Collective motion enhances chemotaxis in a two-dimensional bacterial swarm

Abstract

In a dilute liquid environment in which cell-cell interaction is negligible, flagellated bacteria, such as Escherichia coli, perform chemotaxis by biased random walks alternating between run-and-tumble. In a two-dimensional crowded environment, such as a bacterial swarm, the typical behavior of run-and-tumble is absent, and this raises the question whether and how bacteria can perform chemotaxis in a swarm. Here, by examining the chemotactic behavior as a function of the cell density, we showed that chemotaxis is surprisingly enhanced because of cell crowding in a bacterial swarm, and this enhancement is correlated with increase in the degree of cell body alignment. Cells tend to form clusters that move collectively in a swarm with increased effective run length, and we showed analytically that this resulted in increased drift velocity toward attractants. We also explained the enhancement by stochastically simulating bacterial chemotaxis in a swarm. We found that cell crowding in a swarm enhances chemotaxis if the cell-cell interactions used in the simulation induce cell-cell alignment, but it impedes chemotaxis if the interactions are collisions that randomize cell moving direction. Therefore, collective motion in a bacterial swarm enhances chemotaxis.

Significance

In a two-dimensional crowded environment, such as a bacterial swarm, the typical run-and-tumble behavior, a hallmark of bacterial chemotaxis, is absent because of frequent cell-cell collision. This raised the question whether cells can still perform chemotaxis in a swarm. Here, by studying the chemotaxis performance as a function of cell density, we discovered that chemotaxis is surprisingly enhanced because of cell crowding in a swarm. By combining measurements with simulations of chemotaxis in bacterial swarm, we found that this enhancement is due to spontaneous symmetry breaking of the rotational symmetry directed along the gradient of the chemical stimulus.

Introduction

Motility of flagellated bacteria, such as Escherichia coli, are enabled by rotation of helical flagellar filaments, each driven at its base by a reversible rotary motor (flagellar motor) (1). They show different motile modes, swimming-moving independently in dilute bulk liquid or swarming-moving in groups with high cell density in a thin film of liquid on a moist surface (2, 3, 4, 5). When individual E. coli cells are placed in bulk liquid with low cell density, where cell-cell interactions are negligible, they perform a run-and-tumble behavior of swimming controlled by the direction of rotation of the flagellar motors. When all the flagellar motors on a cell turn counterclockwise (CCW), the flagellar filaments form a helical bundle that pushes the cell steadily forward (a run). When one or more motors switch to clockwise (CW), their filaments come out of the bundle, and the cell tumbles to change orientation (6). By tracking a swimming cell, Berg & Brown found that a swimming E. coli explores the environment in a random walk of alternating run-and-tumble (7). When E. coli cells are inoculated in a nutrient-rich medium on a moist semisolid surface, they elongate, synthesize more flagella, and form a two-dimensional (2d) crowded thin film. Cells in this crowded nutrient-rich surface continuously change their direction by collision with their neighbors, and they move by associating into groups (clusters), resulting in a swarming mode. During swarming, the typical run-and-tumble behavior is inconspicuous (5).

Bacteria move toward chemical attractants and away from repellents (perform chemotaxis) by using the bacterial chemotaxis signal transduction system. In E. coli, the chemotaxis system consists of an interaction network of several types of chemotaxis proteins (8, 9, 10). When the chemical ligands (attractant) bind to the periplasmic domain of the chemoreceptors, the activity of the associated histidine kinase (CheA) is suppressed, and this results in a decrease in the cellular concentration of CheY-P, the phosphorylated CheY (11). CheY-P binds to FliM in the switch complex at the base of the flagellar motor and changes the probability of the motor rotating CCW or CW (12,13) and, accordingly, the probability of cell run or tumble (14). Therefore, the run-and-tumble behavior is a hallmark of bacterial chemotaxis, which was usually studied in a dilute aqueous environment. The absence of the typical run-and-tumble behavior in bacterial swarming raised the question whether bacteria can still perform chemotaxis in a swarm. Furthermore, it was found that a chemotaxis-deficient strain of E. coli (with deletion of the cheY gene) can also swarm, as long as its flagellar motor can switch rotational direction spontaneously with a mutant FliM, revealing that chemotaxis is dispensable for a swarming colony to expand (15).

A recent work studied the chemotaxis of planktonic E. coli cells at various cell densities (for a cell density range with volume fractions below ∼0.1) in a three-dimensional (3d) experimental setting with a microfluidic device (16). In an E. coli swarm, especially near the vigorously moving swarm front, the swarmer cells are morphologically different (e.g., with larger cell body aspect ratio), and move in a 2d environment with a higher cell density (with area fraction as high as 0.7). It is intriguing what the chemotaxis behavior is in a bacterial swarm.

In this study, we intended to investigate whether and how bacteria perform chemotaxis in a swarm by investigating the bacterial chemotaxis behavior on a swarm plate. We referred to swarming exclusively in the context of surface migration on a “swarm” agar (0.45%, w/v), which is different from the swimming within a “swim” agar (0.2–0.4%, w/v) (2,17). We discovered that bacterial chemotaxis in a swarm is surprisingly enhanced by cell crowding.

Materials and methods

Strains and plasmids

The plasmid pMT1 expresses mCherry under control of an isopropyl-β-D-thiogalactoside (IPTG)-inducible promotor in the vector pTrc99a. The plasmid pVS88 expresses both CheZ-eCFP and CheY-eYFP under control of an IPTG-inducible promoter (18). The plasmid pLC113 expresses Tar under a salicylate-inducible promoter (19). The double-mutant CheY^D13KY106W is active without phosphorylation (20) and does not respond to CheZ (15,21). The plasmid pMT2 expresses CheY^D13KY106W under control of an arabinose-inducible promoter in the vector pBAD33. The wild-type E. coli K12 strain AW405 (HCB1) transformed with pTrc99amCherry was used for fluorescent tracking of cell trajectories. Strain HCB1414 (Δtar, tap, tsr, trg, aer, cheY, cheZ) carrying pVS88 and pLC113 was used for the Förster resonance energy transfer (FRET) studies. Strain HCB1736 (ΔCheY) carrying pMT2 was used for control experiments with the chemotaxis-defective mutant strain. AW405 with no plasmid was used for all other studies.

FRET assays

To determine the equivalent α-methyl-DL-aspartate (MeAsp) concentration in a normal swarm agar plate, we estimated the number of swarm cells to be ∼1.1 × 10⁹, which was equivalent to 6.88 × 10⁸ cells/ml when the colony covered two-thirds of the swarm plate. Thus, we used fresh swarm buffer to cultivate the HCB1 strain at 33°C to a concentration of 6.88 × 10⁸ cells/ml (OD₆₀₀ ∼ 0.85) and collected the supernatant by centrifugation. The measurements were performed using a FRET setup described previously (19). During growth of the HCB1414 cells, 1 μM salicylate was used to induce Tar expression to a level approximating that in wild-type cells. The FRET between CheZ-eCFP and CheY-eYFP was used to measure the step response of HCB1414 cells to various concentrations of MeAsp solutions and to 1:500 diluted supernatant of swarm buffer. The ratio of the signals from the yellow and cyan channels was used to represent the FRET value, which was normalized by the average prestimulus value. The initial responses were used to construct the dose-response curve (Fig. S1).

Swarm plates

Swarm agar (0.45% Eiken agar, 1% Bacto peptone, 0.3% beef extract, and 0.5% NaCl) was prepared and melted at 65°C, then allowed to cool down. When cooled to ∼60°C, IPTG that was dissolved in dH₂O and filtered was added to a final concentration of 2 mM. 25 ml of the swarm agar was poured to a polystyrene petri dish (150 mm diameter), which was then allowed to cool without a lid for 20 min inside a sealed large Plexiglas box at a room temperature of 23°C (5,22).

Cells were grown overnight in LB (1% Bacto tryptone, 0.5% yeast extract, 0.5% NaCl) at 33°C (with shaker at 200 rpm). The overnight culture was diluted by 10⁻³, 10^-4, or 10⁻⁵ with swarm buffer (1% Bacto peptone, 0.3% beef extract, and 0.5% NaCl), and a 2.5-μL drop of which was inoculated on the surface of the swarm plate. The plate was covered with the lid and incubated at 30°C and 100% relative humidity. The swarming colony expands to cover two-thirds of the swarm plate in ∼14 h. For the control experiments with chemotaxis-defective strains, swarm agar was supplemented with 0.5% glucose after autoclave (23), which may help the chemotaxis-defective cells to swarm by supplying an additional energy source (24). L-arabinose (final concentration of 5 mg/L) was added to the swarm agar to induce a suitable expression level of CheY^D13KY106W for swarming. 1 mL of overnight cells of HCB1736 carrying pMT2 was washed with 1 mL swarm buffer twice (4000 × g for 2 min), a 2.5 μL drop of which was inoculated on the swarm agar. The colony expanded into a standard circle, 4 cm in diameter, in ∼14 h.

Cell tracking on the swarm plate

Cells of AW405 and AW405 carrying pMT1 were mixed and inoculated on the swarm plate at a ratio of 40:1. For tracking of chemotaxis-defective strains, cells of HCB1736 carrying pMT2 and HCB1736 carrying pMT1 and pMT2 were used. When the swarm edge was expanded to the position of a certain gradient (usually in ∼14 h), the swarm plate was put on a Nikon Ni-E (Nikon, Minato City, Japan) upright fluorescence microscope equipped with a temperature-controlled sample stage. All experiments were performed at 30°C, and the swarm plates were covered with a lid to prevent evaporation in all experiments. The microscope was equipped with a filter-set for mCherry and a sCMOS camera (C11440; Hamamatsu Photonics, Hamamatsu, Japan). For tracking of cells at a normal (undiluted) swarm edge, cells were imaged in epifluorescence at a frame rate of 25 fps with a 40× dry objective (Nikon CFI S Plan Fluor ELWD ADM 40XC, NA 0.6, WD 2.8–3.6 mm). For tracking of diluted cells at the swarm edge, a 2-μL drop of swarm buffer (30°C) was dropped to the swarm edge, then a glass coverslip (24 mm square) prewarmed to 30°C was placed at the drop position and cells were imaged at 50 fps with a Nikon Apo λ 60×/1.40 NA oil-immersion objective.

Establishing MeAsp gradient on a swarm plate

After the 60°C swarm agar was spread uniformly on the petri dish, a drop of MeAsp dissolved in 60°C swarm agar was placed on the surface of the agar plate near the rim (away from future inoculation position of the cells). The plate was then allowed to cool without a lid for 20 min inside a sealed large Plexiglas box at a room temperature of 23°C. The cells were then inoculated on the plate and incubated at 30°C with 100% humidity.

To calibrate the spatial distribution of MeAsp on the swarm plate as a function of time after the initial drop, a drop of fluorescein was used instead of the MeAsp drop, followed with the same incubation procedures. We first made a calibration of the fluorescent intensities with respect to the fluorescein concentration in swarm agar, as shown in Video S1. A sample video of a swarm edge, Document S2. Article plus supporting material A, exhibiting slight nonlinearity at high concentrations. To measure the spatial distribution of fluorescein on the swarm plate at various times after the initial drop, a glass coverslip was used to cover the surface of the swarm plate, and the fluorescence was observed with a Nikon Ni-E upright microscope equipped with the filter-set for fluorescein, a Nikon Apo λ 60×/1.40 NA oil-immersion objective, and a sCMOS camera (C11440; Hamamatsu). We measured the distribution of fluorescein concentration at 2.5–13.5 h (with 1-h step) after adding a 100-μL drop of 1 mM fluorescein, as shown in Fig. S2 B. From the measured distribution, the gradient can be calculated at any position, and the gradient can be adjusted by adjusting the volume or concentration of the initial drop.

Data analysis

Data analysis was done using custom scripts in MATLAB (The MathWorks, Natick, MA). Video frames were processed to extract the positions of individual cells in each frame, and cell tracking was accomplished by identifying the cell with least distance in the next frame for each cell in the current frame. Velocities were calculated from the cell-displacements between consecutive frames, and velocity autocorrelation was calculated as below. For each trajectory, we separated it into two types of segments, toward the attractant (forward) and away from the attractant (backward), using as a reference the line connecting the cell inoculation point and the MeAsp drop position. We calculated velocity autocorrelation separately for the forward and backward segments as (5)

$$\text{Correlation}\left(\Delta t>0\right)=$$

$${\langle \text{cos}({\theta }_i\left(t\right)-{\theta }_i\left(t^{\prime }\right))\rangle }_{t^{\text{′}}-t=\Delta t},$$

where Δt is the time lag, θ_i(t) denotes the angle of instantaneous velocity of the i-th cell at time t with respect to the reference line, and < > denotes average over all forward or backward segments with the time lag Δt. The correlation as a function of time lag was fitted with the function $\text{Correlation}\left(t\right)=A\times e^{-\raisebox{1ex}{$t$}\!\left/ \!\raisebox{-1ex}{$\tau $}\right.}+C$ (A and C are two fitting constants) to extract the persistence time τ.

Simulations of chemotaxis in bacterial swarm

We combined a stochastic model of chemotaxis motion and a modified Vicsek-type model of bacterial swarming to simulate bacterial chemotaxis in a swarm. The Vicsek model describes point-like self-propelled particles that move at constant speed and align their velocity with their neighbors’ in presence of noise (25). The simulations were carried out in a two-dimensional square area of linear size 50 μm, with periodic boundary conditions. Cells moved with a constant speed of 25 μm/s. Cells can be in either run or tumble. The direction of velocity for each running cell was updated by a direction summation of the velocity vectors of the neighbor cells with similar swimming direction (with the angle between the velocities of the neighbor and current cells less than 90°) and the reversed velocity vectors of the neighbor cells with opposite swimming direction (with the angle between the velocities of neighbor and current cell larger than 90°) (26). We slightly modified the original Vicsek model; the velocity for each cell was updated by a direction summation of the velocities of neighboring cells in the Vicsek model, whereas in our simulation, the reversed velocity vector was used in the summation for a neighboring cell with opposite swimming direction (27). Cells stop moving during tumbles. For cells switching from tumble to run, a random number chosen with a uniform probability from the interval (−π, π] was used for the direction of velocity. The neighbor cells were referred to the cells within an interaction radius of R = 3 μm, about one cell length. The time step was Δt = 0.04 s. Each simulation was run for 100 s and was repeated 50 times at each cell density. To simulate the artificial situation when cell-cell collision resulted in randomized moving direction, each cell was assumed to collide with neighboring cells within a radius of 3 μm with a probability of 10%, and the direction of velocity was assumed to be uniformly distributed in (−π, π] when a collision happened.

We simulated chemotaxis using a stochastic model of chemotactic motion (28,29). Specifically, to determine the cell state (run or tumble), a coarse-grained model of bacterial chemotaxis was used (30). The relation between the ligand concentration L, the receptor activity a, and the receptor methylation level m was written as the following:

$$a=\frac{1}{1+e^{N\left(f\left(m\right)+g\left(L\right)\right)}},$$

$$\frac{dm}{dt}=k_R\left(1-a\right)-k_{B}a,$$

where N is the number of chemoreceptors in a Monod-Wyman-Changeux cluster, f(m) is the kinase activity in absence of ligand and is linear in m: f(m) = α(m₀ − m) according previous work (31), and g(L) is the ligand-dependent free energy: g(L) = ln (1 + L/K_I) − ln (1 + L/K_A). All parameter values we used were the same as before (29): K_I = 18.2 μM, K_A = 3 mM, N = 6, α = 1.7, m₀ = 1, k_R = 0.005 s⁻¹, and k_B = 0.010 s⁻¹.

The CheY-P concentration was assumed to be linearly dependent on the receptor activity (32): [CheYp] = k_a × a. As the activity a is 1/3 and [CheYp] is 2.62 μM for a wild-type cell in steady state, the value of k_a is 7.86 μM. The relation between motor CW bias and [CheYp] can be written as follows (33):

$$\text{CW bias}=\frac{{\left[CheYp\right]}^{10.3}}{{\left[CheYp\right]}^{10.3}+{3.1}^{10.3}}.$$

The switch rate of CCW to CW was calculated as k_ccw = CW bias/0.11 (29,34), whereas the switch rate of CW to CCW was assumed to be 5 s⁻¹ because the average tumble time is ∼0.2 s.

Results

Chemotaxis on a swarm plate

To test whether the swarmer cells can perform chemotaxis when put in a dilute bulk liquid environment, we collected some swarmer cells by gently rinsing the leading edge of a swarm (a region extending ∼5 mm into the colony) (22). We tracked their 3d trajectories and found that they showed typical run-tumble behavior. We also directly tested their chemotaxis behavior by putting them in a linear spatial gradient of MeAsp, using a microfluidic device, and found that they can perform chemotaxis in a free environment (see Supporting materials and methods for details).

To directly test whether bacteria can perform chemotaxis in a swarm, we sought to establish a gradient MeAsp for swarming cells on a swarm plate. A drop of high-concentration MeAsp was placed on the swarm plate and allowed to diffuse for over 10 h. To calibrate the spatial distribution of MeAsp, we substituted the MeAsp drop with a drop of fluorescein, which has a similar diffusion constant to MeAsp. Fig. S3 showed a photo image of the distributions of fluorescein on a swarm plate 13.5 h after the initial drops, which were 100 μL of fluorescein of different initial concentrations. The fluorescent intensity of the fluorescein, measured with an epi-fluorescent microscope, was an indicator of the concentration (Video S1. A sample video of a swarm edge, Document S2. Article plus supporting material A), and its spatial distributions were recorded as a function of time after the initial drop. An example of the distributions with a drop of 100 μL of 1 mM fluorescein is shown in Fig. S2 B.

Therefore, the gradient of MeAsp at the swarm edge at the time of observation can be quantified. Changing the initial concentration or volume of the MeAsp drop can change the specific gradient.

A complication is that the swarm agar/buffer is nutritious, containing a high concentration of attractants. To determine the equivalent MeAsp concentration in swarm buffer cultured with bacterium, we first measured the dose-response curve of a Tar-only (the chemoreceptor for MeAsp) E. coli strain by measuring its step response to various concentrations of MeAsp solutions (35). An example of the step responses is shown in Video S1. A sample video of a swarm edge, Document S2. Article plus supporting material A. The step response of the Tar-only strain to 1:500 diluted swarm buffer was then compared with the dose-response curve, which led to an equivalent MeAsp concentration in the swarm buffer of 794 ± 48 μM (Fig. S1 B), so there is a high concentration of background attractant on the swarm plate.

Even with this high background concentration of attractant, the chemotaxis in a bacterial swarm was obvious, as shown in Fig. 1. A protrusion at the swarm edge was present with a drop of 400 μL of 5 mM MeAsp (dissolved in swarm agar) establishing the attractant gradient (Fig. 1 A), whereas it was absent on a control swarm plate with a drop of 400 μL of swarm agar (Fig. 1 B) and a control swarm plate of a chemotaxis-defective strain HCB1736 (CheY^D13KY106W) with a drop of the same MeAsp (Fig. 1 C; Fig. S4).

Figure 1.

Photo images of a swarm colony with (A and C) and without (B) an MeAsp drop (dissolved in swarmer agar) to establish an MeAsp gradient on the swarm plate. A drop of swarm agar instead of MeAsp drop was used in (B). The wild-type strain HCB1 was used in (A) and (B), and the chemotaxis-defective strain HCB1736 was used in (C). The left panels are the images of whole petri dishes, and the right panels are the zoom-in views near the drop position. The dots denote the predicted attractant profile to guide the eyes. To see this figure in color, go online.

Furthermore, we tested chemotaxis of bacterial swarm for various attractants and repellents. Three amino acids (serine, leucine, and valine) and one sugar (glucose) were used to establish the chemical gradient by a similar method. Similar to the case of MeAsp, there was a protrusion at the swarm edge under serine (400 μL 5 mM drop) or glucose (400 μL 50 mM drop) gradient. In contrast, there was a depression under a leucine (400 μL 100 mM drop) or valine (400 μL 100 mM drop) gradient relative to the normal arc-shaped colony edge (Fig. S5 and S6).

Colony growth on a macroscopic scale is affected by many factors besides cell motion, such as nutrient consumption, surface tension, etc. We made sure to use nonmetabolizable MeAsp as the attractant, eliminated possible effects of disturbing the physical environment from adding the MeAsp drop, and performed multiple control experiments to show that the protrusion at the swarm edge is the result of chemotaxis. Nonetheless, colony growth is a qualitative indicator of chemotaxis rather than a quantitative measure. Therefore, we subsequently performed experiments to track individual cells so that we could quantify the chemotaxis behavior.

Quantifying chemotaxis performance in a bacterial swarm

To characterize the chemotaxis behavior in a bacterial swarm quantitatively, we intended to track the trajectories of individual cells on a swarm plate near the swarm edge, but the high cell density made that a difficult task. Therefore, we fluorescently labeled some of the bacteria in the swarm so that the density of the fluorescent cells is sparse enough for us to track individual trajectories (36,37). We recorded the trajectories near the swarm edge for ∼80 s for each swarm plate. A sample video is shown in Video S1.

For each trajectory, we separated it into two types of segments: toward the attractant (forward) and away from the attractant (backward), using as a reference the line connecting the cell inoculation point and the MeAsp drop position. We calculated velocity autocorrelation separately for the forward and backward segments as (5)

$$\text{Correlation}\left(\Delta t>0\right)={\langle \cos \left({\theta }_i\left(t\right)-{\theta }_i\left(t^{\prime }\right)\right)\rangle }_{t^{\prime }-t=\Delta t},$$

where Δt is the time lag, θ_i(t) denotes the angle of instantaneous velocity of the i-th cell at time t with respect to the reference line, and < > denotes average over all forward or backward segments with the time lag Δt. Fig. 2 A showed examples of the correlation curves from recording of one swarm plate at an MeAsp gradient of 80 μM/mm, which was fitted with an exponential function correlation (t) = A × e^−t/τ + C to extract the persistence time τ. The difference between the forward (τ_f) and backward (τ_b) persistence times characterizes the chemotaxis performance. We define the drift index as D_I = (τ_f − τ_b)/(τ_f + τ_b). The chemotactic drift velocity then approximately equals v × D_I, where v is the average cell swimming speed. The averaged persistence times from recording of 30 swarm plates at an MeAsp gradient of 80 μM/mm were τ_f = 0.410 ± 0.014 and τ_b = 0.316 ± 0.007s (mean ± SEM), resulting in a drift index of 0.13 ± 0.02. For comparison, we measured the persistence times of the wild-type strain, without adding the MeAsp drop, and the chemotaxis-defective strain under an identical MeAsp gradient (80 μM/mm), resulting in a drift index of 0.04 ± 0.01 and 0.00 ± 0.01, respectively. In total, we measured the persistence times for seven different magnitudes of MeAsp gradient on swarm plates, and the results are plotted in Fig. 2 B. We did not plot the drift index as a function of the gradient of the logarithmic MeAsp concentration. This was because the average MeAsp concentration we induced at the swarm edge ranges from 10 to 200 μM, whereas the background concentration in the agar is ∼800 μM; thus, the absolute concentration changed very little. For the wild-type strains, the drift index changed from 0.04 ± 0.01 to 0.16 ± 0.02 as the MeAsp gradient increased. In contrast, that of the chemotaxis-defective strain stabilized at 0 as the MeAsp gradient increased. This is similar to that observed in swimming cells (38).

Figure 2.

(A) Examples of velocity correlations for the forward (circles) and backward segments (triangles) for a swarm edge with an MeAsp gradient of 80 μM/mm. The solid lines are fits with an exponential function to extract the persistence time. (B) The drift index as a function of the MeAsp gradient. The circles are from the measurements of the wild-type strain HCB1. The triangles are from the measurements of a mutant defective in chemotaxis HCB1736. ΔC/ΔX of 0 corresponded to the control, swarming in the absence of MeAsp gradient. The symbols with error bars denote mean and mean ± SEM, each averaged from measurements performed on about 30 swarm plates.

Cell crowding enhances chemotaxis in a bacterial swarm

To investigate how the high cell density in bacterial swarm affects the chemotaxis performance, we sought to measure the persistence times as a function of cell density on a swarm plate. It was shown that the upper surface of an E. coli swarm is stationary (39); thus, the cells move between a fixed surfactant layer above and a fixed agar surface below, and placing a solid surface above the swarm plate did not affect their movement (22). We added a 2-μL drop of swarm buffer to the swarm edge to dilute the cell and placed a glass coverslip over the swarm edge so that we could track the cell movement with fluorescent imaging. The cell density of the diluted swarm edge is low initially but kept increasing so that some small cell clusters would appear in several minutes, and in ∼15 min, it recovered to the state of a normal swarm edge (Fig. 3). We tracked the trajectories of individual cells during this process and analyzed the chemotaxis performance as a function of cell density.

Figure 3.

The process of a diluted swarm edge recovering from fully diluted to the normal state. (A) diluted single-cell state at t = 0, (B) multicluster state at t = 3 min, and (C) normal state at t = 15 min.

We made sure that the 2-μL drop of swarm buffer (to dilute the swarm edge) did not noticeably perturb the established gradient of attractant by carrying out the same cell-diluting procedure on the gradient established with fluorescein on a swarm plate and monitoring the gradient before and after adding the 2-μL drop of swarm buffer. We also tested to make sure that adding 2-μL drop of swarm buffer did not perturb the physiology of the swarmer cells: We collected some swarmer cells by gently rinsing the swarm edge and put them in swarmer buffer at 30°C (the same buffer and temperature as a swarm plate). We measured the tumble frequency at various times after collection from swarm edge and found that it kept nearly constant in the range of 0.7–0.8 s⁻¹ in the period of 0–20 min after collection from the swarm plate.

We recorded ∼300 videos of the recovery of diluted swarm edges (each 80 s long) on different swarm plates, all at an MeAsp gradient of 52 μM/mm and analyzed the drift index as a function of cell density (triangles in Fig. 4 A). We fitted them with a Hill function, demonstrating the sigmoidal increase of the drift index with respect to the cell density. The cell density on a normal swarm edge fluctuates but is usually above seven cells per 100 μm².

Figure 4.

(A) The drift index as a function of cell density. Triangles are from measurements on diluted and recovering swarm edges at an MeAsp gradient of 52 μM/mm. Circles are from measurements with no added MeAsp gradient. The solid lines are fits with Hill function. (B) The degree of cell body alignment for the swarm system as a function of cell density. The averages were taken over square regions of size 2.5 × 2.5 L, where L = 5.8 μm was the mean body length of swarmer cells. The results are mean ± SEM. The solid line is the fit with Hill function.

For comparison, we also carried out similar measurements on diluted swarm edges with no added MeAsp gradient. The results are shown in Fig. 4 A as circles. The drift indexes were close to 0, demonstrating that the attractant gradient, possibly induced by cell-consumption of nutrients in the swarm agar, if it existed, is small compared with the MeAsp gradient of 52 μM/mm.

Enhancement of chemotaxis by increased cell density is correlated with increase in the degree of cell body alignment

Previous research found that on a quasi-two-dimensional substrate, collective motion and collision among motile rod-like cells could increase the cell alignment and led to nearly identical cell orientation in short distance (40), exhibiting self-organization akin to nematic liquid crystal ordering at high concentrations (41, 42, 43). The phenomenon was more obvious for myxobacteria because of the larger aspect ratio of the cell body (44,45). E. coli swarmer cells have a larger aspect ratio of the cell body than planktonic cells. It was reasonable to assume that the degree of local cell body alignment varied with the extent of collective motion resulting from changes in cell density in a bacterial swarm. To test this hypothesis, we measured the degree of cell alignment under different cell densities at the swarm edge without an MeAsp gradient.

We defined the degree of cell body alignment (DA) as

where ${\theta }_{ij}\in \left[0,\frac{\pi }{2}\right]$ was the angle between the long axes of the i-th and the j-th cell bodies, the average ⟨···⟩ was taken over all pairs of cells within regions of 2.5 × 2.5 L, where L was the mean body length of swarmer cells (L = 5.8 μm). Further averaging of DA was then calculated over the whole field of view. The results for the bacterial swarm are plotted in Fig. 4 B. The degree of alignment increased with cell density, and this relationship could be fitted with a Hill function. We also calculated the degree of alignment using different region sizes (1.5 × 1.5 L and 2 × 2 L), and the trends were similar (Fig. S7). Both the degree of alignment and the chemotaxis performance increased synchronously with increasing cell density (Fig. 4, A and B) in a way similar to a phase transition. It was therefore reasonable to infer that higher cell density increased the probability of cell body alignment and the size of cell clusters, and this enhanced the chemotactic ability of the swarm.

Analytical understanding of the chemotaxis enhancement in a swarm

Swarming bacteria form dynamic clusters or groups that move collectively (5,46), and cells in a cohesive group move with higher directional persistence (26), leading to longer effective run time. Considering a cluster formed by two cells, and assuming for simplicity that the cluster effectively tumbles only when both cells tumble, the effective run time of the cluster would be larger than that of individual cells, as shown below. If the cluster was running at time 0, denoting Q(t) as the probability of the cluster still running at t, then

$$Q\left(t+dt\right)=Q\left(t\right)-Q\left(t\right)\times 2\times \frac{{\tau }_T}{{\tau }_T+{\tau }_R}\times \frac{dt}{{\tau }_R}$$

where τ_R and τ_T were the average run time and tumble time of individual cells, respectively. This led to

$$Q\left(t\right)\propto e^{-t/{\tau }_{eff}}$$

and

$$P\left(t\right)=\frac{dQ\left(t\right)}{dt}\propto \frac{1}{{\tau }_{eff}}{e}^{-t/{\tau }_{eff}},$$

where P(t) was the distribution of run time for the cell cluster and τ_eff = (τ_T + τ_R)/(2τ_T) × τ_R is the average run time of the cell cluster. Therefore, the average run time of the cell cluster increased by a factor of (τ_T + τ_R)/(2τ_T) relative to that of individual cells.

For timescales much longer than average run time, the drift velocity for individual cells up an attractant gradient (without cell-cell interaction) can be written approximately as the difference between the average run length up and down the gradient divided by the total time, including the tumble time (47).

$$V_d=v\times \frac{{\tau }_{+}-{\tau }_{-}}{{\tau }_{+}+{\tau }_{-}+2{\tau }_T},$$

where v was the cell swimming speed, and τ₊ and τ₋ were the average run times up and down the gradient, respectively. As the average run time of the cell cluster increased by a factor (τ_T + τ_R)/(2τ_T), the drift velocity for the cell clusters is

$$V_d=v\times \frac{\left(\frac{{\tau }_T+{\tau }_{+}}{2{\tau }_T}\right){\tau }_{+}-\left(\frac{{\tau }_T+{\tau }_{-}}{2{\tau }_T}\right){\tau }_{-}}{\left(\frac{{\tau }_T+{\tau }_{+}}{2{\tau }_T}\right){\tau }_{+}+\left(\frac{{\tau }_T+{\tau }_{-}}{2{\tau }_T}\right){\tau }_{-}+2{\tau }_T}$$

$$=v\times \frac{{\tau }_{+}-{\tau }_{-}\left(\frac{{\tau }_T+{\tau }_{-}}{{\tau }_T+{\tau }_{+}}\right)}{{\tau }_{+}+{\tau }_{-}\left(\frac{{\tau }_T+{\tau }_{-}}{{\tau }_T+{\tau }_{+}}\right)+2{\tau }_T\left(\frac{2{\tau }_T}{{\tau }_T+{\tau }_{+}}\right)},$$

which is larger than that of individual cells without cell-cell interaction. Therefore, cell crowding-enhanced chemotaxis performance. For example, for an MeAsp gradient of 10 μM/mm, τ₊ and τ₋ differed by ∼5%: τ₊ ∼ 1.0 s, τ₋ ∼ 0.95 s, and τ_T ∼ 0.15 s (29); thus, using the equations above for individual cells, the drift velocity is ∼0.022v, whereas it is 0.046v for a cluster of two cells.

Simulation of the crowding-enhanced chemotaxis in bacterial swarm

To investigate the detailed mechanism of enhanced bacterial chemotaxis in bacterial swarm, we combined a stochastic model of chemotactic motion (28,29) and a Vicsek-type model for bacterial swarming (25,48) to simulate chemotaxis in bacterial swarm. In the simulation, cells were represented as self-propelled particles moving on a 2d surface. Each cell could be in either run or tumble state, determined by using a coarse-grained model of bacterial chemotaxis. Cells swim with constant speed during runs and stop moving during tumbles. To model the effect that cells aligned their moving direction as they approached or collided with each other (26), we used the following cell-cell interaction scheme. During runs, the velocity direction of a cell at each time step assumes the average velocity direction of the cells in the neighborhood (the reversed velocity was used in the average if the neighboring cell and the current cell are moving toward each other), with some random perturbation added. When a cell switches from tumble to run, a random angle chosen with uniform probability in the interval of (−π, π] was used for its velocity direction.

Using similar parameters as previous studies (25,29), the simulation reproduced the collective behavior in a bacterial swarm. Using a linear gradient of MeAsp concentration of 180 μM/mm with a background MeAsp concentration of 794 μM, the simulation showed that the drift index increased as cell density increased (Fig. 5 A, circles), with a trend consistent with that measured in the experiment. The MeAsp gradient used in the simulation was larger compared with the experiment, probably because the model of the chemotactic motion was based on parameters determined from cells grown in a bulk solution. Nevertheless, the combined simulation demonstrated the similar sigmoidal relationship between chemotaxis performance and cell density as measured in our experiments.

Figure 5.

Simulation results. (A) The drift index as a function of cell density in a linear MeAsp gradient of 180 μM/mm with a background MeAsp concentration of 794 μM. The circles with error bars are simulations with a modified Vicsek-type cell-cell interaction that induced cell alignment. The solid line is a fit with Hill function. The squares with error bars (SEM) are simulations with a cell-cell interaction that totally randomized cell moving direction after collision. (B) The average velocity of the group (normalized by the cell speed of 25 μm/s) as a function of cell density. The error bars are standard deviations. (C) The angle of the average velocity fluctuates randomly with time (left), resulting in uniformly distributed angles (right). (D) Under a linear gradient of MeAsp, the angle of the average velocity peaked toward the gradient. For (C) and (D), the cell density was 10 cells per 100 μm².

To demonstrate that the cell-cell interaction that induces cell alignment is critical for the enhancement of chemotaxis, we also tried a different cell-cell interaction scheme that totally randomized cell moving direction after collision. As shown in Fig. 5 A (squares), the drift index decreased to 0 as cell density increased.

Discussion

Here, we demonstrated that the swarmer cells can perform chemotaxis in their native 2d swarming environment (on a swarm plate). We found that the chemotaxis ability surprisingly increases as cell density increases; thus, cell crowding actually enhances chemotaxis ability, and this enhancement is correlated with an increase in the degree of cell body alignment. We explained this enhancement in a simple analytical model. Cells in a swarm tend to move collectively in clusters. The effective run time of a cell cluster increased compared with that of individual cells, and the factor of increment is larger for the run time up the attractant gradient than that down the gradient, resulting in a larger chemotactic drift velocity for cell clusters than individual cells without cell-cell interaction. By combining a stochastic model of chemotactic motion and a modified Vicsek-type model for bacterial swarm, we performed stochastic simulations of bacterial chemotaxis in a swarm and reproduced the sigmoidal increase of chemotaxis performance as cell density increases. We found that the chemotaxis performance would decrease with cell density if cell-cell interactions that totally randomized the cell moving direction were used in the simulation instead.

Our analytical model uses the idea that cell-cell interaction can increase running time. This does not seem to be explicitly used in our simulation that combines Vicsek-type model and chemotaxis. Nonetheless, it is effectively used. In the simulation, the angular change of velocity in a tumble will be affected by neighbors, so that when a cell tumbles, its angular change of velocity may not be large enough to be classified as a tumble; therefore, the run time is effectively increased.

From the simulation, the cell-crowding-induced enhancement of chemotaxis in a bacterial swarm can also be understood phenomenologically as follows. As cell density increases, the cell population undergoes a kinetic phase transition from near zero average velocity at low cell intensities to finite average velocities (Fig. 5 B). This is through spontaneous symmetry breaking of the rotational symmetry (25). However, in the absence of attractant gradient, the direction of the symmetry breaking is randomized (that is, the direction of the average velocity of the swarm fluctuates with time resulting in a uniform distribution of the direction) (Fig. 5 C). With a gradient of attractant, the symmetry breaking is directed approximately along the gradient, resulting in a peaked distribution of the direction of the average group velocity along the gradient (Fig. 5 D). Because the group velocity (after symmetry breaking) is much larger than typical chemotactic drift velocity of individual cells (tens of percent versus a few percent of the cell swimming speed), this finite average velocity of the swarm as directed along the gradient enhances bacterial chemotaxis in a swarm.

A recent work studied the chemotaxis of planktonic E. coli cells at various cell densities in a 3d environment (16), the difference was that the E. coli swarm, as studied here, is in a 2d environment, with elongated cell body length (aspect ratio ∼6:1), and with a higher cell density (area fraction of 0.1 − 0.7). The 2d geometry, the elongated body length, and the higher cell density tend more easily to induce collective motion of cells because cohesive moving of cells was previously shown to be unique to flagellated bacteria in a 2d environment (26). This collective motion resulted in enhanced chemotaxis for a bacterial swarm. The work of Colin et al. (16) and our work here were complementary for different dimensionalities, cell physiological states, and cell densities.

Although the chemotaxis pathway is dispensable for cells in a bacterial swarm, as long as their flagellar motors can switch direction spontaneously, wild-type cells in a swarm, nevertheless, can still perform chemotaxis. The chemotaxis capability offers the swarmer cells survival benefits when there is a stimulus present ahead by allowing their movement toward the beneficial stimulus. This chemotaxis capability, in turn, is surprisingly enhanced by the collective movement of the bacterial swarm.

Author contributions

J.Y. and R.Z. designed the work. M.T. performed the measurements with help from C.Z. on the microfluidics and FRET experiments. C.Z. performed the simulation; all authors wrote the work. M.T. and C.Z. contributed equally to this work.

Editor: Julie Biteen.

Supporting citations

References (49, 50, 51, 52, 53, 54, 55, 56) appear in the Supporting materials and methods