Run-and-Tumble Bacteria

Active matter · Effective diffusion · Boundary accumulation · Chemotaxis

Bacteria N: 80

Run speed v: 2.0

Tumble rate λ: 0.05

Chemotaxis bias: 0.0

Confinement: box

Mean run length—

D_eff theory—

Boundary frac—

Modefree

Run-and-tumble is the locomotion strategy of E. coli: straight runs (CCW flagella) punctuated by tumbles (CW, random new direction).
Effective diffusion: D_eff = v²/(d·λ_tumble), where d=2 (2D). Longer runs → larger D_eff.
Boundary accumulation: bacteria near walls spend more time there (hydrodynamic + steric trapping), creating ρ(boundary) >> ρ(bulk).
Chemotaxis: E. coli modulates tumble rate based on receptor methylation state — swimming up-gradient suppresses tumbles, implementing a temporal comparison. Run length ∝ exp(χ∇c) in gradient χ.