Research ArticleAPPLIED SCIENCES AND ENGINEERING

Chirality-induced bacterial rheotaxis in bulk shear flows

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Science Advances  10 Jul 2020:
Vol. 6, no. 28, eabb2012
DOI: 10.1126/sciadv.abb2012
  • Fig. 1 Setup and typical trajectories of swimming bacteria in the upper and lower half of the channel.

    (A) A dilute bacterial suspension is injected into a polydimethylsiloxane (PDMS) microchannel (width W = 600 μm, height H = 100 μm, and up to L = 20 mm in length) at a given flow rate Q. (B) Bacteria and passive tracers are recorded at 200 frames per second (fps) using a 63× lens (observation window in the x-y plane, 200 μm by 100 μm) at varying distances z from the bottom wall. The angle Ψ defines the bacteria orientation in the x-y plane, and Θ is the out-of-plane angle. (C and D) Typical trajectories of swimming bacteria in the lower (C) and upper channel half (D). The circles represent the end of the bacteria trajectories. Bacteria drift toward the right with respect to the negative flow direction in (C) and in the opposite direction in (D).

  • Fig. 2 Mean velocities for bacteria and passive tracer beads.

    (A) Bacteria [v¯x(z)] and bead [Vx(z)] velocities obtained by scanning through the z direction. Passive tracer beads with diameter d = 1 μm (empty circles) and bacteria (filled circles) are represented at mean flow rates of Q = 5 (blue), 10 (red), and 20 nl/s (purple). (B) Difference between bacteria and flow velocities v¯xVx. Results from simulations are shown by solid lines. (C) Corresponding mean rheotactic velocities v¯y and bead velocities Vy(z). (D) Rheotactic velocity v¯y normalized by the average bacteria swimming speed v0 as a function of local shear rate γ. controlled by two methods: z scan, scanning through the channel height at given flow rates Q (5,10, and 20 nl/s), corresponding to the data of (B), and Q scan, varying flow rates at fixed channel height (0.11H and 0.21H). Results from simulations are indicated by open symbols and are given for heights 0.2H, 0.3H, and 0.4H.

  • Fig. 3 Velocity and orientation distributions.

    Experimental (symbols) and numerical (solid lines) results of (A) velocity vy and (B) orientation Ψ distributions obtained by varying the flow rate Q at a given distance from the channel bottom wall (zH/4). Local shear rates have been closely matched between experiments and simulations. For better readability, the different curves are shifted in the vertical direction. (C) Sketch of the bacterium orientation Ψ and relation to up- and downstream and left and right orientation.

  • Fig. 4 Color map of rheotactic velocity and orientation distributions as a function of channel height from experiments and simulations.

    (A) Probability density function (PDF) for the rheotacitic velocity vy. (B) PDF for the swimmer orientation Ψ. Different panels correspond to different applied flow rates, as indicated by the corresponding wall shear rates γ.w.

  • Fig. 5 Orientation phase space and simulated probability distributions for nontumbling bacteria in simple shear flow.

    (A) The streamlines of a nonchiral swimmer simply follow Jeffery’s periodic solutions for passive ellipsoids. (B) Chirality breaks the left-right symmetry, which is the main reason for bacterial bulk rheotaxis. The green and blue dots correspond to marginally stable fixed points in the linear regime pointing to the left (Ψ = − π/2, Θ = 0) and to the right (Ψ = π/2, Θ = 0) side of the channel. (C and D) Orientation distributions for nonchiral (C) and chiral (D) swimmers at different shear rates using our standard parameters (ν = 0.06, Dr = 0.057 s−1, α = 5).

  • Fig. 6 Universal scaling of the rheotactic velocity.

    (A) Dependence of the scaled mean rheotactic velocity vy/v0 on the shear rate γ. for nontumbling bacteria in simple shear (simulations) for different parameter sets (rotational diffusion Dr, bacterium aspect ratio α, chiral strength ν). (B) Results as shown in (A) but plotted against the chirality number 𝒞. (C) Data in (B) for α = 5 compared to tumbling bacteria in simple shear flow and Poiseuille flow. (D) Slow algebraic saturation at high shear rates. Color code indicated in (D). Symbol code used in all subfigures: ⋆Dr = 0.057, α = 5, ν = 0.06; ▯Dr = 0.057, α = 5, ν = 0.006; ○Dr = 0.2, α = 5, ν = 0.06; △Dr = 0.057, α = 5, ν = 0.02; ▽Dr = 0.057, α = 5, ν = 0.1; ⊳Dr = 0.1, α = 5, ν = 0.06; ◊Dr = 0.057, α = 3, ν = 0.06; □Dr = 0.057, α = 10, ν = 0.06.

Supplementary Materials

  • Supplementary Materials

    Chirality-induced bacterial rheotaxis in bulk shear flows

    Guangyin Jing, Andreas Zöttl, Éric Clément, Anke Lindner

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