Figure 4. Bacterial trajectories have Lévy walk characteristics.

Analysis using the high magnification. (a) A typical trajectory of a B. subtilis bacterium with turning points marked in red. Trajectory was obtained at the high magnification. (b) The length ΔL of walking segments as a function of its duration Δt, indicating an approximately constant speed. A similar plot was obtained for S. marcescens cells with the same average speed. (c) Distribution of waiting times between turns showing a power-law decay with a slope of −2.5, in agreement with the theory of LWs. Filled circles, squares and diamonds show results with B. subtilis; empty circles, squares and diamonds show S. marcescens. The slope is independent of the cutoff ω. Straight lines are least squares fits. At short and long times (indicated by a vertical dashed line), the fit to a power-law deteriorates.