Bacterial Flagellar Motor: Torque-Speed & Switching

Motor Drive

Proton-motive force 160 mV

Active stator units 8 / 11

Load (viscous drag) bare filament

CW / CCW Switching

Auto-switch via CheY-P

CheY-P level 30%

RUN — flagella co-rotate CCW

Live Readout

Rotation speed

0.0 Hz

Motor torque

0 pN·nm

Mechanical power

0 fW

Regime

—

How it works

The bacterial flagellar motor is a rotary nanomachine embedded in the cell envelope. Protons flowing down their electrochemical gradient (the proton-motive force, PMF) through stator complexes (MotA/MotB) push against the rotor's C-ring (FliG/FliM/FliN), turning the hook and helical filament like a propeller.

Steady-state speed is set by where the motor's torque-speed curve meets the load line. Following measurements from tethered-cell and bead-assay experiments (Berg lab), the curve is a "knee" shape:

T(ω) = T_stall                              for ω ≤ ω_knee   (plateau)
T(ω) = T_stall·(ω_max − ω)/(ω_max − ω_knee)  for ω_knee < ω ≤ ω_max
T(ω) = 0                                     for ω ≥ ω_max

T_stall, ω_knee, ω_max all scale with PMF and with the number
of engaged stators n (up to n = 11 in E. coli).
Load:  T_load(ω) = ζ·ω   (ζ = rotational drag coefficient)

The simulator solves T(ω) = ζ·ω exactly each frame: on the flat plateau, torque stays roughly constant while speed varies with load; past the knee, torque falls linearly to zero at the maximum (zero-torque) speed. A bare filament has low drag and runs near ω_max; a large attached bead (as in real single-motor experiments) loads the motor onto the high-torque plateau at low speed.

Switching: the response regulator CheY-P binds FliM and switches the rotor's sense from counter-clockwise (CCW, filaments form a co-rotating bundle — a "run") to clockwise (CW, the bundle flies apart — a "tumble"). Raising CheY-P raises the switching probability, producing the stochastic run-and-tumble pattern real E. coli use for chemotaxis; toggle "Auto-switch" off to drive the motor manually.

Engaged stator (MotA/MotB) Idle stator C-ring (FliG/FliM/FliN)

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Bacterial Flagellar Motor: Torque-Speed Curve & CW/CCW Switching