Effects of shear-thinning viscosity and viscoelastic stresses on flagellated bacteria motility

The behavior of flagellated bacteria swimming in non-Newtonian media remains an area with contradictory and conflicting results. We report on the behavior of wild-type and smooth-swimming E. coli in Newtonian, shear-thinning, and viscoelastic media, measuring their trajectories and swimming speed using a three-dimensional real-time tracking microscope. We conclude that the speed enhancement in Methocel solution at higher concentrations is due to shear thinning and an analytical model is used to support our experimental result. We argue that shear-induced normal stresses reduce wobbling behavior during cell swimming but do not significantly affect swimming speed. However, the normal stresses play an important role in decreasing the flagellar bundling time, which changes the swimming-speed distribution. A dimensionless number, the “strangulation number” (Str) is proposed and used to characterize this effect.

Figure 1

Mean swimming speed of smooth swimmers in Ficoll (red symbols) and Methocel (black symbols) solutions. The viscosity is the shear viscosity measured at 200 ${\mathrm{s}}^{-1}$. The swimming speed decreases with increased viscosity in Ficoll solutions but increases with increased viscosity in Methocel solutions. Calculated swimming speeds, using a shear-dependent RFT model [6], are plotted using light- and dark-blue symbols, for flagellar shear rates of ${\dot{\gamma }}_f=7000$ and 4000 ${\mathrm{s}}^{-1}$, respectively.

Figure 2

The 2D projection of the swimming trajectories of two individual swimmers. (A) In 0.500% Methocel solution. (B) In motility buffer. It is clearly shown that the trajectory in the Methocel solution is faster and smoother than the trajectory in the motility buffer.

Figure 3

(a) Averaged skewness of swimming-speed distribution of wild-type cells in Methocel (black symbols) and Ficoll (red symbols) solutions at various viscosities. The skewness increases monotonically in Ficoll solutions with increased viscosity. In Methocel solutions, the averaged skewness increases from negative to 0 and then starts to decay. (b). Averaged characteristic run speed of wild-type cells in Methocel (black symbols) and Ficoll (red symbols) solutions at various viscosities. The speed decreases in Ficoll solutions with increased viscosity but increases with increased viscosity in Methocel solutions. (Ficoll results reproduced from Qu et al. [15]).

Figure 4

Smooth-swimmer flagellar motor torque behavior calculated using resistive force theory. The knee speed of the motor is about 100 Hz, which is a bit lower than that found in wild-type cells [8, 15].

Figure 5

Averaged local curvature of all swimming trajectories at different viscosities. Red symbols show the results in Ficoll solutions, and black symbols the results in Methocel solutions.

Figure 6

Shear viscosity of polymer solutions. (a) Methocel solutions. (b) Ficoll solutions.