Bacterial Run-Tumble Chemotaxis

E. coli navigating a chemoattractant gradient — biased random walk

Gradient Field

Statistics

Mean X position
Drift velocity
Tumble fraction
Time elapsed

Adaptation: dm/dt = (C−m)/τ

Tumble rate: λ = λ₀·f(m−C)

Gradient sensing: dC/dt > 0 → ↓λ

Run = straight swim.
Tumble = random new θ.
Temporal comparison of C: ΔC = C(t)−m(t)
More attractant → fewer tumbles → biased drift up-gradient.