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Dynamics of pattern formation and emergence of swarming in Caenorhabditis elegans

  1. Esin Demir
  2. Y Ilker Yaman
  3. Mustafa Basaran
  4. Askin Kocabas  Is a corresponding author
  1. Bio-Medical Sciences and Engineering Program, Koç University, Sarıyer, Turkey
  2. Department of Physics, Koç University, Sarıyer, Turkey
  3. Koç University Surface Science and Technology Center, Koç University, Sarıyer, Turkey
  4. Koç University Research Center for Translational Medicine, Koç University, Sarıyer, Turkey
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Cite this article as: eLife 2020;9:e52781 doi: 10.7554/eLife.52781

Abstract

Many animals collectively form complex patterns to tackle environmental difficulties. Several biological and physical factors, such as animal motility, population densities, and chemical cues, play significant roles in this process. However, very little is known about how sensory information interplays with these factors and controls the dynamics of pattern formation. Here, we study the direct relation between oxygen sensing, pattern formation, and emergence of swarming in active Caenorhabditis elegans aggregates. We find that when thousands of animals gather on food, bacteria-mediated decrease in oxygen level slows down the animals and triggers motility-induced phase separation. Three coupled factors—bacterial accumulation, aerotaxis, and population density—act together and control the entire dynamics. Furthermore, we find that biofilm-forming bacterial lawns including Bacillus subtilis and Pseudomonas aeruginosa strongly alter the collective dynamics due to the limited diffusibility of bacteria. Additionally, our theoretical model captures behavioral differences resulting from genetic variations and oxygen sensitivity.

Introduction

Some animals have remarkable abilities to form complex patterns to cope with environmental challenges (Sumpter, 2010; Martínez et al., 2016; Miller and Gerlai, 2012; Szopek et al., 2013; Ioannou et al., 2012; Stabentheiner et al., 2003; Peleg et al., 2018; Tennenbaum et al., 2016; Gregor et al., 2010). Formation of these biological patterns is particularly initiated by aggregation. At high population density, animals tend to aggregate as animal-to-animal interactions cause instability in uniform distribution (Gregor et al., 2010; Buhl et al., 2006; Liu et al., 2016; Vicsek et al., 1995). Different factors such as motility of animals and chemical cues can trigger these instabilities by altering the behavior of animals. In particular, sensory information plays a primary role in controlling behaviors. Elucidating how environmental factors interplay with the sensory information is essential to improve our understanding of pattern formation in biological systems. However, this is a challenging problem in complex organisms.

Nematode Caenorhabditis elegans allows the use of sophisticated experimental tools and the results provide very precise information regarding the relation between genes, neural circuits, and behaviors (Bargmann and Marder, 2013; Gray et al., 2005; Chalasani et al., 2007; Calarco and Samuel, 2019; Kocabas et al., 2012; Lee et al., 2019). This study is motivated by the possibility of developing a platform that combines both neuronal information and the collective dynamics in this model system.

C. elegans shows a variety of collective responses including, social feeding (de Bono and Bargmann, 1998; de Bono et al., 2002; Macosko et al., 2009; Coates and de Bono, 2002), starvation-induced clustering (Artyukhin et al., 2015), hydrodynamic networking (Sugi et al., 2019) and collective swimming (Yuan et al., 2014; Gray and Lissmann, 1964). Recent studies have shed light on some physical (Sugi et al., 2019; Ding et al., 2019; Oda et al., 2017) and biological (Rogers et al., 2006; Busch et al., 2012; Zhao et al., 2018) aspects of these behaviors and their variations. Oxygen sensitivity is particularly the main source of the variation. Laboratory strain (N2) is known to be solitary nematode with a broad range of oxygen preference while natural isolates exhibit strong aggregation and sharp aerotaxis (Rogers et al., 2006; Persson et al., 2009). Further, oxygen sensing, feeding and aggregation behavior are all intricately related in C. elegans. Bacteria utilize oxygen for growth and C. elegans seeks low oxygen levels for locating the bacteria as a food source. However, in a dense population, all these factors become extremely coupled (Tuval et al., 2005; Gray et al., 2004; Nichols et al., 2017). In this study, we aimed to develop a general model dealing with the dynamics of all these factors.

Here, we report that, C. elegans including the laboratory strain (N2), forms complex patterns during feeding. When thousands of worms are forced to feed together, aggregation-induced bacterial accumulation and oxygen depletion create unstable conditions and further trigger phase separations. The principle of phase separation is mainly based on a sudden change in the animal’s motility (Liu et al., 2016; Cates and Tailleur, 2015). We also found that the dynamics of the entire process is controlled by the sensitivity of the oxygen-sensing neurons, which gives rise to strong variations in animals’ collective response. Further, we also observe the convergence of self-organized patterns to the motile swarming body as a result of complex interactions between oxygen diffusion, bacterial consumption, and motility of animals. Finally, we studied the effects of bacterial diffusibility and biofilm formation of the lawn on the collective dynamics of animals.

Results

To investigate the collective response of C. elegans, we began by imaging animals during food search in a crowded environment. We collected thousands of animals (N2) in a droplet and let it dry on an agar plate. The droplet was put a few centimeters away from food. After drying, worms spread and searched for food by tracing the attractive chemicals. This experimental procedure allowed us to increase the worm density around a bacterial lawn to observe their collective movement. When animals found the bacteria, they usually slowed down and penetrated the lawn. However, we observed that, at high densities the majority of the worms did not penetrate the lawn. After reaching the lawn, they suddenly stopped and started accumulating (Figure 1a). As the worms accumulated, they formed a huge aggregate that covered the entrance. Eventually, this large aggregate gained motility and swarmed across the lawn (Figure 1a,b,c, Video 1). This observation was quite different from the previously reported response of the reference strain N2 which generally behaves solitarily (de Bono and Bargmann, 1998; Gray et al., 2004). Further, we tested different mutant strains deficient in several sensing mechanisms and essential neuromodulators; we observed similar aggregation and swarming responses in a wide range of animals (Figure 1—figure supplement 1). We also used various types of food sources including B. subtilis biofilm, filamentous bacteria, or extremely thick bacterial lawns. Surprisingly, animals showed a very rich collective response ranging from complex pattern formations to large scale swarming (Figure 1d,e,f, Figure 1—figure supplement 2). Altogether, these results suggest that the conditions observed in a dense population can broadly trigger the collective response in C. elegans.

Figure 1 with 8 supplements see all
Collective response and pattern formations in C. elegans.

(a, b) Thousands of animals collectively swarm on a bacterial lawn. (a) While searching for food, worms aggregate around the edge of the bacterial lawn. Small aggregates merge and form a massive swarm. (b) Swarming body eventually gains motility and moves across the lawn while consuming the bacteria. (c) A cryo-SEM image of the swarming body. The heads and the tails of the animals are buried, and the bodies extend on the surface of the swarm. (d, e) Sample images of Turing-like patterns formed by animals on an agar surface under various conditions, such as starvation-induced and on a biofilm. The magnified version of the image is given in the supplementary information. Scale bar, 1 cm (f) Fluorescent image of worms aggregating near the GFP-labeled bacteria. Due to the capillary effect and diffusion of bacteria, worms concentrate the bacteria within the aggregates. Scale bar, 1 mm.

Video 1
Typical swarming response of a laboratory strain (N2) C.elegans.

The video is played 600 X speed and the real elapsed time is indicated in the video (h: min: sec). This video is associated with Figure 1a,b.

This collective response only occurs on a bacterial lawn. Previous studies reported the same conditions for aggregating strains (de Bono and Bargmann, 1998; Gray et al., 2004). However, how the presence of bacteria contributes to this process is unclear. To clarify this point, we used GFP expressing bacteria (OP50, E. coli) to follow the entire dynamics. Time-lapse fluorescence microscopy revealed that the bacteria are concentrated within the aggregates. This bacterial accumulation further promotes the collective behavior of animals (Figure 1f, Figure 1—figure supplement 3, Figure 1—video 1; Video 2). Following the accumulation of bacteria, the motility of animals is strongly suppressed. The naïve hypothesis explaining this observation is that the process is mainly based on the capillary meniscus around the animals (Rabets et al., 2014; Gart et al., 2011). When animals form aggregates, the structure becomes porous. Thus, due to the capillary effect, the porous aggregate can hold more bacterial suspension. Eventually, concentrated bacteria could make the formation of aggregate more favorable by conditioning the oxygen levels. We can conclude that concentrated bacteria is the primary factor triggering the formation and the maintenance of the aggregation.

Video 2
Emergence of swarming response of laboratory strain (N2) around a GFP-labeled bacterial lawn.

Worms accumulate around the lawn and form large aggregates. As large aggregates merge, swarm body appears and gains motility. Bacteria accumulate within the aggregates. The video is played 250 X speed and the real elapsed time is indicated in the video (hr: min: s).

We then focused on the effects of oxygen on the entire process. Previous studies have already shown that the bacterial lawn can decrease oxygen concentration [O2] (Rogers et al., 2006; Gray et al., 2004). To directly observe this effect, we used fiber optic sensors to measure [O2] in both bacterial suspensions and in the swarming body. We observed that the oxygen level drops below 0.1% in the bacterial suspension (Figure 2—figure supplement 1). Moreover, we found similar depletion in [O2] in the swarming body (Figure 2a, Video 3). These results imply that concentrated bacteria deplete [O2] in the swarming body. It should be noted that the fiber optic sensor can only be used to record the oxygen levels in the swarm liquid. Although [O2] is very low, the animals' bodies can extend on the surface of the swarm and they can get sufficient O2 from the environment. Besides the ambient environment, wet agar surface can also provide oxygen by lateral surface diffusion. We independently validated these contributions by covering the aggregate with a glass slide and by using an agar chunk containing oxygen depleting chemical Na2SO3, (Figure 2—figure supplement 2, Figure 1—video 2 and Figure 1—video 3 ). Moreover, we observed that Na2SO3 based oxygen depletion on the agar surface could initiate aggregation behavior in the bacteria-free region (Figure 1—video 4). We also tested animals responses on a very thick bacterial lawn which can significantly decrease the oxygen level. We found that npr-1 worms did not form clusters on the thick bacterial lawn and they avoided extremely thick regions of the lawn (Figure 1—video 5). As a final control experiment we tested the aggregation responses of worms on a dead OP50 lawn. Interestingly, dead bacterial suspensions have different oxygen kinematics and result in small clustering (more discussions about dead bacteria are available in the review file). From these results, we can conclude that animals effectively experience the average O2 levels defined by the ambient environment and the swarm liquid. Altogether, ambient oxygen levels and oxygen depletion are essential factors for aggregation.

Figure 2 with 4 supplements see all
Oxygen sensitivity and the dynamics of pattern formation.

(a) Accumulation of bacterial suspension depletes oxygen in worm aggregates. Oxygen levels measured by the fiber optic sensor while the swarm passes through the sensor. Initially fiber optic sensor records ambient [O2] on the surface and the sudden drop is originating from the complete coverage of the fiber by the swarm body. (b) Oxygen-dependent motility of animals. The average speed of the worms as a function of ambient oxygen. The slope of the curve defines the aerotactic response of the animals. The comparison of velocity profiles of N2 (red) (on food), npr-1(blue) (on food), and off-food-N2 (green) response show the difference between the strains. Colored regions indicate the dispersive, stationary and aggregation phases. Error bar indicates the s.e.m. = ± 18 μm/s. For each experiment, 25 individual animals were imaged. Measurement error is defined by the error in image processing steps. (c) Schematic representation of each phase. The competition between animal dispersion (D) and aerotactic response (β) defines the collective behavior of worms. (d) Simulation results of the model at time 10 min after randomization of the patterns with various initial animal densities. The pattern formation strongly depends on worm density. At low density, worms create clusters. As the worm density increases, clusters converge to stripes and hole patterns. (e, f) Experimental results of density-dependent pattern formation. (e) At low worm densities (500 worms/cm2), N2 worms do not form patterns. As the density increases, we observed stripes (2000 worms/cm2) and holes (6000 worms/cm2). (f) The strong aerotactic response of npr-1 strain enables worms to form patterns even at low densities. An increase in the worm density causes a change in the instability conditions and tunes the patterns. Scale bar, 1 mm.

Video 3
Measurement of [O2] in a swarming body.

The fiber optic sensor is placed on a bacterial lawn and ambient [O2] is set to 21%. Ambient set [O2] and measured [O2] are indicated in the video as O2 set (green) and O2m (black), respectively. This video is associated with Figure 2a.

To quantify the effects of [O2] on the motility of animals, we measured the response of the animals under changing oxygen concentrations. Figure 2b compares the velocity profiles V(O) of both, aggregating strain npr-1 (DA609) and solitary strain N2 and the velocity of the animals moving in the bacteria-free region (off-food). Both strains responded to very low [O2] by increasing their velocities, which mainly triggers dispersive behavior (Video 4). On the contrary, npr-1 suppressed its motility around intermediate oxygen levels (7–10%) and showed a sharp response when oxygen levels exceeded 15%. In contrast, N2 suppressed its motility in more broader range of oxygen levels, but their velocity slowly increased as [O2] reached 21% or more. These differences appear to be originating from the sensitivity of the oxygen-sensing neurons URX, AQR and PQR that shape the overall oxygen preferences of the animals (Oda et al., 2017; Busch et al., 2012; Zimmer et al., 2009). Although both npr-1 and N2 perform aerotaxis at 7–10% oxygen, N2 shows a weaker aerotactic response, thus, they have a broader range of oxygen preference. All these critical features of the strains can be extracted from oxygen-dependent response curve V(O) which is directly related to neuronal sensitivity.

Video 4
Oxygen-dependent motility response of individual animals (npr-1).

In order to minimize the animal to animal interaction isolated bacterial slots were used. This video is associated with Figure 2b.

Motility suppression behavior has been observed in a variety of organisms ranging from bacteria to mussels (Cates and Tailleur, 2015; Cates et al., 2010; Liu et al., 2013; Liu et al., 2014; Dervaux et al., 2017; Liu et al., 2011; Garfinkel et al., 2004). Generally, animals tend to slow down when they come together. The entire process is represented by the density dependence of the animal movement which can lead to the formation of patterns. However, in C. elegans we observed indirect density-dependent suppression. Without bacteria, animals move fast (Figure 2b). In striking contrast, the presence of bacteria results in oxygen depletion and motility suppression. These findings suggest that in the dynamics of oxygen, bacterial concentration and animal motility are the essential physical factors controlling the collective behaviors of C. elegans.

To gain a more quantitative representation of pattern formation, we developed a mathematical model. Many different models have been used to describe the dynamics of pattern formation. Particularly, dryland vegetation models share similarities in terms of dynamic variables and feedbacks (Gilad et al., 2007; Gilad et al., 2004). However, in our system, we have to implement the activity of the worms based on oxygen concentrations. To do so, we followed the notation and the framework developed for active chemotactic particles (Liebchen and Löwen, 2018). We set two separate differential equations to represent worm density (W) and oxygen kinematics (O) in two-dimensional space. V(O) is the oxygen-dependent motility response of individual animals. This factor served as an experimentally measurable sensory curve of the animals. This curve defines competition between diffusivity and aerotactic motility. Both effects became minimal around the optimum oxygen level (7–10%) at which the animals were almost in a stationary phase (Figure 2b). In low oxygen region, dispersion and reversal of aerotaxis promoted motility. On the other hand, at high oxygen levels, aerotaxis dominated the dynamics and promoted aggregation (Figure 2c). These are the Keller-Segel like equations (Keller and Segel, 1970; Wang, 2010) with both, nonlinear diffusion and chemotactic sensitivity (Materials and methods);

(1) Wt=DWW+βWO
(2) Ot=DO2O+fOam-O-kcW

Here, DW=V22τ represents motility-dependent dispersion of the worms, DO  is the diffusion coefficient of oxygen on the surface, β=V2τVO is the aerotactic coupling coefficient indicating the strength of the animal response to oxygen gradient. f is the penetration rate of the oxygen from the air to the water surface, Oam is the ambient oxygen level, and kc  is the rate of oxygen consumption by worms and bacteria. kcW term in the model covers the hydrodynamics related to the bacterial concentration. Here, we assume that bacterial density is linearly proportional to worm density (Figure 1—figure supplement 3b). Furthermore, the time scale of the bacterial consumption is much longer than the aggregation time, thus we ignore the bacterial consumption term in the equations.

First, we focused on the instability criteria. Following the linear stability analysis of the solution in the uniform phase, we predicted that instability occurs when Weqβkc>fDW . The detailed derivations are given in Materials and methods. This criterion suggests that population density and aerotactic response favor instability; however, dispersion of animals opposes it. To verify these conditions, we performed simulations by tuning initial worm density. Depending on the density, we observed the formation of uniform distribution, dots, stripes, and holes (Figure 2d). These are the basic patterns that are frequently seen in many biological systems (Liu et al., 2016; Chen et al., 2012).

Our simulations also predict that under low aerotactic response, the increase in population density could complement the instability criteria and give rise to pattern formation. This is because the multiplication of density and aerotactic response simply shifts the dynamics to a new instability zone. This prediction could explain the response of solitary N2 in a dense population. N2 shows weak aerotactic response which results in broad oxygen preference and patterns only appear in a dense environment. On the other hand, the strain npr-1 with sharp aerotactic response can form similar patterns even at low population density. We tested this hypothesis experimentally (Figure 2e and f, Videos 5 and 6) and found that N2 forms stripes and hole-like patterns only at high population density, whereas npr-1 could form small aggregation patterns even at a low density.

Video 5
Typical structural patterns formed by the animal at high population density under different oxygen levels.

Top images show N2 and bottom images corresponds to npr-1 strain. The circular region is the bacterial lawn. This video is associated with Figure 2d–f and Figure 3.

Video 6
Typical structural patterns formed by the animal at low population density under different oxygen levels.

Top images show N2 and bottom images corresponds to npr-1 strain. The circular region is the bacterial lawn. This video is associated with Figure 2d–f and Figure 3.

Ambient oxygen is the second experimentally controllable factor driving the dynamics of the system. The onset of the pattern formation can be controlled by tuning the ambient oxygen levels at a fixed population density. Further, we tested the contribution of ambient oxygen levels to pattern formation. To be able to control the [O2], we performed the experiments in a chamber where the flow of O2/ N2 mixture is precisely controlled (Figure 2—figure supplement 3). First, we measured the [O2] in a large aggregate accumulated around the bacterial lawn. We started the experiment at 21% O2 and sequentially decreased the [O2] to 1%. We observed that the aggregates respond to decreasing O2 level by increasing their surface area (Figure 3a, Figure 3—figure supplement 1, Video 7). However, [O2] in the aggregate remained low until it reached 7% (Figure 3b). Below this level, the pattern became very porous and oxygen would directly leak into the fiber sensor which led to small fluctuations in readings. It should be noted that the [O2] at 1% completely randomized the patterns by increasing motility and reversing aerotaxis. Subsequently, we increased the [O2] which resulted in similar stripe and hole patterns across the region (Figure 3c, Figure 3—figure supplement 2). We noticed that patterns formed by N2 strain did not change significantly during oxygen scans (Figure 3—figure supplement 3). This was expected, because N2 exhibits low and almost flat aerotactic response within the same range of oxygen levels.

Figure 3 with 4 supplements see all
Combinatorial effect of ambient oxygen and worm density.

(a) Schematics show the response of worm aggregates to changing ambient oxygen levels. As oxygen level increases, the size of the clusters shrink and form circular aggregates which balance the oxygen penetration and diffusion. (b) Measured oxygen concentration in worm aggregates. The dashed red line shows the ambient oxygen level. Error bar indicates the s.e.m. = ± 0.1% (c, d) Simulation and experimental results of pattern formation under various worm densities and ambient oxygen levels. Patterns are formed when the instability criterion is satisfied. The instability zone is bounded by the uniform stable population. Scale bar, 1 cm. Image snapshots representing simulation results are taken at time 10 min after randomization of the patterns. Worm densities vary between 5–60 worms / mm2 (Martínez et al., 2016) in the experiments.

Video 7
Typical response of the swarm formed by N2 to changing ambient oxygen.

We further explored the combinatorial effects of oxygen and worm density on pattern formation. As predicted by the instability criterion, in two-dimensional parameter space, the onset of dot, stripe and hole patterns is observed around the zone bounded by high and low uniform animal densities (Figure 3d). An increase in worm density or a decrease in ambient oxygen levels transforms the dot-shaped structure to stripe and hole patterns.

The other interesting feature of the pattern formation is the coarsening event. We sought to know how the shape of the patterns evolves in time at a fixed oxygen level. Our time-lapse imaging and simulation results validate the coarsening of characteristic domain size (Bray, 1994Figure 4a–c, Figure 4—figure supplement 3, Videos 8,9). In later stages, patterns merge and form a large cluster. This type of a large cluster shares visual similarities with our initial swarming experiments (Figure 1a and b). Interestingly, unlike simulation the width of the of the cluster reaches saturation before they dissociate. Arrested phase seperation was also observed in bacterial system due to birth and death dynamics (Cates et al., 2010). We noticed that, in our case, the consumption of bacteria is significant within the cluster and may limit the growth of the clusters. The similar effect of bacterial depletion was also proposed to explain the motion of the aggregating strain npr-1 (Ding et al., 2019). To investigate the details, we measured the bacterial concentration. GFP signal revealed different bacterial concentrations across the swarm; the front edge of the swarm has more bacteria than the back (Figure 4d–f). Worms in the swarm consumed bacteria and the food continually diffused from the front edge toward the back. As the swarm grows, the gradient profile gradually extends into the swarming body with the average decay length of around λ ~2–4 mm (Figure 4g–h). λ the characteristic length scale of the gradient profile can be simply defined by the bacterial diffusion coefficient (Db) and consumption rate (fb), λ 2 = Db/fb. This decay length defines the width of the swarm body. The small clusters show symmetric GFP distribution and do not form a gradient profile (Figure 4—figure supplement 1d).

Figure 4 with 3 supplements see all
Coarsening event and the emergence of swarming behavior.

(a, b, c) After the formation of patterns, animals locally consume bacteria which eventually increases the motility of animals. (b) Further, patterns merge and coarsen. (c) Consumption of food eventually results in the formation of a large aggregate which resembles the swarming body. Scale bar, 1 cm. (d, e, f) Different stages of a swarming response observed during food search behavior in a dense population. (d) Worms accumulate around the lawn. Unlike isolated worms, diffused bacteria cause the worms to slow down and then the worms form a band around the edge of lawn which eventually converges to aggregates. (e) Small aggregates concentrate bacteria and further accumulate the incoming worms. Consumption and diffusion of bacteria from the lawn leads to a bacterial gradient within the aggregate. (f) Following the formation of a gradient, large aggregate gains motility. The swarm moves through the lawn until finishing the entire lawn and then dissociates. (g) Superposition image of swarming animals and GFP-labeled bacteria indicating the gradient formation across the swarm. (h) A gradient profile gradually extends into the swarm at different time points.

Video 8
Sample simulation results of representing the coarsening process.
Video 9
Typical response of npr-1 to changing ambient oxygen.

Bacterial depletion promotes coarsening and the emergence of swarming. This video is associated with Figure 4.

Next, we tested whether this concentration profile could change the activity of the animals. The activity of the animals increased towards the back which suggests that the animals crawling at the front edge encountered more bacteria than those at the back. To quantify the activity profile, we measured the mean velocity of animals using Particle Image Velocimetry (PIV) analysis. Indeed, the velocity increased toward the back (Figure 4—figure supplement 1a–c). This response is consistent with our V(O) curve where the animals perform off-food response. Without the availability of bacteria, animals start moving fast. On the whole, due to the balance between bacterial consumption and diffusion, swarm body gains motility and moves across the bacterial lawn (Figure 4—figure supplement 2).

So far we have studied the interplay between oxygen levels and animal density. Our observations suggest that diffusion of bacteria on the lawn and swarm fluid is an essential factor and physical properties of the bacterial lawn could also play a significant role during pattern formation. To gain more understanding, we tested the responses of the animals on different biofilm-forming bacterial lawns. B. subtilis can form a biofilm which consists of an elongated chain of cells. Due to their long chaining structure, diffusibility of the bacteria could be relatively limited. We used GFP-labeled B. subtilis and overexpressed sinI protein (Yaman et al., 2019) to drive biofilm formation on regular NGM plates. Figure 5 shows the time evolution of animal accumulation on this chaining biofilm. Interestingly, as animals accumulate dark regions appear across the lawn. These regions indicate the bacteria depleted domains that eventually grow and form open holes (Video 10). The appearance of these holes triggered by local bacterial depletion which can be considered as noise in the concentration. These structures Tjhung et al., 2018 strongly resemble the noise-induced bubbly phase seperation (Tjhung et al., 2018) in active particles. In order to get more insights we tested the dynamics of holes in a swarming body moving on isolated E. coli lawn (OP50). Interestingly, on E. coli based swarm, holes gradually disappeared (Figure 5—figure supplement 1). This difference suggests that the dynamics of holes depend on the physical properties of the bacterial lawn. This difference could be related to the reversal of Ostward process observed in active fluids (Tjhung et al., 2018). We leave the details of this process for future work. The naïve explanation behind this process is that on biofilms the diffusibility of the bacteria decreases and could not compensate the local oxygen penetration which further promotes animal motility around these depleted domains.

Figure 5 with 1 supplement see all
Emergence of periodic holes on biofilms.

(a–d) Snapshots of aggregating N2 animals on GFP labeled B. subtilis biofilm. Limited diffusibility of the chaining bacteria allows local bacterial depletion and oxygen penetration. An increase in the local oxygen concentration results in periodic hole structures by triggering the animals' motility.

Video 10
Accumulation of N2 animals on a biofilm-forming B. Subtilis bacterial lawn.

GFP-labeled bacteria show the concentrated and depleted regions. Depleted regions converge to periodic open holes. This video is associated with Figure 5.

As a final step, we focused on the collective response of animals on pathogenic bacteria. It has been known that pathogenic bacteria Pseudomonas aeruginosa (PA14) trigger immune response and avoidance behavior in C. elegans (Reddy et al., 2011; Zhang et al., 2005). In order to analyze the collective dynamics, we first measured the V(O) curves of both N2 and npr-1 strains on the lawn formed by PA14. The responses of these strains are very different from the behaviors observed on regular OP50; N2 animals are always active on the lawn, on the other hand npr-1 shows a narrowed slowing down window between 3% and 5% oxygen (Figure 6a,c). Further, we tested their swarming behaviors in a dense population. As expected from the V(O) curves N2 does not swarm but npr-1 shows accumulation around the lawn (Figure 6—video 1 and Figure 6—video 2). Long-time lapse imaging experiments showed that the consumption of pathogenic bacteria is extremely slow which takes more than a day to finish the lawn completely.

Figure 6 with 5 supplements see all
Dynamics of collective response of both N2 and npr- one on pathogenic bacteria Pseudomonas aeruginosa (PA14).

Oxygen-dependent motility of the laboratory strain N2 (a) and (c) npr-1 on PA14. Error bar indicates the s.e.m. = ± 18 μm/s. Snapshots of distribution high-density animals N2 (b) and np1-1 (d) on PA14. For each experiment N = 25 individual animals were imaged.

The striking feature we observed in these experiments is the accumulation of N2 worms around the edge of the lawn (Figure 6—video 1). Figure 6b shows these clusters. The most parsimonious hypothesis explaining this observation is that bacteria can diffuse from the biofilm lawn and form a thin layer of isolated bacteria which is sufficient to change the oxygen concentration in the liquid layer on NGM surface. Previous studies showed the instability of the edge of bacterial biofilms (Yaman et al., 2019; Semmler et al., 1999). Thus, pathogenic PA14 show substantial structural differences between biofilms and edges. The bacteria in the biofilm are tightly packed and attached to the extracellular polymeric substances (EPS) matrix, however around the edge they are motile, and they can disperse using their fimbriae. Further we used GFP-labeled PA14 and observed single layer finger-like structures around the lawn (Figure 6—figure supplement 1). The width of this layer is about 1.6 mm for 3 days old PA14 bacterial lawn.

In contrast to N2, npr-1 animals form a large aggregate (Figure 6d). When we randomize the pattern and set the ambient oxygen to a higher level, we also observed transient clustering on the lawn (Figure 6—video 2). This observation is consistent with our diffusion concept. Animals can initially concentrate the isolated bacteria available on the surface but eventually they cannot get enough bacteria from the biofilm to sustain the aggregation.

Finally, in order to gain more information about the differences between OP50 and PA14, we imaged the dynamics of the bacteria around a single worm during locomotion. We observed that on the OP50 lawn, worms could concentrate the bacteria (Video 11). In contrast, on the PA14 biofilm animals only make a trench but do not concentrate the bacteria (Figure 6—video 3). However, around the edge of the PA14 biofilm animals can concentrate the isolated bacteria (Figure 6—video 4). Altogether these observations suggest that biofilm structure and diffusibility of the bacteria play essential roles during aggregation and pattern formation.

Video 11
Dynamics of bacteria around a single worm on a GFP-labeled OP50.

Bacteria can diffuse and the worm accumulates the bacteria around the trench left behind.

Discussion

The dynamics of pattern formation in biological systems depend on many intricately related factors. The theory of pattern formation in active particles provides a powerful framework to explain the complex interactions between these factors (Cates et al., 2010; Liebchen and Löwen, 2018). Using Keller-Segel model (Keller and Segel, 1970; Wang, 2010) and motility-induced phase separation principles (Liu et al., 2016; Cates and Tailleur, 2015), this study throws light upon new physical and biological insights of this complex dynamics. We revealed four essential factors; First, hydrodynamic interactions between worms initiate the process of bacterial accumulation within the aggregates, which is the first, and a critical step in the pattern formation. Second, the oxygen-dependent motility of the animals controls the competition between aerotaxis and animal dispersion. This competition links the neuronal sensitivity to the collective response of the animals. Third, the population density can compensate for the neuronal sensitivity to convert the behavior of solitary animals to aggregation. Further, a gradient profile is formed across the aggregate due to the consumption of bacteria, which leads to the initiation of forward motility and swarming behavior. Finally, we observe that bacterial diffusibility and biofilm formation of the lawn strongly alter the collective dynamics of animals. Our results show that collective dynamics and pattern formation of C. elegans is particularly driven by slowing down response of animals. Our work also raises the questions of how the activities of sensory neurons coordinate motility and slowing down response of worms. Particularly how head and tail neurons separately sense the oxygen levels and synchronize forward and backward locomotion. Moreover, the relation between slowing down response and pathogenic avoidance behavior should be investigated. Future experiments will help identify the details of the circuit dynamics controlling these behaviors. Altogether, experimental results and mathematical models of this study will shed light on understanding the complex dynamics of biological systems.

Materials and methods

Derivation of the mathematical model

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The motion of worms is described as a random walk with oxygen-dependent speed of worms denoted by VO. Worms can change their direction at a rate of τ. The continuity equation reads as:

(3) Wt=-J

where W is the density of worms and J is the worm flux and given by the following expression:

(4) J=-VOnτVOW

n is the dimensionality and equals to 2 in our 2-D model. Substituting Equation 4 into Equation 3 leads to:

(5) Wt=[V(O)2τ(V(O)W)]
(6) =12τ[V2W+VWV]
(7) =12τ[V2W+VWVOO]
(8) =[DWW]+[βWO]

In the equation above, DW=V22τ is worm diffusivity and β=V2τVO is the aerotactic coupling coefficient. The oxygen kinematics can be controlled by three contributing factors. First, oxygen diffuses through the two-dimensional wet agar surface. The second is the penetration of the ambient oxygen from the air to the aggregate. The last contribution is the consumption of oxygen by worms and bacteria. Since the local density of worms and bacteria are linearly correlated as shown in Supplementary Figure 3b, the oxygen consumption can be described with the worm density. Hence, the following equation accounts for the oxygen dynamics on an agar surface:

(9) Ot=DO2O+fOam-O-kcW

Here, DO is the diffusion coefficient of the oxygen on the surface, f is the penetration rate of the oxygen from the air to the water, Oam is the ambient oxygen level and kc is the rate of oxygen consumption by worms and bacteria. We ignore the distribution of the bacteria, since it is linearly correlated with the local worm density.

Linear stability analysis

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Our equations are:

(10) Wt=DWW+βWO
(11) Ot=DO2O-kcW+fOam-O

At the homogeneous equilibrium state, where W and O are constant over time and space, we have the following solution:

(12) kcW=fOam-O

We denote the equilibrium state as:

(13) Weq,Oeq=Weq,Oam-kcfWeq

Then we introduce small perturbations into this homogeneous equilibrium condition as follows:

(14) Wx,t=Weq+ΔWx,t
(15) Ox,t=Oeq+ΔOx,t

By applying these variable replacements to Equation 10 and Equation 11, we obtain

(16) ΔWt=x[DWx(Weq+ΔW)]+x[β(Weq+ΔW)x(OamkcfWeq+ΔO)]
(17) =x[DWx(ΔW)]+x[β(Weq+ΔW)x(ΔO)]
(18) =DWxΔWx+DW2ΔWx2+βxWeqΔOx+βWeq2ΔOx2
(19) ΔOt=DO2x2(OamkcfWeq+ΔO)kc(Weq+ΔW)+f(Oam(OamkcfWeq+ΔO))
(20) =Do2ΔOx2kcΔWfΔO

Second-order terms in perturbations are neglected. We assume:

(21) ΔWx,t=ΔWtsinkx
(22) ΔOx,t=ΔOtsinkx

By doing so, we have decoupled spatial structure and temporal dynamics. By definition, DW and β are:

(23) DW=V22τ
(24) β=V2τVO

Therefore, the partial derivatives of diffusivity and aerotactic coupling coefficient with respect to x  are:

(25) DWx=12τ2VVx
(26) =VτVOOx
(27) βx=12τ(VOVx+Vx(VO))
(28) =12τ((VO)2Ox+V2VO2Ox)

In terms of perturbations around the equilibrium, the equation (12) becomes:

(29) DWx=VτVOΔOx
(30) βx=12τVO2ΔOx+V2VO2ΔOx

Since each term in the expressions of diffusivity and aerotactic coupling coefficient parameter is first order in small perturbations, their multiplication with another first-order term will be negligible. Therefore, we neglect all higher order terms in Equation 18. Finally, these equations become:

(31) sinkxΔWt=-DWk2sinkxΔW-βWeqk2sinkxΔO
(32) ΔWt=-DWk2ΔW-βWeqk2ΔO
(33) sinkxΔOt=-DOk2sinkxΔO-kcsinkxΔW-fsinkxΔO
(34) ΔOt=-DOk2ΔO-kcΔW-fΔO

Using a linear algebra notation:

(35) tΔWΔO=-DWk2-kc-βWeqk2-DOk2-fΔWΔO

We need to find the eigenvalues of the matrix at Equation 35 and check the signs of their real parts.

(36) -DWk2-λ-βWeqk2-kc-DOk2-f-λ=0
(37) -DWk2-λ-DOk2-f-λ-βWeqk2kc=0
(38) λ2+DWk2+DOk2+fλ+DWk2DOk2+f-βWeqk2kc=0
(39) λ=12-DWk2+DOk2+f±DWk2+DOk2+f2-4DWk2DOk2+f-βWeqk2kc

Eigenvalue must be positive for an unstable condition. Since all the terms before ± are negative, the square root term must be positive and sufficiently large in order to make the real part of the eigenvalue positive. Therefore, the condition for a positive real part is:

(40) DWk2+DOk2+f<(DWk2+DOk2+f)24(DWk2(DOk2+f)βWeqk2kc)
(41) (DWk2+DOk2+f)2<(DWk2+DOk2+f)24(DWk2(DOk2+f)βWeqk2kc)
(42) DWk2(DOk2+f)<βWeqk2kc

If this inequality holds, the homogenous equilibrium state is unstable. By solving the inequality for k2, we find:

(43) WeqβkcDWf>DOk2

Since k2 and DO are positive, we get the following result for instability:

(44) Weqβkc>fDW

Numerical solution

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We used numerical methods to solve the coupled partial differential equations. To solve the equations in time and space, we used COMSOL Multiphysics, finite element methods and periodic boundary conditions in space. The coupled partial differential equations are implemented by using general form coupled differential equations:

(45) Wt=V22τW+V2τVOWO
(46) Ot=DO2O+fOam-O-kcW

Here, we replaced the dispersion and aerotactic coupling coefficients with their definition. In our simulations, we used V as a parabolic function of O which has the following expression:

(47) V=aO2+bO+c

At the beginning of the simulations, worms are uniformly distributed with additional noise. The parameters used in the simulations are given below. f and kc are chosen to acquire the width of experimentally observed domain boundaries and time dynamics. DO, DW, β, Weq,Oam and velocity parameters are experimentally defined. Realistic worm densities and diffusion were measured by imaging the worms cluster by setting ambient oxygen to 0.

  • Parameters of velocity (m/s): a=1.89E-2, b=-3.98E-3, c=2.25E-4

  • Tumbling rate: τ=0.5 1/s

  • Oxygen diffusion coefficient: DO=2E-5 cm2/sec

  • Oxygen penetration rate: f=0.65 1/sec

  • Oxygen consumption rate by worms and bacteria: kc=7.3 E-10 1/sec

  • Ambient oxygen level Oam ranges between 0 and 0.21

  • Worm density W, in the uniform stage is around ~ 1–90 worms/mm2

  • Width and height of the simulation window; L=2cm

C. elegans strains

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Strains were grown and maintained under standard conditions unless indicated otherwise. All the strains were obtained from Caenorhabditis Genetics Center (CGC).

Strain List: npr1 (DA609), npr1 (CX4148), gcy35 (AX1295), cat2 (CB1112), tph1 (MT15434), bas1 (MT7988), bas1 and cat4 (MT7983), tax2 (PR694), tax4 (PR678), tax2 and tax4 (BR5514), nsy1 (AWC off killed-CX4998), eat2 (DA465), mec4 (CB1611), mec10 (CB1515), osm9 (VC1262), trpa1 (RB1052), dig1 (MT2840), trp4 (VC1141), lite1 (ce314), daf19 and daf12 (JT6924), npr-1(ad609) X.

Swarming protocol

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Nematode growth media (NGM) plates having a diameter of 9 cm were used for maintaining the worms. NGM plates were seeded with 1 ml of OP50 culture. After the worms consumed the bacteria, three NGM plates were washed with 1 × M9 buffer and the wash was centrifuged twice at 2000 rpm for 30 s. Centrifugation was repeated (up to six times) until a clear supernatant was obtained. Since multiple centrifugation cycles might affect the activity of worms, the cycles subsequent to the first two cycles were carried out for 10 s at 2000 rpm. After cleaning the worms, a 150 µl worm droplet was put on a 6 cm plate seeded with 100 µl (0.5 × 1 cm) of OP50 culture. The optimum swarming pattern was observed in 6-day-old plates and hence 6-day-old plates were used in all further experiments unless indicated otherwise. For NGM plates, M9 buffer preparation and worm synchronization were done based on the standard protocols given in the wormbook.

Oxygen control and measurements

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A plexiglass chamber was used to control the ambient [O2] (Figure 2—figure supplement 4). A 50 sccm mixture of O2 and N2 was used and flow rates were controlled by a flow controller. [O2] was measured by using a normal oxygen sensor (PreSens, Microx TX3). During [O2] measurements the sensor probe should be inserted entirely into swarm fluid in order to read valid signals. The fiber optic sensor has a polymer coating and O2 can easily diffuse from the open air-exposing regions and can quench the fluorescence signal. During fiber optic removal, capillary meniscus around the fiber also affects the reading, we only read the ambient signal [O2] when the meniscus breaks.

At the beginning of the swarming experiments, the oxygen levels in the chamber were adjusted to 21%. After swarming was first observed, oxygen levels were sequentially decreased to 10%, 7%, 3%, and 1% at an interval of ten minutes. Then, oxygen levels were increased in reverse order. The experiments were recorded using Thorlabs DCC1545M CMOS camera with a Navitar 7000 TV zoom lens.

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Decision letter

  1. Sandeep Krishna
    Reviewing Editor; National Centre for Biological Sciences‐Tata Institute of Fundamental Research, India
  2. Aleksandra M Walczak
    Senior Editor; École Normale Supérieure, France
  3. Vishwesha Guttal
    Reviewer; Indian Institute of Science Bangalore, India
  4. Davide Marenduzzo
    Reviewer; University of Edinburgh, United Kingdom

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Acceptance summary:

The manuscript describes the rich phenomenology of swarming behavior of C. elegans worms on a bacterial lawn, forming Turing-like patterns under conditions of low density and oxygen. The study integrates a comprehensive array of experiments with a simple theory, which allows the authors to show that a combination of ambient [O2] and bacterial structure and diffusibility play ‎critical roles during this collective swarming behavior.

Decision letter after peer review:

Thank you for submitting your article "Dynamics of pattern formation and emergence of swarming in C. elegans" for consideration by eLife. Your article has been reviewed by Aleksandra Walczak as the Senior Editor, a Reviewing Editor, and three reviewers. The following individuals involved in review of your submission have agreed to reveal their identity: Alon Zaslaver (Reviewer #1), Vishwesha Guttal (Reviewer #2); Davide Marenduzzo (Reviewer #3).

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

All the reviewers have found the swarming behavior intriguing and interesting. However, they have raised some concerns about the interpretation of the observations. In particular, they have suggested some control experiments and additional analyses to rule out alternative explanations and probe the underlying assumptions you have made. Please address the comments in the three reviews attached below in your revision.

Reviewer #1:

The authors describe an interesting complex behavior of C. elegans worms as they collectively swarm ‎through a bacterial food lawn: Initially, solitary worms reach the edge of the bacterial lawn and start to ‎pile up. The intricate concentrate of worms in the aggregate reduces [O2] and as a result worms remain ‎in the aggregate. The accumulated pile of worms then gets motion once the worms consume the bacteria ‎within the aggregate. The swarm moves along the lawn and consumes all the bacteria, after which the ‎worms disperse. In sum, a combination of ambient [O2] and bacterial structure and diffusibility play ‎critical roles during this collective swarming behavior.‎

Parts of the data presented in this manuscript had been shown before (e.g, [O2] reduction within the ‎worms' aggregate, the speed of various mutants across a wide range of [O2], and worm's [O2] ‎preference; see for example: Gray… et al., 2004, and Rogers etal…, 2006.‎

Yet, the authors herein put all these data, as well as additional supporting results and including a ‎mathematical model, in a nice comprehensive framework that describes this intriguing collective ‎behavior.‎

Essential revisions:‎

1) The authors interpret that worms' aggregate makes the bacteria more ‎concentrated (Results section). The edge of the bacterial lawn is considerably thicker than the inside ‎of the lawn, especially when using several-days old lawns, as described in this study. The ‎worms therefore have much space to burrow into this thick border of bacteria and feed on them. ‎This by itself suppresses motion. Solitary worms reaching such edges also typically suppress ‎motion and remain in the lawn periphery. Once this region is consumed, the worms, which are ‎already piled up to form an aggregate, continue swarming along the bacterial lawn. It may be that there is no need to ‎concentrate the bacteria further to get the observed behavior as suggested.‎ Could the authors comment on that or maybe discuss this as an alternative explanation?

2) The assumption throughout the manuscript is that the bacteria deplete [O2] in the aggregate (for ‎example, Figure 1—figure supplement 2). It could, however, be that the viscous solution of ‎bacteria is poorly permeable to ambient O2. The authors can easily check if it is actually ‎bacterial respiration that consumes all O2 by measuring O2 level in an aggregate consisted of dead ‎bacteria (e.g. heat killed bacteria). This will help to support this claim.

‎3)‎ Figure 2B: not understood at all. Is the average speed of individual worms shown in the graph? ‎This is not indicated in the legend nor in the Materials and methods section. The green data points which indicate off-‎food, are they for the N2 or the npr-1 strain? Also, the legend says error bars are SEM, but no ‎error bars appear in the graph. Does this mean that the indicated 18% SEM hold for all data ‎points?‎

‎4)‎ Figure 3B: legend indicates of error bars but these are not presented. Also, does it show a ‎representative measure or an average of several measurements?‎

‎5)‎ Results section: It is noted that glb-5 can form small clusters even at low densities, but no value is ‎given for these densities. How is this value compared to N2 and npr-1 worms? The change in ‎cluster shown in Figure 3C regarding glb-5 different, is it statistically significant different from ‎what is found in npr-1 and N2 worms? ‎

‎6)‎ Substantial grammar, punctuation, and style revisions are required. Some parts of the manuscript ‎were very difficult to understand.‎

Reviewer #2:

I really enjoyed reading the article on dynamic pattern formation and emergence of swarming in C. elegans. Authors conduct a remarkably comprehensive array of experiments which are exceptionally well matched with a simple theory that the authors develop/modify based on existing models of the literature. Authors show that C. elegans form Turing-like patterns under conditions of low density and oxygen conditions. Such integrative studies are rare, and hence authors deserve much appreciation for the rigour of the work and very fascinating results they have demonstrated. I am not an expert on C. elegans or its mechanisms of motility or swarming. So my review is broadly based on the novelty and comprehensiveness of the study.

I do not have any major comments that I would like the authors to address. However, I am keen to know whether the local positive feedback + long-range inhibition (also called scale-dependent feedback), which is thought to be a fairly universal principle behind such regular Turing-like patterns, is also true in this system. I would appreciate if the authors comment on this aspect. One reference that may be useful in this context is the paper by Rietkerk and van de Koppel, 2008. Although this is written from the perspective of ecosystems and pattern formation, the broader principle of how scale-dependent feedbacks shape patterns will be relevant.

I would also like to see a short discussion on potential alternative mechanisms that may explain these patterns, and also some future directions based on this work.

Reviewer #3:

The authors describe the pattern formation in a system with C. elegans on bacterial lawns or biofilms. They argue that the patterns form because motility decreases with oxygen so that motility-induced phase separation sets up. On top of this, bacteria are consumed by worms and this sets up a swarming behaviour at sufficiently late times. I think this work shows very interesting experiments and the videos are useful to understand the very rich phenomenology.

The main concern that I think should be addressed in full before publication is with the numerical simulation of the continuum model, which is based on a combination of Keller-Segal equations and motility-induced phase separation ideas. I think the overall motivation/basis of the modelling is sound, but it is unclear to me whether more than quite a qualitative comparison can be made. An important feature concerns coarsening, or macroscopic phase separation versus microphase separation. This is briefly discussed in Figure 5 and in some of the supplementary Videos it is shown that late-time behaviours feature patterns coarsening into a single swarming pattern. But this applies to experiments only and it is related according to the authors to bacteria consumption.

In the simulations, the times at which the various snapshots in Figure 2 and Figure 3 are shown is not specified. Presumably the times are all the same but it should be mentioned. If I understand correctly, from the dispersion relation it seems to me that in the simulations, which assume no bacterial consumption, there is still coarsening rather than microphase separation and the formation of multiple stable patterns as for instance in MIPS with logistic bacterial replication (Cates et al., 2010). Can the authors clarify whether this is the case? In other words, they should discuss the fate of the simulation patterns at late times. If all patterns coarsen, then it is important to motivate the choice of the intermediate times at which snapshots are shown (as, if this were the case, the end result would be in all cases complete phase separation). Related to this, I did not have the impression that the patterns would coarsen experimentally at timescales for which bacterial consumption becomes relevant. It would be good to comment on this as well.

https://doi.org/10.7554/eLife.52781.sa1

Author response

Reviewer #1:

The authors describe an interesting complex behavior of C. elegans worms as they collectively swarm ‎through a bacterial food lawn: Initially, solitary worms reach the edge of the bacterial lawn and start to ‎pile up. The intricate concentrate of worms in the aggregate reduces [O2] and as a result worms remain ‎in the aggregate. The accumulated pile of worms then gets motion once the worms consume the bacteria ‎within the aggregate. The swarm moves along the lawn and consumes all the bacteria, after which the ‎worms disperse. In sum, a combination of ambient [O2] and bacterial structure and diffusibility play ‎critical roles during this collective swarming behavior.‎

Parts of the data presented in this manuscript had been shown before (e.g, [O2] reduction within the ‎worms' aggregate, the speed of various mutants across a wide range of [O2], and worm's [O2] ‎preference; see for example: Gray et al., 2004, and Rogers etal., 2006.‎

Yet, the authors herein put all these data, as well as additional supporting results and including a ‎mathematical model, in a nice comprehensive framework that describes this intriguing collective ‎behavior.‎

We thank the reviewer for a general review and emphasizing the contribution of the manuscript.

Essential revisions:‎

1 The authors interpret that worms' aggregate makes the bacteria more ‎concentrated (Results section). The edge of the bacterial lawn is considerably thicker than the inside ‎of the lawn, especially when using several-days old lawns, as described in this study. The ‎worms therefore have much space to burrow into this thick border of bacteria and feed on them. ‎This by itself suppresses motion. Solitary worms reaching such edges also typically suppress ‎motion and remain in the lawn periphery. Once this region is consumed, the worms, which are ‎already piled up to form an aggregate, continue swarming along the bacterial lawn. It may be that there is no need to ‎concentrate the bacteria further to get the observed behavior as suggested.‎ Could the authors comment on that or maybe discuss this as an alternative explanation?

We would like to thank the reviewer for pointing out this interesting point. The reviewer is predicting that around thick bacterial region worms do not need to concentrate bacteria and they should not form aggregates.

We fully agree with the reviewer’s prediction, based on our model worms should not form aggregates if the bacterial layer is thick enough. Bacterial thickness is the main parameter controlling the effective oxygen level. First, we classified this scenario into three different conditions,

1)in athin bacterial layer, animals need to concentrate the bacteria to create preferred oxygen levels (7-10%). This is the condition we observe on regular NGM plates. Bacteria cannot grow efficiently and form only a thin layer (5-10 mic). The edge of the lawn is relatively thick but still thinner than the worm thickness. We verified this edge thickness using a digital microscope (Author response image 1). The other important factor here is the worm’s motion, they can easily spread and flatten the thick bacterial regions around the edge.

Author response image 1
3D topography of 10 days old OP50 bacterial lawn on regular NGM plate.

The edge thickness is around 16 μm.

2) The second case is the relatively thick bacterial layer (~50 mic). If the layer is comparable with the worm thickness, they do not need to form aggregates. On a regular plate, we may rarely observe this condition locally, but again worms can easily damage these concentrated regions.

3) The last case is the thick bacterial layer (>50 mic). In this condition, bacteria cover the entire worm’s body and they can only experience very low oxygen. Thus, they should definitely escape from these regions.

We decided to test these conditions experimentally, particularly we tried to observe the last two cases. We added yeast extract to NGM plates to promote aggressive bacterial growth (OP50). We tested the aggregation response of npr-1 worms on this very thick bacterial lawn. We transferred the worms from regular NGM plate to thick bacterial lawn. As predicted, animals do not form aggregates. Figure 2—figure supplement 3 compares the aggregation responses of npr-1 worms on both plates. It is evident that worms do not form clusters. We further imaged the worms for several days and observed that worms escape from very thick bacterial regions (Video 8 dark area around the center). During this long time-laps imaging we do not observe any aggregate. After 4 -5 days they become very crowded and depleted the bacteria. After then we started seeing the aggregates.

We have added all these control experiments to the manuscript. We would like to thank the reviewer for this prediction. We think that this is a significant contribution to support our model.

2) The assumption throughout the manuscript is that the bacteria deplete [O2] in the aggregate (for ‎example, Figure 1—figure supplement 2). It could, however, be that the viscous solution of ‎bacteria is poorly permeable to ambient O2. The authors can easily check if it is actually ‎bacterial respiration that consumes all O2 by measuring O2 level in an aggregate consisted of dead ‎bacteria (e.g. heat killed bacteria). This will help to support this claim.

We thank the reviewer for this suggestion. We agree that other factors could have additional effects on oxygen kinematics. Our previous experiment (Video 7) shows that the presence of oxygen depleting chemicals such as NaSO3 could also induce aggregation response without bacteria. In order to test the effects of dead bacteria, we performed additional experiments. We used heat-killed bacterial lawn (overnight grown OP50, 1hour, 65 0C). As a control experiment, an LB plate was seeded with 100 μl bacterial suspension and we did not observe any colony. We found that npr-1 worms can aggregate on a dead bacterial lawn. We also noticed that overnight grown bacterial suspension has very low oxygen levels ([O]~ 0.1%). Killing bacteria does not increase this oxygen level. This suggests that there is no difference between live and dead bacteria if we use their native solution. Therefore, we washed the dead bacteria with fresh M9 buffer and seed the plate with these dead bacteria. Again, we observed slow accumulation around the edge. The Author response image 2 shows the snapshots of these accumulated worms after 30 minutes. Accumulation dynamics are very different.

Author response image 2
Aggregation behaviors of npr-1 worms on dead bacterial lawns.

Op50 bacterial suspension was heat-killed 65 0C before seeding. Bacterial lawns were prepared (a) with native suspension (b) fresh M9 washed suspension. npr-1 worms can form aggregation on a dead bacterial lawn.

Further in order to clarify this point, we measured the permeability of dead bacterial suspension washed with fresh M9 buffer. We sandwiched the fiber optic sensor with cover glass and let the oxygen diffuse only from the open end. Before loading the dead bacterial suspension, we shook the sample to saturate oxygen. Later we set the ambient oxygen level to 0% and then 21% and measured the oxygen dissociation rate. Successively we repeated the same procedure with M9 buffer, 1X, 10x and 50 X concentrated dead bacterial suspension. Author response image 3 below shows that M9 buffer and dead bacterial suspensions have different dissociation rates depending on the bacterial density. These results suggest that suspensions with dead bacteria have low oxygen capacity. On the other hand, dead bacteria with its own overnight suspension has very low oxygen content and it is definitely enough to decrease oxygen on the surface.

Author response image 3
Oxygen dissociation rate measurements of dead bacterial suspensions.

Dense bacterial suspensions quickly release oxygen.

When we use M9 washed-dead bacteria as a lawn, animals form small clusters. Unfortunately, in these small clusters, measuring oxygen concentration by using a fiber optic sensor is not possible. Although we do not know the exact mechanism, we can conclude that dead bacteria can decrease the oxygen both in their native solution or in fresh M9 buffer. Furthermore, dissociation rates of oxygen in dead bacterial suspension are different, it can quickly release oxygen. This simply suggests that worms on this layer can consume oxygen very quickly. At this stage we are not able to make a strong claim about the permeability or the solubility of oxygen in these suspensions. More effort is needed to understand the exact mechanism behind the effects of dead bacteria. We also tested Sephadex (G-50) beads and observed small but notable clusters around the beads. Our experiments are not conclusive enough at this stage, so we would like to leave these results and the discussion in the review file.

We have modified the following paragraph to emphasize this point.

“We also tested animal responses on a very thick bacterial lawn which can significantly decrease the oxygen level. We found that npr-1 worms did not form clusters on the thick bacterial lawn and they avoided extremely thick regions of the lawn (Video 8). As a final control experiment we tested the aggregation responses of worms on a dead OP50 lawn. Interestingly dead bacterial suspensions have different oxygen kinematics and results in small clustering (more discussion about dead bacteria can be found in the review file). From these results we can conclude that animals effectively experience the average O2 levels defined by the ambient environment and the swarm liquid. Altogether, ambient oxygen levels and oxygen depletion are essential factors for aggregation.”

‎3)‎ Figure 2B: not understood at all. Is the average speed of individual worms shown in the graph? ‎This is not indicated in the legend nor in the Materials and methods section. The green data points which indicate off-‎food, are they for the N2 or the npr-1 strain? Also, the legend says error bars are SEM, but no ‎error bars appear in the graph. Does this mean that the indicated 18% SEM hold for all data ‎points?‎

We clarified this figure with additional explanations. We would like to thank the reviewer for highlighting the invisibility of error bars. We have fixed this problem in the graph. The green curve corresponds to N2 worms. Npr-1 worms also have a very similar response but not given in the figure. We also clarified this point.

Error bars show the error of measurement. In these experiments, low magnification and image processing steps define the error of the speed measurement. Particularly, this is important for slow worms we observe around 10% oxygen levels where the worms are almost stationary. We prefer indicating the measurement error. We have explained this part in the figure legend.

‎4)‎ Figure 3B: legend indicates of error bars but these are not presented. Also, does it show a ‎representative measure or an average of several measurements?‎

Figure 3B is a single measurement. Synchronization and averaging different measurements are not possible here. The error of the measurement was calculated by averaging independent oxygen measurements

‎5)‎ Results section: It is noted that glb-5 can form small clusters even at low densities, but no value is ‎given for these densities. How is this value compared to N2 and npr-1 worms? The change in ‎cluster shown in Figure 3C regarding glb-5 different, is it statistically significant different from ‎what is found in npr-1 and N2 worms? ‎

We agree that this part of the work is not well supported, and the quantitative comparison is not possible at this stage. We have decided to remove all the experiments about glb-5.

‎6)‎ Substantial grammar, punctuation, and style revisions are required. Some parts of the manuscript ‎were very difficult to understand.‎

We have edited some parts of the manuscript to readability of the text, and we received comments particularly from colleagues with different backgrounds to improve the flow of the paper.

Reviewer #2:

I really enjoyed reading the article on dynamic pattern formation and emergence of swarming in C. elegans. Authors conduct a remarkably comprehensive array of experiments which are exceptionally well matched with a simple theory that the authors develop/modify based on existing models of the literature. Authors show that C. elegans form Turing-like patterns under conditions of low density and oxygen conditions. Such integrative studies are rare, and hence authors deserve much appreciation for the rigour of the work and very fascinating results they have demonstrated. I am not an expert on C. elegans or its mechanisms of motility or swarming. So my review is broadly based on the novelty and comprehensiveness of the study.

We would like to thank the reviewer for motivating comments and a general review of the manuscript.

I do not have any major comments that I would like the authors to address. However, I am keen to know whether the local positive feedback + long-range inhibition (also called scale-dependent feedback), which is thought to be a fairly universal principle behind such regular Turing-like patterns, is also true in this system. I would appreciate if the authors comment on this aspect. One reference that may be useful in this context is the paper by Rietkerk and van de Koppel, 2008. Although this is written from the perspective of ecosystems and pattern formation, the broader principle of how scale-dependent feedbacks shape patterns will be relevant.

I would also like to see a short discussion on potential alternative mechanisms that may explain these patterns, and also some future directions based on this work.

We thank the reviewer for bringing up this point. Following the reviewers’ suggestions, we checked the literature particularly about ecological pattern forming examples. We noticed that vegetation patterning has strong similarities with our system. We linked these seemingly unrelated systems by comparing their feedbacks and variables. Water limited dryland vegetation can form complex patterns. The models representing their dynamics are based on three variables, biomass density, water content and surface water thickness. Interestingly the first similarity appears between these variables. Our model has worm density, oxygen content and bacterial layer. Like bacterial diffusion in our system vegetation patterns strongly depend on the flow properties of the surface water layer. On the other hand, water infiltration by biomass acts as local feedback and water flow sets long-range feedback on the system. In our case, oxygen consumption is local and oxygen penetration and diffusion can be considered as competing for long-range feedback on the system. From the activator-inhibitor perspective there is no one to one similarity. This is because, in our model, worm diffusion is not constant, and it includes oxygen taxis component which depends on animals’ motility. We can only define an effective diffusion coefficient. For low oxygen regime we can claim that worm density activates lack of oxygen and lack of oxygen inhibits worm density. Here, worm density can be considered as an activator and the lack of oxygen is the inhibitor. However, for higher oxygen regime, worms have negative effective diffusion due to oxygen taxis. In this regime we cannot define inhibitory feedbacks. We have added this additional information to emphasize the similarities and differences.

Besides strong similarities between these systems, the main difference is the active matter nature of the worms. This is completely different from the dynamics of passive particle models. Although, we are not able to fully implement all the properties, motility-based diffusion can provide some of them. Comments of the last reviewer are all about these differences. As a future direction we are proposing to use optogenetic perturbation approach to fully extract the internal dynamics. These experiments will allow us to control not only the neural activity but also the speed of the worms and will reveal the activity-based contributions leading to pattern formation. We modified the manuscript as given below and shortly added this discussion.

“To gain a more quantitative representation of pattern formation, we developed a mathematical model. Many different models have been used to describe the dynamics of pattern formation. Particularly dryland vegetation models share similarities in terms of dynamic variables and feedbacks. However, in our system we have to implement the activity of the worms based on oxygen concentrations. To do so we followed the notation and the framework developed for active chemotactic particles.”

Reviewer #3:

The authors describe the pattern formation in a system with C. elegans on bacterial lawns or biofilms. They argue that the patterns form because motility decreases with oxygen so that motility-induced phase separation sets up. On top of this, bacteria are consumed by worms and this sets up a swarming behaviour at sufficiently late times. I think this work shows very interesting experiments and the videos are useful to understand the very rich phenomenology.

We would like to thank the reviewer for his comments and a general assessment of the work.

The main concern that I think should be addressed in full before publication is with the numerical simulation of the continuum model, which is based on a combination of Keller-Segal equations and motility-induced phase separation ideas. I think the overall motivation/basis of the modelling is sound, but it is unclear to me whether more than quite a qualitative comparison can be made.

We would like to thank the reviewer for raising this point. Many of the quantities used in the simulation were experimentally verified. Dw, DO, V(O), β(Ο) worm densities etc. We are actually very close to quantitative comparison. The only exemption is the kc (rate of oxygen consumption) and f (the penetration rate of oxygen). These two variables are still arbitrary. We have chosen them to match the experimentally observed time dynamics and also the penetration depth around the domain boundary of worm clusters. The figure below shows the sample simulation results of the worm density and oxygen profiles. Using these quantities, the penetration depth is about ~200-400 µm. This penetration is around a few worm thicknesses which is reasonable compared to our experimental observation. We tried to extract these variables experimentally however, our fiber optic sensor has a very poor spatial resolution. The smallest sensor tip is around 100 μm. Currently, it is not possible to further verify these two quantities experimentally. Very recently we have found an alternative approach to measure oxygen profile precisely in micron-scale. This method depends on the photoconversion of GFP to RFP under a low oxygen regime (in vivo oxygen imaging using green fluorescent protein, Takahashi, 2006). This interesting method is very promising but depends on photobleaching upon strong light exposure. We are still having some difficulties with the implementation of this approach. Because, strong light exposure triggers avoidance of the worms which quickly disrupts the measurements. We added Figure 3—figure supplement 4 and explain how we set the physical quantities in our simulation to clarify this point.

An important feature concerns coarsening, or macroscopic phase separation versus microphase separation. This is briefly discussed in Figure 5 and in some of the supplementary Videos it is shown that late-time behaviours feature patterns coarsening into a single swarming pattern. But this applies to experiments only and it is related according to the authors to bacteria consumption.

We observe both coarsening and also the convergence of clusters to the swarming phase. We thank the reviewer for highlighting this confusion. We modified the text and use coarsening to define the initial growth of the structures.

In the simulations, the times at which the various snapshots in Figure 2 and Figure 3 are shown is not specified. Presumably the times are all the same but it should be mentioned.

We have updated the simulation results; all the images are taken at time t=10 min after the randomization of the pattern. This time window is experimentally reasonable because we do not observe significant bacterial consumption within this duration.

If I understand correctly, from the dispersion relation it seems to me that in the simulations, which assume no bacterial consumption, there is still coarsening rather than microphase separation and the formation of multiple stable patterns as for instance in MIPS with logistic bacterial replication (Cates et al., 2010). Can the authors clarify whether this is the case? In other words, they should discuss the fate of the simulation patterns at late times. If all patterns coarsen, then it is important to motivate the choice of the intermediate times at which snapshots are shown (as, if this were the case, the end result would be in all cases complete phase separation). Related to this, I did not have the impression that the patterns would coarsen experimentally at timescales for which bacterial consumption becomes relevant. It would be good to comment on this as well.

The referee is correct that patterns in our simulation are coarsening. In order to clarify this point we calculated the characteristic domain size of simulated patterns and compared them with the experimental measurements. The figure below shows that the exponent of the curve is close to the universal value of 1/3. On the other hand, experimental results reach saturation around L~ 2mm. After this time bacterial depletion dominates the dynamics and all the clusters dissociate. Here we are speculating that this saturation is defined by the bacterial diffusion and consumption within the worm clusters. GFP labeled bacterial gradient provides a comparable length scale. This mechanism resembles the arrested phase separation mechanism due to bacterial death (Cates et al., 2010). Our simulation unfortunately does not have bacterial consumption dynamics. This made the simulation unstable. We were not able to find realistic parameters forming patterns yet. We added Figure 4—figure supplement 3 to the manuscript and modified the text to clarify this point.

“The other interesting feature of the pattern formation is the coarsening event. We sought to know how the shape of the patterns evolves in time at a fixed oxygen level. Our time-lapse imaging and simulation results validate the coarsening of charanteristic domain size (Figure 4A-C, Figure 4—figure supplement 3, Video 13, Video 14). In later stages, patterns merge and form a large cluster. This type of a large cluster shares visual similarities with our initial swarming experiments (Figure 1A, 1B). Interestingly, unlike simulation the width of the of the cluster reaches saturation before they dissociate. Arrested phase seperation was also observed in bacterial system due to bird and dead dynamics. We noticed that, in our case the consumption of bacteria is significant within the cluster and may limit the growth of the clusters. The similar effect of bacterial depletion was also proposed to explain the motion of the aggregating strain npr-1. To investigate the details, we measured the bacterial concentration. GFP signal revealed different bacterial concentrations across the swarm; the front edge of the swarm has more bacteria than the back (Figure 4D-F). Worms in the swarm consumed bacteria and the food continually diffused from the front edge towards the back. As the swarm grows, the gradient profile gradually extends into the swarming body with the average decay length of around λ ~ 2–4 mm (Figure 4G-H). λ the characteristic length scale of the gradient profile can be simply defined by the bacterial diffusion coefficient (Db) and consumption rate (fb), λ 2 = Db/fb. This decay length defines the width of the swarm body. The small clusters show symmetric GFP distribution and do not form a gradient profile (Figure 4—figure supplement 1D).”

https://doi.org/10.7554/eLife.52781.sa2

Article and author information

Author details

  1. Esin Demir

    Bio-Medical Sciences and Engineering Program, Koç University, Sarıyer, Istanbul, Turkey
    Contribution
    Data curation, Formal analysis, Observed the swarm response, Performed swarning experiments and mutant screens, Wrote the manuscript
    Contributed equally with
    Y Ilker Yaman
    Competing interests
    No competing interests declared
  2. Y Ilker Yaman

    Department of Physics, Koç University, Sarıyer, Istanbul, Turkey
    Contribution
    Conceptualization, Data curation, Software, Formal analysis, Investigation, Methodology, Performed the pattern formation experiments, designed the imaging systems, developed the mathematical models, performed the simulations and carried out image processing analysis of experiments, Wrote the manuscript
    Contributed equally with
    Esin Demir
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0003-4094-616X
  3. Mustafa Basaran

    Bio-Medical Sciences and Engineering Program, Koç University, Sarıyer, Istanbul, Turkey
    Contribution
    Conceptualization, Data curation, Software, Formal analysis, Investigation, Methodology, Performed biofilm experiments, Developed the COMSOL implementation, Wrote the manuscript
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-1895-254X
  4. Askin Kocabas

    1. Bio-Medical Sciences and Engineering Program, Koç University, Sarıyer, Istanbul, Turkey
    2. Department of Physics, Koç University, Sarıyer, Istanbul, Turkey
    3. Koç University Surface Science and Technology Center, Koç University, Sarıyer, Istanbul, Turkey
    4. Koç University Research Center for Translational Medicine, Koç University, Sarıyer, Istanbul, Turkey
    Contribution
    Conceptualization, Resources, Data curation, Software, Formal analysis, Supervision, Funding acquisition, Validation, Investigation, Visualization, Methodology, Project administration, Performed the pattern formation experiments, designed the imaging systems, developed the mathematical models, performed the simulations and carried out image processing analysis of experiments, Performed biofilm experiments, Wrote the manuscript
    For correspondence
    akocabas@ku.edu.tr
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-6930-1202

Funding

European Molecular Biology Organization (IG 3275)

  • Askin Kocabas

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

This work was supported by an EMBO installation grant (IG 3275); The Science Academy, Turkey, (BAGEP) young investigator award and TUBITAK (project no115F072 and 115S666). We thank Tevfik Can Yuce for computational support. We thank Mario de Bono and his group members for discussions and suggestions about the initial observation of the swarming response. We thank Prof FM Ausubel for providing GFP labeled PA14 strain. We also thank H Kavakli, M Iskin, F Balci, P A Ramey for the comments and critical reading of the manuscript.

Senior Editor

  1. Aleksandra M Walczak, École Normale Supérieure, France

Reviewing Editor

  1. Sandeep Krishna, National Centre for Biological Sciences‐Tata Institute of Fundamental Research, India

Reviewers

  1. Vishwesha Guttal, Indian Institute of Science Bangalore, India
  2. Davide Marenduzzo, University of Edinburgh, United Kingdom

Publication history

  1. Received: October 16, 2019
  2. Accepted: April 5, 2020
  3. Accepted Manuscript published: April 6, 2020 (version 1)
  4. Version of Record published: May 6, 2020 (version 2)

Copyright

© 2020, Demir et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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