Wall accumulation of bacteria with different motility patterns

We systematically investigate the role of different swimming patterns on the concentration distribution of bacterial suspensions confined between two flat walls, by considering wild-type motility Escherichia coli and Pseudomonas aeruginosa, which perform Run and Tumble and Run and Reverse patterns, respectively. The experiments count motile bacteria at different distances from the bottom wall. In agreement with previous studies, an accumulation of motile bacteria close to the walls is observed. Different wall separations, ranging from 100 to $250\mu \mathrm{m}$, are tested. The concentration profiles result to be independent on the motility pattern and on the walls' separation. These results are confirmed by numerical simulations, based on a collection of self-propelled dumbbells-like particles interacting only through steric interactions. The good agreement with the simulations suggests that the behavior of the investigated bacterial suspensions is determined mainly by steric collisions and self-propulsion, as well as hydrodynamic interactions.

Figure 1

(a), (b) Swimming patterns: Run and Tumble of E. coli (a); Run and Reverse of P. aeruginosa (b). (c) Sketch of the experimental setup: a drop of the bacterial suspension is closed between two glass coverslips with separation $h$, and it is observed in a bright field along the $z$ direction from below with focal plane $(x,y)$ parallel to the walls. The scale bar in the zoom of the field of view corresponds to $5\mu \mathrm{m}$. (d) Sketch of the model used in the simulations: for illustration purposes, we plot bodies of different anisotropy: the multicolored ones are made by $M=4$ beads and are characterized by a head (red) and a tail (green) bead. The active force $F_a$ is applied to each bead pointing along the tail-head direction. The yellow bodies are less anisotropic ($M=3$). In this case no head-tail direction is highlighted since these bodies describe nonmotile cells ($F_a=0$). Note that our simulations consider active and passive bodies with the same anisotropy (same $M$).

Figure 2

Top: Experimental concentration profiles obtained for MG1655 E. coli (full squares) and wild-type P. aerugionosa (full circles). The corresponding results from the simulations of the Run and Tumble (RT) (empty squares) and Run and Reverse (RR) (empty circles) models are reported for comparison. In this case the slit height $h\approx 100\mu \mathrm{m}$ and $75\%$ of the bacteria are motile. Bottom: Zoom of the concentration profiles near the walls.

Figure 3

Concentration profiles for different separations $h$ between the walls in the case of experimentally observed MG1655 E. coli (a) and wild-type P. aeruginosa (b) and numerically simulated Run and Tumble (RT) swimmers. The plots report the number of swimming cells $N$ normalized to the average number $N_0$ of the central plateau as a function of the distance $z$ from the walls in the near-wall regions.

Figure 4

(a) Concentration profiles of Run and Tumble swimmers confined in a slit of height $h\simeq 100\mu \mathrm{m}$. Different symbols refer to different values of the active force and hence of the average speed. Note that for higher values of the average speed, the aggregation of the active swimmers near the walls increases. (b) Concentration profile of Run and Tumble swimmers for different body aspect ratio. In the legend $M$ is the number of beads forming a single cell. For all cases, the Péclet number is $\text{Pe}=420$ corresponding to a body average speed of $\sim 50\mu \mathrm{m}$/s. The concentration of particles is $\sim 5\times {10}^8$ CFU/ml. The system is confined within a slit of height $h=97\mu \mathrm{m}$.

Figure 5

(a) Velocity-velocity correlation function $C\left(t\right)$ for Run and Tumble swimmers (a) and Run and Reverse swimmers (b) obtained for several values of the number of beads $M$. Time is given in units of the characteristic time of the Lennard-Jones interaction ${\tau }_{LJ}=\sigma {(m/\epsilon )}^2$. By fitting the curves by an exponential, the values of $D_r$ can be obtained. The higher the anisotropy, the smaller the decay rate, hence the value of $D_r$. Data refer to a collection of Run and Tumble swimmers where $F_a=300$ and concentration is $5\times {10}^7{\mathrm{ml}}^{-1}$. Data refer to a collection swimmers with $F_a=300$ and concentration $5\times {10}^7{\mathrm{ml}}^{-1}$.

Figure 6

Time dependence of the ratio $M\mathrm{MSD}\left(t\right)D_r/\left(2dt{v}^2\right)$, where $\mathrm{MSD}\left(t\right)=\langle {[\mathbf{r}\left(t\right)-\mathbf{r}\left(0\right)]}^2\rangle$, for Run and Tumble cells. Different curves refer to different values of the number of beads $M$ forming each cell. Data refer to a collection swimmers with $F_a=300$ and concentration $5\times {10}^7{\mathrm{ml}}^{-1}$.

Figure 7

(a) Detention time distribution of Run and Tumble (RT) and Run and Reverse (RR) swimmers in the layer of width $\mathrm{\Delta }z=3\mu \mathrm{m}$ closest to the wall (outer layer). Note that time is given in units of the average run time ${\tau }_R$. Both distributions display an exponential decay whose time scale has been estimated by an exponential fit (see values in the legend). (b) Distribution of the angle $\alpha$ between the cell axis and the wall for Run and Tumble (RT) and Run and Reverse (RR) swimmers near a wall. Data refer to a collection of swimmers where $F_a=200$ and concentration is $5\times {10}^8{\mathrm{ml}}^{-1}$.