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Motile bacteria in a critical fluid mixture

Nick Koumakis, Clémence Devailly, and Wilson C. K. Poon
Phys. Rev. E 97, 062604 – Published 11 June 2018
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  • INTRODUCTION
  • METHODOLOGY
  • RESULTS
  • ACKNOWLEDGMENTS
    • Supplemental Material
    References

    Abstract

    We studied the swimming of Escherichia coli bacteria in the vicinity of the critical point in a solution of the nonionic surfactant C12E5 in buffer solution. In phase-contrast microscopy, each swimming cell produces a transient trail behind itself lasting several seconds. Comparing quantitative image analysis with simulations show that these trails are due to local phase reorganization triggered by differential adsorption. This contrasts with similar trails seen in bacteria swimming in liquid crystals, which are due to shear effects. We show how our trails are controlled, and use them to probe the structure and dynamics of critical fluctuations in the fluid medium.

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    • Received 6 September 2017

    DOI:https://doi.org/10.1103/PhysRevE.97.062604

    ©2018 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Fluctuation mediated interactions
    1. Physical Systems
    BacteriaLiving matter & active matter
    Polymers & Soft MatterPhysics of Living Systems

    Authors & Affiliations

    Nick Koumakis, Clémence Devailly, and Wilson C. K. Poon

    • SUPA and School of Physics & Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, Scotland, United Kingdom

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    Vol. 97, Iss. 6 — June 2018

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    Images

    • Figure 1
      Figure 1

      (a) Phase-contrast microscopy image snapshots of a single swimming E. coli at different times, showing an occurring trail in a phase-separating fluid (brighter than the background). The image contrast was increased for clarity. (b) Experimental phase diagram of the temperature versus the concentration of C12E5 in the motility buffer, without bacteria, highlighting the experimental area. Points show the measured upper and lower bounds of the phase separation, while the line is a guide to the eye. (c) Schematic of how the trail intensity profiles are extracted from the images.

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    • Figure 2
      Figure 2

      Snapshots of bacteria at a temperature near criticality/phase separation (≈−0.1K), with the concentration of C12E5 at (a) 1.1wt.%, (b) 1.6%, and c) 2.2%. Note the appearance of bacterial aggregates for (b) and (c).

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    • Figure 3
      Figure 3

      Main: Plot of three intensity profiles at a near-critical temperature (ε=3.310−4, or Tc−T≈0.1∘C) after subtraction of the background for τ=0.5 (red), 1.5 (blue), and 3.0s (green). Dots are from analysed data, while solid lines are the Gaussian fits to the data. Insets: (a) A contour plot of the intensity profiles as a function of time, for the analyzed data and for the fitted curves. The height, (b), and variance, (c), of the Gaussian fits as a function of time, including a linear fit in (c), from which a diffusivity can be extracted [Eq. (7), here D≈0.15μm2/s].

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    • Figure 4
      Figure 4

      Fitting of the diffusivity for a specific temperature (ε=6×10−4), by numerically integrating Fick's second law over the experimental data, showing the experimental data and the fitting. The range of fitting is restricted to 5μm from the center of the track. (a) The starting configuration for the model integration, a short time after the trail has been formed (t0=0.7s) and (b) the end configuration (0.7+0.2s). (c) The starting configuration at a further time (t0=1.4s) after the trail formation and (d) the corresponding end configuration (1.4+0.2s). Note the improvement of the fitting quality between (b) and (d).

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    • Figure 5
      Figure 5

      Figure showing the selection of data for the averaging process. The fitted diffusivity (Fig. 4) is plotted against the squared peak value of the trail, multiplied by the reciprocal of the sum of squared deviations between the fit and the experimental data (K). The ten diffusivities scoring the highest K are then averaged (noted by the vertical line). The points corresponding to Fig. 4 are highlighted.

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    • Figure 6
      Figure 6

      Diffusivity as a function of normalized distance from criticality, D(ε), measured by fitting trail intensity profiles (▪) and from differential dynamic microscopy (•). Lines are fits to D∼εϕ with ϕ=0.56±0.08 and 0.60±0.03, respectively.

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    • Figure 7
      Figure 7

      (a) DICFs [26] for several wave vectors at a fixed temperature corresponding to ε=5×10−4. Markers: experimental data; lines: corresponding fit with a single exponential decay. (b) Diffusion coefficient extracted from DICF adjustment at each wave vector q for several temperatures.

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    • Figure 8
      Figure 8

      (a) Ising model simulation at T=2.8 (ε≈0.23) of a trail formed by an Gaussian-shaped energy inclusion [peak value =5.6kBT, standard deviation = 4 pixels (px)] traveling at a speed of 0.05px/ts towards the right. (b) Average spin profile from the center of the inclusion, corresponding to different time scales, showing a reduction of the peak in time, as indicated by the color-coded vertical dashed lines in (a).

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    • Figure 9
      Figure 9

      Simulations of 64-site wide trails with different initial conditions embedded in a COP Ising lattice at TBulk=2.7 (ε≈0.19). Snapshots are shown at time t=0 and two other times in units of Monte Carlo time step, ts, and plots of the average energy as a function of the distance from the center of the profile, which decay towards the background energy value with increasing time (l). (a) A stripe initially at a higher temperature, T=4 (ε≈0.76). (b) A stripe initially with all up-spins at T=2.7.

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