Role of tumbling in bacterial swarming

Typical wild-type bacteria swimming in sparse suspensions exhibit a movement pattern called “run and tumble,” characterized by straight trajectories (runs) interspersed by shorter, random reorientation (tumbles). This is achieved by rotating their flagella counterclockwise, or clockwise, respectively. The chemotaxis signaling network operates in controlling the frequency of tumbles, enabling navigation toward 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 collectively swarming cells do change direction at the level of the individual cell, often exhibiting reversals, it has been suggested that chemotaxis does not play a role in multicellular colony expansion, but the change in direction stems from clockwise flagellar rotation. In this paper, the effects of cell rotor switching (i.e., the ability to tumble) and chemotaxis on the collective statistics of swarming bacteria are studied experimentally in wild-type Bacillus subtilis and two mutants—one that does not tumble and one that tumbles independently of the chemotaxis system. We show that while several of the parameters examined are similar between the strains, other collective and individual characteristics are significantly different. The results demonstrate that tumbling and/or flagellar directional rotor switching has an important role on the dynamics of swarming, and imply that swarming models of self-propelled rods that do not take tumbling and/or rotor switching into account may be oversimplified.

Figure 1

Swarming colonies of B. subtilis. (a) A microscopic phase-contrast image of the edge of a wild-type colony along with the velocity and vorticity fields. Black arrows indicate the local velocity and colors indicate local vorticity (units in rad/s). (b) Same as (a) for the NCbRS (nonchemotactic but rotor switcher) strain. (c) Same as (a) for smooth-swimmers strain.

Figure 2

Collective swarm statistics. Left column: velocity; right column: vorticity. (a) The spatial correlation functions of the velocity and vorticity fields of the three strains decay similarly. (b) The temporal correlation functions of the velocity and vorticity fields of all strains decay similarly. (c) Velocity and vorticity distributions of the wild-type swarmers, and the NCbRS (nonchemotactic but rotor switcher), obey a Gaussian curve while the smooth swimmers exhibit deviations from the Gaussian.

Figure 3

Correlation between speed and vorticity. (a) The average speed of the swarming cells at three different vorticity ranges (in absolute values). Correlation is found for the smooth swimmers only. (b) Speed distribution for different vorticity ranges; the smooth swimmers show different distributions, but the wild-type and the NCbRS (nonchemotactic but rotor switcher) strains show similar distributions independent of the vorticity.

Figure 4

Microscopic statistics of individuals in the swarm. (a) Fluorescent microscopy showing the fluorescently labeled bacteria only. (b) Mean square displacement of single bacteria. A slope of $\sim 1.6$ is obtained for all cells, independently of strain type. (c) The distribution of cell displacements of wild-type cells along each axis between a fixed number of frames. Following a scaling of $\mathrm{\Delta }{t}^{1/\beta }$, the distribution approximately fits a Lévy-stable distribution with parameter $\beta =1.27$. (d) Same as (c) for the NCbRS (nonchemotactic but rotor switcher) with $\beta =1.24$. (e) Same as (c) for smooth swimmers with $\beta =1.30$.

Figure 5

Differences in directions. (a) An example trajectory of an individual bacterium (light-blue line), superimposed with the collective flow (black arrows), cell orientation (purple bar), and instantaneous cell velocity (orange arrow). (b) Distribution of angles between the cell velocity and the flow vector field at the same position and time. Smooth-swimming cells (red crosses) are more aligned with the flow while wild-type cells (blue diamonds) and the NCbRS (nonchemotactic but rotor switcher; green triangles) exhibit much larger deviations. (c) Distribution of angles between the cell velocity and its orientation. Smooth-swimming cells tend to be aligned with the actual direction of motion while wild-type bacteria and the NCbRS exhibit significantly larger deviations. (d) Distribution of angles between cell orientation and the flow vector field at the same position and time. Smooth-swimming cells tend to be aligned with the flow while wild-type and NCbRS exhibit larger deviations.