Abstract

Artificial linking of two isolated culture dishes is a fascinating means of investigating interactions among multiple groups of microbes or fungi. We examined artificial interaction between two isolated dishes containing Euglena cells, which are photophobic to strong blue light. The spatial distribution of swimming Euglena cells in two micro-aquariums in the dishes was evaluated as a set of new measures: the trace momentums (TMs). The blue light patterns next irradiated onto each dish were deduced from the set of TMs using digital or analogue feedback algorithms. In the digital feedback experiment, one of two different pattern-formation rules was imposed on each feedback system. The resultant cell distribution patterns satisfied the two rules with an and operation, showing that cooperative interaction was realized in the interlink feedback. In the analogue experiment, two dishes A and B were interlinked by a feedback algorithm that illuminated dish A (B) with blue light of intensity proportional to the cell distribution in dish B (A). In this case, a distribution pattern and its reverse were autonomously formed in the two dishes. The autonomous formation of a pair of reversal patterns reflects a type of habitat separation realized by competitive interaction through the interlink feedback. According to this study, interlink feedback between two or more separate culture dishes enables artificial interactions between isolated microbial groups, and autonomous cellular distribution patterns will be achieved by correlating various microbial species, despite environmental and spatial scale incompatibilities. The optical interlink feedback is also useful for enhancing the performance of Euglena-based soft biocomputing.

1 Introduction

Societal formation and ecological development are underpinned by interactions between groups of organisms, manifesting in nature as an ecological balance between two or more species [16, 19, 37]. In the microbial world, cooperative interaction is exemplified by the symbiosis between coral and zooxanthella [3, 33, 36, 38], in which the coral shelters the zooxanthellae and receives nutrients from their photosynthesis. By contrast, competitive interactions involve attack and repulsion, such as the coexistence of phage and bacteria [6, 13, 34]. In these examples, the cooperative or competitive interaction [10,12, 18] drives the microbial cell distribution into optimal spatiotemporal patterns. Therefore, by artificially controlling these interactions, we can realize biocomputing information processing such as optimum pattern formation or combinatorial optimization [1, 2, 26, 32]. Indeed, the dynamical control of spatial network configuration by an artificial feedback mechanism has been explored for spatially represented combinatorial optimization, where the autonomously formed spatial network was further reconfigured through connectivity-analyzing feedback [20], showing a high potential for interaction feedback of network optimization and analysis. However, even with available gene-modification technologies, the artificial control of natural microbial interactions is extremely difficult. Encouraging two microbial species to interact is further limited by habitat differences and by the scale difference between their body sizes. Consequently, no laboratory-scale artificial microbial interactions have been examined.

A promising means of inducing interaction among microbial cells is offered by phototaxis or chemotaxis. For instance, Euglena gracilis is photophobic to strong blue light. When exposed to such a light, it escapes by changing its swimming direction [5, 8, 9, 23, 24]. We have developed an optical feedback system in which an arbitrary blue light pattern is projected on a closed micro-aquarium containing a group of Euglena cells [27]. Using the optical feedback system, we performed Euglena-based neural computing and demonstrated strong performance in searching for multiple solutions to a simple combinatorial optimization problem [29]. In this previous demonstration, video images of Euglena cells swimming in the micro-aquarium were processed on a personal computer (PC) to obtain the feedback illumination pattern of blue light. When the data of swimming Euglena cells in two discrete feedback systems is transferred from one PC to another, the Euglena cells contained in the separate systems can be correlated with each other, enabling an artificial interaction between the two Euglena groups.

In this report, we demonstrate artificial interaction between two isolated Euglena cell cultures by means of an optical interlink feedback that transfers data between the separate feedback systems. Under digital interlink feedback, we explore simple rules for correlating the cellular distribution patterns in the two dishes, and elucidate the relationship between various rule combinations and their resulting patterns. Analogue interlink feedback is also examined by projecting patterns of blue light onto one dish with intensity proportional to the cell density in the counter dish. In this experiment, we analyze the temporal evolution of the cell-distribution patterns. The artificial interlink feedback is potentially expandable to different microbial species and to networks of multiply-interlinked dishes.

2 Experiments

2.1 Feedback System

Figure 1 is a block diagram of the optical feedback system used in our interlink experiments. The main components are an optical microscope (Olympus, BX51) with a 5× objective lens, a polydimethylsiloxane (PDMS) micro-aquarium contained in a culture dish, a video camera (Trinity, IUC-200CK2), a liquid-crystal projector (Sanyo, LP-XU84) with reduced-projection lenses, and a PC (Fujitsu, MG/D70N) for data processing. 200–400 Euglena gracilis cells were confined in each of two micro-aquariums. The dishes containing the micro-aquariums were placed on individual microscopes, and illuminated from their bottom sides by a blue light pattern produced by the PCs and projectors. The key function of the feedback system was to project a strong blue light with an arbitrary spatial pattern onto the micro-aquarium so as to evacuate the Euglena cells from the illuminated areas through their photophobic responses. The feedback system is detailed in our previous reports [27].

Figure 1. 

Signal-flow diagram of interlink feedback system. The data set of TM, calculated by processing the captured images, was transferred to the counter system. For each system, an illumination pattern was independently generated according to the rule imposed on the system and the exchanged TM data set, and projected to the micro-aquarium in the dish. Blue-light illumination induces the photophobic response of Euglena cells in the micro-aquarium.

Figure 1. 

Signal-flow diagram of interlink feedback system. The data set of TM, calculated by processing the captured images, was transferred to the counter system. For each system, an illumination pattern was independently generated according to the rule imposed on the system and the exchanged TM data set, and projected to the micro-aquarium in the dish. Blue-light illumination induces the photophobic response of Euglena cells in the micro-aquarium.

Euglena gracilis strain Z is an ideal target microbe for artificial interaction via optical interlink feedback, since the cells are blue-light photophobic, sufficiently large for observation, and easily cultured by photosynthesis [21, 25, 30, 35]. The cells generally swim forward, but change their swimming direction in the presence of a strong blue light [5, 8, 9, 23, 24]. Because of this photophobic response, the probability that a cell enters the illuminated area is heavily reduced, and the cell density declines in the illuminated area. The cells suspended in Cramer-Myers (CM) medium [7] in the micro-aquariums survived for a week or longer, requiring no extra nutrition. The cell movements were observed with red light, which induces no photophobic response. The micro-aquariums were of two designs: one with 16 spokes around a central circle extending to an outer diameter of 2.5 mm (Figure 2a), the other with 25 squares connected by short pathways and an outer edge of 2.8 mm (Figure 2f). The depth of each micro-aquarium was 150 μm, which allows the cells to swim across without collision, even for a large number of cells (more than ten thousand). When the number of Euglena cells in the micro-aquarium was reduced below 100, the fluctuation of TM values (for TM values, see the next subsection) became too large to stabilize illumination versus non-illumination status on the spokes or squares. The minimum number of cells required for the successful computation was thus estimated to be approximately 100. When the cell number exceeded 1000, the chance of flipping between illumination and non-illumination was reduced by too small fluctuation of TMs, which resulted in a longer computing time. Therefore, the optimum number of Euglena cells in the micro-aquarium for successful computation is 100–1000.

Figure 2. 

(a, top left) Whole real image of a 16-spoke micro-aquarium, captured by a video camera. The outer diameter of the 16-spoke pattern is 2.5 mm. (b, top middle) Enlargement of the real image in (a). Euglena cells were observed as black rods (typical size 3 × 9 pixels). (c, top right) Differentiated and binarized image produced from two subsequent real images. Extracted movements of Euglena cells are plotted as red spots. To guide the eye, the outer edge of the micro-aquarium and areas of blue-light illumination are superimposed on the image. (d, bottom left) Trace image produced by superimposing 10 differentiated and binarized images. Swimming trajectories of Euglena cells are indicated as red lines. The movement extracted from the 10th frame is shown in white to indicate direction of motion. (e, bottom middle) Whole view of a trace image of the 16-spoke micro-aquarium. (f, bottom left) Whole view of a trace image of the 25-square micro-aquarium. The outer edge of the 25-square pattern is 2.8 mm.

Figure 2. 

(a, top left) Whole real image of a 16-spoke micro-aquarium, captured by a video camera. The outer diameter of the 16-spoke pattern is 2.5 mm. (b, top middle) Enlargement of the real image in (a). Euglena cells were observed as black rods (typical size 3 × 9 pixels). (c, top right) Differentiated and binarized image produced from two subsequent real images. Extracted movements of Euglena cells are plotted as red spots. To guide the eye, the outer edge of the micro-aquarium and areas of blue-light illumination are superimposed on the image. (d, bottom left) Trace image produced by superimposing 10 differentiated and binarized images. Swimming trajectories of Euglena cells are indicated as red lines. The movement extracted from the 10th frame is shown in white to indicate direction of motion. (e, bottom middle) Whole view of a trace image of the 16-spoke micro-aquarium. (f, bottom left) Whole view of a trace image of the 25-square micro-aquarium. The outer edge of the 25-square pattern is 2.8 mm.

The two feedback systems were interlinked by exchanging the evaluation data of swimming Euglena cells via a LAN cable connecting the two PCs, as described in Section 2.2. Although the data exchange between the two systems was not synchronized completely, the time delay observed was within 2–3 time steps (within 5 s) in most of the experiments, which did not unduly affect the results. The data flow (image, signal, value, and light) is presented in Figure 1.

2.2 Evaluation of Cell Activity

To evaluate the swimming activity of Euglena cells in specific areas (16 spokes or 25 squares) of the micro-aquarium, the captured images of the cells were processed as follows.

  • Capture an image of the micro-aquarium (real image; see Figure 2a). Euglena cells were observed as black or gray rods typically sized 3 × 9 pixels, as shown in Figure 2b.

  • Binarize the differential between two subsequent real images with a fixed threshold. This process extracts the moving cells, as shown in Figure 2c.

  • Superimpose ten subsequent binarized differential images to produce a trace image. This process yields the trajectories of moving cells, as shown in Figure 2d and e.

  • Count the number of “on” pixels inside the 16 spokes (or 25 squares in Figure 2f) in each trace image. The resulting counts, called trace momentums (TMs) in this article, represent the swimming activity of Euglena cells in the corresponding areas.

  • Use the TMs to illuminate the blue-light pattern generated by the imposed rule (algorithm), as described in the next subsection (2.3).

  • Proceed to the next cycle by flashing the superimposed trace image.

Steps (i) to (vi) were executed in a single time step, consuming approximately 1.6 s of running time. A single experiment was conducted in 4000 time steps.

The measured TM directly reflects the cell activity in the area, which depends on the number and speed of cells swimming in the area. Since Euglena cells frequently entered or departed a particular spoke or square, TM was a dynamic, spontaneously changing variable. Furthermore, TM gradually decreased in blue-light-illuminated areas, as the cells deserted the region. The time constant of the TM decrease (increase) at a step change of illumination off to on (on to off) was approximately 1 min (20 s) for the micro-aquarium with 16 spokes. The large difference between the two time constants is due to whether Euglena cells migrate out from the spokes with rotation (when illumination was turned on) or they swim straight in (when illumination was turned off). The TM values cannot follow the illumination changes faster than these time scales. Therefore, the temporal evolution of the interlink feedback is governed mainly by the illuminations (and non-illuminations) sustained longer than the two time constants.

2.3 Interlink Feedback Algorithm

The algorithm in the feedback system generates illumination patterns from the set of observed TM values. During the interlink feedback experiments, the TM values obtained from one culture dish (dish A) were instantly transferred to the PC of the counter system, and an illumination pattern to the counter dish (dish B) was generated by the counter PC, and vice versa. Digital and analogue feedback operations were examined in the 16-spoke and 25-square micro-aquariums, respectively.

In digital feedback experiments, the algorithm selected (illuminated) eight out of 16 spokes, according to two individual rules (out of four listed below) imposed on the systems. The four rules were formulated as follows:

  • (1) 

    Select the eight least popular (smallest TMs) spokes in the counter dish.

  • (2) 

    Select the spokes opposite the eight most popular (largest TMs) spokes in the counter dish.

  • (3) 

    Select the spokes immediately to the right of the eight most popular spokes in the counter dish.

  • (4) 

    Select the eight most popular spokes in the counter dish.

The digital feedback experiments adopted two of the above rules, each imposed on one of the systems. The number of spokes illuminated by blue light was always eight for both dishes. Some combinations of the above rules (e.g., (1) and (2)) can be satisfied by a stable illumination pattern, whereas the rule combination (1, 4) cannot be stably satisfied by a fixed pattern. More specifically, the rule combination (1, 2) is satisfied when the same spokes are illuminated in each dish while maintaining the opposite spokes non-illuminated. Note that neither system knows the rule imposed on the counter system. Instead, each system seeks stable solutions to its individually imposed rule. The intensity of blue light was approximately 12 mW/cm2.

Figure 3 shows an example of the temporal evolution of the observed illumination pattern under the rule combination (1, 2). At time step t + dt, blue light was projected on dish B according to rule (1), referring to the eight least popular spokes in dish A at time step t. Conversely, dish A was illuminated according to rule (2), referring to the eight most popular spokes in dish B at time step t. Illuminating a particular spoke induces the escape of Euglena cells from that region, reducing the local TM in the following time steps. In Figure 3, three or four of the eight most popular spokes remain under illumination, showing that the illumination patterns appearing during these time steps were not stable.

Figure 3. 

Production of blue-light illumination patterns, shown as a flowchart. The eight most popular spokes (numbered 1–8 in the chart, where 1 is the most popular) were selected by TM count. The illumination patterns in the next time step were generated by exchanging TM data sets with those of the counter dish, and applying the imposed rule to each system. In this chart, rule (1) was to select the eight least popular (smallest TMs) spokes of the counter dish, while rule (2) was to select the spokes opposite to the eight most popular (largest TMs) spokes of the counter dish. Illumination induces the photophobic response of Euglena cells in the next time step. As the Euglena cells enter and exit the spokes, the TMs change spontaneously. The entry probability is reduced by illuminating the spoke with blue light, in turn reducing the TMs of that spoke in the following time steps.

Figure 3. 

Production of blue-light illumination patterns, shown as a flowchart. The eight most popular spokes (numbered 1–8 in the chart, where 1 is the most popular) were selected by TM count. The illumination patterns in the next time step were generated by exchanging TM data sets with those of the counter dish, and applying the imposed rule to each system. In this chart, rule (1) was to select the eight least popular (smallest TMs) spokes of the counter dish, while rule (2) was to select the spokes opposite to the eight most popular (largest TMs) spokes of the counter dish. Illumination induces the photophobic response of Euglena cells in the next time step. As the Euglena cells enter and exit the spokes, the TMs change spontaneously. The entry probability is reduced by illuminating the spoke with blue light, in turn reducing the TMs of that spoke in the following time steps.

In the analogue feedback experiments using the 25-square micro-aquariums, the intensity of blue light in square i in dish A was determined as
formula
where and denote the TM of square i and the largest TM, respectively, in dish B, and k is a constant (20 mW/cm2). Similarly, the blue-light intensity in square i in dish B was determined by
formula
Since the threshold intensity of blue light that triggers a photophobic response differs widely among Euglena cells, the cell density in a specified square decreases with increasing blue-light intensity, reducing the TM in that square. The analogue interlink algorithm, governed by Equations 1 and 2, therefore models competition between the cell densities of square i in dish A and dish B.

3 Results

3.1 Pattern Operation with Digital Interlink Feedback

Figure 4a shows the temporal evolution of a digital feedback experiment imposing rules (1) and (2) on dish B and dish A, respectively. The figure displays the number of spokes satisfying each rule as a function of time. Prior to time step 400, the feedback was inactive; that is, no blue light was projected on either dish, but approximately half of the spokes satisfied both rules accidentally with stochastic fluctuations. Shortly after feedback illumination was initiated at time step 400, the number of spokes satisfying the rules rapidly increased, and both rules were completely satisfied by time step 1162. Although occasional changes of illumination pattern were observed thereafter, the illumination pattern established at time step 1162 stably remained.

Figure 4. 

(a, top) Temporal evolution of the number of spokes satisfying rules (1) and (2). For rule (1), the number of spokes with the same illumination status (on or off) as the counter dish was counted. For rule (2), the number of spoke pairs (a spoke and its direct opposite) with one illuminated and one non-illuminated spoke was counted. The interlink feedback was suspended (no application of blue light) until the 400th time step. The number of spokes satisfying both rules converges, indicating that rules (1) and (2) were simultaneously and stably satisfied after 1162 time steps. (b, bottom) The trace images of the micro-aquarium at the 4000th time step. The number of cells in dish A is smaller than in dish B. All cells in dish A and the vast majority in dish B remained in the non-illuminated spokes and the central circle, due to photophobic responses. A small number of cells occupied the illuminated spokes in dish B, indicating that they were insensitive to blue-light illumination at the given intensity.

Figure 4. 

(a, top) Temporal evolution of the number of spokes satisfying rules (1) and (2). For rule (1), the number of spokes with the same illumination status (on or off) as the counter dish was counted. For rule (2), the number of spoke pairs (a spoke and its direct opposite) with one illuminated and one non-illuminated spoke was counted. The interlink feedback was suspended (no application of blue light) until the 400th time step. The number of spokes satisfying both rules converges, indicating that rules (1) and (2) were simultaneously and stably satisfied after 1162 time steps. (b, bottom) The trace images of the micro-aquarium at the 4000th time step. The number of cells in dish A is smaller than in dish B. All cells in dish A and the vast majority in dish B remained in the non-illuminated spokes and the central circle, due to photophobic responses. A small number of cells occupied the illuminated spokes in dish B, indicating that they were insensitive to blue-light illumination at the given intensity.

Since the number of illuminated spokes is always eight in the experiment, the variation of possible patterns is 128702. Rules (1) and (2) are simultaneously satisfied by only 256 patterns out of 128702. Thus, the probability of establishment of the solution pattern by chance alone is vanishingly small. The successful achievement of one of the solution patterns shown in Figure 4 indicates that digital interlink feedback has a strong driving force in searching for a solution pattern satisfying the two imposed rules simultaneously. The driving force of the feedback system originates from the photophobic responses of Euglena cells, the spontaneous fluctuation of TMs due to random cell movements, and the existence of a small number of photoinsensitive cells, as discussed in our previous study on Euglena-based neurocomputing [29]. The first factor preserves the illumination pattern that satisfies the imposed rules, while the latter two alter the combination of illumination patterns, also to satisfy the rules.

The cell distributions in the two dishes at the 4000th time step are shown in Figure 4b. In dish A, containing fewer Euglena cells than dish B, all cells occupied the non-illuminated spokes and the central circle of the micro-aquarium. A similar distribution was observed in dish B, although a small minority of the cells were swimming in the four illuminated spokes. In this interlink feedback experiment under the rule combination (1, 2), four spokes in both dishes were directly correlated at each time step: one spoke and its opposing spoke in dish A, and two corresponding spokes in dish B. When an illumination pattern on a set of these four spokes satisfied both imposed rules, the illumination remained unchanged in the next time step, reducing the TMs in the illuminated spokes through the photophobic response of the Euglena cells. In turn, the declining TM in the illuminated spokes enhanced the probability that the non-illuminated spokes were selected for the eight most popular spokes, further stabilizing the illumination pattern. This positive feedback mechanism accelerates the achievement of a solution pattern that simultaneously satisfies both imposed rules and widens the TM deviation between the illuminated and non-illuminated spokes (see Figure 4b).

Whether the illumination patterns converge depends on the difficulty of simultaneously satisfying both imposed rules. Figure 5 shows the temporal evolution of the TMs in two pairs of opposite spokes (indexed as 1 and 9, or 2 and 10, clockwise from the top), obtained in the digital feedback experiments executed under rule combinations (1, 2), (2, 3), and (1, 4). The imposed rule combination (2, 3) is simultaneously satisfied by only two out of all possible patterns (128702), whereas the combination (1, 4) cannot be satisfied by any patterns. Despite large fluctuations, the four TMs satisfying the rule combination (1, 2) split and converged into high (spokes 1 and 2) and low (spokes 9 and 10) levels after a time step of 1100–1200 (low levels remained below 200 after a time step of 1122), corresponding to the achievement of a solution at a time step of 1162. Under the rule combination (2, 3), the four TMs switched between high and low levels after around 2200 time steps, suggesting that the illumination patterns had settled near an approximate, but not an exact, solution. One of the two solutions was achieved at 3680 time steps, but repeatedly deviated from thereafter, revealing that the solution had not been established stably by 4000 time steps. Under the rule combination (1, 4), the four TMs continuously fluctuated in a middle range, indicating that the illumination pattern of each dish never converged to a specific pattern.

Figure 5. 

Temporal evolutions of 40-point moving-averaged TMs in two spoke pairs (a spoke and its direct opposite; indexed by 1 and 9, or 2 and 10). Rule combinations used in the digital feedback experiments were (a) rules (1, 2), (b) rules (2, 3), and (c) rules (1, 4). The imposed rule combinations (1, 2) and (2, 3) can be satisfied by 256 patterns and two patterns, respectively, out of all possible patterns (128702), given by the condition that the number of illuminated spokes is always eight in each dish. The rule combination (1, 4) cannot be simultaneously satisfied. The interlink feedback was suspended (no application of blue light) until the 400th time step. The solution pattern was achieved at time step 1162 in (a) and 3680 in (b). The convergence of TMs indicates that the illumination patterns stably satisfy the two rules.

Figure 5. 

Temporal evolutions of 40-point moving-averaged TMs in two spoke pairs (a spoke and its direct opposite; indexed by 1 and 9, or 2 and 10). Rule combinations used in the digital feedback experiments were (a) rules (1, 2), (b) rules (2, 3), and (c) rules (1, 4). The imposed rule combinations (1, 2) and (2, 3) can be satisfied by 256 patterns and two patterns, respectively, out of all possible patterns (128702), given by the condition that the number of illuminated spokes is always eight in each dish. The rule combination (1, 4) cannot be simultaneously satisfied. The interlink feedback was suspended (no application of blue light) until the 400th time step. The solution pattern was achieved at time step 1162 in (a) and 3680 in (b). The convergence of TMs indicates that the illumination patterns stably satisfy the two rules.

The results from the digital interlink feedback experiments revealed that the artificially interlinked systems autonomously evolved to satisfy both individually imposed rules by composing an and pattern solution. In this process, the artificial interlink forces the Euglena cells in the separated dishes to cooperate when following the imposed rules (tasks). Using the interlinked system, we can artificially design interactions among separated groups of microbes by introducing various rules (logics) and algorithms that optimize the cellular distribution and its autonomous evolution. In this way, the system proves a useful implement in soft biocomputing.

3.2 Habitat Separation with Analog Interlink Feedback

One variation of interlink feedback is analogue blue-light feedback. The number of Euglena cells showing the photophobic response depends on the blue-light intensity. Since the intensity required to trigger photophobia differs among the cells [5, 8, 9, 23, 24], some cells escape from areas illuminated with a specific intensity while others remain, unlike the situation in the digital feedback experiments.

Analogue interlink feedback was examined in two 25-square micro-aquariums, as shown in Figure 2f. Blue light was irradiated onto each square at individual intensities calculated from Equations 1 and 2, with reference to the TMs in the counter micro-aquarium. Figure 6 illustrates typical trace images captured throughout an analogue-interlink-feedback experiment of 4000 time steps. Up to 400 time steps, when interlink feedback was suspended, the cellular distributions in both dishes were uniform, showing natural deviations and fluctuations (Figure 6a). The averages and standard deviations of 25 TMs in dishes A and B were 1868 ± 614 and 1242 ± 348, respectively. The respective ratios of standard deviation to average were 0.33 and 0.28. These results showed that, while the cell density was 1.5 times higher in dish A than in dish B, the uniformity of cell distribution was essentially the same in both dishes.

Figure 6. 

Trace images observed in an analogue feedback experiment at time steps 5 (top), 505 (middle), and 2005 (bottom). The interlink feedback was suspended (no application of blue light) until the 400th time step. In each panel, the two numbers are the ratios of the standard deviation to the average, computed from 25 TMs in micro-aquariums A and B. Prior to feedback, the cells spread uniformly, but gradually concentrated into certain squares once the feedback started. The cell concentration patterns in dish A are complementary to those in dish B. As the feedback cycles proceeded, isolated squares of high density converged into a larger group of squares. The autonomous pattern formation of highly populated squares with its reversal pattern in the counter dish is similar to habitat separation exhibited by organisms in nature.

Figure 6. 

Trace images observed in an analogue feedback experiment at time steps 5 (top), 505 (middle), and 2005 (bottom). The interlink feedback was suspended (no application of blue light) until the 400th time step. In each panel, the two numbers are the ratios of the standard deviation to the average, computed from 25 TMs in micro-aquariums A and B. Prior to feedback, the cells spread uniformly, but gradually concentrated into certain squares once the feedback started. The cell concentration patterns in dish A are complementary to those in dish B. As the feedback cycles proceeded, isolated squares of high density converged into a larger group of squares. The autonomous pattern formation of highly populated squares with its reversal pattern in the counter dish is similar to habitat separation exhibited by organisms in nature.

Once the feedback was initiated, a stronger (weaker) blue light was irradiated on a square if the cell density of the corresponding square in the counter dish was higher (lower) than in other squares. Under stronger (weaker) illumination, the TM of the square was decreased (increased) by the photophobic response of the Euglena cells. In turn, the decreased (increased) TM at time t reduced (enhanced) the blue-light intensity irradiated onto the corresponding square in the counter dish at t + dt, and the TM of the corresponding square in the counter dish was increased (decreased) through the photophobic response of the cells. Overall, the algorithm of Equations 1 and 2 generated a positive interlink feedback effect that amplified the cell density differences among the squares, and induced the reversal distribution pattern of cell density in the counter dish. Figure 6b shows the cell distribution and illumination intensity pattern after 505 time steps, when the cells were concentrated into some squares in dish A and into the complementary squares in dish B. The ratio of standard deviation to average was 0.72 and 0.50 in dishes A and B, respectively, indicating that cell aggregation was larger in dish A than in dish B.

As the feedback progressed, the cell distribution pattern was autonomously changed, as shown in Figure 6c at a time step of 2005. The densely occupied squares were rather isolated and dispersed in Figure 6b, but were clustered in Figure 6c. Most of the cells were concentrated into nine squares surrounding the center in dish A, whereas in dish B they occupied 14 or 15 edge squares. The ratio of standard deviation to average increased to 0.95 and 0.78 in dishes A and B, respectively. The concentration of cells into several squares arose from a geometrical factor, whereby many Euglena cells diffused from the highly populated squares into the neighboring squares.

The autonomous formation of complementary patterns of densely occupied squares in the two dishes is similar to the habitat separation exhibited by various organisms in nature. In this context, we have realized artificial habitat separation between two isolated groups of Euglena cells via the analogue interlink feedback operation governed by blue light illuminations. When illumination was terminated, the cells in the highly populated squares dispersed into the neighboring squares, and the uniform distribution was recovered. In repeat trials of the analogue interlink feedback generated from Equations 1 and 2, the same group of Euglena cells occupying the same dishes spontaneously formed diverse patterns of densely occupied squares. Even when we repeated the same experiments with the same dishes, the resulting patterns of densely occupied squares differed every time. This indicates that the initial fluctuation of cell density in each square plays an important role in the formation and grouping of densely occupied squares. In the final stage of the experiments, however, the densely occupied squares in one dish usually gathered into a small number (mostly one or two) of groups.

4 Discussion

Here, we have examined a small variety of feedback rules and algorithms over relatively short time scales (1–2 h). Since Euglena cells undertake a range of longer-term survival strategies, such as adaptation to blue light, temporal resting, and change of swimming trajectory, the implementation of these strategies in the micro-aquariums will alter the cell distribution therein. Such temporal changes in cell distribution will cause transition among solution patterns (in pattern logic operation) or dynamic changes of cell distribution patterns (in habitat separation). Both effects will enhance the optimum-solution-search capability of the system under specified rules (tasks). In addition, time-variant rules and algorithms are useful for operating sequential logic patterns or for optimizing density patterns.

From our separated experiments for single-dish feedback with comparing digital and analogue feedback, we found that using analogue feedback in Euglena-based neurocomputing is promising in incorporating the diversity of photo-responses of Euglena cells to enhance the solution-search capability for combinatorial optimization problems and to utilize the adaptive reaction of Euglena cells [28, 31]. In contrast to analogue feedback, pattern transition in digital feedback converges faster and more firmly. Therefore, the analogue and the digital approaches in the interlink feedback are suited for different applications: Digital feedback is suitable for the problems of on-off decision making in two separated conditions, whereas analogue feedback is suitable for those with trade-off or frustrated or ambiguous conditions.

The artificial interlink feedback examined in this study is potentially applicable to other photosensitive microbes such as Chlamydomonas reinhardtii [14, 39, 42], Synechocystis spp. [17, 40, 41], and Physarum polycephalum [4, 15, 22]. Since our interlink feedback scheme uses separate culture dishes, we can realize artificial interaction among various target microbes inhabiting different environments. As indicated by the emergent habitat separation, our proposed interlink feedback system may also lead to artificial microbial colonies or communities. By forming a network of multiple culture dishes via the interlink feedback, we can realize more complicated and advanced pattern logic operations or density optimizations.

Variations in interlink feedback rules, algorithms, micro-aquarium configurations, and microbial species will enrich the applicability of the optical interlink feedback scheme toward micro-organism-driven soft biocomputing.

5 Conclusion

Artificial interaction between two isolated culture dishes containing Euglena cells was realized by introducing digital and analogue interlinking feedback, governed by blue-light illumination. By imposing a separate rule on each dish, the feedback algorithm generated illumination patterns dependent on the exchanged sets of TM values, which represent the swimming activity of the cells in specified areas of the counter dish. In the digital pattern logic operation, a cell-distribution pattern simultaneously satisfying two individually imposed rules was autonomously generated by cooperative interaction between the paired dishes. In the analogue interlink feedback, blue light proportional to the cell density in a specified square was irradiated onto the corresponding square in the counter dish. This manipulation induced competitive interaction, thereby amplifying initial fluctuations in the cell density distribution. Consequently, artificial habitat separation was realized as a particular pattern of densely populated squares in one dish and its reverse pattern in the counter dish. According to the results of this study, optical interlink feedback between two isolated culture dishes is potentially useful for investigating artificial interactions among various microbes. Especially, it circumvents the difficulties in matching different species, different environments, and different spatiotemporal scales. By varying the interlink feedback rules, algorithms, micro-aquarium configurations, and microbial species, the scheme also offers a promising approach for developing high-performance soft biocomputing.

Acknowledgments

The authors would like to thank Dr. Kengo Suzuki, Ms. Sharbanee Mitra, and Ms. Ayaka Nakashima at Euglena Co. Ltd. (http://euglena.jp/english) for supplying the Euglena cells and culture medium, together with information on cell culture. The authors also wish to acknowledge financial support for this study by the Ministry of Education, Science, Sports and Culture, under Grant-in-Aid for Scientific Research (B), 21360192, 2009-2012, and 25280092, 2013-2016. This research was also partially supported by a National Research Foundation of Korea (NRF) grant funded by the Ministry of Education, Science and Technology (No. 2010-0014809).

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Author notes

Contact author.

∗∗

Bioengineering Lab, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan. E-mail: ozasa@riken.jp (K.O.)

Department of Mechanical Convergence Engineering, Hanyang University, 17 Haendang-dong, Seongdong-gu, Seoul, 133-791, Korea.