What is swarming growth

Some bacteria such as E. While cells do get to the bottom of the colony, they rarely migrate to the upper parts of the colony, which contain mostly liquid. It was found that secreted biosurfactants keep bacteria away from the swarm-air upper boundary, and that added antibiotics at the lower swarm-surface boundary lead to their migration away from this boundary.

Formation of the antibiotic-avoidance zone is dependent on a functional chemotaxis signaling system, in the absence of which the swarm loses its high tolerance to the antibiotics. Once again, we see that the biological properties of cells repulsive chemotaxis affects the physics of the system and the environment each cell senses.

One of the striking observations in swarming bacterial colonies is that swarms can carry or transport materials, such as small beads [ 10 ] or even other organisms. It has been shown that P. While the precise mechanism in which P. Some species, such as myxobacteria [ 72 , , , ], migrate collectively on surfaces using motive organelles different than flagella. These include, for example, motors that are based on pili, and gliding slime.

Studies on myxobateria revealed that periodic reversals in their motion on agar allow them to spread efficiently, and that mutants lacking some genes migrate poorly [ ]. Other studies demonstrated, experimentally and theoretically, the role of a biochemical signaling system where intracellular dynamics, contact-mediated intercellular communication, and cell motility all lead to group behavior producing collective motion and intricate periodic patterns in a form of waves [ 64 , 69 , ].

Theoretical myxobacteria-related studies include discrete [ 69 , 97 , 98 ] and continuum [ 27 ] models, each suggesting different types of interactions between the individuals among the group. In [ 68 ], Jeckel et al. Using machine learning clustering techniques, they identified 3 distinct dynamical states: a low-density single-cell phase; a high-density rafting phase with a high percentage of comoving cells and a biofilm phase characterized by long, unseparated cells.

Two coexistence phases were also observed. Bacterial swarms are a fascinating natural system exhibiting collective motion in which millions of cells participate in generating complex motion patterns. One of the main reasons for the difficulties in deciphering the basic principles underlying the swarm formation and its dynamics is that both physics and biology play a pivotal role.

It is clear that cells obey the laws of physics and are constrained by the physical principles governing collectively moving dense suspensions of active micro-swimmers. In this review, we tried to highlight a complementary approach, suggesting that physics pose not only constraints, but also an opportunity for the cell.

Under harsh conditions, bacteria develop sophisticated survival mechanisms. In order to flourish and invade new territories, bacteria may have evolved to manipulate the cellular mechanical properties as well as the physical properties of their medium, in order to create advantageous dynamics. In this sense, the biology of swarming bacteria promotes favorable physics to aid in their survival.

Despite considerable progress, much of the physical principles underlying swarms are still far from fully understood. For example, the theory of collective motion predicts a phase transition between a disordered phase at low densities and an ordered one at higher densities.

Such a transition has not been observed experimentally in collectively moving bacteria. One reason that phase transitions were not observed is the technical difficulty in manipulating some of the fundamental global properties of the swarm such as control of the density and aspect ratio. It is expected that a natural habitat for swarms will typically include several species proliferating and moving in complicated, heterogeneous environments.

In such mixed colonies, species may differ in both their biological e. Understanding the physics of mixed systems takes the next step towards understanding how real and natural bacterial swarms behave. The claim that the average cluster size of ordered particles is larger than the size of disordered clusters is problematic because of the method Chen et al. Since the minimal distance is fixed for all measured densities and is smaller than the typical cell length but much larger than the width , it is expected that the width of clusters in the direction perpendicular to the mean cluster orientation will be proportional to density, while the length of clusters is approximately independent of density because cells cannot crowd in this direction.

Indeed, Fig. See also [ ], Figs. As a result, the number of cells in a cluster is expected to be proportional to the overall density [ 33 ], Fig. This observation is a result of the way clusters were defined and may not be of particular physical or biological nature. A similar problem occurs in the finding that correlations are scale-free, i. Because clusters are defined as close cells that have similar orientations, large clusters are, by definition, more aligned or the other way around — ensembles that are more aligned will be classified as in larger clusters.

As the direction of the velocity is correlated with the direction of the cell body, it is expected that large clusters will show larger correlation lengths. In other words, the scale free property may be an artifact of the way clusters were defined. The occurrence of large number fluctuations is related to what is termed motility-induced phase separation [ 29 , 41 , 87 ] in which cells or particles with reduced motility self-separate to form large immotile-clusters.

This theory is not relevant for swarming bacteria because [ 29 ] assume that dense regions move slower — the opposite than observed with bacteria. In bacterial swarms, dense clusters move faster.

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The transition as a function of density is pronounced in the spatial correlation functions Fig. The transition region is narrow, suggesting a critical phenomenon.

Further examination reveals that the jump in the standard deviation of measurements is mostly due to density fluctuations in time Fig. A time series analysis reveals a sharp increase in the Hurst exponent, which quantifies the roughness of temporal fluctuations, indicating that the density varies sharply in time Fig.

For small aspect ratios, the Hurst exponent is around 0. See Supplementary Note 2 and Supplementary Fig. The gray rectangle represents the transition region. From an active matter perspective, our results reveal some successful theoretical predictions upon comparison to earlier work on simulations 17 , 18 , 21 , 23 , 24 , 33 , 34 and experiments with artificial inanimate systems 35 , However, the swarming phase diagram also has several unique characteristics that are not observed in other active systems.

For example, several phases that have been observed in simulations, such as the bio-nematic and laning phases 21 , 34 , were not realized. Other predictions, such as the emergence of bimodal cluster-size distributions Fig. See Supplementary Note 3 for further discussions. Collective motion of bacteria changes, quite dramatically, if the aspect ratio is increased above a threshold value around 10 for B.

Strikingly, above densities of around 0. This transition is reminiscent of behavior of self-propelled rods with short-range alignment interactions typically due to volume exclusion in simulations and experiments; see ref. The observed cluster-size distributions are in line with a kinetic theory describing occurrence of LCs as a specific type of microphase separation characteristic for rod-shaped moving particles like bacteria 18 , DCS is also related to the increase in temporal fluctuations.

We hypothesize that large temporal fluctuations correlate with the occurrence of giant number fluctuations, which indicate the occurrence of LCs, similar to previous findings in bacterial systems 19 , 20 and in contrast to experimental reports and theoretical predictions, e. We conclude that, in the SC and LC phases, collective behavior is dominated by short-range alignment or excluded volume interactions.

This is in line with findings for filamentous, very large aspect ratio mutants of Escherichia coli that display behavior dominated by short-range alignment interaction At small aspect ratios, the collective behavior deviates from the self-propelled rod paradigm. We rationalize that this is due to long-range hydrodynamic interactions, which suppress the clustering and density inhomogeneities. This is in accordance with recent simulation findings, e.

Thus our observation should stimulate more detailed model studies. While jamming of high-density active systems has been predicted theoretically 21 , 30 , 34 , the IM phase does not occur in typical active matter systems. This includes swimming not swarming bacteria in bulk or thin films 2 , 42 , in driven inanimate particles 35 , 36 , or most models of self-propelled particles, either discrete or continuous, e.

During swarming, on the other hand, the reason for the absence of motion of isolated individuals or cells at very low densities is unclear. It has been suggested that the cells are trapped in areas that are temporarily too dry 8.

In such regions, the surface may exert a large drag force that the thrust of the flagella cannot overcome. Another possibility is that quorum sensing or some sort of quorum signaling may play a role in the onset of swarming. Indeed, it is known that the quorum sensing in B. Therefore, introducing quorum signaling to current bacterial swarming models may be crucial for successfully modeling the transition between the IM and the motile phases.

However, in the swarming regimes that are considered in this work, corresponding to extremely high bacterial densities in the interior of the colony, surfactin at the colony edge is abundant 46 , and we do not expect that quorum sensing plays a major role in the dynamics of the cells in the outer band. In particular, the absence of motion of sparsely distributed cells does not seem to be the result of quorum signaling effects, which does not fluctuate on the micrometer scale; individual cells that are placed on the agar with the system already above the threshold for surfactant secretion are still immobile.

Indeed, the increase in the average speed as a function of cell density can be explained in terms of collective-motion models that do not take quorum sensing into account 30 , Overall, many of the prominent features of the swarm dynamics, including the non-trivial Hurst exponent marking the SC—LC transition and the lack of phase changes at small aspect ratios cannot be explained by current theories.

Therefore, the phase diagram, Fig. As a result, it has direct biological consequences in terms of the ability of bacteria to swarm efficiently. With a typical aspect ratio of 7 and a wide range of densities 0. Within the S region, the swarming statistics were not sensitive to the density as well as to small changes in the aspect ratio, suggesting that the collective behavior of WT swarming cells is particularly robust to fluctuations in density and cell shape.

Thus the physical robustness of the swarming phase S may be advantageous for maintaining efficient swarming, particularly under stress. Thus we expect their phase diagram to be qualitatively similar.

Moreover, the difference between phase states may be a critical determinant that differentiates temperate from robust swarmers and thus the kinds of surface hardness a bacterium can traverse. Bacterial swarming is a natural state, i. The phase diagram discussed above describes the range of possible dynamical regimes for the swarm, highlighting the subtle interplay between the physical and biological characteristics of the swarm. We find that under standard conditions bacteria inhabit a region of phase space in which the swarm dynamics is highly robust and insensitive to fluctuations.

In this regime, bacteria do not cluster and do not form an orientational order that would bias the bacterial flow toward a particular direction. Global alignment would reduce the assumed biological function for swarming, which is rapid isotropic expansion given no external directional cues. In addition, the super-diffusive property of trajectories does not deteriorate at high surface densities.

These conditions are pivotal for rapid spreading and mixing of bacteria within the swarm, which may be crucial for efficient growth and colony expansion. Four different variants of B. All mutants were obtained from the same laboratory Daniel B. Kearns, Indiana Supplementary Table 1 lists the strain name and the mean aspect ratio with the standard deviation the table includes strain DS too, with which we performed few control tests only.

The mean was obtained from randomly chosen cells in the active part of swarm, close to its edge. In most cases, the large variety of cell lengths in a specific sample is due to proliferation and cell division, thus the mean cell length does not have a Gaussian distribution the size is bounded in the range 1—2 times the length of a single cell.

For each aspect ratio, at least 30 independent plates were created. In each experimental plate, individual cells were identified using a custom tracking software implemented in Matlab.

The number density at each frame was estimated by counting the number of cells. Surface density was estimated by measuring the area of a threshold filter applied to either the pixel intensity or the local entropy of the image. Snapshots were binned according to densities with a width of 0. In some of the figures, results with very sparse or very dense bins e. The tracking algorithm receives as input a video of bacteria given as a sequence of frame images.

It outputs the trajectories of all cells in the video. The algorithm is separated into two conceptual parts: image analysis and motion reconstruction. In the image analysis step, following standard filtering and sharpening preprocessing, the location and orientation of every bacterium in each frame is obtained by thresholding an intensity histogram and segmenting cells compared to the background. Cells that overlap or are too close to be distinguished are separated using two custom algorithms.

The first estimates the orientation of a bacteria using axis matching. The second applies a skeleton cutting algorithm as suggested in ref. Finally, the motion reconstruction algorithm matches cells in consecutive frames using a nearest-neighbor greedy algorithm to approximate continuous trajectories. The dynamical properties of single cells and the swarm were quantified using several measurements and observables, which were calculated from the binned trajectory data.

Mean squared displacement MSD exponent of trajectories. We compute the standard deviation, the kurtosis centered, scaled fourth moment , and the histogram of densities within all subsections. Clusters are defined as connected components of the graph obtained using the above definition.

The spatial velocity correlation is then given by. Similarly, the angle correlation cell orientation is given by. Figure 4 shows both the correlation lengths obtained by averaging over all experiments in the density range Fig. We study three auto-correlation functions in different vector fields r t : the instantaneous velocity, normalized instantaneous velocity direction of movement , and cell orientation.

Hurst exponent H : Given a time series, the Hurst exponent quantifies the roughness of fluctuations in the series. Large number fluctuations : Cells with particular aspect ratio and density were partitioned into 1—30 bins in each dimension.

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