Hydrodynamic Surface Interactions Enable Escherichia Coli to Seek Efficient Routes to Swim Upstream

Escherichia coli in shear flow near a surface are shown to exhibit a steady propensity to swim towards the left (within the relative coordinate system) of that surface. This phenomenon depends solely on the local shear rate on the surface, and leads to cells eventually aligning and swimming upstream preferentially along a left sidewall or crevice in a wide range of flow conditions. The results indicate that flow-assisted translation and upstream swimming along surfaces might be relevant in various models of bacterial transport, such as in pyelonephritis and bacterial migration in wet soil and aquatic environments in general.

Figure 1

E. coli cells in a laminar flow channel with three balanced inlets (a). Bacterial suspension is injected into the center inlet. (b) The central channel (width 150 or $300\mu \mathrm{m}$, height $50–450\mu \mathrm{m}$) receives the flows and is imaged from below. The bacteria attach with a $-x$ direction (or “leftward”) bias on glass (c) and PDMS (d) surfaces when buffer (PBS) is injected into the side streams. Images are the average of 100 individual snapshots, resulting in the clear depiction of attached bacteria within the field of view. The scale bars represent $20\mu \mathrm{m}$.

Figure 2

E. coli body angles at either surface of a $300\mu \mathrm{m}$ wide channel for a total flow rate of $9\mu \mathrm{L}/\min $. Average body angle is extracted via a Gaussian fit to the cumulative frequency histogram for E. coli cell bodies suspended in LB broth and imaged at the glass (a) and PDMS (b) surfaces. Bacterial body angle is measured in the $x\mathrm{\text{−}}y$ plane of the given surface. Here, the dominant body angle is 19.5° on glass and 18.5° on PDMS. (c) Average body angle within five equal-width sections across the surface width. The center point on either plot corresponds to the average angle in the middle strip of the respective surface; the PDMS surface is wider than glass for the channel cross-section in this example [see Fig. 3b]. (d) Average body angle as a function of cell aspect ratio. Error bars represent the 95% confidence interval in each peak position.

Figure 3

Shear rate along the $z$ direction on the surface determines the body angle. (a) Average bacterial body angle in central channel strip near PDMS and glass surfaces as a function of flow rate for a $300\mu \mathrm{m}$ wide channel of variable depth ($206–378\mu \mathrm{m}$); deeper channels yield higher curves. (b) Cross section of device 7 mm from where the inlets meet to form the main channel, depicted here as an example. (c) Velocity field computed by COMSOL Multiphysics from different channel cross sections (shown here for the cross section in (b) for a flow rate of $9\mu \mathrm{L}/\min $) yields the shear rate in the $z$ direction along each surface. Shear rate in the $x\mathrm{\text{−}}y$ plane over glass or PDMS is negligible compared to that along the $z$ direction of either surface. (d) Average bacterial body angle as a function of average velocity gradient across that strip for several geometries. The angles for PDMS surface are virtually coincident with those for glass.

Figure 4

Some of the relevant hydrodynamic forces and torques acting on a motile bacterium near a surface and one possible mechanism that we propose to explain our observations. For clarity, axial torques on the cell body and the flagellar bundle, as well as viscous reaction forces and torques, are not shown. (a) In the absence of flow, the propulsive force of the flagella causes the nose of the cell to dip slightly, and the bacterium swims in a circular, clockwise trajectory at the surface [3, 4]. (b) We propose that at low shear rates ($\sim 10{\mathrm{s}}^{-1}$ or less), flagellar propulsion still dominates and causes the nose to dip. The resulting hydrodynamic torque on the cell body along the $z$ axis counterbalances the clockwise torque due to swimming at two distinct angles, (i) and (ii) (see text). (c) Shear flow rates above $\sim 10{\mathrm{s}}^{-1}$ dominate over bacterial propulsion and the downstream end of the bacterium dips towards the surface. In this regime, bacteria drifting leftward and downstream at a stable angle (i) vastly outnumber others.

Figure 5

Bacteria imaged within the narrow trenches [such as (i) and (ii) depicted in Fig. 3b] between the glass surface and the PDMS side walls of a microfluidic channel that is $150\mu \mathrm{m}$ wide and $93\mu \mathrm{m}$ deep. At most flow rates, the vast majority of cells within either trench swim upstream. Cells show a specific preference for the trench under the left sidewall along the glass surface [i.e., trench (ii) in Fig. 3b; top row of images]. The sequential images depicted here correspond to a 2 s interval for a total flow rate of $3\mu \mathrm{l}/\min $. The images show cells swimming upstream at different speeds.