Length heterogeneity of flexible bacteria enhances swarming

Abstract

Bacterial swarming is a phenomenon characterized by the rapid migration of microorganisms on a surface powered by flagella. While extensive studies have explored various factors influencing swarming dynamics, the impact of length variation within a single strain on swarming remains to be elucidated. Here, we investigate the effect of length variants within a single strain, Vibrio alginolyticus, as an ideal model to explore the cooperative mechanisms driven by a heterogeneous, flexible population. Through individual cell tracking, we found that cell length directly impacts collective organization. Long, flexible cells move faster and more persistently than shorter cells, promoting the emergence of large-scale, coordinated flow. In contrast, shorter cells slow down due to frequent reverse movements, which create spaces and prevent jamming within the dense colony. This division of labor, where longer cells act as leaders and shorter cells serve as buffers, facilitates efficient collective movement and demonstrates the significant advantage of phenotypic heterogeneity within a single strain for robust swarming. Our findings suggest that the diversity in length of active matter may facilitate efficient spreading across soft interfaces.

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I. Introduction

Bacterial swarming is a phenomenon in which large numbers of bacteria rapidly migrate across a semi-solid surface using flagella,^1,2 and is influenced by surface conditions and cell physiology.^3–7 During swarming, bacteria can exhibit coordinated movement and self-organization, often forming complex patterns with spatiotemporal fluctuations in density.⁸ To initiate swarming from the planktonic state, it is essential for a series of differentiations in the bacterial phenotype to occur. The elongation of the cells and the increase in lateral flagella enhance cell-to-cell contact, allowing bacteria to transfer more efficiently across surfaces.^9,10 However, this elongation is also related to inhibition of cell division, which may further contribute to the enhanced bacterial coordination and surface movement.^11–13

From a dynamic perspective, numerous studies have explored the flow fields observed in bacterial swarming to gain a comprehensive understanding of swarming dynamics, ranging from smaller to larger scales. These studies encompass chaotic trajectories,^14,15 active turbulence,^16–18 and active nematic defects.^19–21 Central to these analyses are the correlations and the distributions of velocity and vorticity, with particular emphasis on their temporal and spatial characteristic scales. These swarming dynamics are known to be influenced by long-range hydrodynamic interactions and short-range repulsion due to volume exclusion.^19,22–24

Recently, the effect of different cell aspect ratios on these dynamics has been studied.^13,25,26 One study on a single-strain with length-mutated Bacillus subtilis (hereafter B. subtilis) has shown that the strain with an aspect ratio close to the wild-type cell exhibits faster movement. In contrast, for the system of two length-mutated strains, a small proportion of longer cells enhanced the movement of the entire population while the longer cells tended to move more slowly.²³ Despite these findings, the measurements were often averaged across entire strains, potentially masking the specific roles of individual cells with different lengths. This raises intriguing questions about the contribution of individual variants within the same strain to swarming behavior.

To investigate this issue, we experimentally examine the dynamics of mono-layered bacterial swarming of variants of Vibrio alginolyticus (strain YM19), an elongated flexible bacterium that exhibits a range of lengths within a single strain. By tracing the positions of single cells, we found that longer cells are more motile and contribute to the aligned collective motion observed in swarming, while shorter cells tend to exhibit more lateral movements and reversals, which create space within the swarm. This combination of behaviors enhances the overall motility of the cell swarm. As a result, swarming bacteria with length heterogeneity are able to travel quickly and effectively together, demonstrating that length variation can be advantageous for collective movement.

The paper is organized as follows: in Section II, we provide a detailed explanation of our experimental methods and image analysis. Section III presents the length distribution of cells within a single strain and explores the diverse motions of cells with varying lengths. Section IV discusses the impact of cell lengths on the coherent and density fields. In Section V, we identify the lengths of swarming clusters and examine the role of long cells within these clusters. Finally, Section VI summarizes our conclusions.

II. Experimental method

Cell growing

V. alginolyticus is a Gram-negative and halophilic bacterium that flourishes in the marine environments^27,28 equipped with two flagella systems, polar flagella (Pof) and lateral flagella (Laf), and generates thrust in aqueous or higher viscous environments, including the surface. During swarming on agar surfaces, V. alginolyticus reduces division and elongates, producing heterogeneous length distribution. A polar flagella-defective strain of V. alginolyticus (YM19, Pof⁻, Laf⁺) was used throughout this study.²⁹

Prior to the plate making, a scratch of YM19 is taken from −80 °C stock and cultured overnight in 5000 µL autoclaved growth medium (supplemented with 3% NaCl, 0.5% polypeptone, 0.5% yeast extract, 0.4% K₂HPO₄, and 0.2% glucose) at 30 °C. As representative bacteria in the group of robust swarmers, YM19 exhibits swarming behavior on hard agar surfaces, in contrast to the temperate swarmers.^9,12,25 0.5 µL YM19 overnight culture was then inoculated at the center of a 30 mm glass-bottom Petri dish filled with 1% agar, as shown in Fig. 1(a). A swarming colony expanded after a lag phase, and it was recorded approximately 6 hours after inoculation.

Fig. 1 (a) The inoculation process of YM19 at the center of the agar dish (bottom). The middle and the top images are the swarming colony and its protrusions under a 4× objective lens, respectively. (b) The spatial distribution of bacteria under a 60× objective lens, color-coded according to bacterial lengths L, where the white dots mark one of the ends of the bacterium. (c) The bacterial length distribution and the four colored sections of length groups. (d) The spatial distribution of bacteria within the same region as (b), color-coded by four length groups, and (e) the averaged field 〈L〉 of the bacterial length distribution, respectively. 〈L〉 is calculated using Gaussian smoothing with a standard deviation σ = 1.76 µm and a spatial smoothing window of approximately 50 µm².

Recording and image analysis

Monolayer regions can be observed through a phase contrast microscope (Nikon Ti-U) with a 4× objective lens, as the region shown in the first inset of Fig. 1(a). Their detailed swarming motion was then captured under a 60× objective lens (Nikon, S plan fluor ELWD 60×) with a CCD camera (AVT Prosilica GT1910). This setup captures full HD images with a resolution of 1920 × 1080 pixels at 50 frames per second. Tracking individual cells is crucial for determining variations in cell length. However, the YM19 strain possesses a long and curved body, which makes tracking and segmentation more challenging compared to previous studies on B. subtilis. Neither point-tracing methods,⁸ nor machine learning approaches^30,31 can consistently recognize the shape of bacteria in dense populations, particularly long and flexible YM19. To obtain a stable and comprehensive dataset of the position and shape of each bacterium, we employed the ImageJ plugin JFilament, which implements the ‘Stretching Open Active Contours’ algorithm³² to semi-automatically separate the bacteria from the background. Then, we manually corrected the cell images obtained from the previous process to improve the accuracy in dense images.

To investigate individual cell dynamics, we analyzed 500 frames of images over 10 s intervals and tracked ∼240 cells (∼10% population) in each frame, which is sufficient for active cells to traverse the field of view and provide a representative sampling of swarming dynamics. For the study of bacteria spatial distribution, we separately analyzed two 10-frame bursts separated by 10 s, yielding snapshots of ∼2300 to 2400 cells per frame that capture collective organization. Since the swarm evolves continuously under non-equilibrium growth, two bursts with a finite sampling window capture spatial organization at a well-defined stage of colony expansion. We also used another ImageJ plug-in, OrientationJ,³³ to extract the orientation of bacterial arrangement and the alignment coherence.

Data analysis and statistics

Individual bacterial velocity v⃑ or speed |v⃑| was calculated from the midpoint displacements between consecutive frames, divided by the frame interval (0.02 s). It provides a reproducible metric of motility at our experiment resolution.

Identification of swarming cluster, representing the rapid collective behavior, requires a robust measure to prevent misclassifications caused by local motion of elongated cells. To achieve this, we computed body-averaged speeds by choosing points along the cell centerline and averaging their displacement between consecutive frames. Active motile cells were defined as those with a body-averaged velocity greater than 10 µm. We then connected nearby candidate bacteria based on spatial proximity, using a threshold distance of 0.95 µm (∼1.2 × cell width). Clusters containing at least 2 members were classified as swarming clusters to effectively represent collective motion. After the initial grouping, an optional refinement step was performed to ensure that the mean velocity difference within each group was within 25 µm s⁻¹. Although this step rarely changed the results, it helped to confirm that identified clusters exhibited robust collective motion.

Statistical significance among different groups based on cell length or cluster size was evaluated using Kruskal–Wallis test followed by Dunn's post-hoc test with Dunn–Šidák correction, which are suitable for non-parametric data distribution.

III. Individual variants within a strain and their interaction

To examine the effect of length variants on swarming dynamics, we first identify individual cells and determine the distribution of cell lengths L within a single strain of YM19. Fig. 1(b) illustrates the spatial configuration of the monolayered swarming bacteria, color-coded according to the bacterial lengths in a dense population. This configuration reveals that the degree of cell elongation induced by surface sensing, varies significantly among individuals, resulting in a wide distribution of cell length, as shown in Fig. 1(c). Cell lengths range from 1.3 µm to more than 20 µm. Since cell widths are narrowly distributed from 0.6 to 0.8 µm, the aspect ratios of length to width are predominantly influenced by this considerable heterogeneity in cell lengths. We classified cells into four groups based on the length distribution, each spaced by intervals of 2.55 µm. As depicted in the colored sections of Fig. 1(c), these four groups are denoted with the center value of the section, such as 3.1, 5.7, 8.2, and >9.5 µm. This classification aids in understanding the role of length variants in the dynamics of bacterial swarming. Based on this category, as shown in Fig. 1(d), recolored bacteria exhibit the spatial arrangement of YM19 across different length groups. Fig. 1(e) presents the averaged bacterial length field, denoted as 〈L〉, derived from the spatial configuration of bacteria with various lengths. It was obtained through Gaussian smoothing with a standard deviation of σ = 1.76 µm and applied to an observed window of approximately 50 µm². The cells are spatially non-uniformly distributed, which demonstrates a clear spatial segregation of YM19 bacteria by length. This indicates that longer and shorter cells do not mix randomly but occupy distinct regions within the swarming bath.

Next, we turn our attention to the individual behavior of cells. Since the spatial configuration of bacteria is not uniform, their motions can be different. Fig. 2(a) and Movie S1 demonstrate the diverse motions of several bacteria. The cell trajectories were determined by tracking the midpoint of the bacteria over a 2-second period. We observed three distinct patterns of the trajectories: (i) the short runs accompanied by the irregular rotation, (ii) the wiggle motions, and (iii) the long and smooth trajectories. Longer cells (yellow-green) show smooth and persistent navigation, and short cells (green) prefer to exhibit irregular rotations and intermittent dash runs. Cells of intermediate length tend to follow curved paths that lie between the aforementioned trajectory styles.

Fig. 2 (a) Trajectories (pink dashed line) of example bacteria on the snapshot of the microscope within 2 s, where the example bacteria are colored based on their lengths. (b) and (c), mean square displacement and the midpoint speed distribution of the bacteria according to their group of lengths, respectively. The gray lines in (b) are the fitting curves according to eqn (1) and the inset in (b) indicates the persistence time, τ, for the four length groups. (d) and (f) The sketches of the measurement on θ_Rv and θ_v, respectively. The sketches below are the criteria for (d) the active and passive motion and (f) the forward and reverse motion. Green lines, red arrows, and the dotted green arrow denote the measured bacterium in time series, the velocity at the nearby time, and the main axis of the bacterium, respectively. (e) The histogram of the angle θ_Rv between the main axis R⃑ of each bacterium and the velocity v⃑ at the middle point, where the gray area belongs to the active motion. (g) The histogram of the angle θ_v between the midpoint velocity of the bacteria v⃑_t and v⃑_t+dt in the time nearby with the time interval 0.02 s and the measurement based on the sketch in (f), where the gray area belongs to the forward motion. Different lines in (e) and (g) represent different length groups of bacteria as the color label in (c).

To quantify the motility of the cells, we calculated the mean square displacement: MSD = 〈|r⃑(t + Δt) − r⃑(t)|²〉, where Δt is the lag time and r⃑ is the position vector of the cells. As shown in Fig. 2(b), MSD values of the longer cells are higher than those of shorter cells, indicating the longer cells move faster. Furthermore, the cells exhibit super-diffusive behavior at short times, with scaling exponents α ranging from 1.6 to 1.8 and the Brownian-like diffusion at long time scales [Fig. 2(b)], regardless of the length groups. Thus, with two exponents of Brownian-like and ballistic-like motions, we can rewrite the MSD as follows:³⁴

MSD = 2D_A[Δt − τ(1 − e^−Δt/τ)] (1)

where τ is the persistent time of bacteria, indicating how long bacteria move persistently. Here, D_A represents the diffusion coefficient of bacterial motion. The persistence time, τ, is obtained by fitting MSD with eqn (1). It increases with increasing bacteria length and eventually saturates, as shown in the inset in Fig. 2(b). These findings reveal that cells move faster and more persistently as their length increases. We also checked the speed distributions, P(v⃑), for each length group. Here, velocity is defined v⃑ = [r⃑(t + Δt) − r⃑(t)]/Δt at the middle point vector, r⃑, of the cell. The stretched tails in P(v⃑) of the long cell groups compared to those of the shorter counterpart groups further illustrate this trend [Fig. 2(c)]. This finding is inconsistent with the previous study,²³ which found that shorter cells move faster. It may come from the fact that YM19 has a flexible body in contrast to the rigid body of B. subtilis. Additionally, the groups of short bacteria display an exponential decay in their speed distribution, indicating that these short cells do not retain a memory of their motion [Fig. 2(c)]. Importantly, these behaviors are not solely determined by the number of lateral flagella but are also shaped by intercellular interactions.

Further analysis explores additional possible factors that contribute to the intricate interaction among cells. Propelled by the flagella, the rod-like swarming bacteria can only navigate along their main axis. However, in a densely populated environment, jostling motion becomes inevitable, leading to lateral movements. The sketch in Fig. 2(d) illustrates these two possible movements (active and passive motions) of the bacterium. The former indicates the motion powered by itself, and the latter is induced by the collision with other cells. While bacteria typically exhibit a combination of both types of motion, the dominant motion can be classified according to the prevailing mode. The passive and active motions can be quantified by assessing the angle θ_Rv and the velocity v⃑ = [r⃑(t + Δt) − r⃑(t)]/Δt, where θ_Rv is measured between the end-to-end vector R⃑ of the cell. In the figure, the gray area represents the active dominant motion with |θ_Rv| smaller than 45° or greater than 135°, and the other belongs to the passive motion. The probability density function (PDF) of θ_Rv, P(θ_Rv), in Fig. 2(e) shows that P(θ_Rv) of short cells at the passive region is higher than that of other groups, indicating that the motion of short bacteria is more likely to be affected by neighbors.

Additionally, YM19 displays a bilateral motion, as shown in Fig. 2(a). It moves backward when its movement is restricted by its surroundings, indicating that bacteria adapt to reverse motion to avoid jamming. As shown in Fig. 2(f), the degree of reverse motion is measured by the angle change θ_v between the velocities over time v⃑(t) and v⃑(t + Δt) with Δt = 0.02 s (red arrows). The reverse motion is identified when |θ_v| is greater than 90°; otherwise, the bacteria continue moving with the same midpoint considered as the forward motion. The histogram of θ_v in Fig. 2(g) shows that short cells exhibit reverse motion more frequently than long cells.

IV. Interaction with the environmental fields

In the previous section, we focused on the motions of individual cells involved in complex intercellular interactions. Here, we shift our attention to the environmental fields, including coherence, density, and velocity fields. In particular, the study of these fields emphasizes the significance of collective motion and the role of self-organization in creating group patterns. Fig. 3 depicts the coherence field, coh, of the bacteria alignment, and the density field, ϕ, in the left and right panels of Fig. 3(a) and Movie S2, respectively. The groups (dashed circles) with the maximum coh at their center move persistently for a long time and navigate through less crowded areas. Following the movement of the swarming group, several low-density and disordered areas remain, denoted by the white arrows. This creates new spaces that can be filled by incoming cells, which not only aids in the disintegration of the swarming groups that have already passed but also allows for the realignment and emergence of new clusters in a dynamic cycle.

Fig. 3 (a) The snapshots of the environmental fields at 1 s, where the right and left panels are color-coded by local density ϕ and coherence coh of the bacteria alignment θ, respectively. The gray arrows and dashed lines in the panels indicate the emergence of dense and coherent packs, as well as their direction of movement, while the white arrows highlight the sparse areas left behind by these dense and coherent packs. (b) The speed |v⃑| and the local coherence coh near the example bacterium (5.7-length group) over time, where the background with yellow intervals indicates the moments when passive motion occurs. (c) 2D Joint histograms of the phase space projections, constructed by coh, ϕ, or |v⃑|, of the longest and the shortest length groups. (d) The average of coh (light blue line), ϕ (deep blue line), and |v⃑| (pink line) over bacteria length groups. Error bars were obtained from bootstrap using 1000 resamplings of size 1000.

The re-alignment process is closely linked to cellular interactions, as illustrated in Fig. 3(b). We compared the midpoint speed |v⃑| and coh surrounding a specific bacterium to the moment of its passive motion (yellow intervals) over time. As also demonstrated in Movie S3, passive motion is caused by jostling between individuals and is correlated with decreased local coh. It is clear that the cell experiences a reduction in velocity, |v⃑|, during passive motion, followed by an immediate increase in speed afterward. This behavior arises from a series of realignments driven by collisions within the dense population, allowing the bacterium to navigate quickly and directly by joining a swarming group with high coh. Shorter cells, being more influenced by their neighbors, contribute to improved local swarming efficiency through this passive motion.

This phenomenon is illustrated in 2D joint histograms for two groups, the shortest (3.1 µm) and longest (>9.5 µm) length groups, as shown in Fig. 3(c). In both groups, ϕ is strongly correlated with coherence coh. However, the cells in the longest length group are localized in the region where both ϕ and coh are high. These longest cells exhibit higher velocity, primarily localized at higher ϕ and coh. In contrast, the cells in the shortest length group move slowly but are distributed over the entire ϕ and coh. These observations highlight the relationship between cell length and their swarming dynamics as well as their collective behavior. The long cells are found in highly aligned and concentrated swarming areas, whereas the short cells are less aligned with their neighboring cells, even in regions of high concentration.

Fig. 3(d) presents the average values of the coherence field 〈coh〉, density field 〈ϕ〉, and the speed 〈|v⃑|〉 for four different length groups. These values support the trends visually observed in Fig. 3(c) and (d) and further highlight the difference between short and long cells. The density 〈ϕ〉 remains steady at around 0.8 across all lengths, reflecting that bacteria, especially longer cells, spend most of their time within dense packs. Moreover, the mean velocity 〈|v⃑|〉 exhibits a clear upward tendency with increasing bacterial length, consistent with previous findings in Fig. 2(b), (c) and 3(c). In contrast, the coherence field 〈coh〉 also increases with cell length, largely due to the benefits of volume exclusion presented by longer cells.³⁵ This property enhances the organization of neighboring cells, intensifying the clustering effect. However, the saturation of 〈coh〉 can be attributed to the flexible structure of long YM19 cells, which allows for greater adaptability to varying environmental conditions.

V. Bacterial swarming clusters

Configuration in the bacterial swarming clusters

We now determine the size of swarming clusters based on coherence and velocity fields, which is a crucial factor to characterize the swarming dynamics of bacteria. Fig. 4(a) and (b) illustrate the velocity fields in magnitude |v⃑| and direction field v_θ within 0° to 360°, respectively. When a high-velocity group emerges, the alignment of bacterial cells along their swarming directions becomes important. The clusters are predominantly composed of bacteria with similar movement patterns. The alignment of cells fosters positive feedback in collective motion, allowing high-speed cells to carry surrounding cells through slight realignments by collisions. These active swarming clusters, mostly colored in light blue, are apparent and associated with faster motion, close to 40 µm s⁻¹, deviating from most other bacteria, which are colored in deep blue [Fig. 4(a)]. In contrast, in less active regions (deep blue), bacterial motion is characterized by frequent reversals, irregular rotations, and short runs, as noted in Fig. 2(a). Moreover, the areas with inhomogeneous v_θ reflect slower velocities or even the immobility of cells, indicating that the bacteria are jammed due to the surrounding bacteria having different alignments since YM19 can only move toward its end directions.

Fig. 4 (a) and (b) The snapshots of the bacteria color-coded by the fields of velocity in magnitude and directions v_θ from 0° to 360°, respectively. (c) The spatial correlation function g(r) of coh, |v⃑|, and v_θ denoted in different lines. The solid gray lines are the references. (d) The configuration of bacteria color-coded by different swarming clusters with similar speed, where the bacteria colored in gray and white are the bacteria in an inactive region or with the number of cluster members n smaller than the criterion 2, respectively. (e) The percentage for the area (left chart) and the number (right chart) of bacteria in the swarming cluster, small active cluster, and inactive cluster. (f) The cluster size distribution on a logarithmic scale.

Fig. 4(c) shows the spatial correlation g(r) in relation to coh, |v⃑|, and v_θ, which is defined as

where M_r0 refers to a variable at distance r₀ and M_r0+r pertains to the variable at a distance r away. Here, μ and σ² represent the mean and the variance of M throughout the space. The variable M includes coh, |v⃑|, and v_θ for each g(r) curve, respectively. An exponential decay was observed in three of the g(r) curves. The v_θ curve exhibits the steepest decay rate, with a corresponding correlation length of v_θ (about 2.2 µm), which is shorter than that of |v⃑| (about 4.0 µm). The correlation length of coh falls in between these two values, as coherence can be enhanced in both active and inactive regions through the jostling of bacteria, as shown in Fig. 3(b). The rapid decline of all the spatial correlations indicates a short-range interaction between cells associated with the limitation of velocity coupling. Only nearby cells significantly influence each other's velocities, resulting in localized interactions where dynamics heavily depend on the local cell configuration.

As previously discussed, since swarming clusters are characterized by rapid and collective motion, we can determine their size based on experimentally obtained information. Although high-speed cells predominantly maintain their speed as they move in a consistent direction, a small fraction may occasionally deviate from this path, though such instances are infrequent and typically short-lived. Therefore, we identified swarming clusters by selecting actively motile cells (body-averaged speed ≥10 µm s⁻¹, based on Fig. 4(a)) and grouping those in close proximity. Clusters with more than two members exhibited stable collective motion and were classified as swarming clusters (see Methods for details). In this context, we define the size of a swarming cluster, denoted as n, as the total number of bacteria within the cluster. We note that only swarming clusters with n > 2 are considered since they effectively represent collective motion. Fig. 4(d) illustrates the spatial configuration of the resulting swarming cluster within the observed window, depicted in distinct vibrant colors. Bacteria colored in white and gray are associated with the small active region and inactive region, respectively. Those swarming clusters tend to form a comet-like shape with a stretched tail, followed by a mass of bacteria that contributes to higher motility within the colony.³⁶ The left and right panels of Fig. 4(e) compare the occupied area to the number of bacteria, categorized into three regions: the swarming cluster, the small active region, and the inactive region. For the swarming cluster, the number fraction decreases in comparison to the area fraction, indicating that longer cells are predominantly found in this area, while shorter cells are mainly concentrated in the inactive region.

Fig. 4(f) shows the size distribution of the swarming clusters with an average size of approximately 20 cells. The temporal variations in the sizes of these swarming clusters result from splitting and merging clusters or active cells over time. Several studies^37,38 assuming cells as rigid rods showed that it has a power law decay, p(n) ∼ n^−β, whose scaling exponent β is between 0.9 and 1.3. However, in our system, β is approximately 1.7, which can be attributed to the long and flexible bodies of cells, as well as the diversity of cell lengths. It also agrees well with the experiment of a 2D model of Myxococcus xanthus³⁵ and the simulation of the dense system of flexible self-propelled rods, interacting by a soft volume exclusion.^39,40

Composition of individual variants in swarming clusters

As discussed above, the individual variations in cell lengths are related to swarming behaviors, which raises further questions about bacterial length fraction within a given size of swarming clusters and its relationship to swarming clusters. To check this, we computed the enrichment ratio F^L_n ≡ f^L_n/f^L_tot for four predefined length groups within the given cluster size n, where f^L_n is the fraction of a given length group within clusters of size n, and f^L_tot is the corresponding fraction of the entire population. This ratio tells us whether specific length groups are preferentially enriched (F^L_n > 1) or diminished (F^L_n < 1) in swarming clusters of a given bacterial size. As shown in Fig. 5(a), regardless of the cluster size, the value of F^L_n for long cells is always greater than 1, indicating that the swarming clusters contain more long cells. Furthermore, F^L_n of long cells even increases with increasing sizes of swarming clusters. The medium-sized cells are also enriched in the clusters. In contrast, the population of the shortest group of cells is less than 1, indicating that many short cells are located in the non-cluster areas. These observations are in accordance with the implications presented in Fig. 4(e). We also measure the cell velocity in the same clusters. Within the cluster, all cells move together, regardless of their length. Moreover, as the swarming clusters grow larger, the mean bacterial speed rises. Thus, when a large number of longer cells are in the swarming system, the swarming cluster becomes larger and swarming efficiency improves [Fig. 5(b)].

Fig. 5 (a) Enrichment ratio F^L_n ≡ f^L_n/f^L_tot is shown for four bacterial length groups within all the swarming clusters (left panel). The right panel shows a breakdown by five cluster sizes n shown within each group. The ratio F^L_n quantifies the enrichment or depletion of specific length groups in cluster size n, relative to their abundance in the overall population. Asterisks denote significance (Dunn's test). (b) The mean bacteria velocity, 〈v⃑〉, within clusters is shown for different n. Error bars represent the standard error of the mean. (c) and (d) The configuration of the long cells among swarming clusters (multiple colors correspond to different swarming clusters) and inactive regions (pink), where the long cells belong to the top one (c) and two (d) longest length groups separately. The white and gray bacteria are the small cells inside and outside the swarming clusters, respectively.

Fig. 5(c) and (d) depict the bacterial clusters (represented by white cells), emphasizing the top one (c) and two (d) longest cell groups in colors. The bacteria colored in pink are the long cells that do not belong to the swarming clusters. Fig. 5(c) shows that most of the long cells (the longest group) move within or in proximity to the swarming clusters, addressing the significant role of the long cells in the formation of swarming clusters again. When the criteria for long cells are adjusted to include a shorter length range (top two longest length groups), a noticeably greater number of long cells are found outside the cluster, as shown in Fig. 5(d). These indicate that the long cells move fast and lead the movement of the shorter cells, which constitute a majority of the population.

VI. Discussion and conclusion

This study experimentally investigated the effect of individual cell length variation within the single strain of robust swarmer V. alginolyticus (YM19) on swarming dynamics. The elongation of this bacteria during differentiation provides significant intra-strain phenotypic diversity,^9,12 making it an ideal model to dissect the roles of individual variants. Our investigation, centered on the monolayer collective motion of YM19 with its intra-strain cell length variations, helps uncover the mechanisms driving cooperative behavior among individual variants in swarming colonies.

The key finding in this swarming system is that the heterogeneity in cell length within the same strain provides a functional advantage that enhances the efficiency of bacterial swarming in the compact state. This effect is achieved through a cooperative division of labor among cells of different lengths. The longer cells exhibit higher motility and typically lead the swarming clusters, while the shorter cells, which make up the majority of the population, act as a buffer. This observation contrasts with previous findings in B. subtilis, where the motility of long cells is lower than that of short cells.^13,25 This discrepancy can be attributed to the characteristics of V. alginolyticus, which possesses a longer and more flexible body than B. subtilis. As a result, V. alginolyticus can maneuver around obstacles by bending, avoiding the formation of immobile clusters that occur in the more rigid, rod-like B. subtilis. Consequently, the trajectories of longer V. alginolyticus cells display sustained and smoother patterns of movement.

Beyond individual motility enhancement, cell length also significantly impacts collective alignment through volume exclusion, a crucial factor in dense monolayer systems.³⁵ Our analysis reveals that when short cells collide, they may simply deflect, experiencing relatively weak geometric constraints that would force perfect alignment. In contrast, the long cells impose stronger geometric restrictions, which limit their rotational freedom, enhancing their tendency to align with neighbors and the local flow. This length-dependent enhancement of alignment, stemming directly from cell shape, appears to be a key factor promoting the large-scale coordinated flow and emergent order characteristic of bacterial swarms. Cell length, therefore, directly amplifies the organizational impact of volume exclusion on collective dynamics.

These microscopic interactions and alignment tendencies collectively shape the macroscopic structure and dynamics of the swarm, such as density and alignment coherence across space and time. These fields exhibit distinctive swarming patterns, with local fluctuations reflecting the intensity of collective movement. High-coherence regions correlate with high density, signifying the presence of strong collective motion, where bacteria move swiftly as a cohesive swarm. In addition to alignment driven by volume exclusion, the realignment through jostling between cells is crucial in indirectly enhancing both coherence and propagation speed, promoting the stability of swarming clusters. Conversely, low-density regions lead to decreased coherence, resulting in the disintegration of swarming clusters or the formation of new ones.

These swarming clusters are crucial to the population transport, with bacteria motility amplified by collective interactions that strengthen as the cluster grows. The long cells play a crucial role in driving and maintaining swarming clusters despite their relatively small portion of the total population. Moreover, the presence of long cells directly influences the size of the clusters. Hence, as the clusters grow larger, the number of cells with the longest length increases consistently. In contrast, although the short cells constitute the majority of the population, a smaller number of cells than the average number of short cells in the total population participated in the swarming clusters, suggesting that they are either accompany the swarming clusters as background cells or are even excluded.

By integrating these observations, we propose that long and short cells play distinct yet cooperative roles in swarming. The long cells move quickly, align strongly, and appear to initiate and drive the dense, rapidly moving clusters. A large portion of short cells is located in lower-density regions between clusters. Here, they may act as buffers, mitigating alignment between clusters, potentially preventing jams between clusters, and maintaining open pathways. The fact that larger clusters contain more short cells suggests a system where the group's capacity and efficiency benefit from this teamwork between different cell lengths. Such collaboration, using a mix of lengths, might not be possible in groups where all cells are the same short length.

In conclusion, this study highlights the importance of cell length variation in understanding microbial collective motion. By analyzing the behavior of V. alginolyticus with varying lengths within the same strain, we discovered that longer cells drive collective motion and alignment within clusters, while shorter cells create buffers for new cluster fronts, which demonstrates how heterogeneity can be a crucial factor in enabling efficient and robust collective behavior. Our findings provide insights into the fundamental principles of self-organization in active matter, potentially enhancing our understanding of collective dynamics in other biological systems. Further investigations are necessary to explore these principles across different species and environmental contexts.

Conflicts of interest

The authors have no conflicts to disclose.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Supplementary information (SI) is available. See DOI: https://doi.org/10.1039/d5sm00798d.

Acknowledgements

The authors would also like to acknowledge M. Homma at Nagoya University for generously providing the YM19 strain essential to this work. This work has been supported by the National Science and Technology Council of Taiwan under Grants No. 112-2112-M-008-030 – (Y. J.) and No. 113-2112-M-001-059-MY3 (C.-J. L.).

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