Bacterial Flagellar Motor: Run-and-Tumble Motility (2D)

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 — swimming straight

Live Readout

Rotation speed

0.0 Hz

Motor torque

0 pN·nm

Swim speed

0.0 µm/s

Path so far

0 µm

Tumbles

Net displacement

0 µm

How it works (2D model)

This 2D companion solves the exact same torque-speed physics as the 3D flagellar-motor model — but instead of rendering the motor's internal parts in 3D, it uses the motor's own solved rotation rate to drive a second, independent simulation: the cell's actual swimming trajectory, viewed from above.

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
Load:  T_load(ω) = ζ·ω,  solved exactly each frame for ω

Top panel: a top-down schematic of the C-ring and stator ring, spinning at the solved rate ω. Bottom panel: run-and-tumble motility — while CCW (run), the flagella bundle co-rotates and the cell swims in a straight line at a speed proportional to ω; when CheY-P triggers a CW switch (tumble) the bundle flies apart, the cell nearly stops translating and its heading randomizes, then the next run sets off in a new direction:

run:    x += cos(θ)·v·dt,  y += sin(θ)·v·dt     (v ∝ ω, straight line)
tumble: θ → θ + Δ  (Δ random, roughly uniform)   (v ≈ 0, no net translation)

This biased random walk — long straight runs interrupted by reorienting tumbles — is exactly the mechanism E. coli uses for chemotaxis: biasing run duration (not direction) toward favorable conditions turns this random walk into a directed drift. Here CheY-P level sets the tumble rate directly so you can see how a higher switching frequency shortens runs and produces a tighter, more localized random walk, while a low CheY-P level produces long, ballistic-looking excursions.

Proton-motive force / active stators / load — set the solved rotation rate ω exactly as in the 3D version; ω in turn sets swim speed during runs.
CheY-P level — sets the auto-switch tumble probability; higher CheY-P means more frequent, shorter runs.
Path so far / net displacement — the ratio of path length to net displacement is the real experimental signature of run-and-tumble motion: frequent tumbles keep net displacement much smaller than total path length (diffusive), while rare tumbles let net displacement approach total path length (ballistic).

Motor (top-down)

Swimming trajectory

Run (CCW) Tumble (CW)