In-situ swarming studies e. One known example, which may be of medical importance, is swarming of P.
The swarming colony — a multiscale view. Frame indicates the region where optical flow measurements are performed. Multiple flagella are visible. Swarming may be largely divided into two categories according to the thickness of the swarm. In this regime, the advancing colonial edge is relatively sparse, where the bacteria migrate rapidly, forming only a thin, single layer of moving cells.
Towards the interior of the colony, cells become more crowded, swirl much faster, but still occupy only a monolayer. Further back inside the colony, cells become less active and pile in some cases they exhibit sporulation or biofilm formation. The physical mechanisms that play a role during swarming, as well as the characteristics of the swarming patterns, are known to depend on both the cell characteristics and the environmental conditions.
The first includes cell density [ ], cell aspect ratio [ 65 ] and cell rigidity [ 14 , 62 ], flagellar density [ ], flagellar number and structure [ 36 , 55 ] and flagellar propulsion power and activity [ 58 , ], interactions between flagella of adjutant cells [ 38 ] and the ability to secrete biosurfactant [ 10 ].
Environmental conditions studied include temperature, humidity, food level [ 11 ], agar rigidity [ 11 , 73 ], oxygen availability [ ], nearby interacting colonies [ 13 ] and the presence of antimicrobial agents [ 19 ], attractants and repellents [ 57 ]. As detailed above, many of the biological studies on swarming bacteria describe in detail the biochemical manifestations of this phase [ 40 , 60 , 74 , 75 , 93 , ].
However, such studies provide limited information on the collective macroscopic properties of swarms that can consist of millions of cells. To this end, and at a risk of over-simplification, physicists tend to look at swarming cells as elongated rod-shaped self-propelled particles. The first quantitative physical-inspired works on collectively moving bacteria focused on swimming cells in sessile drops, or concentrated suspensions e.
More recently, with better imaging abilities, swarming colonies were studied as well [ 6 , 11 , 12 , 19 , 33 , 40 , , ]. However, the common denominator of all such examples is not only its phenomenological visible outcome of coherent swirling and dynamic clusters, but also the physics-motivated approaches and tools used to analyze them.
Most swarm experiments take place in a standard Petri-dish 8. Nutrients vary depending on the species, but in many cases standard LB, peptone or some other yeast extracts and tryptone, are used. The collective bacterial motion is typically analyzed using particle image velocimetry PIV algorithms e. In principal, high-resolution in time and space movies are streamed into the computer, separated into frames, and after standard pre-processing for noise reduction and smoothing, the software identifies changing patterns in between consecutive frames.
See an example in Fig. The denser the swarm, the more reliable will be the OF that does not track individual particles per-se.
Such generic methods generate velocity fields, indicating the instantaneous motion of the flow in the observed field of view. Several derivatives of the flow fields are typically calculated, such as the vorticity field the curl of velocity, or tendency of rotating , the distributions of velocities and vorticities, spatiotemporal correlation functions, indicating the characteristic length the typical size of vortices in the flow and time scales the typical life-time of a vortex of the dynamic flow.
See Fig. Below, we distinguish between monolayer and multilayer swarms. The observed swarming dynamics strongly depends on several factors such as the species under study or the specific strain , the nutrients levels, and the wetness or humidity. Multilayer swarms are usually more localized as far as the expansion of the colony is concerned. These differences are also manifested in several characteristics of cells. For example, the same species is typically longer in monolayer swarms compared to thicker swarms.
Because nature does not provide easy-to-find habitats for swarming, there is no single protocol for lab experiments and it is important to test different conditions. It is expected that the ability of bacteria to move effectively will depend on the available nutrients energy source and medium type. This motivated research to explore the dynamical properties of collective behavior under a variety of conditions, in particular adverse environments.
In canonical conditions, namely when cells are not starved peptone experiments , the substrate is moist, and humidity and temperature are favorable for the cells, B. The dynamic patterns that are formed yield spatiotemporal correlation functions that decay exponentially, both in time and space; hence, B.
This is also true for P. Manipulation of the substrate by addition of surfactants does not change these observations, although the colonial expansion speed and the microscopic speed may vary. Increased resistance of swarming bacteria to antibiotics was linked specifically to swarming motility and not to other types of movement [ 76 , 90 ]. In particular, it cannot be attributed to antibiotic-resistant mutations [ 78 ]. This raises the question of how antibiotics affect the physical properties of the swarming dynamics?
Understanding these effects may shed light on the mechanisms underlying antibiotic resistance. For B. It was found that this anomalous, non-Boltzmann dynamics is caused by the formation of a motility-defective subpopulation that self-segregates into clusters. This observation was verified both experimentally, using a mixture of motile and immotile B. Interestingly, although the microscopic speed was dramatically reduced, the expansion rate of the colony edge, and the number of live cells extracted from the leading edge were not affected by kanamycin [ 19 ]. The answer is that addition of kanamycin increases the fraction of immotile cells in the population.
If motile and immotile cells were mixed, then the entire colony may become jammed [ 26 , ] and unable to grow. However, the system segregates into clusters of immotile cells, while the unaffected cells migrate freely. As a result, the expansion of the colony is not affected. The appearance of islands, corresponding to immotile, antibiotic affected bacteria, can be explained in terms of the physical properties of granular materials, as discussed below.
In other words, the colony survives thanks to a physical phenomenon, rather than a biological one. In Fig. Antibiotics resistance — segregation into clusters. Red regions are very-slowly moving cells corresponding to the motility defective bacteria. Segregation is relatively constant in time and space, so that the red regions remain in the same places. Most swarming species can easily swim in liquid bulk.
If the cells are sparse enough, interactions between individuals are negligible, and their motion has typically the form of run-and-tumble, characterized by straight trajectories runs interspersed by shorter, random reorientation tumbles [ 16 , ]. During runs, cells rotate their flagella in a counterclockwise direction, which creates a bundle that propels them forward. However, the mean run-time is not constant, but can slowly change in time [ 18 , 21 ]. During tumbles, the flagella rotate in a clockwise direction and the bundle opens; as a result, the cells randomly obtain a new direction in which a new run event takes place.
The chemotaxis signaling network operates in controlling the duration of runs, enabling navigation towards or away from desired regions in the medium. In contrast, while in dense populations, flagellated bacteria exhibit collective motion and form large dynamic clusters, whirls, and jets, with intricate dynamics that is fundamentally different than trajectories of sparsely swimming cells.
Although swarming cells do change direction at the level of the individual cell and may exhibit reversals [ ], it has been suggested that chemotaxis does not play a role in multicellular colony expansion [ 24 , 84 ]. Instead, changes in cell direction stems from flagellar rotor switching that are uncorrelated with the chemical cues [ ]. One method for studying the role of tumbling on the swarm dynamics is by comparing wild type WT cells with mutants that do not tumble, or with mutants that tumble at random times — independently of the chemotaxis system.
Smooth swimming bacteria are cells that do not tumble, either because these species simply do not tumble, or because they were genetically modified in the lab not to do so.
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These cells exhibit the run phase only, meaning that they swim in relatively straight trajectories. If inoculated on agar, the growing colony expands much slower, and on the microscopic scale the cells do not show the characteristic whirls and jets, but some weak motion. These include spritzing of water on the colony to enhance wetness, initial inoculation of a much larger volume compared to the regular case e.
In all cases the swarm is still different compared to WT colonies. In some studies, it was suggested that the role of tumbling, or perhaps the role of rotor switching between the run and the tumble, during motion on agar or swarming has additional functionality, such as pumping liquid from the agar [ ] or stripping off lipopolysaccharide LPS from the Gram-negative outer membrane to enable wetting of the surface [ , ].
In the absence of tumbling or rotor switching, the local wettability is poor and the cells are stuck. Therefore, in order to test the role of tumbling, it is important to disconnect the chemosensory system from the rotor switching, and test mutants that do tumble but do not have a functional chemosensory system. To the naked eye, the colony seems to swarm because it expands rapidly, but the microscopic picture shows the poor motion at the edges. In contrast to smooth swimming mutants, S. These cells, which tumble at random times that are independent of the chemotaxis system, were found to swarm very similarly to the WT.
To the naked eye, their motion looks similar to WT swarming. In addition, spatiotemporal correlation functions as well as the distribution of velocities is similar [ ].
On the other hand, non-chemotactic cells that do tumble exhibit the same behavior as the WT. This demonstrates that chemotaxis per-se does not function during swarming even though that tumbling, or rotor switching, does play a role during swarming.
As will be discussed below, the subtle differences in the flow statistics of WT and smooth-swimming cells results in slightly different geometrical properties of cell trajectories. In particular, WT cells have a slightly larger diffusive exponent [ ]. This means that the displacements of a WT cell with rotor switching in a swarm are on average slightly larger than that of a smooth-swimmer. This is counter-intuitive as one would expect that tumbling would lower super-diffusion.
Zero To Infinity The Foundations Of Physics Ws 2007
Once again, we see that the biological properties of cells in this case rotor-switching affect the physics of the system and the environment each cell senses. The theory of active matter, in particular, in relation to self-propelled rod-shaped particles, predicts that the shape of cells should play a central role in determining the flow pattern and its statistics. This is due to the fact that both excluded volume effects and hydrodynamic interactions produce an effective alignment mechanism that depends on the cell aspect-ratio [ 3 , 97 , , ].
Quantitative statistical studies of collectively swimming bacteria, and on gliding ones [ ], were performed prior to flagellated swarming e. In theoretical studies that model bacteria as self-propelled rods, particles with small aspect ratios formed tightly packed clusters that prohibited the formation of swarming a jammed state [ , , ].
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To test the role of cell aspect ratio on bacterial swarming, several variants of B. In general, all strains formed a swarm pattern, and the changes between the cases were measured. Firstly, the average microscopic speed was found to depend on the aspect ratio in a non-monotonic way, with slower motion for colonies composed of short and long strains, and faster motion for the WT colonies Fig.
Moreover, the velocity of both shorter and longer cells has an anomalous, non-Gaussian, distribution. While WT cells have a kurtosis of approximately 3 Gaussian , both long and short cells show a higher kurtosis, which can be up to 5, indicating a heavier tail.
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Similar results are obtained for the distribution of the vorticity and the temporal correlation function e. Effect of cell aspect ratio.
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