Watching the flagellar motor at work

by Lucas Le Nagard
 

Figure 1. Three rotating polystyrene beads attached to in­dividual flagellar motors on an E. coli cell. By the au­thor

If you look at the movie displayed in Figure 1, you will see three small beads attached to an Escherichia coli cell, each spinning at about 300 rps (revolutions per second). How do I know this? I tracked them! As it turns out, this "bead assay" is not just a pretty experiment, but also a powerful tool to probe the me­chan­ical output of the bacterial flagellar motor. You will see how in a minute, but let's first zoom out and introduce the basic principles of bacterial self-propulsion in liquids.
 

Swimming E. coli cells typically cover a distance equivalent to the radius of a human hair each second. It might not seem very impressive… But for a 2 µm bacterium, it corresponds to 10 body lengths per second! Much better than the swimming speed of our best athletes, which barely exceeds one body length per second. So, how does E. coli achieve this?
 
 

Figure X. Swimming E. coli cells with fluorescent bodies and flagella bundles. Source

The answer is simple: swimming requires thrust, and, for their size, E. coli cells generate a lot of it by rotating their helical flagella. They alternate between forward propulsion, or "runs," and "tumbles," during which their body stays mostly stationary but actively reorients before the next run. By adjusting the duration of each mode in response to chemotactic signals, cells are able to bias their motion towards attractants and away from repellents. In the "run" mode, all the flagella rotate counter‑clockwise, and hydrodynamic interactions between filaments produce a tight bundle of flagella at the back of the cell (Figure 2). The rotation of this helical propeller generates a propulsive force, until one or several flagella start to spin clockwise when a signal protein, called CheY, binds to the mo­tor(s). At this point, the bundle disassembles and the cell "tumbles."
 

The immediate drop in swimming speed observed during a tumble illustrates the physics of self-propulsion at the microscale: if the propulsive force vanishes, the fluid's friction on the bacterium makes the cell stop in less than a millisecond! The situation is different for larger organisms: a single stroke propels a human swimmer for at least a few seconds, because this motion is dominated by inertia rather than friction. Comparing bacterial to human swimming earlier was thus akin to comparing apples to oranges as far as physics is concerned, but I like to think of bacteria as tiny Olympic swimmers, and it seems I am not the only one! Another consequence of living in a friction-dominated world is that microswimmers can only self-pro­pel by performing a non-reciprocal sequence of movements. This is E.M. Purcell's "scallop the­orem," which states that a microscopic scallop only able to open and close its shell cannot go anywhere, although the situation would be more complex in non-Newtonian fluids. In the case of E. coli, the rotation of helical flagella is a non-reciprocal motion well-suited to generate thrust. And fortunately for scallops, they are much larger than bacteria, so they can rely on inertial forces to swim. If you would like to delve deeper into this topic, I recommend E.M. Pur­cell's classic paper Life at low Reynolds number (Open Access PDF).
 

(click to enlarge)
Figure 3. Schematic structure of flagella (top), of the fla­gellar motor (bottom left), and corresponding electron microscopy images (bottom right). Adapted from Sour­ce and Source

But now to the motor driving the rotation of the flagella. As previously discussed on this blog here, and here, the flagellar motor comprises a "rotor" made of several rings able to rotate with respect to the cell's membrane, and a "stator" composed of peptidoglycan-anchored subunits that sup­ply the torque required for the rotor to spin (Figure 3). The rotor drives the rotation of a central rod, which transmits this spinning motion to the flagellum through a flexible structure called the hook.
 

Of course, this description does not do justice to the beauty of this biological nano-machine, nor to the efforts going into revealing those structural characteristics, recently reviewed here. But it does raise the question: since motor rotation implies mechanical work, where does the energy come from? The motor does not "consume" energy carriers such as ATP or NADH, but rather draws energy from the inward flux of a specific cation (proton or sodium, depending on the species) through its stator units. In the case of E. coli, it works thanks to the proton motive force (PMF), an electrochemical gradient of protons that cells maintain across their cytoplas­mic membrane by exporting protons through respiration or ATP consumption. Proton translo­cation through the motor converts the potential energy stored in the PMF into mechanical work, and the motor can spin. A special engineering treat is the switching between "run" and "tumble" modes without interrupting the PMF, as detailed in Hey flagellum, shift into reverse gear!.
 

This leads to the final question: "how fast does a flagellum spin?" Let's go back to the bead assay of Figure 1. This gold-standard technique is actually quite simple! First, shorten the flagella by passing the cells multiple times through some narrow tubing. Then, immobilize the cells onto a substrate, and attach micron-sized beads to the flagella stubs (for this, you need a mutant strain that produces "sticky" flagella). Record a bead's trajectory to get the speed of its motor, and voilà! Experiments conducted early on with this or similar approaches showed that the motor speed increases with the magnitude of the PMF. Researchers also found that the performance of the motor is load-dependent: not just that its speed decreases as the size of the "load" increases (which it does, see Figure 4), but also that the torque delivered by the motor changes. So, as for any man-made motor, we now have a characteristic torque-speed curve for the bacterial flagellar motor! Furthermore, the bead assay is also well-suited to study the dynamic association of stator units with the motor, which is still an active area of research.

 

Figure 4. Larger loads lead to slower rotation frequen­cies. Movies are slowed down 50×. By the author

So, next time you see some research about the flagellar motor's behavior, check which method was used. Even if authors rarely publish their bead assay movies, it is possible that they had, like me, the joy of looking at those tiny "spinners" for hours during the course of their research. Some have even liked it so much that they also tried to "listen" to their bacteria, or even let them play the drums!
 

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Lucas is a postdoc in the Pilizota lab at the University of Edinburgh, where he studies the link between bacterial motility and physiology by combining bulk swimming measurements with single-motor assays.