A statistical physics view of swarming bacteria

Abstract

Bacterial swarming is a collective mode of motion in which cells migrate rapidly over surfaces, forming dynamic patterns of whirls and jets. This review presents a physical point of view of swarming bacteria, with an emphasis on the statistical properties of the swarm dynamics as observed in experiments. The basic physical principles underlying the swarm and their relation to contemporary theories of collective motion and active matter are reviewed and discussed in the context of the biological properties of swarming cells. We suggest a paradigm according to which bacteria have optimized some of their physical properties as a strategy for rapid surface translocation. In other words, cells take advantage of favorable physics, enabling efficient expansion that enhances survival under harsh conditions.

Fig. 1

The swarming colony – a multiscale view. a A macroscopic top-view of a swarm colony grown on an agar plate, indicating the region where microscopic analysis is performed (the size of the frame is a bit larger than the entire field shown in (b)). b A microscopic view of the colony; cells are nearly resolved in the multilayered structure. Frame indicates the region where optical flow measurements are performed. c The highest magnification of the colony (taken using a 60X objective lens), d TEM images of bacteria taken from the swarm. Multiple flagella are visible. e The velocity and vorticity fields of the region in (c). Black arrows indicate instantaneous (and local) velocity, and colors indicate vorticity (scale bar in rad/sec)

Fig. 2

Definitions and formulae

Fig. 3

Antibiotics resistance – segregation into clusters. a and b are two images showing the same field of view, 1 s apart. 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

Fig. 4

Effect of cell aspect ratio. a and b are top-view images of the swarm for short (aspect ratio = 3.8) and long (aspect ratio = 8) cells. c The mean microscopic speed of the cells depends on the aspect ratio in a non-monotonic way. Cells that are close to the WT in aspect ratio exhibit faster speeds (and vorticity). d The kurtosis (indicating the deviation from Gaussian) of the distribution of velocities and vorticities exhibit a non-monotonic trend with a minimum for the WT and strains with similar aspect ratios

Fig. 5

Swarming in a monolayer. a The cells are sparse and move on the agar in a single layer. A surfactant layer secreted by the cells is obtained ahead of the colony. b A larger view of a monolayer swarm. Cells move in dynamic clusters that split and merge. Colors indicate cells that “belong” to different clusters

Fig. 6

Individual cells within a dense swarm. a Trajectories of fluorescently labelled cells. b The mean-squared displacement shows super-diffusive behavior. Each line shows the statistics obtained for a single cell. c Following proper scaling, the displacement of positions of cells (along the x or y axes) collapse on a master curve which is approximately a Lévy stable law. d A trajectory of a single bacterium showing the instantaneous cell-orientation, velocity and the flow around it

Fig. 7

Chiral movement of swarms. a A macroscopic view of the curls formed when P. dendritiformis type-C grow on agar. No particular curvature is obtained, but the direction is the same. b The microscopic view of a colony similar to the one seen in (a). The “roads” of bacteria are thin curls. The elongated rod-shaped cells move along these roads back and forth