Slowdown of surface diffusion during early stages of bacterial colonization

We study the surface diffusion of the model cyanobacterium Synechocystis sp. PCC6803 during the incipient stages of cell contact with a glass surface in the dilute regime. We observe a twitching motility with alternating immobile tumble and mobile run periods, resulting in a normal diffusion described by a continuous-time random walk with a coefficient of diffusion $D$. Surprisingly, $D$ is found to decrease with time down to a plateau. This is observed only when the cyanobacterial cells are able to produce released extracellular polysaccharides, as shown by a comparative study between the wild-type strain and various polysaccharides-depleted mutants. The analysis of the trajectories taken by the bacterial cells shows that the temporal characteristics of their intermittent motion depend on the instantaneous fraction of visited sites during diffusion. This describes quantitatively the time dependence of $D$, related to the progressive surface coverage by the polysaccharides. The observed slowdown of the surface diffusion may constitute a basic precursor mechanism for microcolony formation and provides clues for controlling biofilm formation.

Figure 1

Experimental setup. (a) Closed cavity where the bacterial cells (dots) sediment and diffuse on the lower surface. (b) Protocol followed with the microfluidic cell: The first experiment is carried out similar to that in (a) but in a microfluidic cell with controllable flow. After sedimentation is completed and having let the bacteria diffuse enough on the lower surface, a pressure gradient is applied to detach the cells from the surface. Then the flow is stopped and the sedimentation-diffusion process starts again. In both setups, bacterial cells are observed with the same equipment (optical microscope coupled to a CCD camera).

Figure 2

(a) For five different experiments, temporal evolution of the number of cyanobacterial cells detected on the hard surface divided by the final number of cells. The plain line corresponds to Eq. (1). (b) Mean-square displacement at several observation times for a selected experiment, computed according to Eq. (A1). The MSD is plotted for observation times ranging from $t=100$ to 2900 s in steps of 400 s. Increasing observation time is indicated by the arrow. The inset shows a snapshot of a typical experiment where bacteria appear as dark spots on the gray background (scale bar $50\mu \mathrm{m}$). (c) Symbols show the temporal evolution of the diffusion coefficient for experiments similar to (a); the black line is the fit based on Eqs. (2) and (3) (see the discussion Sec. 4c for details on the fitting procedure). The inset shows the experimental MSD at long times (circles) and as computed from numerical simulations (line). The dashed black line indicates the slope given by Eq. (2).

Figure 3

(a) Temporal evolution of the coefficient of diffusion for experiments carried out in the microfluidic system [see Fig. 1]. Renewal of the bacterial cell population due to the liquid flow occurs during the period corresponding to the vertical gray bar. (b) Temporal evolution of the diffusion coefficient normalized by its initial value $D_0$ for various Synechocystis strains. Data are the result of averaging over two different experiments. The black (dark) dashed line shows $\mathrm{\Delta }\mathrm{s}ll1875\text{−}\mathrm{sll}1581$, the black (dark) solid line $\mathrm{\Delta }\text{sll0923}–\text{sll5052}$, the red (light) solid line the wild type, and the red (light) dashed line $\mathrm{\Delta }\text{sll1581}$.

Figure 4

(a) Trajectory of a bacterial cell (668 s). Runs correspond to (red) lines and tumble to (blue) dots. The inset shows a representation of a diffusion step by the continuous-time random-walk model (left) and the corresponding experimental diffusion step where the distance traveled during a run $l_{\mathrm{run}}$, the corresponding run duration ${\tau }_{\mathrm{run}}$, and the tumble duration ${\tau }_{\mathrm{tumble}}$ are indicated (right). Also shown are displacement probabilities along one direction for (b) experimental trajectories at the plateau and (c) simulated trajectories. The distributions are given for time intervals $\mathrm{\Delta }=2$, 5, 10, 20, 40, 60, and 80 s. Increasing time interval is indicated by the arrow.

Figure 5

Temporal evolution of (a) $\langle {\tau }_{\mathrm{run}}\rangle$, (b) $\langle {\tau }_{\mathrm{tumble}}\rangle$, and (c) $\langle V_m\rangle$. Here ${\overline{V}}_m$ is indicated by the arrow. Data are normalized by their initial value for the various Synechocystis strains. The lines are defined as in Fig. 3.

Figure 6

(a) Fraction of surface area covered by trajectories in various experiments as a function of time (dot-dashed lines). The thick black solid line is a curve fitted with Eq. (3) (see the discussion in the text). (b)–(d) Colonization maps of the surface for the times indicated in (a). Colormaps indicate the cumulated number of visits in the considered pixel (dark areas indicate empty sites whereas bright areas indicate sites visited more than 20 times).

Figure 7

Variation of $\langle \tau \rangle$ (dashed lines) and $\langle {\tau }_{\mathrm{run}}^2\rangle$ (dotted lines) as functions of the fraction of distinct visited sites $S\left(t\right)$ for five different experiments. The solid lines are linear interpolations.

Figure 8

Coarse-grained velocity $V_{\delta }$ [solid (gray) line] and instantaneous velocity $v$ (dashed line). The black solid line indicates the selection of run periods according to the criteria explained in the text (set to 1 when a run is detected and 0 otherwise). The velocity threshold $V^{★}$ is indicated with an arrow.

Figure 9

Distribution of (a) tumble times, (b) run times, and (c) average velocity during runs $V_m=l_{\mathrm{run}}/{\tau }_{\mathrm{run}}$. Experimental data (points), corresponding to the experiment leading to $D_{\infty ,1}$ described in Sec. 3b, are fitted with expressions given in Appendix pp3 (solid lines), which are used for numerical simulations.