overnight culture solution is transferred to of T-Broth (NaCl , trypton , pH7.2), and the inoculated cultures are incubated at and agitated at 150 rpm for about 6 hours. After reaching an optical density of $0.4$, the culture medium is centrifuged at 3000 rpm at room temperature for 10 minutes to concentrate the bacterial suspension density to $20-25\% v/v$.

The straight swimming of bacteria was measured in a bulk fluid, and the fluctuation of the heading angle $\theta(t)$ was analyzed. Single bacteria are considered as self-propelled points particle, with a position $\bm{r}(t) = (\bm{x}(t), \bm{y}(t))$ and an orientation $\bm{d}(t)$(Fig.\[figs\_diffusion\](a)). For two-dimensional coordinates, the orientation of single bacteria is expressed by the unit vector along the long-axis of bacteria $\bm{d} = \bm{d}(\theta(t)) = (\cos\theta(t) , \sin\theta(t))$. Because the mean-square angle displacement (MSD) is given by $\langle \bigl[\bm{d}(\theta(t)) - \bm{d}(\theta(0))\bigr]^2 \rangle_t = 2(1-\exp[-D t])$ with time interval $\delta t$ and the angular diffusion coefficient $D$ that reflects the fluctuation of bacterial orientation at single cell level[@jain](Fig.\[figs\_diffusion\](b)). The obtained coefficient $D$ is 0.12 rad$^2$/sec, indicating that RP4979 bacteria persistently swim in one direction at a low density in bulk.

![**Straight swimming of single bacteria in bulk.** (a) Typical trajectory of swimming single bacteria 