Research ArticleBIOPHYSICS

Swimming bacteria power microspin cycles

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Science Advances  19 Dec 2018:
Vol. 4, no. 12, eaau0125
DOI: 10.1126/sciadv.aau0125
  • Fig. 1 Dense suspensions of confined E. coli form microspin cycles.

    (A) Schematic of the experimental setup. An emulsion of a bacterial culture and mineral oil is sandwiched between two coverslips. The distance between coverslips is h ~ 25 μm. The bacterial culture is confined within roughly disc-shaped droplets of radius R. High-speed differential interference contrast (DIC) microscopy is used to capture the flow of bacteria within the droplet. (B) Time sequence of a representative droplet. The flow field is shown with magenta arrows. A single clockwise-rotating vortex at time 3.0 s transitions to a counterclockwise rotating and returns to clockwise rotation at 7.2 s. The average period is approximately 3.4 s, and the droplet is approximately 30 μm in diameter. (C) The order parameter (blue line; see text for definition) varies in time as a square wave, providing a quantitative measure of the periodic behavior of the system. (D) The maximum velocity in the droplets oscillates in a roughly sawtooth pattern at half the period of the order parameter.

  • Fig. 2 The two-phase bacterial fluid model recreates the microspin cycles.

    (A) A free swimming bacterium exerts a thrust force F0 on the fluid, which causes the bacterium to swim with velocity V0 in the direction d. (B) The thrust from the flagella and resistive drag on the entire bacterium (black arrows) produce a dipole-distributed stress on the fluid, which induces a local flow pattern (purple arrows). (C) Random movements and hydrodynamic interactions cause the bacteria to align in a volume fraction–dependent manner. We assume an approximately sigmoidal dependence of the orientational order on the volume fraction. (D) Gradients of the fluid flow (purple arrows) that are perpendicular to the long axis of the bacteria exert a torque that causes the bacteria to rotate. (E) Our mathematical model replicates the behavior observed in Fig. 1B with a slightly faster period (~2.9 s). The color map shows the bacterial volume fraction. (F) The simulations reproduce well the dynamics of the order parameter. (G) As was observed in the experiments, the maximum velocity in the simulations undulates in a roughly sawtooth-like pattern at half the period of the order parameter.

  • Fig. 3 Length modulates flow pattern.

    (A) As cell body length increases, the probability of observing different flow patterns changes from that of E. coli–like, periodic reversals (blue) to B. subtilis–like, stable vortices (red). Sporadic droplets (gray) are more common at transitional lengths, and single vortices (purple) are uncommon across all lengths. (B) Flow field of a droplet containing 5.9-μm-long E. coli, showing a flow pattern with counterrotation at the boundary (light blue), reminiscent of the flows produced by B. subtilis. The counterflow arrows are not drawn to scale. (C) Azimuthal velocity as a function of radial position. Counterrotation at the periphery increases with cell length, and the location of the peak velocity shifts inward toward the center of the droplet. The half-period of periodically reversing E. coli droplets does not depend on (D) bacterial cell length, (E) droplet diameter, or (F) medium viscosity. (D to F) Numbers above the data points are the sample size. (E) Data points represent the average value for droplets with diameters within ±5 μm of the data point. The correlation between the half-period and the diameter (E) is not significant (P > 0.9). Error bars show SEM.

  • Fig. 4 Dependence of reversals on diameter, swimming speed, and density distribution.

    (A) Flow velocity depends linearly on droplet diameter and does not depend strongly on volume fraction. Data points represent the average value and SEM for droplets with diameters within ±10 μm of the data point. (B) The inverse of the half-period scales linearly with the swimming speed of the bacteria. The simulations predict that there is an asymmetric density distribution for droplets that periodically reverse (C), whereas the distribution is symmetric for droplets with stable vortices (D). The color map in (C) shows the volume fraction of the bacteria. FM 4-64 was used to fluorescently stain the bacterial membranes. Images represent the fluorescent intensity in the droplets averaged over 1 s for a droplet undergoing periodic reversals (E) and one undergoing stable vortical motion (F). The color maps in (E) and (F) are in arbitrary units. The plots underneath the images show the order parameter (Ψ) versus time for these droplets. Scale bars, 10 μm.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/12/eaau0125/DC1

    Supporting Methods

    Fig. S1. Characteristic dynamics of the order parameter for representative droplets.

    Fig. S2. The effect of droplet diameter and cell swimming speed on the probability of different flow patterns.

    Fig. S3. Model predictions for the effect of bacterial length on the flow dynamics.

    Fig. S4. Counterrotations are not affected by che mutants.

    Fig. S5. The effect of volume fraction on the probability of different flow patterns.

    Fig. S6. The effect of fluid viscosity on the probability of different flow patterns.

    Fig. S7. The effect of growth time on single-cell velocities.

    Table S1. Model parameters.

    Movie S1. Confined E. coli forms microspin cycles.

    Movie S2. Simulations of our two-phase model for collective motion of bacteria predict two types of flows for a given set of parameters, either periodic reversals or stable vertical flow, which depend on the initial conditions.

    Movie S3. E. coli cells treated with cephalexin are longer and, for cells over 3.0 μm in length, will produce counterrotating vortices reminiscent of B. subtilis.

    Movie S4. Confined E. coli mutants form microspin cycles.

    Movie S5. The bacterial membranes were stained with the fluorescent dye FM 4-64.

    References (3137)

  • Supplementary Materials

    The PDF file includes:

    • Supporting Methods
    • Fig. S1. Characteristic dynamics of the order parameter for representative droplets.
    • Fig. S2. The effect of droplet diameter and cell swimming speed on the probability of different flow patterns.
    • Fig. S3. Model predictions for the effect of bacterial length on the flow dynamics.
    • Fig. S4. Counterrotations are not affected by che mutants.
    • Fig. S5. The effect of volume fraction on the probability of different flow patterns.
    • Fig. S6. The effect of fluid viscosity on the probability of different flow patterns.
    • Fig. S7. The effect of growth time on single-cell velocities.
    • Table S1. Model parameters.
    • Legends for movies S1 to S5
    • References (3137)

    Download PDF

    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). Confined E. coli forms microspin cycles.
    • Movie S2 (.mp4 format). Simulations of our two-phase model for collective motion of bacteria predict two types of flows for a given set of parameters, either periodic reversals or stable vertical flow, which depend on the initial conditions.
    • Movie S3 (.mp4 format). E. coli cells treated with cephalexin are longer and, for cells over 3.0 μm in length, will produce counterrotating vortices reminiscent of B. subtilis.
    • Movie S4 (.mp4 format). Confined E. coli mutants form microspin cycles.
    • Movie S5 (.avi format). The bacterial membranes were stained with the fluorescent dye FM 4-64.

    Files in this Data Supplement:

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