Motile Living Biobots Self-Construct from Adult Human Somatic Progenitor Seed Cells

As a result of these analyses, we conclude that there is a statistically significant relationship between the Anthrobots’ developmental morphology and their behavior, and we show visual examples of this relationship with categorical examples on Figure 4B. We further represent this relationship by a decision tree in the form of a Waddington Landscape – a formalism often used to characterize cell‐ and body‐level properties by mapping out the sequential logic of decision‐points in transcriptional space or morphospace.[ 24 ] Figure 4C shows the Waddington Landscape for the Anthrobot. The single cell at the top of the diagram represents the single cell that will develop into the multicellular Anthrobot. During this process of self‐construction, the Anthrobot moves through the developmental landscape, negotiating certain points of morphological possibility to reach its final architecture. We conclude that the unique and spontaneous 3D multicellular morphogenesis of adult airway cells into Anthrobots is consistent; the final form of the Anthrobot displays a degree of variability and exhibits discrete characters with easily recognizable primary features that also map on to phenotypic behavior.

The above metrics all focused on the global structure of the bot. Next, we studied the local characteristics that connect the movement of bots to their morphology, by looking for a difference in bilateral symmetry, or lack thereof, between the two major types of displacing bots (linear and circulars) through symmetricity measurements across plane coincident with their direction of movement. One hypothesis is that Anthrobots have bilateral symmetry that underlies their ability to move in straight lines (as observed in many existing species[ 25 ] and even synthetic forms[ 26 ]); this hypothesis predicts that Anthrobots with circular motion should have more asymmetry across their movement axis compared to other planes. This hypothesis was tested by running a PCA and unsupervised clustering algorithm on a point cloud quantifying Anthrobot cilia distribution patterns through four major bilateral symmetry‐related measurements: total cilia points on a given bot (measured by “tot”), difference in number of cilia points between the two hemispheres (halves of the bot that are separated by the movement axis) of a given bot (measured by “diff”), this difference normalized by total cilia points (measured by “difftot”), and finally the bilateral symmetry index along the movement axis (measured by “Chamfer distance,” see methods for more details). Results of this analysis (Figure 4D) yielded two major clusters that, in a statistically significant manner, each correspond to one of the two major types of displacing bots (linear and circulars). The group consisting predominantly of linear bots scored significantly higher on the bilateral symmetry measurement (via Chamfer Distance axes, which inversely correlate with bilateral symmetry measurement).

This result provides preliminary evidence in support of the hypothesis that Anthrobots with linear movement trajectories may have higher degrees of bilateral symmetry.

In order to further test this hypothesis, while also controlling for the globally homogeneous cilia distribution in linear bots posing a potential confounding factor for bilateral symmetry measurements, we compared the bilateral symmetricity of linear and circular bots against arbitrary axes other than the axis of movement. The initial hypothesis that linear Anthrobots may have higher degrees of bilateral symmetry compared to circular bots automatically suggests that for linear bots, we would expect there to be no other axis than the axis of movement along which the bilateral symmetry is higher; and for circular bots, we would expect there to be other axes than the axis of movement in respect to which the bilateral symmetry is higher. We tested this postulation by measuring linear and circular Anthrobots bilateral symmetry indices separately along each bot's axis of movement versus its farthest rotated (i.e., 90‐degree rotated) counterpart (as the control axis). As a result (Figure 4E), we indeed observed that while for the linear bots there exists no other axis in respect to which the bilateral symmetry is higher than that of the axis of movement, for the circular bots, there exists other axes than the axis of movement in respect to which the degree of bilateral symmetry is higher (p = 0.048). (See Figure S8, Supporting Information for comparison with other control axes that have rotational angle smaller than the farthest possible 90‐degrees.) Taken together, these findings support our hypothesis that Anthrobots with distinct movement types have distinct local bilateral symmetry profiles, with linear bots showing higher bilateral symmetry. This suggests that these synthetic forms recapitulate a fundamental morphological property observed in many wild‐type species.

One possible use of these living biobots is to manipulate other tissues, in vitro or in vivo, in future biomedical or bioengineering applications. How will biobots react to environments different from those that their component cells face in their native configuration in vivo? Thus, Anthrobot behaviors need to be characterized outside of a bare culture dish context, and especially in environments that airway epithelia do not normally encounter. Having characterized their baseline movement and morphology, we wanted to assay this novel motile form for potentially useful behaviors and ways in which it may interact with other somatic tissues, especially sites of damage. Because we are interested in surprising examples of behaviors in such novel constructs, we sought to confront them with a scenario which would not be natural for these airway cells, either in vivo or in their evolutionary history. We decided to study the ability of Anthrobots to move across live tissues that have been damaged, taking advantage of a common model system: the monolayer scratch assay in vitro.[ 27 ] We produced 2D confluent layers of human neurons derived from human induced neural stem cells (hiNSCs) based on a previously established method,[ 28 ] and introduced a scratch of 400–1000 microns by mechanically scratching away the neuron layer in a long swath. We chose hiNSC‐derived scratches, instead of (for example) smooth and regular polydimethylsiloxane (PDMS) channels, because complex borders of such in vitro live tissue scratches featuring live cells constitute more biologically realistic in vitro proxies. We are interested in developing aspirational models for more complex scratched multi‐layered live tissues which are more prone to reveal novel and interesting interactions compared to gels or other artificially‐smooth surfaces.

Anthrobots were placed within these neuronal scratch environments in order to characterize their dynamics in this novel biological environment. Bots were allowed to freely move on their own and timelapse videos were recorded (Figure 5A, and Videos S6 and S7, Supporting Information). These videos were then tracked, and specific indices were calculated from the tracked files (Figure 5B). Among these indices, we characterized the degree to which bots interact with the native tissue surrounding the scratch (measured by “proportion of bot on tissue”), bots’ tendency to assume a circular motility profile (measured by “bot's rotational tendency”), and bots’ displacement speed in traversing the scratch (measured by “instantaneous velocity”). More specifically, we investigated the relationship between bots’ efficiency in traversing the scratch as a function of the circularity of their movement pattern (Figure 5C). We observed a significant positive relationship (slope = 1.5, p = 0.01), confirming our baseline assumption that although circling bots are less efficient in forward motion, they are better at covering the most unique coordinates in the scratch. We have further observed that the instantaneous velocity also had a significant positive relationship with bots’ efficiency in moving across the scratch (slope = 0.0082, p = 0.031 (Figure 5D), presumably due to increased collisions with the tissue. Taken together, these data reveal that Anthrobots are capable of efficiently moving across damaged tissues, and that bots that have a higher rotational tendency and or higher speed have higher degrees of unique coordinate coverage by moving across a higher percentage of the scratch interface.

Having observed the behavior of these bots in scratches, we focused on the interactions between various scratch edge patterns and bots’ ability to track along them. In order to do so, we first constrained the dataset to trajectories that could be used to further understand this relationship. We specifically focused on bots that were not extreme in their rotational tendencies, had ample contact with the scratch and had viable tracking videos (see Experimental Section). This enabled us to isolate the tendency of the bot to turn consistently in the same direction (measured again by “bot's rotational tendency”) and the correlation between the trajectory and scratch edge (measured by “scratch‐trajectory correlation”). With our constrained dataset, we saw that gyration had a quadratic effect on scratch‐trajectory similarity (Figure 5E) with p = 0.006, suggesting that there is a specific range for gyration where the scratch‐trajectory correlation can be maximized: Anthrobots can be chosen to specifically maximize coverage efficiency based on their rotational tendency.

One of the most important aspects of exploring synthetic morphogenesis is the opportunity to observe novel behaviors that are obscured by standard, default phenotypes. Having seen that these airway cell‐derived constructs can move along and settle in neural scratches, we decided to check for the effects of their presence on the surrounding cells. A characterization of their wild‐type capabilities is important not only for understanding biological plasticity but also for establishing a baseline for future efforts in which biobots are augmented with additional synthetic circuits for pro‐regenerative applications.

Inspired by collective behavior and swarm intelligence, and more generally, how in nature collectives can accomplish tasks that individuals cannot, we decided to create “superbot” assemblies by facilitating random self‐aggregation of distinct Anthrobots that fuse to form larger structures. We accomplished this without using molds or any other external shape‐giving equipment, but by simply constraining multiple Anthrobots in a relatively smaller dish, while keeping everything else constant. Akin to how ants cross openings that are too wide for a single ant to cross by forming a bridge through aggregation of their bodies,[ 29 ] we placed these superbots into arbitrary sites along the tissue scratch such that they span the entire width of the scratch, enabling them to “bridge” two sides of the damaged tissue in order to see if we can induce any kind of repair of the scratched monolayer by bridging the two sides, akin to a mechanical stitch. Figure 6A shows a superbot on a scratch upon its placement on day 0, as well as the resulting bridge configuration on subsequent days of day 1 and day 2.

Strikingly, within the next 72 h upon inoculation of the superbot into the tissue scratch on day 0, we observed a substantial regrowth of the native tissue taking place (i.e., gap closure), resulting in the formation of a stitch right underneath the “superbot bridge,” connecting the two sides of the scratch (Figure 6B). This gap closure was observed solely at the site of superbot inoculation, and at no other place along the long scratch (Figure 6C). A quantitative analysis (Figure 6D) of these gap closure sites shows that while the neuron pixel coverage density of the gap closure site is as high as the native tissue outside the scratch (see Figure S10, Supporting Information), the rest of the scratch space, whether adjacent or far, had significantly less density of coverage. Thus, the density of the induced gap closure area that formed as a result of the presence of the superbot represented full (statistically indistinguishable from 100%) recovery of the original tissue and was uniquely different from the surrounding scratch area. Further quantification of superbot bridge‐assisted neuronal gap closure formation showed an average aspect ratio of 0.7 on average. Finally, in order to test whether simple (passive) mechanical contact was sufficient to induce the same effect, we incubated neuronal scratches for 4 days with a piece of agarose on top to provide mechanical loading; this induced no repair (see Figure S11, Supporting Information).

Biorobotics and bioengineering have at least two main areas of impact. One is the production of useful living machines.[ 2a–c ] The other is the use of unconventional configurations for living materials at all scales, to probe the macro‐scale rules of self‐assembly of form and function.[ 3 , 30 ] Specifically, by confronting evolved systems with novel contexts, we can learn about the degree of plasticity that cells and control pathways can exhibit toward new anatomical and functional endpoints, as well as develop protocols to alter default outcomes. Here, we used human patient cells to begin the journey toward immunologically‐acceptable, active, living biomedical constructs, and to begin to probe the morphological and functional capabilities of mammalian, adult cells.

Self‐motile, fully‐organic biobots have been demonstrated with frog cells[ 7 ]; however, it was unknown whether the surprising properties of Xenobots depend strongly on their amphibian genome and evolutionary history, as well as their embryonic state. Specifically, the plasticity of amphibian tissues, and the propensity of embryonic cells to self‐assemble into structures were thought to be unique features that may not be available to engineers working with adult patient‐derived cells. We show that despite spending their entire life in a flat, tracheal architecture (a cycle of over 4–8 decades for our donors), these human cells, with a wild‐type genome and no introduction of scaffolds or nanomaterials, are able to implement a novel set of morphogenetic classes and motile behaviors. Another surprising finding, given the usually tight mapping between genomes and species‐specific form and function, is that the Anthrobots adopt some of the morphological and functional properties similar to Xenobots despite their highly divergent genomes.

Anthrobots’ overall shape and behavior are similar to that of Xenobots, but not identical. Anthrobots are ≈20 to 300+ micrometers in size, whereas Xenobots range from an average of 487±39 µm for the smallest cut explants to 602±30 µm for the largest30. Xenobots likewise offer discrete motion types, and their behavior transition profile is similar. The interconversion between linear and circular is very small for Xenobots (0.5% and 1.6%) and Anthrobots (0.2% and 0.3%), while their consistency of Circular behavior is extremely high for Xenobots (95%) just like for Anthrobots (92%). However, Xenobots’ linear behavior consistency was not as high (67%) when compared to Anthrobots (80%). Despite their highly divergent genome, age, and tissue origin, the two platforms assemble into very similar types of creatures, illustrating the importance of generic laws of morphogenesis[ 31 ] in addition to species‐specific genomic information.

Another difference from existing biorobotics is that the Xenobots’ construction depended on a rate‐limiting process of extracting source cells from frog embryos. Here we show a protocol for enabling the self‐construction of Anthrobots: living structures made from epithelial cells that traverse aqueous environments. The process is highly scalable, and produces Anthrobots in the course of 3 weeks, with minimal manual input beyond weekly media changes. At the end of their 4–6 weeks life span, they safely degrade by becoming unviable debris.

Anthrobots exhibit several distinct movement and morphological classes, which are significantly correlated. This is especially important because the structure and function of this novel construct is not that of a familiar organism (despite a wild‐type genome), and it was not yet known whether its morphospace possessed specific attractors, how reliable the cells’ navigation of that morphospace was, or how the movement patterns would relate to its specific morphology. Anthrobots showed clear and consistent active movement types, quantified over 30 second periods: circulars, linear, curvilinear, and eclectics, with the last category including the non‐displacing bots, i.e., wigglers, as well as distinct morphotypes that are best distinguished by Anthrobot size, shape, and cilia localization patterns. While more work needs to be done to establish a causal relationship between these morphotypes and the movement types, our analyses showed significant correlation between the non‐displacing (wiggler or non‐mover) movement type and morphotype 1, linear movement type and morphotype 2, and finally circular movement type and morphotype 3. Such correlation has implications for future control of higher‐order behaviors (such as movement types) by way of controlling Anthrobot morphology through synthetic morphogenesis, as well as real‐time physiological signaling. In the future, machine learning classifiers may help predictively identify different movement types from phase contrast images of live bots, without needing to perform immunostaining on them. Furthermore, such classifiers will use artificial intelligence tools to correlate initial physiological parameters with final outcomes, as part of the effort for using Anthrobots as a platform for cracking the morphogenetic code.

Analysis of movement and morphology has further revealed the ability of the Anthrobots to establish bilateral symmetry, which is an interesting aspect of self‐assembly in a symmetrical environment and will enable future studies of the still poorly‐understood question of how multicellular amniote embryos bisect themselves to establish a single midplane for their bodyplan.

We found that Anthrobots can traverse neural tissues and defects therein. This popular but highly simplified injury model[ 27a ] is just the beginning for understanding how Anthrobots will deal with traversing complex multifaceted 3D tissues. Most remarkably, we found that Anthrobots induce efficient healing of defects in live human neural monolayers in vitro, causing neurites to grow into the gap and join the opposite sides of the injury. Passive materials did not recapitulate this effect, but it is not yet known which of the many possible biochemical and biophysical aspects of Anthrobot presence are required for this. Although the complex in‐vivo dynamics (e.g., immune components, migratory cells, inflammatory signaling and so on) that may otherwise be observed in actual wounded tissues are not present in this simplified in‐vitro neuronal injury model, so are the endogenous repair cues (e.g., chemical gradients that normally guide such repair processes), yet the Anthrobots were still able to facilitate the repair of a scratched neuronal monolayer. Future work will examine the functionality of Anthrobots in complex injury sites in vivo and identify which of their properties and active processes are mediating the effects.

Furthermore, the size of the Anthrobot to facilitate this repair can be adjusted. The tendency of the bots to fuse together and thus form different sized collectives (i.e., superbots) for different scratches can be controlled by modulating the number of Anthrobots cultured together in the same well for fusion, which happens only on days immediately following dissolution while the Anthrobot basal layers are still exposed and thus can mediate the bot‐to‐bot fusion. The finding is unexpected given these tissues’ normal roles in the human body – the fact that wild‐type cells from trachea will move over and heal neural tissues could not be predicted from any current molecular or tissue‐level models. Thus, it is likely that screens for engineered interactions between body tissues in the context of motile bio‐robotics and other preparations should be performed to uncover novel capabilities of cells and multicellular constructs. Likewise, future molecular biophysics and machine learning efforts could identify the specific signaling modality that is used by Anthrobots to induce neural repair in their vicinity, and thus harness this effect for therapeutic purposes.

Anthrobots are derived from adult human tissue, and in the future could be personalized for each patient, enabling safe in‐vivo deployment of these robots in the human body without triggering an immune response. Once inoculated in the body via minimally invasive methods such as injection, various applications can be imagined, including but not limited to clearing plaque buildup in the arteries of atherosclerosis patients, bulldozing the excess mucus from the airways of cystic fibrosis patients, and locally delivering drugs of interest in target tissues. The possible applications will represent those arising from exploiting surprising novel behaviors of cells and engineering new ones via future synthetic biology payloads, such as novel enzymes, antibodies, and other ways to manipulate the cells they traverse and interact with. They could also be used as avatars for personalized drug screening,[ 32 ] having the advantage of behavior over simple organoids, which could be used to screen for a wider range of active, dynamic phenotypes.

We quantified in detail the morphogenetic and behavioral capacities that self‐organized, clonally‐derived biobots can develop in culture from adult, genetically wild‐type, human cells. We found correlations between their specific form and several modes of autonomous (self‐driven) motile function, and characterized the space of discrete characters of form and function that are not currently inferable from the standard target morphology associated with the human genome. We also found a surprising non‐cell‐autonomous functionality of Anthrobots – a repair property that likewise could not have been guessed in advance from existing frameworks describing the uses of organoids and other bioengineered structures.

Anthrobots may be able to be generated from other ciliated cells in the human body (e.g., oviductal epithelia or brain ependymal cells), and other cell types can be used for bots when autonomous motility is not needed (they can still perform various functions such as the healing we report here, or sensing/reporting, etc.). It may also be possible to induce a ciliation program in other body cell types. These data establish a research program with many unanswered questions for subsequent work. What other cells can Anthrobots be made of? What other behaviors might they exhibit, and in what environments? What other tissue types can they repair or affect in other ways? Can transcriptional or physiological signatures be read out in living bots, that reflect their past and immediate interactions with surrounding cellular or molecular landscapes? Do they have preferences or primitive learning capacities,[ 33 ] with respect to their traversal of richer environments? More fundamentally, these data reveal additional morphogenetic competencies of cells which could have implications for evolutionary developmental biology, as evolution of anatomical and functional features could be affected by the ability of the same genome to produce very diverse forms in different environments. Finally, this kind of new model system is a contribution to two key future efforts. The study of synthetic biological systems[ 3 , 34 ] is an essential complement to the standard set of phenotypic defaults available in the natural phylogenetic tree of Earth, revealing the adjacent possible in morphological and behavioral spaces.[ 35 ] Moreover, these systems offer a safe, highly tractable sandbox in which to learn to predict and control the surprising and multi‐faceted system‐level properties of multiscale complex systems.

NHBEs were sourced from Lonza Walkersville, MD (CC2540S). The cells were first thawed and seeded on a T150 flask containing bronchial epithelial growth medium (BEGM, Lonza CC‐3170) for 2D cell culture growth. Once the NHBEs were ≈80% confluent, they were passage into a 24‐well‐plate of Matrigel (Corning #354 230) beds for 3D cell culture. The NHBEs were not passed past the 3rd passage. Each Anthrobot bed contained 500 µL of 25% Matrigel, 0.1% 0.5 nM retinoic acid (Sigma–Aldrich R2625) and in bronchial epithelial differentiation medium (BEDM, which is 50% BEGM without T3 and 50% high glucose Dulbecco's Modified Eagle Medium (DMEM) without Sodium Pyruvate from Sigma #11‐965‐092) that was centrifuged for 5 s at 100 x g and prepared at least 4 h before passaging the cells. We usually made 6 beds, but this number can be adjusted at discretion. The cells were re‐suspended in 5% Matrigel, 95% BEDM and 0.1% 0.5 nM Retinoic Acid (RA) and seeded directly onto the Matrigel beds with 500 µL per well at a 30 000 cells mL−1 concentration. Once seeded, the NHBEs were centrifuged for 5 s at 50 x g. On days 2 and 8, the NHBEs received a top feed containing 750 µL 5% Matrigel, 95% BEDM, and 0.1% RA. On day 14, 500 µL of the wells’ contents was aspirated and 500 µL of dispase (#D469) at concentration 2 mg mL−1 was added to each well. A mini cell scraper was used to break up the Anthrobot clumps and then followed by a 0.05% Triton coated pipette tip to mix up the Anthrobot with the dispase. The dispase was then incubated at 37 °C for 1 h with the pipetting process repeated every 15 min. During incubation, Pluristrainer Mini's with a 40 µm pore size (Fisher Scientific #431 004 050) were placed in wells of a fresh 24‐well‐plate that contained 2.5 mL of 0.05% Triton.

After the incubation period, 250 µL of 1% 5 mM EDTA in Dulbecco's Phosphate Buffered Saline (D‐PBS) was added into each well. The media in each well was then drawn up, using the Triton‐coated tip, and added to the Triton‐coated strainers. The NHBE spheroids in the strainer were rinsed with 1 mL of D‐PBS then expelled onto a low adhesive dish by inverting the strainer over the dish and expelling 5 times of 1 mL of BEDM through the bottom of the strainer. After all spheroids were in one dish, they were divided evenly among multiple 60 mm dishes by using a Triton‐coated pipette tip and a microscope to manually draw up and divide them. 0.5 µL of 0.5 nM retinoic acid was added into each dish once divided. For the next 14 days as the spheroids started moving, they required 0.5 µL of 0.5 nM RA every other day and a media change every 4 days. The media change was performed by swirling the Anthrobots to the center of the dish then collecting 2 mL of old media and adding 3 mL of fresh BEDM.This was done under a microscope to ensure no Anthrobots got aspirated. Finally, it was created “superbot” assemblies by facilitating random self‐aggregation of distinct Anthrobots that fuse to form larger structures. It was accomplished this by transferring one well's equivalent of Anthrobots into a 60 mm dish, while keeping everything else constant.

Timelapse videos of the Anthrobots were collected at 2.5 s intervals for a duration of 5 h. The videos were contrast‐enhanced using the video editing software ImageJ for optimal tracking and data that are within one bot length (≈100 um) from the edge of the vessel were omitted to prevent edge effect as a confounding factor. They were then processed to extract the trajectories of the Anthrobots utilizing the trackR function in the trackR package (version 0.5.1) for R developed by the Swarm Lab of New Jersey Institute of Technology (NJIT). The software parameters were chosen manually in order to increase the accuracy of the tracking, following the instructions in the trackR package's help. Tracking errors such as the swapping, deletion or insertion of tracks were subsequently manually corrected using the trackFixer function from the same package.

From the extracted trajectories, the following metrics were computed: i) the linear distance between the current position and the immediately preceding one; ii) the linear speed at each position, approximated as the distance moved between the current position and the immediately preceding one during the time interval between these two positions; iii) the heading of the bot at each position, approximated as the angle between the vector formed by the current position and the immediately preceding one and that formed by the Anthrobot position and the immediately following one; iv) the angular speed of the bot at each position, approximated as the difference between the heading at the immediately preceding position and that at the current one during the time interval between the corresponding three positions required to calculate these two headings; v) the time difference between each position.

Behavioral classification was then performed on non‐overlapping 30 s blocks of trajectory. To determine how predictable a position change was, the linear speed, heading, and angular speed were estimated at each position to predict the coordinates of the following position. The error (Euclidean distance) between the predicted coordinates and the actual coordinates was then computed. For each complete 30 s block of trajectory (i.e., a block with no missing timestamp), total error over the entire block was calculated and normalized by the total distance traveled during that block to account for the artificial error amplification caused by predicting over longer distances. To separate active from inactive blocks, an automated classification method was used on the distribution of total normalized errors. A gamma mixture model with two components was fit to the data using the expectation maximization algorithm in the REBMIX function from the rebmix package (version 2.12.0) for R.[ 36 ] The 30 s periods in the resulting cluster with the highest total normalized error were considered as inactive and excluded from further classification.

We then derived two metrics to describe each trajectory: i) a “straightness” index computed as 1 minus the circular variance of the headings during the block (a value of 1 indicates a perfectly straight line) and ii) a “gyration” index computed as 1 minus the circular variance of the angular speed during the block divided by the circular variance of the same angular speeds and their additive inverse, which helps in taking into account the magnitude of the angular speeds themselves (a value of 1 indicates a trajectory following a perfect circle).

The need for two indices arises from the fact that a straightness index alone cannot fully tease apart all different movement types due to its aggregate view of a trajectory. In other words, a low straightness index does not automatically translate into a perfectly circular bot, as we can see in Figure S6A.1,A.2 (Supporting Information) with the arc trajectory. This is due to the fact that the straightness index does not account for the time‐dependent dynamics and thus ignores individual variations across frames. This is where the second movement metric, the gyration index, comes into play. To account for temporal information, we calculate the angular speed, which is the difference between successive headings divided by time between frames and thus has units of radians/ second. Figure S6B (Supporting Information) shows a bent trajectory and Figure S6C (Supporting Information) shows an arc trajectory, both of which have similar straightness indices. However, when we start looking at their temporal relationships using angular speeds, the behavior is entirely different. For the arc (Figure S6C, Supporting Information), the variance of the angular speed is very small since the change in heading of the trajectory each time is relatively consistent (the distribution shown in the histograms).

For the bent trajectory (Figure S6B, Supporting Information), the variance of angular speed is much larger than the arc since for most of the trajectory the angular speed is close to 0 (it goes straight), but the bent portion has a very high angular speed, i.e., the angle changes very quickly. In general, the greater the absolute value of the angular speed the sharper the turn in the trajectory (zero is straight) and the greater the variance of the angular speeds, the less the consistency of the turns in the trajectory. A circle or arc usually has absolute values of the angular speed much greater than zero and low variation of angular speed. However, the gyration index alone cannot differentiate between all behavior either. Let's look at a circular trajectory (Figure S6D, Supporting Information). Even though the absolute values of the angular speeds between arcs and circles are different, the circle also ends up having a gyration index close to 1 since all the turns in a circle are highly consistent like in an arc and thus the variance of the angular speed for both is very small. This fact means the gyration index cannot segregate between arcs and circles, among other things, by itself. Interestingly, the straightness index is exceptional at separating arcs and circles. This shows that though either index alone cannot distinguish all movement types well, together they can accomplish much more.

To separate the trajectory blocks into categories of similar behavior after calculating the movement metrics, a cross‐entropy clustering algorithm was used,[ 37 ] and implemented in the cec function of the CEC package (version 0.10.2) for R.[ 38 ] This yielded us six categories, of which trajectories from categories numbered 3 and 4 were merged into categories numbered 1 and 2 respectively due to the difference being phenotypically minimal. In the “behavioral space” as defined by the straightness and gyration indices, cluster 3 had the same straightness index range as cluster 1 and a lower gyration range between roughly 0.65 and 0.95, which represented trajectories that were highly circular but fell short of cluster 1 which represented “prototypical circulars”. Similarly, Cluster 4 had a slightly smaller straightness index range than cluster 2 (0.7 to 1 instead of 0.6 to 1) and higher gyration range between 0.1 and 0.55 which represented trajectories that were mostly linear but did not have a high enough gyration to be curvilinear or low enough gyration to be Cluster 2, a “prototypical linear”. The merge of the two clusters increased the average dissimilarity of the cluster, but it is a testament to how similar clusters 1 and 3, and 2 and 4 were already that their dissimilarity still remains very low at ≈0.09 and ≈0.14 respectively. Last, to understand how the bots’ behaviors are distributed relative to each other, transition probabilities between each behavioral category were estimated by calculating the proportion of times a block of a given category is followed by a block of the same or another category. This was then presented in the form of a Markov Chain.