t n = −300 to t n = 0 of Figures 6E–H and Figure 7E–H were used to determine the final states. Figures 6I–L and Figures 7I–L show the distributions of the above data. The peak angles obtained from the distribution were used as the characteristic angle of the day for the following statistical analysis of the daily change.

Figure 8 shows the classification of network formation according to the daily change in characteristic angle. The typical daily changes are shown in Figures 8B–F. In Figure 8B, the major tube orientations are always parallel to the direction in which the tip of the plasmodium was advancing (Type 0). This indicates that the network is always a tree. In Figures 8C–F, the orientation of tubes changes to multidirectional on Day 4–1, respectively (named type 1–4, respectively). Here, the multidirectional tubes indicate that the network is mesh type. As shown in Figure 8A, Type 0 and 1 are the majority in the control experiment, while Type 2–4 are the majority in the Quinine experiment. This quantitative analysis supports the observations of the typical case described at the beginning of this section.

As shown in §3.1.3, it was confirmed that the network morphology changed during the learning process of “habituation” in the Quinine experiment. This indicates that the network morphology relates to the state of the learning memory of the plasmodium. To verify this hypothesis, Day 5 experiments were performed to see whether memory status changes when the network of the start blocks is artificially disrupted or when the start blocks are placed at different orientations. Figure 2 shows a typical view of plasmodium spreading on bridges after these manipulations. In the control experiment, there is not much change in the area after cutting the network (Figure 2E; Supplementary Movie S5) compared to the intact case (Figure 2D). On the contrary, in the Quinine experiment, after cutting or changing direction of the network, the area is smaller than in the intact case (Figures 2F–I; Supplementary Movie S6). These results can be statistically confirmed through the quantitative analysis of the area, as shown in Figure 4. In addition, in the Quinine experiment, when the network is manipulated, the speed of crossing the bridge becomes smaller than for the intact case, as shown in Figure 5. Taken together, these results suggest that there is a strong relationship between learning memory and the maintenance of network morphology.

As shown in §3.1.3, the network formation differed between the control and Quinine experiments. To investigate how these different networks are formed, the type of tube connection between the start and goal blocks was examined (Figure 9). There are four types of connections: there is no connection between the start block and the goal block, as shown in Figure 9A (Type n); the number of connection tubes is single, double, and triple, as shown in Figures 9B–D (Type s, d, and t), respectively. Note that type t also categorizes the case where the number of connection tubes is greater than three. The observation ratio of Type n increases with the passage of days, regardless of whether the experiment is control or Quinine (Figures 9E, F). It should be noted that the values grow much larger in the Quinine experiments, especially on Days 2–4. On the contrary, the ratios of Types s and d significantly decrease with the days in the Quinine experiments, while they are almost constant in the control experiments (Figures 9G–J). Finally, on Day 4, the case that the start and goal blocks are strongly connected is dominant in the control experiments, whereas the case of no-connection is dominant in the Quinine experiments. This suggests that the strength of connection affects network formation on the goal block.

To confirm this assumption, the ratio of connecting types was examined for each type of network formed in the goal, as shown in Figure 10. In the control, tree networks are very common, and the results are concentrated in the cases of strong connections (Type s, d, and t; Figure 10A). A small number of mesh networks can also be observed in the control experiments, but they are more common in the absence of connections (Type n; Figure 10B). In contrast, in the Quinine experiments, Type n connection is the most frequently observed in the mesh networks, as shown in Figure 10D.

To summarize the above results, a tree-type network is formed when start and goal blocks are connected through transport tubes. Conversely, if plasmodia on both blocks are separated by bridges containing repellent materials, the network will be formed only within the goal block, resulting in a mesh-type network. In the control experiment environment, the plasmodium on the start and goal blocks remained strongly connected via tubes developed on the bridges (Figures 9B–D). In this dumbbell-shaped morphology of the plasmodium, the cytoplasm of the plasmodium frequently moves back and forth between the start and goal, autocatalytically strengthening the connection between the two portions (Nakagaki et al., 2000b; Takamatsu et al., 2000). Thus, the reciprocal flow of protoplasm from the start to goal direction (arrow direction shown in Figure 6A) may have led to the development of transport tubes parallel to this direction, resulting in the formation of a tree-shaped network. Meanwhile, in the Quinine experiment environment, the start and goal blocks became separated as the number of experimental days passed, and the networks were formed only on the goal block (Figure 9A). Of course, plasmodia sometimes remain in the start block as well; however, we will ignore them here because they will not be used in the next day’s experiment. The reason for the division of the two blocks is supposed to be due to the tendency of the plasmodium to escape from aversive chemicals contained in the bridge blocks. Within a limited area on the goal block, no cross-sectional cytoplasmic flow over the goal block is observed. In addition, the goal contains nutrition, on which it is known that a mesh-type network is formed (Takamatsu et al., 2009; Ito et al., 2011). Due to both above effects, a mesh network would be formed in the later days of the Quinine experiment.

Based on the above results, after crossing a Quinine bridge, a tree network is formed in the goal block on Day 1 or 2 in most cases, and a mesh network is formed on Day 3 or 4. Meanwhile, the area of plasmodium on a bridge increases with the passage of days, and the relative crossing speed also increases. To investigate how these different morphologies of networks affect the bridge-crossing behavior of the plasmodium, the thickness oscillation of the plasmodium at the start blocks was investigated. Figure 11 shows the oscillation frequency in the Quinine experiments normalized by the median of the control data on the same day (see Supplementary Figure S6 for the original data). The frequencies are lower on Days 1 and 2 compared to the control data (denoted by 1.0 of the normalized angular frequency) and then become higher on Days 3 and 4. The results suggest that higher frequency of thickness oscillation assists the plasmodium to pass through the Quinine bridge, increasing its speed and spreading area. To confirm this hypothesis, the relations between oscillation frequency and the quantitative indices of behavior of the plasmodium on the bridges, such as area and speed, were analyzed. However, it was difficult to find direct correlations between the frequency and the behavioral indices (Supplementary Figure S7), which might be due to the wide dispersion of the data.

Then, the oscillation frequency data were analyzed separately for each network morphology to clarify what causes the oscillation frequency to rise on the later days, as shown in Figures 12A, B. Regardless of whether it was a control or Quinine experiment, the frequency of plasmodium oscillations in the mesh networks was always higher than in the tree networks. This indicates that the network morphology is a factor in controlling the oscillation frequency.

Similarly, the effect of network morphology on behavioral indices was investigated, as shown in Figures 12C–F. Both area and speed were found to be greater when the plasmodium placed at the start formed a mesh network than a tree network in the Quinine experiment, while there was no significant difference in network morphology in the control experiment.

We trained plasmodium of true slime mold P. polycepharum to cross a bridge containing Quinine, an aversive substance, in accordance with the procedure of Boisseau et al. (2016). As shown in the results of §3.1.1 and §3.1.2, we confirmed that “habituation learning” was established after 4 days of training in Quinine experiment, which agreed with the results of Boisseau et al. (2016), who conducted the first habituation experiment with plasmodium. The experiments performed by Boussard et al. (2019) showed that the uptake and retention of the stimulants given during the learning process are deeply involved in the mechanism of habituation. However, it is unclear how the uptake chemicals act on the plasmodia themselves to bring the memory function and how this memory results in changes in the behavior of the plasmodia.

We hypothesized that the key to the answer lies in the transport tube network of plasmodium, and we quantitatively examined the network morphology formed in the goal, as shown in §3.1.3. In the Quinine experiment, most formed a tree network in the goal on the first day, and their morphology changed to a mesh network over the course of daily repetitive stimulation (Figure 7; Figure 8). If the retention of the aversive chemical taken into the cell is the only factor important for memory retention, then disrupting the network should not result in a change in habituation behavior (memory deletion). However, when the network formed after learning was disrupted or redirected, the behavior changed as if the memory had been deleted (§3.2). Therefore, it is reasonable to hypothesize that not only the uptake of the chemical, but also the morphology of the transport tube network would assist the habituation behavior in some manner.

In fact, it has already been shown that the morphology of the network depends on the chemical substances in the environment (Takamatsu et al., 2009). From this, it can be deduced that the uptake of chemicals from the environment changes the internal state of the plasmodium, namely, the physical properties of the intracellular sol and/or outer gel, which leads to a change in the network morphology. For “habituation memory”, the uptake of chemicals into the cell would be necessary to rewrite the internal state, and the change in network morphology would be necessary as a gateway to the output (Figure 13).

The learning mechanism connecting from network morphology to habituation behavior has not been elucidated. As a candidate mechanism, we expected that the thickness oscillation of plasmodium would act as a pump because of the following reports: it is known that different network morphologies produce different spatio-temporal oscillation patterns (Takamatsu et al., 2001); it has been reported that the oscillation frequency of plasmodium is high in the attractive environment and low in the aversive environment (Takahashi et al., 1997). Our experiment results confirmed that the oscillation frequency is higher when a mesh network is formed (§3.4; Figure 12B). Meanwhile, the behavioral indices of habituation, the area and speed of plasmodium spreading on the Quinine bridges, were higher when a mesh network was formed than when a tree network was formed, (Figure 12D, F). The results of these two quantitative analyses lead to the inference that the formation of the mesh network may assist the action of crossing the Quinine bridge by increasing the oscillation frequency. However, no direct evidence was found to support the hypothesis that thickness oscillations act as a pump to support the bridge cross. Further investigation is needed on this.

The following questions also remain. In the Quinine experiments, as discussed previously, the relationship between habituation behavior and network morphology was clear: the plasmodium was inactive in crossing the Quinine bridge when the network was a tree, and it was active when it was a mesh. In contrast, in the control experiment, there was little change in behavior whether the network was a tree or mesh. This does not lead to the conclusion that the morphology of the network simply causes changes in behavior. Actually, the environment for the plasmodia of the goal blocks is complicated in this experimental setup: the goal block contains a nutrient medium, while the learned plasmodium additionally uptakes an aversive chemical substance. These complex factors need to be investigated in future studies.

In this paper, from the memory deletion experiment, we have shown that transport tube network in addition to the retention of the chemicals plays an important role in habituation behavior in plasmodium. There would be advantages for the system where information input from the outside is not only stored internally in the form of concentration of chemical substance, but also converted into transport tube network morphology. This is because external stimuli can take various forms, such as thermal and mechanical stimuli in addition to stimuli by chemical substances. It was mentioned in the Introduction section that the transport tubes of plasmodium have neuron-like properties. Moreover, the thickness of transport tubes can be strengthened or weakened by the relationship between the oscillations of the parts (phase difference of the oscillation), resulting in the formation of different morphologies of transport tube networks. This reminds us of strengthening synapses in neurons and the formation of neural networks. Although learning functions in various single-celled organisms are widely reported, plasmodium may be the closest single-celled organism to a neural network because of the transport tube network. It would be important to study such primitive networks to hypothesize their evolution into more sophisticated neural networks.

We thank all members of “Ethological dynamics in diorama environment”, Grant-in-Aid for Transformative Research Areas (A), MEXT, Japan for their useful discussion.

This work was supported by the MEXT KAKENHI Grant-in-Aid for Transformative Research Areas (A) 22H05693 for AT and JSPS KAKENHI Grant-in-Aid for Scientific Research (C) 19K03774 for AT.

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

The manuscript presents research on animals that do not require ethical approval for their study.

AT contributed to conception and design of the study. EY developed the experimental system and performed the experiments. EY and AT performed the data analysis of the results. EY wrote the first draft of the manuscript in Japanese. AT rewrote the manuscript. All authors contributed to the article and approved the submitted version.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fcell.2023.1249165/full#supplementary-material

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.