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

The question of whether a single-celled organism without a brain could have functions such as learning and memory has been the subject of much debate in recent years. The plasmodium of the true slime mold, Physarum polycephalum, is an ideal model organism for such a question. The plasmodium exhibits behaviors that resemble intelligence, including solving mazes, mimicking optimal rail transportation networks, predicting the weather, and solving traveling salesman problems. In addition, the plasmodium has recently been shown to have the simplest form of learning: habituation. In the experiments in which plasmodia were repeatedly allowed to cross bridges containing aversive chemicals, the habituation behavior has been confirmed. It has been shown that the habituation process involves chemicals that are stored internally. However, it is not clear how these chemicals result in change in the behavior of plasmodium during habituation learning. This study focused on the transport tube network formed in plasmodium during the above experiments. Then, the role of the network morphology in the habituation learning process was investigated. The results showed that the network morphology changes from tree to mesh type during habituation learning, and disrupting the learned network reduces habituation behavior. In addition, it was shown that the thickness oscillation frequency depends on the network morphology. The study found that in the plasmodium of P. polycephalum, a primitive organism without a brain, transport tube networks, instead of neuronal networks, play an important role in habituation learning and the resulting decision making.

Keywords: slime mold, memory, habituation, transport tube, network, Physarum polycephalum

The question of whether single-celled organisms without brains have functions such as learning and memory has been much debated in recent years, and the importance of this question has been widely recognized (Dussutour, 2021; Gunawardena, 2022; Wright et al., 2023). Although the definition of learning has long been discussed for animals with brains and nervous systems, it can be extended to single-celled organisms as follows: “learning” is a change in the internal state of a system in response to external stimuli, followed by an appropriate change in the behavior in response to the same stimuli (Barron et al., 2015). From this perspective, the learning function has been reported in a variety of single-celled organisms; examples include E. coli (Yi et al., 2000), Stentor (Rajan et al., 2023), Spirostomum (Eisenstein et al., 1982), and Paramecium (French, 1940; Hanzel and Rucker, 1972).

In this context, the plasmodium of the true slime mold, Physarum polycephalum, is an ideal model organism. Although it is a single-celled organism, it behaves as if it has “intelligence” in a diorama environment artificially constructed in a laboratory (Nakagaki, 2021). After Nakagaki et al. demonstrated in 2000 that the plasmodium of P. polycephalum can solve mazes (Nakagaki et al., 2000a), a variety of important studies relating to their “intelligence” have been conducted. The slime mold can find the shortest path (Nakagaki et al., 2004), optimize railway networks (Tero et al., 2010; Watanabe et al., 2011), predict weather (Saigusa et al., 2008), solve traveling salesman problems (Zhu et al., 2013; Zhu et al., 2018), and more.

The plasmodium is a vegetative form of the true slime mold of P. polycephalum. It is a very large amoeboid cell, ranging in size from a few millimeters to several meters. It crawls around in the environment while changing its shape (William et al., 1986). Because the plasmodium has many nuclei within its single-cell body, it can survive even if part of it is separated from the rest of the cell. Then, the separate parts behave as individuals. Meanwhile, there is a network structure of transport tubes, i.e., veins, inside the cell body (Takamatsu et al., 2017). These tubes are responsible for transporting the contents of the cell, cytoplasm (including the nucleus, nutrients, and oxygen), throughout the body. This is an essential structure for the plasmodium that must maintain a large cell body. The outer part of the transport tube is a harder structure consisting of gel, while the inner part consists of a softer material, cytosol. As the plasmodium crawls and spreads through the environment, the hard and soft parts can change their states with each other through sol-gel transformation (Kamiya, 1959). This allows the transport tube network to change shape easily, resulting in an efficient network that responds to the surrounding environment (Takamatsu et al., 2009; Tero et al., 2010; Ito et al., 2011; Takamatsu et al., 2017). For example, in an environment with aversive chemicals or under starvation, the network forms a dendritic or tree structure; in a nutrient-rich environment, it forms a mesh structure with a thin sheet-like structure at the front (Takamatsu et al., 2009).

Recently, studies have directly examined the learning function in plasmodium of P. polycephalum (Boisseau et al., 2016; Vogel and Dussutour, 2016; Boussard et al., 2019). These studies have focused on the simplest form of learning, habituation. Habituation, classified as non-associative learning, is a phenomenon in which the response to repeated stimuli decreases. To determine this phenomenon as a form of learning, nine criteria were initially established (Thompson and Spencer, 1966), and later, a tenth was added (Rankin et al., 2009). In the above studies, seven criteria were met: decreased response to repeated stimuli, sensory recovery, dependence on stimulus frequency, dependence on stimulus intensity, stimulus specificity, and dishabituation (Boisseau et al., 2016; Vogel and Dussutour, 2016) or long-term habituation (Boussard et al., 2019). This learning memory is found to be closely related to the cellular uptake and retention of stimulus chemical substances given during learning (Boussard et al., 2019), but it is not known how exactly the chemicals from the environment act on the internal system of the plasmodium, nor how the information is stored and how they cause changes in the behavior of plasmodium.

This study focused on the transport tube network formed in plasmodium. The transport tubes of plasmodium adaptively change in thickness in response to the flow rate of the cytoplasm (Tero et al., 2007). The thickening follows nonlinear dynamics and then generates bipolar states, such as thick or thin; this property is analogous to the phenomenon of neuronal firing. Furthermore, it was shown by a combination of experimental analysis and mathematical modeling that information applied locally can be retained in the spatial gradient of transport tube thickness, and it was suggested that a single transport tube itself could have a memory function (Kramar and Alim, 2021). It is expected that networks composed of transport tubes with such properties will provide plasmodium with more advanced information processing functions beyond that of a mere single cell.

Inspired by the habituation experiments of Boisseau et al. (2016) on plasmodium , this study examined the relationship of transport tube network morphology to the learning process and memory of habituation, and we discuss how memory information is read out and output to plasmodium behavior.

Prior to the following procedure, plasmodia of P. polycephalum are cultured on 1.5 w/v% agar medium (FUJIFILM Wako pure chemical industries), fed oat flakes (Premium Pure Oats, Nippon food manufacture), and incubated for approximately 1 day at 25°C in the dark.

The basic experimental setup consists of a start block, bridge block, and goal block, as shown in Figure 1. The start and goal blocks are food blocks made of 1.0 w/v% agar containing 10 g w/v% oat-flake-grind extract (Takamatsu et al., 2009). They are circular in shape, 18 mm in diameter and 3–4 mm thick. The bridge block is made of 1.0 w/v% agar with or without containing 0.5 mM Quinine hydrochloride dihydrate (FUJIFILM Wako pure chemical industries), which are used for Quinine experiments or control experiments, respectively. Quinine was used to inhibit the plasmodium from crossing bridges for habituation training in the same manner as in the experiments of Boisseau et al. (2016). Quinine is an alkaloid and an aversive chemical substance for the plasmodium. It was reported that application of this substance slowed the flow of cytoplasm (Kamiya, 1959), and temporarily inhibited the progress of the plasmodium on agar medium containing this substance (Takagi et al., 2007). The bridge blocks are rectangular, 18 × 18 mm in size, and 3–4 mm thick. The bridge blocks are placed between the start and goal, as shown in Figure 1B.

Thirty setups shown in Figure 1B (almost half of them were for Quinine experiments, while the rest were for control experiments) were placed on two large plastic plates (square bio assay dish, 245 × 245 mm, Corning Inc.) for a single experiment set. To avoid systematic effects, Quinine and control setups were alternately placed on the large plates. In total, eight sets of experiments were performed on different days in different seasons (October and November 2019; July, August, October, and November 2020; and February and March 2021) in Shinjuku, Tokyo. The samples were illuminated with transmitted light by yellow-LED illumination plate (around 580 nm; LM8C 311X455-35Y AItec) to avoid light and thermal response of plasmodia (Ueda et al., 1988). The experiments were performed in a thermostatic and humidistatic chamber at 25 ± 0.3°C, with a relative humidity of 85% ± 3% (PR2KT; ESPEC Corp, Japan).

The transmitted light images were recorded with a digital camera (body: EOS RP; lens: EF24 mm F2.8 IS USM, Canon Inc.) at 5 min intervals for approximately 24 h. Image resolutions were 0.06–0.08 mm/pixels. For the analysis of thickness oscillations, the images were captured at 5 s intervals for 10 min. The original raw images were converted linearly to 8-bit gray scale images using image processing software [Photoshop, Adobe Inc; Fiji (Schindelin et al., 2012)]. The images in the figures have been linearly adjusted in brightness and contrast according to their purpose, so that any description can be easily understood. In Figure 1A, Figure 3A, and Figure 9, the treatment focuses on the entire plasmodium on the three blocks. In Figures 1C, D, Figures 2D–I, the treatment focuses on the plasmodium on the bridge. In Figures 2A, B, Figure 3C, Figure 6 and Figure 7, the treatment focuses on the network formed by the plasmodium on the goal block.

Eight datasets were used for behavior analysis, including measuring area and speed. Six datasets were used for network analysis. Three datasets were used for connection analysis. One dataset was used for thickness oscillation analysis.

A single set of experiments lasted for 6 days, from Day 0 to Day 5. For these experiments, plasmodia are cut from the fan-shaped frontal part of the cultured plasmodium (§2.1) so that the total amount is 0.085 g. As the wounds of the freshly collected plasmodia are not sufficiently healed, the Day 0 procedure is performed before the test experiments of Day 1–5 are begun. The fresh plasmodia are transferred to the start block on Day 0 (Figure 1A). The plasmodium begins to spread on the bridge block, then reaches the goal block, and finally covers it. The goal block covered by the plasmodium is detached from this setup, and then used for Day 1’s experiment (Figure 1C). On Day 1, the plasmodium at start position begins to spread on the new test bridge, then reaches and covers the new goal. These procedures are repeated until Day 4.

On Day 5, the goal plasmodia of Day 4 are divided into 4 groups named intact, cutoff, horizontal, and reverse, respectively as shown in Figure 2. The first group (intact) of the goal plasmodia are placed intact at the start of the Day 5 experiment, the same as the experiments of Days 1–4 (Figures 2D, F). The second group (cutoff) of the goal plasmodia are placed at the start after being cut in a Y-shape so that the transport tube network becomes disconnected (Figures 2B, C, G). In this procedure, the plasmodium are scratched 2–3 mm wide by gently sliding a spatula over the agar surface. Care is taken not to damage the agar surface. This procedure divides the single plasmodium into three parts as shown in Figure 2B. Note that the block are placed at starting position after their wound has healed and the three separate parts become a single body. The third and fourth groups (horizontal and reverse) of the goal plasmodia of Day 4 are placed after rotating their orientations by 90 o and 180 o from the original direction at the start positions of Day 5, respectively (Figures 2H, I).

The procedure of placing the start block of Day N is performed at almost the same time in 1 day, which is defined as time 0 in actual time (Figure 3). Then, the experiment day finishes at actual time = 1440 min, including preparation time for the next-day experiment (Figure 3B).

Two different time definitions are introduced: stage time (Figures 3A, B) and network time (Figure 3C). The stage time t = t 0 = 0 is defined when the plasmodium on the start block begins to cross the test bridge (Figure 3A). Then, at time t e , the plasmodium reaches the upper edge of the bridge block, which is in contact with the goal block. The plasmodium then enters the goal block followed by the covering state. The goal block has finished being covered by the plasmodium at t = 320 in this example. Through this event, the transport tube network is formed on the goal block. This network formation is observed until the time for preparation of the next day’s experiment begins, which is defined as network time t n = 0 (Figure 3C). Therefore the value of the network time t n is negative during covering state, whose definitions are used in Figures 6A–H and Figures 7A–H.

Areas of plasmodium on the bridges were estimated using Fiji (Schindelin et al., 2012). The background image, which is the image at t 0 (second part of Figure 3A) was subtracted from the image at t e (third part of Figure 3A; Supplementary Figure S1A). Only the part of plasmodium on the bridge was extracted by thresholding the image (Supplementary Figure S1B) so that it is binarized (Supplementary Figure S1C). Then, the pixels were counted.

The speed of the plasmodium on the bridge was estimated as [bridge length (mm)]/[t e − t 0 (min)]. The speed of progression strongly depends on the environment of the day (wind exposure in the thermostatic and humidistatic chamber, season, and parentage of the plasmodium). To compensate for such effects, the speed data were normalized with the mean speed of the samples of a control experiment performed on the same day.

The tube networks at goals were characterized by two-dimensional Fourier transform analysis that captures the spatio-periodic structure. The goal image at time t n was cropped into a square for Fast Fourier transform (FFT) analysis using the Fiji plugin (Supplementary Figure S2A), and then the power spectrum was obtained (Supplementary Figure S2B), which includes direction angles and power values. The angle values were weighted by power value, and then the distribution of tube orientation was obtained (Supplementary Figure S2C). Note that the 180o − 360o data were not included in the analysis because the spectrum is point symmetric. Finally, the major orientation angles of transport tubes in a goal network at time t n were estimated as the mode of the distribution, as shown Supplementary Figure S2C, which was obtained by density estimation using the R software (R Core Team, 2023). Note that the estimated angle values are orthogonal to the orientation direction of the tube, as shown in Supplementary Figure S2D.

Characteristic angles of the day were estimated from the time course of the orientation angles. The characteristic angles were plotted in terms of daily change. These plots were manually classified from Type 0 to Type 4 with the conditions blindfolded. See §3.1.3 for details.

The thickness oscillations of plasmodia on the start block during the 10 min before they begin to cross the bridge were analyzed (Supplementary Figure S3). The area of 320 × 320 pixels (about 20 × 20 mm2) was divided into smaller areas of 10 × 10 pixels, and then the transmitted light intensity of the plasmodium of this area was averaged for each smaller area to obtain the time series data, as shown in Supplementary Figure S3A. The time series data were smoothed by locally-weighted polynomial regression using the R “lowess” function to remove noise. The oscillation periods were estimated as the times between two successive peaks of this waveform. Then, the mode of the period distribution was used as the measure of period T of the small area, and the value was converted into angular frequency as 2π/T. Supplementary Figure S3B shows the spatial distribution of the angular frequencies. Supplementary Figure S3C shows a histogram of the angular frequency obtained from the data of Supplementary Figure S3B. Note that the data above half (more strict threshold than usual) of the Nyquist frequency (2π ⋅ [f n /2], where the Nyquist frequency f n = 0.1) were omitted as noise. The median of this distribution was taken as the representative value of the oscillation frequency of the plasmodium on the start block, whose value was used in §3.4.

To determine the significance of the data, the normality and equal variance of the data groups were first subjected to the Shapiro and Bartlett tests, respectively. For data groups for which the normal distribution and equal variance were not rejected, the Dunnett test was applied as a multiple test, and for the other data groups, the Steel test was applied. The results of statistical analysis are summarized in Supplementary Table S1. These statistical analyses were performed using R.

The experimental process is divided into two phases. The first phase is the process of learning “habituation” in Day 1–4, and second phase is the process of deletion of “learning memory”. It should be noted that the terms such as “habituation” are used here according to the findings by reports on plasmodium of P. polycephalum (Boisseau et al., 2016; Vogel and Dussutour, 2016; Boussard et al., 2019), not in the original psychological sense. Control and Quinine experiments were always simultaneously performed.

The habituation experiments were performed from Days 1–4. On each day, the start block, which is the goal block of the previous day’s experiment and is covered with the plasmodium, was placed in contact with the bridge, as shown in Figures 1B–D. The plasmodium began to spread on the bridge (t = t 0 in Figure 3A) after 10 min to several hours (Supplementary Figures S4A, B), irrespective of control or Quinine experiments. The tip portion of the plasmodium finish the bridge crossing at t = t e (Figure 3A). It took 1–2.5 h for the control and 1.5–3.5 h for the Quinine experiments to finish the bridge crossing (Supplementary Figures S4C, D), whose details are discussed in §3.1.2. Then, the plasmodium covered the goal block over a 3–10 h period (Supplementary Figures S4E, F). The time for covering took longer with the passage of days in both the control and Quinine experiments. Finally, the tube network of plasmodium was formed over the start, bridge, and goal blocks, as shown in the final panel of Figure 3A (t = 1275; details are discussed in §3.3). The above behaviors can be seen in Supplementary Movie S1 for control experiments and Supplementary Movie S2 for Quinine experiments. The difference in characteristics of control and Quinine experiments appeared in the area on the bridges (§3.1.1) and speed of crossing them (§3.1.2), as Boisseau et al. (2016) reported.

As seen in Figure 1, the shape and area of the plasmodia on the bridges over the Day 1–4 experiments were quite different between control and Quinine experiments. In the control experiments, the plasmodium spread in thin sheets over the bridge, with little daily variation in shape (Figure 1C). The area on the bridge also changed little over the days, but tended to decrease slightly on Day 4, as shown in Figure 4A. On the contrary, in the Quinine experiments, the shape (Figure 1D) and area (Figure 4B) changed markedly over the days. On Day 1, the shape is string-like and the area is very small. Each day thereafter, the shape changed to a branch-like shape with the sheet area increased (Figure 1D), and the area increased significantly (Figure 4B). These trends are consistent with the results of Boisseau et al. (2016).

With respect to the raw data of speed of the plasmodium crossing the bridge, the results differed slightly from those of Boisseau et al. (2016). As shown in Supplementary Figure S5A, the speed in the control experiment decreased over days, whereas the results of Boisseau et al. showed no change. In the Quinine experiment, the speed seemed to increase slightly over days but not statistically significantly, whereas the results of Boisseau et al. showed a significant increase.

The difference between Boisseau et al.’s experimental setup and ours is in the preparation method of the start and goal blocks and in the concentration of Quinine in the bridge. The start and goal blocks contained 10% blended oat flakes in their setup, whereas ours contained 10 g w/v% oat-flake-grind extract because it was needed to increase the light transparency of the blocks for observation of the transport tube network. The latter is less attractive as nutrition than the former. This would affect the result of speed reduction in the control experiment. In addition to this, the tendency of reduction was not always observed: half of the eight sets of experiments showed a different tendency. As mentioned in §2.6, the speed would be affected by the environment condition of the day of experiment. Therefore, speed was evaluated using values normalized by those of the control experiment of the same date.

Figure 5 shows the speed of the Quinine experiment normalized with the mean speed of the control samples performed on the same day. Then, it is concluded that the normalized speed increases statistically significantly over days.

Together with the results of §3.1.1 and §3.1.2 and compared with the results of Boisseau et al., it can be concluded that the plasmodium learnt to overcome the danger of the bridge under repeated experiences, thus learning of “habituation” was established.