Rigid body rotation and chiral reorientation combine in filamentous E. coli swimming in low-Re flows

TL;DR

This work quantifies swimming behaviors in two different flow rates and observes rheotaxis in addition to preferential orientation of bacterial bodies, which constrains wiggling bacteria trajectories and orientations compared to those observed in slower flow.

Abstract

When treated with antibiotics below the minimum inhibitory concentration, bacterial cell division turns off, but cell growth does not. Thus, rod-like bacteria, including E. coli, can elongate many times their length without increasing their width. The swimming of these filamentous bacteria through small channels may provide insights into how bacteria that survive antibiotic treatment can reach channel walls. Such swimming behaviors in settings like hospital tubing may signal precursors to adhesion, biofilm formation, and infection. Despite the importance of understanding the behavior of bacteria not killed by antibiotics, the swimming of filamentous bacteria in external flows has not received much attention. We study the swimming behavior of stressed, filamentous E. coli. In quiescence, highly elongated E. coli swim with a sinusoidal undulating motion, suggesting rigid body rotation of long, rigid, buckled cell bodies. In low-Re pressure-driven microchannel flow, the undulation becomes irregular; it may even stop and start within a particular trajectory. We refer to this behavior in flow as "wiggling". Rigid body rotation persists in flow, appearing as a high-frequency change in body orientation on top of a slower one that can be explained by chiral reorientation. We quantify swimming behaviors in two different flow rates and observe rheotaxis in addition to preferential orientation of bacterial bodies. Faster flow constrains wiggling bacteria trajectories and orientations compared to those observed in slower flow, with rheotaxis taking bacteria toward the wall. But not all bacteria in flow wiggle. Populations of non-motile "non-wiggling" filamentous E. coli follow streamlines, without preferential orientation of their bodies. Non-motile bacteria do not behave like chiral rods propelled by rotating flagellar bundles, but like rigid rods. Motility slows swimmers in comparison.

Figures (7)

• Figure 1: (a) shows seven E. coli isolated from a single image where $Q=0.25$$\mu$L/min. Each has been rotated so its the long axis is horizontal. Solid lines denote parabolic fits to the bacteria shape. The inset depicts the methodology for calculating the deflection, $\delta$. (b) shows concavity $a$, in blue, and deflection $\delta$, in green, as a function of time for a single bacteria swimming in $Q=0.25 \mu$L/min. The lines are to guide the eye. (c) shows the Fourier transform of $a(t)$ shown in (b). Horizontal lines represent the mean, $\langle |P(f)|\rangle = 0.003$, and two standard deviations above the mean, $|P|=0.009$. Because the maximum in $|P(f)|$, at $f=9.625$ Hz, is more than two standard deviations above the mean, the maximum frequency is denoted $f_0$ and this bacteria categorized as a wiggler.
• Figure 2: Trajectories of 38 wiggling bacteria at $Q=0.1 \mu$L/min, in (a), and 80 at $Q=0.25 \mu$L/min, in (b). Trajectories begin at the blue dots and end at the red dots. Different colors of the solid lines represent different trajectories. Each image is $36\mu$m in the $x$ direction and $58\mu$m in the $y$ direction. The upper right corner defines the axes; flow is in the $y$ direction and the scale bar refers to both panels. The wall is located on the right hand side of each image at $x=0$indicated by a thicker vertical line. A few trajectories are highlighted in each panel to show examples of wiggling bacteria that swim away from the wall.
• Figure 3: (a) shows the definitions of the three angles used to define the orientation of an E. coli and its trajectory. While the axes are centered on the bacteria for ease of viewing, the location of $x=0$ in flow is at the wall. Flow proceeds in the $y$ direction. The remaining Panels (b), (c), and (d) show examples of the three most common orientations of the average trajectory, $\beta$, average bacteria orientation $\alpha$, and the angle between these, $Z$. The percentages indicate below each panel correspond to the percentage of wiggling E. coli at both flow rates that exhibit the behavior pictured.
• Figure 4: Histograms of the three angles defined in Figure \ref{['DefineAngles']}(a). Panels (a), (b), and (c) depict wiggling E. coli, while (d), (e), and (f) depict non-wiggling E. coli. (a) and (d) show distributions of trajectories $\beta$. (b) and (e) show E. coli orientation with respect to the trajectory, $\alpha$. (c) and (f) show the orientation of the bacteria directors with respect to their own trajectory directions, $Z$. In (a), (b) and (c) the histograms represent $N=38$ and 80 at $Q=0.10$$\mu$L/min and $Q=0.25$$\mu$L/min, respectively. In (d), (e) and (f) the histograms represent $N=50$ and 66 at $Q=0.10$$\mu$L/min and $Q=0.25$$\mu$L/min, respectively.
• Figure 5: (a) Shows eight examples of $\alpha(t)$ for non-wiggling E. coli. (b) Shows the definition of $\alpha$. (c) Shows six examples of $\alpha(t)$ for wiggling E. coli, all in the faster flow, at $Q=0.25 \mu$L/min. Measurements are shown in red, with fits to $\alpha = A_0 \sin (f_0t) + A_c \sin (f_{c}t)$ shown in blue. The horizontal lines correspond to the average $\left<\alpha\right>$ for both measurements (in red) and fit (in blue). The faster frequency $f_0$ corresponds to the wiggling rigid body rotation frequency identified by the procedure in Figure \ref{['DefineWiggle']}, while the slower frequency $f_c$ likely arises from chiral reorientation. In the first example shown in (c), the vertical dashed lines indicate the period corresponding to $1/f_c$, in purple, and to $1/f_0$, in green. On the time axis, each tick mark represents 0.5s in both (a) and (c).