Geometric control of bacterial surface accumulation

Rachel Mok, Jörn Dunkel, and Vasily Kantsler

Phys. Rev. E 99, 052607 – Published 24 May 2019

Abstract

Controlling and suppressing bacterial accumulation at solid surfaces is essential for preventing biofilm formation and biofouling. Whereas various chemical surface treatments are known to reduce cell accumulation and attachment, the role of complex surface geometries remains less well understood. Here, we report experiments and simulations that explore the effects of locally varying boundary curvature on the scattering and accumulation dynamics of swimming Escherichia coli bacteria in quasi-two-dimensional microfluidic channels. Our experimental and numerical results show that a concave periodic boundary geometry can decrease the average cell concentration at the boundary by more than 50% relative to a flat surface.

Received 15 March 2019

DOI:https://doi.org/10.1103/PhysRevE.99.052607

Physics Subject Headings (PhySH)

Locomotion Swimming

Bacteria

Langevin algorithm Molecular dynamics Optical microscopy

Physics of Living Systems

Authors & Affiliations

Rachel Mok^1,2, Jörn Dunkel², and Vasily Kantsler³

¹Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307, USA
²Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307, USA
³Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 99, Iss. 5 — May 2019

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Typical trajectories of swimming cells for flat, sinusoidal, and semicircle boundary geometries as observed in experiment and simulations (see also Video 1 in the Supplemental Material [38]). The start and end of each trajectory are indicated by the yellow and red circle, respectively. Each trajectory is 10 s long. Bacteria align with the surface in the flat geometry leading to significant surface accumulation for the experiment and simulation models. The sinusoidal ( $A = 5.25 μ m$ , $λ = 28 μ m$ ) and concave semicircle ( $R = 12 μ m$ ) boundary geometries redirect the bacteria away from the surface in the experiments and simulations. Scale bars 10 $μ m$ .
Reuse & Permissions
Figure 2
Segmented raw data for the experiment and simulations, used in the statistical analysis. The segmented trajectories (red dots) are acquired at 10 fps. Each red dot represents a bacterium's center at a specific moment in time. The experimental raw data exhibit higher curvature than the simulation raw data likely due to hydrodynamic effects, which are not accounted for in the simulations. Scale bar 10 $μ m$ .
Reuse & Permissions
Figure 3
Mean bacteria surface accumulation for the sinusoidal surface over a range of amplitudes $A$ and wavelengths $λ$ (see also Video 2 in the Supplemental Material [38]). Accumulation at the surface is measured by comparing the number of bacteria within $5 μ m$ from the surface to the number of bacteria in the same area $50 μ m$ away from the surface (gray and blue regions in Fig. 4, respectively). (a) The location of the circles indicates the 20 combinations $(A, λ)$ of the scan with the mean accumulation bilinearly interpolated in between the points. The size of the circle represents the standard deviation of each point. The white numbers indicate the number of experiments per point. See also Fig. 5 for a noninterpolated pixelated heatmap of the experimental and simulation data. (b, c) Three simulations were performed for the same pairs $(A, λ)$ as in the experiments and bilinearly interpolated. The BD and RT simulations agree qualitatively with experiment, revealing an optimum max curvature that reduces accumulation. The set of parameters corresponding to the optimum curvature $k^{*}$ is delineated by the white curve $A = (k^{*} / 4 π^{2}) λ^{2}$ where $k^{*} \approx 0.31 μ m^{- 1}$ . Typical images for the BD and RT simulations are shown in panels (d) and (e), respectively, for $A = 7 μ m$ , $λ = 21 μ m$ (circle), $A = 5.25 μ m$ , $λ = 28 μ m$ (square), and $A = 1.75 μ m$ , $λ = 49 μ m$ (triangle). Scale bars 10 $μ m$ .
Reuse & Permissions
Figure 4
Sampled raw data and accumulation histograms for the flat, sinusoidal ( $A = 5.25 μ m$ , $λ = 28 μ m$ ), and concave semicircle ( $R = 12 μ m$ ) boundary geometries for the experiment and simulations. To visualize the spatial cell distributions, the raw data, acquired at 10 fps for 5 min, were projected onto a single wavelength (the flat surface is assumed to have the same wavelength as the semicircle surface) and sampled such that the bulk density is the same in all cases (a–c), (e–g), and (i–k). Both the experiments and simulations qualitatively show a depletion zone above the boundary for the sinusoidal and semicircle geometries. Due to the differences in the surface accumulation, the total cell numbers differ for the three geometries. The accumulation histograms (d), (h), and (l) quantify this effect, with accumulation defined as the ratio of the number of bacteria in each surface bin area [gray regions near surface for first bin in (a–c), (e–g), and (i–k)] to the number of bacteria in a congruent area $50 μ m$ away from the surface [blue regions away from the surface in (a–c), (e–g), and (i–k)]. The results are independent of the shape of the bulk reference area (see Fig. 6). Histograms (d), (h), and (l) were computed from 20 independent subsamples of the raw data. The bulk accumulation value 1 is indicated by the dashed black line. The accumulation histograms show that the concave semicircle geometry is the most efficient at suppressing accumulation in the experiment and simulations. Bin width 5 $μ m$ . Scale bars 5 $μ m$ .
Reuse & Permissions
Figure 5
Noninterpolated experimental and simulation data for the mean bacteria surface accumulation for the sinusoidal surface over a range of amplitudes $A$ and wavelengths $λ$ .
Reuse & Permissions
Figure 6
Sampled raw data and surface accumulation bar graphs for the flat, sinusoidal ( $A = 5.25 μ m$ , $λ = 28 μ m$ ), and semicircle ( $R = 12 μ m$ ) boundary geometries for the experiment and simulations. To visualize the spatial cell distributions, the raw data, acquired at 10 fps for 5 min, were projected onto a single wavelength (the flat surface is assumed to have the same wavelength as the semicircle surface) and sampled such that the bulk density is the same in all cases (a–c), (e–g), and (i–k). Due to the differences in the surface accumulation, the total cell numbers differ for the three geometries. Accumulation is defined as the ratio of the number of bacteria in each surface bin area (gray regions) to the number of bacteria in an equally sized area $50 μ m$ away from the surface. Two shapes of equal area are considered for the bulk area: a shape which follows the surface contour (blue) and a rectangle (green). For each geometry in (d), (h), and (l), the blue and green bar show the mean surface accumulation calculated with the surface contour and rectangle as the bulk area, respectively, for 20 samples of the raw data. The error bars represent the standard deviation. The blue and green bars are nearly equal for each case, demonstrating that the surface accumulation estimation is independent of the shape taken for the bulk reference area. Bin width 5 $μ m$ . Scale bars 5 $μ m$ .
Reuse & Permissions

Physical Review E

covering statistical, nonlinear, biological, and soft matter physics