Holographic Imaging Reveals the Mechanism of Wall Entrapment in Swimming Bacteria

Self-propelled particles, both biological and synthetic, are stably trapped by walls and develop high concentration peaks over bounding surfaces. In swimming bacteria, like E. coli, the physical mechanism behind wall entrapment is an intricate mixture of hydrodynamic and steric interactions with a strongly anisotropic character. The building of a clear physical picture of this phenomenon demands direct and full three-dimensional experimental observations of individual wall entrapment events. Here, we demonstrate that, by using a combination of three-axis holographic microscopy and optical tweezers, it is possible to obtain volumetric reconstructions of individual E. coli cells that are sequentially released at a controlled distance and angle from a flat solid wall. We find that hydrodynamic couplings can slow down the cell before collision, but reorientation only occurs while the cell is in constant contact with the wall. In the trapped state, all cells swim with the average body axis pointing into the surface. The amplitude of this pitch angle is anticorrelated to the amplitude of wobbling, thus indicating that entrapment is dominated by near-field couplings between the cell body and the wall. Our approach opens the way to three-dimensional quantitative studies of a broad range of fast dynamical processes in motile bacteria and eukaryotic cells.

Popular Summary

When swimming bacteria encounter a wall, they tend to accumulate on its surface. The resulting thin films of bacteria can lead to highly resistant infections. Understanding the mechanisms responsible for this “wall entrapment” can provide insight into how these films form, as well as provide guidance on how to design devices that move populations of bacteria. Conventional microscopes, however, cannot reveal the three-dimensional trajectories and orientations of individual bacteria that are needed to disentangle the underlying physical mechanisms. We have combined holographic imaging with laser entrapment to show how bacteria interact with a wall and what forces are responsible for holding them there.

In our setup, cells of E. coli bacteria are released near a glass surface over a range of approach angles. An optical trap, which uses an infrared laser to hold cells in place, provides consistent control over the initial distance and orientation of the cells. Holographic images of the bacteria are generated by illuminating the cells at different angles with three beams of light—one red, one blue, and one green. We find that, as each bacterium approaches the wall, the wall reaction force works to align the cell so that its long axis is parallel to the surface. Hydrodynamics, however, prevents full alignment. The cell becomes trapped as it tries to swim against the wall.

The quantitative disagreement between our findings and numerical simulations suggests that a more refined description of the cell-wall interaction could be required. Further insight might be gained by studying mutant strains of E. coli against a variety of surfaces. Our technique could also be used to study other self-propelled cells such as spermatozoa and some algae.

Figure 1

Working principle of three-axis holographic microscopy. (a) The sample is illuminated by three partially coherent beams having different colors and directions. (b) The resulting hologram arising from the interference between scattered and unscattered light is acquired by a RGB camera. (c) A volumetric image of the sample is obtained as the overlap of three independent reconstructions obtained by numerically backpropagating the holograms (see also Ref. [48]).

Figure 2

(a) Sequence of volumetric reconstructions of swimming cells during a wall-entrapment event. (b) A close and lateral view of another cell colliding with the wall. Time intervals between reconstructions are 0.2 s in both figures. (c) For the same cell as in (b), the wall distance is plotted as a black line, while the red line plots the angle of the cell-body axis. In both curves, three stages can be identified: approach to the wall, reorientation, and surface swimming. The grey shaded areas help to visualize these three stages.

Figure 3

(a) Gray lines plot the body pitch $\theta$ as a function of the normalized distance $(z-b)/(a-b)$. Blue, green, and red lines refer to bacteria approaching the wall with, respectively, high, intermediate, and low impact angles. The black dashed line represents the contact condition [$(z-b)/(a-b)=|\sin \theta |$]. (b) Collision angle at first impact plotted versus the corresponding starting value (red dots). Error bars represent $+/-$, the standard deviation over cells with a start angle falling in the same 5° bin interval. The solid black line is the theoretical prediction for cells reorienting with a purely diffusive motion ($D_r=0.06{\mathrm{rad}}^2/\mathrm{s}$), while the shaded area represents the corresponding standard deviation. (c) The blue line plots the vertical component of the velocity as a function of the cell-wall distance for a bacterium approaching the glass wall almost perpendicularly ($\theta \approx 90°$). The velocity has been normalized to its bulk value, while the cell-wall distance $z$ is divided by the cell-body half-length $a$. The same quantity, averaged over all bacteria having an angle $\theta >70°$, is shown as a blue line. The black line plots a theoretical prediction that only accounts for an increase of the cell-body drag due to the presence of the wall [see Eq. (1)]. (d) Time evolution of $\tan \theta$ during reorientation. Color coding is the same as in (b). For each curve, the time origin has been shifted so that the cell first hits the wall at time $t=0$.

Figure 4

Scatter plot of the time-averaged pitch angle $\overline{\theta }$ and the wobbling angle ${\theta }_w$ for cells that are swimming close to the surface. Green vertical and horizontal lines represent the mean over all the analyzed bacteria. An anticorrelation between $\overline{\theta }$ and ${\theta }_w$ is visible. Three selected cells’ trajectories with small, average, and large wobbling are also shown. The black line represents the trajectory of the center of mass, while blue and red lines represent, respectively, the back and front poles.