Research ArticleBIOPHYSICS

Flagellar number governs bacterial spreading and transport efficiency

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Science Advances  26 Sep 2018:
Vol. 4, no. 9, eaar6425
DOI: 10.1126/sciadv.aar6425
  • Fig. 1 Bacterial motility patterns.

    (A) Illustration of three strains of B. subtilis with different number of flagella. (B and C) Planar projections of quasi–two-dimensional (2D) experimental (B) and simulation (C) paths. A few trajectories are randomly chosen and translated so that the first point is located at the origin. The simulation parameter values are extracted from experimental data. (D) Directional persistency of the run phase p (circles) and asymptotic rotational-diffusion coefficient Dr (squares) for different strains.

  • Fig. 2 Run-and-tumble statistics.

    (A) The mean run and tumble speeds for different strains (open symbols). Full symbols indicate the results for different cultures of each strain. Horizontal lines show the mean values over all strains. (B) The probability distribution of the run speed. (C) Fluorescence images of the bundles of a WT strain. Scale bars, 3.5 μm. Dashed lines indicate the approximate position of the cell body. (D) The average run (circles) and tumble (diamonds) times. Horizontal lines indicate the average values over all strains. (E) The probability distribution of observing a run time longer than a given duration t. (F) The turning-angle probability distribution R(ϕ). (G) The average turning angle 〈|ϕ|〉 (triangles) and R = 〈cosϕ〉 (squares) for different strains. The bright red curves in (B), (E), and (F) indicate the distributions for different cultures of the WT strain. pdf, probability density function.

  • Fig. 3 Spreading and transport properties.

    (A) Probability distribution of the turning angle ϕ when switching from the run to the tumble phase. (B) Probability distribution of the dimensionless quantity Embedded Image, reflecting the bending of tumble trajectories. Inset: A typical tumble trajectory extracted from experiments. The arrow shows the direction of motion. (C) Evolution of the MSD for different strains, obtained from experiments (thick bright color lines), simulations (symbols), and the model via Eq. 13 (thin dark color lines). Errors of experimental curves are smaller than their line thickness throughout the curves. The simulation errors bars are smaller than the size of the symbols. Inset: The asymptotic diffusion coefficient D for different strains. The analytical predictions (circles) are compared to the experimental results (squares).

  • Fig. 4 Phase diagram of the influential parameters.

    (A) A typical sample trajectory of B. subtilis with run-and-tumble dynamics. (B to D) Three cross sections corresponding to (B) R = 〈cosϕ〉 = 0.56, (C) Embedded Image, and (D) p = 〈cosθ〉 = 0.97 of the 3D phase diagram in the (R, p, Embedded Image) space. The color intensity reflects the magnitude of the asymptotic diffusion coefficient D. Marked regions indicate the accessible range of parameters in our experiments with B. subtilis. (E) MFPT, scaled by MFPT at p = 0 versus the directional persistency p of the run phase. Inset: Optimal persistency popt versus the effective system size L/. (F) Schematic picture depicting how different aspects of transport efficiency vary with Nf.

  • Fig. 5 Sample trajectory with detected tumbling events.

    (A) The trajectory is color coded with respect to speed. (B) The detected tumbling events are indicated with red color. The arrow shows the direction of swimming.

  • Table 1 Parameter values extracted from experiments.

    The values in parentheses are obtained from 25% of the tracks that are more concentrated close to the center of the chamber.

    StrainEmbedded ImageEmbedded ImageEmbedded ImageEmbedded ImagepR
    swrA+ +23.310.

Supplementary Materials

  • Supplementary Materials

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.avi format). A sample bacterial trajectory.

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