The Bacterial Flagellar Motor

What motor do bacteria use to swim?

• The bacterial flagellar motor is a rotary molecular machine embedded in a bacterium’s cell envelope—the membrane and supporting layers surrounding the cell. It rotates a long external flagellum, whose helical shape generates thrust in liquid.
• Distinguish the motor from the flagellum: the motor generates rotation; the external filament acts as the propeller. Together with the connecting structures, they form the flagellar apparatus.
• The motor converts energy stored in an electrochemical ion gradient into mechanical rotation. Most familiar examples use protons, ${\mathrm{H}}^{+}$; some bacteria use sodium ions, $\mathrm{N}{\mathrm{a}}^{+}$.
• Not all bacteria possess flagella, and flagellar swimming is not the only form of bacterial movement.

Think of the apparatus as an ion-powered rotary motor connected through a flexible coupling to a helical propeller.

The main components

• You can divide the apparatus into three functional regions: the motor, the shaft and hook, and the filament. Their precise architecture varies among species.

• Stator anchoring is essential: to exert useful torque on the rotor, the stator needs mechanical support against which to push.
• The hook is more than a connector. Its flexibility allows the filament to adopt an effective swimming orientation without requiring the entire apparatus to form a rigid, straight axle.
• Although the filament is often described as “whip-like,” its propulsion here comes from rotation of a helix, not from a back-and-forth whipping stroke.

The energy source: an electrochemical gradient

• An electrochemical gradient is a difference in an ion’s electrochemical potential across a membrane. It has two contributions:
  • A chemical contribution: a difference in ion concentration.
  • An electrical contribution: a difference in electrical potential, or voltage.
• For a positively charged ion, movement toward a lower concentration is chemically favorable, while movement toward a more negative electrical potential is electrically favorable. The combined effect determines the energetically preferred direction.
• For transfer from outside to inside the cell, the molar free-energy change is:

• Here, $R$ is the gas constant, $T$ is absolute temperature, $c$ is ion concentration, $z$ is the ion’s charge number, $F$ is Faraday’s constant, and $\psi$ is electrical potential.
  • If $\Delta G_{\mathrm{out}\to \mathrm{in}}<0$, inward transfer releases free energy.
  • For both ${\mathrm{H}}^{+}$ and $\mathrm{N}{\mathrm{a}}^{+}$, $z=+1$.
• In proton-powered motors, the electrochemical driving force is called the proton-motive force. Its chemical component is associated with a pH difference, because pH measures proton activity.
• Bacterial metabolism maintains the gradient. The membrane restricts uncontrolled ion passage, allowing the cell to store energy in this difference.

An electrochemical gradient is not merely a concentration difference: membrane voltage matters too.

• The motor does not directly use ATP hydrolysis to power each turn. Its immediate energy input is ion movement down an electrochemical gradient. Metabolism supplies and maintains that gradient.

How ion flow becomes rotation

• Ion conduction: Ions cross the membrane through pathways provided by the stator complexes.
• Molecular coupling: Ion interactions within the stators drive changes in protein configuration and interactions that exert force on the rotor.
• Torque generation: Because these forces act around the rotor’s axis, they generate torque, the rotational analogue of force.
• Mechanical transmission: Rotation passes from the rotor through the rod and hook to the filament.

• For a tangential force $F_{\mathrm{t}}$ acting at radius $r$, torque is:

• The motor’s mechanical power depends on both its torque and its angular speed:

• Here, $\tau$ is torque, $\omega$ is angular velocity, and $P$ is mechanical power.
• The electric-motor analogy is useful because both systems have rotating and stationary components. However, the bacterial motor couples ion transport to protein motion, rather than using the electromagnetic machinery of a conventional electric motor.

Why a rotating helix produces swimming

• The filament’s helical geometry couples rotation to thrust along its axis. As the helix rotates, it exerts forces on the surrounding liquid; the liquid exerts corresponding forces on the filament.
• Bacterial swimming occurs at low Reynolds number, where viscous effects dominate inertial effects:

• Here, $\rho$ is fluid density, $U$ is a characteristic swimming speed, $L$ is a characteristic cell size, and $\mu$ is dynamic viscosity. For bacterial swimming, $\mathrm{Re}\ll 1$.
• This does not mean water becomes intrinsically more viscous around a bacterium. Rather, the bacterium’s small size makes inertia relatively unimportant.
• Consequently, a swimming bacterium coasts essentially no distance after propulsion stops. Continued movement requires continued thrust.

At bacterial scales, swimming is dominated by viscous resistance, not momentum.

Direction changes and chemotaxis

• Chemotaxis is movement biased by chemical conditions, such as the presence of nutrients or harmful substances. Chemical receptors influence signaling pathways that regulate the motor’s switch.
• In a familiar example, Escherichia coli has several flagella and swims through alternating runs and tumbles:

• The cell does not simply point a flagellum toward a detected nutrient source. Instead, it senses whether chemical conditions are improving or worsening as it moves.
  • Improving conditions tend to prolong runs.
  • Worsening conditions tend to increase reorientation.
• This produces a biased random walk: individual direction changes are not precisely aimed, but the accumulated movement favors beneficial conditions.
• Run-and-tumble swimming is not universal. Different numbers and arrangements of flagella support different swimming and reorientation patterns.

Common misconceptions

• “The flagellum itself is the motor.” The filament is the propeller; the motor lies in the cell envelope.
• “The motor burns fuel internally.” Its immediate power source is an ion gradient maintained by cellular metabolism.
• “Only ion concentration matters.” Both concentration and membrane voltage contribute to the driving force.
• “The filament swims by whipping back and forth.” Bacterial flagellar propulsion uses rotation of a helical filament.
• “Bacteria coast after the motor stops.” At low Reynolds number, viscous resistance rapidly removes motion.
• “All bacteria navigate by running and tumbling.” This is an important example, not a universal strategy.

Check your understanding

1. What is the difference between the rotor and the stators?
   The rotor turns; anchored stators conduct ions and exert torque on it.

2. What two factors determine an ion’s electrochemical driving force?
   Its concentration difference across the membrane and the membrane’s electrical potential difference.

3. Why is stator anchoring necessary?
   It provides mechanical support against which the stators can exert torque on the rotor.

4. Why does the filament’s shape matter?
   Its helical geometry converts rotation into thrust through the surrounding liquid.

5. Why does a bacterium barely coast when propulsion stops?
   Its low-Reynolds-number environment is dominated by viscous resistance rather than inertia.

6. How can run-and-tumble motion lead toward nutrients without precise steering?
   Longer runs when conditions improve bias the overall random walk toward favorable regions.