Extended Data Fig. 3: Anticorrelation between bacterial wobbling and motility enhancement.

a, The swimming speed versus the wobble angle of individual bacteria in pure buffer (black squares) and in a suspension of colloids of radius R = 500 nm and volume fraction ϕ = 4% (blue triangles). The data are obtained by averaging the swimming speed of many bacteria binned over a small range of wobble angles. The raw data for each individual bacteria in the 4% colloidal suspension are also shown as the background (grey triangles). For clarify, we do not show the data of individual bacteria in buffer, which show a similar degree of scattering. V₀ = 13 μm/s and θ₀ = 45° are the average swimming speed and the average wobble angle of bacteria in buffer, respectively. As a comparison, the average swimming speed versus the average wobble of bacteria in polymer solutions of different concentrations from ref. ¹⁸ is also shown (red discs). b, A violin plot showing the probability distribution of the wobble angle of bacteria in buffer and in the 4% colloidal suspension. The interquartile range (IQR) gives the difference between the 75th and 25th percentiles of the data. a shows that at a given wobble angle, the swimming speed of a bacterium is nearly constant, independent whether it swims in buffer or in colloidal suspensions. b shows that the average swimming speed of bacteria increases in colloidal suspensions, because there are more weakly-wobbling bacteria in the suspensions.