BRIEF SUMMARY
* Peritrichously flagellated bacteria, such as Escherichia coli (E. coli) are found to interact strongly with shear flow near a surface. Balance of hydrodynamic torques and forces on each bacterium results in a, steady, average bias in body orientation with respect to the flow direction.
* As a result, bacteria continuously swim to one side. In a closed flow channel, they engage a "left-handed" helical trajectory over the inner surfaces as they drift downstream with the flow.
* This phenomenon allows them to "sample" the flow channel surfaces, and ultimately, to locate crevices or imperfections on the surface, along which they get hydrodynamically trapped to swim upstream
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Laminar Flow
If you have ever had cream or milk with your morning coffee, you may have noticed that mixing of the two fluids involves turbulence. At the scale of a coffee cup, convective mixing is the most dominant process. It is rapid, too; all is needed is the introduction of fluid flow through a few seconds of stirring. Turbulence takes care of the rest.
As dimensions shrink and flow velocities are reduced, turbulence starts to disappear. Such conditions can be found in the very vicinity of a solid surface in a flow field. The same is true within the tiny flow channels of microfluidic devices. The predominance of laminar flow (i.e., non-turbulent flow) within micro-scale flow channels means mixing of solutes happens via diffusion alone. Turbulence is a nonlinear phenomenon and is rather difficult to calculate and predict precisely. Diffusion, on the other hand, is rather easy to predict and control. For that reason, diffusion-dominated flow characteristics within microfluidic devices offer a fine control over the spatial and temporal extent of the concentration of virtually any solute. What is more, complex concentration gradients may also be created within microfluidic devices simply by using diffusion alone.
Chemotaxis
The process by which motile cells direct their movement in response to a given chemical in the environment is known as chemotaxis. Bacteria find food, immune cells track invading micro-organisms, and neurons in a developing embryo know exactly in which direction to grow, all thanks to specialized receptor and mobility mechanisms that respond to concentration gradients of various chemicals in their vicinity. Bacterial pathogenesis, fetus development, wound healing, and cancer angiogenesis are only a few examples where understanding the exact biomolecular mechanisms of chemotactic transduction are extremely vital for medical applications and new drug discovery.
An E. coli bacterium has several flagella on its body, which, when all rotating counterclockwise, form a helical bundle that propels the cell forward (a "run"). The counterclockwise rotation of the flagellar bundle is balanced by the clockwise rotation of its cell body along its axis. Away from any boundaries, the cell swims in a straight line until at least one of the flagella in the bundle spontaneously reverses direction and breaks the flagellar bundle (a "tumble").
The tumble allows the cell to randomly reorient before it starts another run. An E. coli bacterium chemotaxes by modulating the interval between runs and tumbles. If it happens to be running up a concentration gradient of a chemical that it likes (a "chemoattractant"), the modulation between the runs and the tumbles favors longer run intervals. A chemorepellent, on the hand, has the opposite effect.
Enter Microfluidics
The capability to create and control precise concentration gradients within microfluidic devices offers a very attractive path to pursue detailed studies of chemotaxis. As such, there have been many microfluidic device designs reported in various journals within the context of chemotactic studies. Such studies are extremely valuable, as they quantify the physiological response of cells to concentration levels and gradients of a given chemical. Nevertheless, continuous flow is necessary to sustain these chemical gradients within microfluidic devices. This fact typically restricts the use of these micro-scale chemotaxis chambers to eukaryotic cells that strongly adhere to the underlying substrate (such as neutrophils on glass). Bacteria, on the other hand, are simply swept away from the field of view by the same flow that establishes the chemotactic gradient. We at the Koser Lab have been developing novel microfluidic devices that allow continuous chemotactic studies on bacteria without disturbing their natural swimming behavior, thereby bypassing this shortcoming.
Hydrodynamics of Bacterial Swimming
Attempts have been made to overcome the shortcoming mentioned above by simply studying cells at the far downstream of the flow channel, with the expectation that the bacteria will still chemotax during the time that they drift with flow. Recent research at the PI’s laboratory has shown that this expectation is not justified. In fact, we have determined that the presence of flow, particularly near the channel surfaces, has a profound effect on how the bacteria swim. In particular, we have shown that Escherichia coli (E. coli) in flow near a surface exhibit a steady propensity to swim towards the “left” (within the relative coordinate system) of that surface (Fig. 1). Here, we define “left” for a given surface with respect to the flow direction; if you could stand on that surface as a miniature version of yourself, facing directly upstream, the referred direction would be your left.
 Fig. 1. (a) A simple microfluidic channel, made out of poly-dimethylsiloxane mold attached to a microscrope slide, is used to study the hydrodynamics of E. coli swimming near surfaces in the presence of flow. (b) The bacteria are imaged from below. Cells introduced from the center inlet are observed to be attaching most preferentially to the "left" side (-x direction) of each surface (both glass (c) and PDMS (d)) in the absence of any chemotactic gradients. The attachment bias increases downstream. The scale bar denotes 20 microns (or 20 thousandths of a millimeter). For comparison, bacteria in the picture are only about 1 micron wide and several microns long. Figure adopted from [1].
This bias is only present with motile E. coli. Control experiments with non-motile strains of E. coli have yielded no such bias. With measurements of bacterial body angles from thousands of images, we have found that the reason for the leftward swimming bias is actually an orientation preference (Fig. 2).
 Fig. 2. E. coli body angles at either surface of a 300 μm wide channel for a flow rate of 9 μL/min in the main channel. Dominant population average angle is extracted via a Gaussian fit to the cumulative frequency histogram for E. coli cell bodies imaged at the bottom (a) and top (b) surfaces. Bacterial body angle is measured in the x-y plane of the given surface. (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 top surface is wider than the bottom for the channel cross-section in this example. (d) Average body angle as a function of cell aspect ratio. Error bars represent the 95 % confidence interval in each peak position. Figure and caption adopted from [1].
The orientation bias, it turns out, arises from a balance of torques (due to viscous drag) on the cell body due to bacterial propulsion and fluid shear. The length of a given bacterium (as in Fig. 2d), its swimming speed and the local shear rate (as in Fig. 2c) appear to determine the orientation angle. In fact, once the bacterial lengths and swimming speeds are averaged out, the local shear rate appears to uniquely determine the average orientation angle on the surface (Fig. 3). The observed effect is indeed hydrodynamic in nature.
Fig. 3. Average bacterial body angle as a function of average velocity gradient for several geometries. It is the shear flow rate (i.e., gradient) along the normal direction over either surface (bottom glass or top PDMS) that determines the average body angle for E. coli. Figure adopted from [1].
In [1], we have proposed one hydrodynamic mechanism through which this angle bias may be accounted for. Below is a brief summary of what is already known about E. coli in motion, and how our findings fit in.
What was already known: An E. coli bacterium normally "runs" straight when far away from boundaries. Near a surface, however, there is increased drag between the bacterium and that surface, which affects the bacterium's trajectory. The forward momentum of the cell as it swims, combined with viscous drag from the quiescent fluid and the increased friction with the surface, results in the front of the cell (i.e., the end opposite the flagellar bundle) dipping slightly towards that surface (Figure 4-left). With the cell body dipping down and rotating clockwise (as viewed from the flagellar end) as it is propelled forward, the bacterium continuously swerves to the right (as viewed from above as in Figure 4-left). The net effect is the display of circular trajectories.
New insight gained from this study : We have determined that the presence of flow near a surface modifies this classic hydrodynamic picture significantly:
- The flow exerts a drag force on the bacterium towards the downstream direction. (This is the most obvious modification.)
MOVIE
Below is a movie (in two formats) of bacteria swimming "left" as they get dragged downstream (as in Figure 4-right). They are on the top (PDMS) surface; the "left" of the surface is the same as the camera view.
- Since the boundary condition of Newtonian flow is typically that of no-slip (i.e., the flow velocity diminishes at the surface), there exists a shear flow on the bacterium. This shear flow tends to roll the cell downstream when viewed from the side (Figure 4-right, bottom). If the cell is motile and the flagellar bundle is intact, the bacterium may resist that roll simply through the sheer length of its body and flagellar bundle combined. The hydrodynamic torque due to shear flow in the y-z plane causes the cell body to be slightly pointed above the surface at steady-state.
- In the x-y plane of Figure 4, the tendency of the bacterium to swerve right and swim a clockwise circle is balanced by another hydrodynamic torque on the cell body that tries to rotate it counterclockwise. The origin of this torque is the slight angle of the cell body in the y-z plane: the back (i.e., the flagellar end) of the cell now dips down towards the surface and creates a pivot point around which the shear flow tends to rotate the cell body counterclockwise.
- The combination of the hydrodynamic effects summarized in 1 through 3 results in a stable bacterial orientation and a trajectory that is towards the "left" (i.e., in the -x direction in Figure 4) and downstream.
Fig. 4. An E. coli bacterium exhibits circular run trajectories just over a surface in the absence of flow. When a shear flow is introduced, the resulting hydrodynamic forces and torques combine to yield a trajectory in which the bacteria swim towards the "left" and get dragged downstream. For simplicity, axial forces and torques on the cell body, as well as viscous drag forces, are not depicted here. Figure adopted from [1].
Swimming Upstream
Why do we ultimately care if bacteria swim to one side on a surface in the presence of flow? Simple: two reasons.
MOVIE
Below are two movies (in two formats each) of bacteria swimming upstream in crevices along the channel sidewalls. They are on the bottom (glass) surface; the "left" of the surface is actually right in the camera view.
150 µm x 93 µm channel, 0.9 µl/min
150 µm x 93 µm channel, 3.0 µl/min
First, we have observed that the overall effect of the flow is the hydrodynamic trapping of cells along the surface. This means that a given cell will most likely be swimming towards the "left" for extended periods of time. In fact, using dilute bacteria concentrations in the flow channel, the PI was able to track a given bacterium through the entire length of the microfluidic channel (over 4 cm) as it traced a left-handed helical screw trajectory along the interior walls. Such a trajectory enables the cell to continuously "sample" the inner walls and eventually find a surface crevice, crack or imperfection that would offer it shelter from the strong shear flow region.
Second, if the bacterium actually finds such a crevice, it gets hydrodynamically trapped to stay in it and swim upstream. Now, this is a phenomenon that is interesting from a medical perspective. It means that, as long as there is flow, the bacteria will be able to "seek" the most efficient routes (crevices or surface imperfections) through which they can swim upstream. At the size scale of E. coli, almost all surfaces will have such imperfections or crevices that are large enough for bacteria to utilize for upstream swimming.
The overall conclusion is that upstream swimming of E. coli (and other peritrichously flagellated bacteria, such as Salmonella) in the presence of flow will be a factor that strongly determines and possibly enhances their pathogenecity in a wide range of flow conditions. To our knowledge, this is the very first time that a natural propensity to swim upstream has been discovered and described in bacteria. Upstream swimming allows these cells to eventually locate large reservoirs that provide richer sources of food and better conditions for multiplying. In particular, upstream swimming of bacteria might be relevant to the transport of E. coli in the upper urinary track; it might also explain the high rates of infection in catheterized patients and the incidence of microbial contamination at protected wellheads.
The next time you find bacteria in your pressure tank or your water heater at home, try to remember if you have ever left the garden house under pressure in contact with the soil!
References
[1] J. Hill, O. Kalkanci, J. L. McMurry, and H. Koser, "Hydrodynamic surface interactions enable Escherichia coli to seek efficient routes to swim upstream," Physical Review Letters, 98 (6), pp. 68101, 2007. |
