Shear-Induced Wobbling and Motility Suppression in Swimming Bacteria

TL;DR

This study addresses how steady shear flow near surfaces alters the wobbling gait of flagellated bacteria and its impact on motility. Using microfluidic shear, high-speed imaging, and dual fluorescence labeling, the authors quantify the wobble angle $\theta_w$, off-axis angle $\alpha$, and orientation $\Psi$, and interpret the results with Resistive Force Theory to connect geometry to propulsion. They find that flow increases $\theta_w$ up to a plateau near $20^{\circ}$, that $\alpha$ tracks flow in a similar way, and that the wobble frequency $f'_w$ rises with flow due to wall-induced rolling; shorter cells show stronger responses and overall mean speed is suppressed by wobbling, up to about $15\%$. Mechanistically, flow- and chirality-induced torques on the flexible flagellar hook couple with the intrinsic body-flagella misalignment, enabling an elastohydrodynamic pathway that governs near-wall motility and microbial transport in realistic shear environments.

Abstract

The intricate wobbling motion of flagellated bacteria, characterized by the periodic precession of the cell body, is a determinant factor in their motility and navigation within complex fluid environments. While well-studied in quiescent fluids, bacterial wobbling under ubiquitous flow conditions remains unexplored. In this work, we investigate the wobbling dynamics of \textit{Escherichia coli} swimming near surfaces under steady shear flow. Our experiments reveal that the wobbling amplitude intensifies with flow strength before reaching a plateau, with this amplification exhibiting a strong dependence on the swimming orientation relative to the flow direction. It turns out that the enhanced wobbling remains governed by the misalignment between the cell body and the flagellar bundle. Furthermore, we observe that the wobbling frequency increases monotonically with flow strength, and that shorter bacteria exhibit more pronounced variations in both amplitude and frequency. By linking the wobbling motion to the intrinsic body-flagella misalignment, we attribute the flow-enhanced precession to a combination of shear- and chirality-induced torques acting on the flexible flagellar hook. This mechanical coupling ultimately suppresses the net migration velocity as the flow rate increases. These findings elucidate the elastohydrodynamic mechanisms by which shear flow modifies bacterial locomotion near surfaces, with implications for microbial transport in physiological and ecological environments.

Figures (6)

• Figure 1: Experimental setup and kinematic characterization of bacterial wobbling. (a)Schematic of the microfluidic platform (height $H = 100~\mathrm{\mu m}$, width $W = 600~\mathrm{\mu m}$). A syringe pump maintains a controlled shear flow of the bacterial suspension. (b) Typical zigzag trajectory of an E. coli cell swimming in a quiescent motility buffer, captured $1~\mathrm{\mu m}$ above the bottom surface. Inset: High-magnification view of the trajectory segments. The mean cell body length is approximately $2~\mathrm{\mu m}$. (c) Definition of the wobbling angle $\theta_{w}$, determined as half of the peak-to-peak amplitude of the time-evolving cell-body orientation $\Psi$, called as polar angle in $x-y$ plane. The lower-right panel displays a representative periodic time trace of $\Psi$, and $\theta_w = (\Psi_{\text{max}} - \Psi_{\text{min}})/2$. (d) Measurement of the off-axis angle $\alpha$, quantifying the misalignment between the cell body's major axis and the rotation axis of the flagellar bundle. The lower-right panel illustrates the temporal variation of $\alpha$ measured via dual fluorescent labeling.
• Figure 2: Dependence of bacterial wobbling on flow rate and cell body orientation. (a) Wobbling angle $\theta_w$ as a function of the flow rate $Q$. The amplitude of $\theta_w$ intensifies with increasing flow before reaching a plateau at high flow rates. Each data point represents an ensemble average of over 1000 cells; error bars denote the sample standard deviation. (b) Probability distribution of bacterial orientation $\Psi$ at various flow rates. Symbols represent bin centers, and solid lines are Gaussian-like fits provided as guides to the eye. The shift in orientation reflects a dynamic balance between wall-induced hydrodynamic torques, the weathervane effect, and chiral drifting torques, leading to a preference for upstream and transverse rheotactic alignment. (c) Orientation-dependent wobbling angle $\theta_w$ under different flow conditions (indicated by color). For a given flow rate, $\theta_w$ is minimized when the cell aligns with the streamlines and reaches its maximum when the orientation is perpendicular to the flow direction.
• Figure 3: Correlation between bacterial wobbling and body-flagella misalignment in flow. (a)Mean off-axis angle $\alpha$ as a function of the flow rate $Q$. The trend mirrors that of the wobbling angle: $\alpha$ initially increases with $Q$ before reaching a plateau at a critical shear rate of approximately $40\,\mathrm{s^{-1}}$. (b)Similar trends between off-axis angle and wobbling angle are observed under both static and 20 nL/s flow conditions, with minimal differences at corresponding off-axis angles.Each small dot represents the off-axis angle and wobbling angle measured from an individual bacterium. The blue dots correspond to the off-axis and wobbling angles of bacteria in a quiescent environment, while the brown dots correspond to those at a flow rate of 20 nl/s. The larger dots represent the mean values within the corresponding intervals, and the error bars indicate the standard deviation of the bacterial wobbling angle within each interval.(c)Schematic of the force and torque driving hook deformation. In a simplified upstream-swimming configuration, the cell exhibits a "nose-down" tilt $\theta_0$ while the flagellar bundle is initially misaligned by $\alpha_0$. The coupling between the shear flow and the helical flagellum generates a shear torque and a chirality-induced transverse force $F_c$. These external loads are balanced by the elastic restoring torque of the hook, inducing a dynamic increase in the off-axis angle $\alpha$ as the flagellum reorients relative to the flow vorticity.
• Figure 4: Modulation of wobbling frequency by wall-induced rolling in shear flow. (a)Representative time-lapse snapshots (top view) of a bacterium undergoing rolling motion along the surface at various flow rates. (b)Apparent wobbling frequency $f^{'}_{w}$as a function of the flow rate $Q$, showing a monotonic increase with flow strength, in contrast to the decrease of pure wobbling with $\alpha$ (flow-induced) without rolling. (c)Schematic illustration of the frequency compensation mechanism. While the increasing off-axis angle $\alpha$ induced by flow would theoretically lead to a decay in the intrinsic wobbling frequency, the no-slip boundary condition at the wall generates a shear-induced rolling motion. This rolling component superimposes onto the precessional dynamics, effectively compensating for the frequency decay and resulting in the observed rise in the total wobbling frequency with increasing flow rate.
• Figure 5: Variation of bacterial wobbling with flow for different body length. (a)Different colors represent different body length. With an increase in bacterial cell body length, the variation in wobbling angle in response to changes in the flow decreases. (b) With an increase in bacterial cell body length, the variation in wobbling frequency in response to changes in the flow also decreases.