Bacterial Chemotaxis in a Gradient

Run-and-tumble chemotaxis (Berg & Brown 1972): E. coli alternates between runs (straight swimming, flagella bundled, ~1s) and tumbles (random reorientation, flagella unbundled, ~0.1s). In a chemical gradient, the tumble rate λ(c) decreases when swimming up-gradient (experiencing increasing concentration), extending runs in favorable directions. The Keller-Segel drift velocity is v_d = v·χ·∇c / (λ₀ + β|∇c|), where χ is chemotactic sensitivity and β is adaptation rate. The chemotactic index CI = cos(θ) measures alignment with the gradient (CI→1 = perfect, CI→0 = random). Adaptation via methylation of receptor MCP (CheR/CheB) maintains sensitivity over 5 decades of background concentration.