Quenching active swarms: effects of light exposure on collective motility in swarming Serratia marcescens

Abstract

Swarming colonies of the light-responsive bacteria Serratia marcescens grown on agar exhibit robust fluctuating large-scale flows that include arrayed vortices, jets and sinuous streamers. We study the immobilization and quenching of these collective flows when the moving swarm is exposed to intense wide-spectrum light with a substantial ultraviolet component. We map the emergent response of the swarm to light in terms of two parameters-light intensity and duration of exposure-and identify the conditions under which collective motility is impacted. For small exposure times and/or low intensities, we find collective motility to be negligibly affected. Increasing exposure times and/or intensity to higher values suppresses collective motility but only temporarily. Terminating exposure allows bacteria to recover and eventually reestablish collective flows similar to that seen in unexposed swarms. For long exposure times or at high intensities, exposed bacteria become paralysed and form aligned, jammed regions where macroscopic speeds reduce to zero. The effective size of the quenched region increases with time and saturates to approximately the extent of the illuminated region. Post-exposure, active bacteria dislodge immotile bacteria; initial dissolution rates are strongly dependent on duration of exposure. Based on our experimental observations, we propose a minimal Brownian dynamics model to examine the escape of exposed bacteria from the region of exposure. Our results complement studies on planktonic bacteria, inform models of patterning in gradated illumination and provide a starting point for the study of specific wavelengths on swarming bacteria.

Keywords: active jamming; active matter; bacterial swarms; light response of bacteria.

Figure 1.

Characteristics of swarming and expanding colony. (a) Far from the edge of the swarm, the active flows show intense vortical patterns: colour here indicates strength of the vorticity fields ω(x, y). Overlaid on this colour map are velocity vectors obtained by PIV. We observe clockwise and counter-clockwise vortices that are arrayed and form periodically. Additionally, we observe interspersed streaming and flocking flows. (b) Combining computed spatial and temporal correlations of the swarming base state (before exposure to light) with analysis of the energy spectra, we deduce that vortical structures are correlated over characteristic lengths ≈20 μm and over characteristic times ≈0.25 s. (c) Snapshot of a Serratia marcescens colony on an agar substrate, during exposure to high-intensity light from a mercury-arc lamp. PIV-derived velocity fields are overlaid in colour. Swarming motion is pronounced approximately 50 μm from the expanding colony front. The inset shows pre-exposure bacterial alignment ≈150 μm from the colony front. (Online version in colour.)

Figure 2.

Phase space for collective motility after exposure. (a) Changes in flow features of swarming Serratia marcescens—relative to the unexposed base state—depend strongly on intensity and duration of light exposure. We use a wide spectrum mercury lamp (bare intensity I₀ = 980 mW cm⁻² at 535 nm) with filters to selectively expose regions of the swarm to a filtered maximum intensity I. Experiments were conducted a minimum of three times per condition, and the resultant phase behaviour was observed to be robust. From subsequent PIV analysis, we classify the response into one of three types: (I) always active, (II) temporarily passive and (III) always passive. The yellow (dashed) and pink (dotted) curves are phase boundaries (equation (3.3)) consistent with a lower threshold in intensity for irreversible response. (b) Velocity fields taken 10 s post-exposure are shown for each phase. Colours reflect speed with the arrows denoting polar orientation. Collective motility of temporarily immobile bacteria is recovered in approximately 15 s past exposure. (c) We plot the average speed of the swarm in the central region, highlighted by the box in (b) for times encompassing pre-exposure, exposure (yellow band) and post-exposure. Pre-exposure, the average swarm speed fluctuates between 25 and 50 μm s⁻¹. For case (I), the bacteria briefly slow down during exposure, but recover in 6 s. In (II), the swarm speed approaches zero during exposure and recovers in 12 s. In (III), the collective swarm speed drops to very low values (close to zero) and remains steady. The data for the PIV were sampled at 60 fps, we only show around four points for every 25 s for clarity. For light intensities that fall within region (II) of the phase plot, it is likely that some bacteria are more impaired mobility-wise than others due to the natural variations in resistance to light-induced damage. We see no evidence from our videos of bacteria re-animated by the swarm when they are in the fully passivated region (region III). The averaged speed remains consistently zero until the active region (phase) starts to convect the paralysed bacteria away. Here, τ is the time of exposure and I is the intensity. (Online version in colour.)

Figure 3.

Thresholding using intensity fluctuation fields. (a) We calculated the intensity fluctuation difference map |I*(r, t + Δt) − I*(r, t)|, here with Δt = 0.1 s. Intensity fluctuations are low (black) in the regions where the swarm is not moving. Suitably thresholding the result allows us to identify the boundary position (blue curve). The quenched (black blob) phase shrinks with time as is observed by examining the extent of the region at t = 1 s (top) and t = 40 s (bottom) as measured post-exposure. The exposure duration τ = 80 s and intensity (at 535 nm) was 3 W cm⁻². (b) Thresholding of PIV-derived velocity (speed) fields confirms the boundary location obtained from the intensity fluctuation maps. The diffuse boundary may also be located using phase field approaches [33,42]. (Online version in colour.)

Figure 4.

Thresholding using PIV-derived fields allows for analysis of the evolution of the quenched region. (a) PIV-derived bacterial velocity fields before (tile 1) and during (tiles 2–5) light exposure. We note from tile (5) that as the exposure is continued, the paralysing effects persist only a short distance into the active unexposed region as evident from the vortical structures seen near the edge. (b) The azimuthally averaged velocity 〈v〉(r) shown as a colour map highlights the creation of an immotile quenched domain within the exposed region. When the light is switched off, the active bacteria from the unexposed regions penetrate into the quenched domain, eroding it away. The filtered maximum intensity =500 mW cm⁻². We note the brief lag after the light is switched on (the lag here being t_on), the gradual increase and (possible subsequent saturation) to a finite size as t → t_off and the rapid erosion and mixing with the grey interphase region t > t_off. (c) Using averaging filters that effectively smooth the fields in (b) yields less resolved fields. Note the difference in the manner intensities are plotted on the bars shown on the right of (b) and (c). (Online version in colour.)

Figure 5.

Growth, shape and dissolution of the quenched domain. (a) Inset: two-dimensional interface boundaries at various instants in time obtained from thresholding the ΔI (x, y) fields but prior to azimuthal averaging. Pink, red and green curves correspond to exposure times of 10, 20 and 100 s (aperture size 60 μm, 20× objective). These shapes yield effective radii of quenched region that are consistent with values obtained from PIV data based first on thresholding using a cutoff 〈v〉 = 10 μm s⁻¹ and subsequent azimuthal averaging (not shown). (a) Using a larger aperture size and longer exposure time allows us to probe the dynamics of growth in more detail. The effective radius as identified by taking thresholding the averaged PIV data is shown. The effective radius of the quenched region grows during exposure (lag time t_lag ≈ 50 s) and asymptotes to a constant as long as the light source remains on. For comparison, a square root dependence is shown as the red dashed curve. Post-exposure, the effective radius decreases to zero in finite time. The aperture size is 120 μm. (b) The maximum extent R_max ≡ r_eff(t = t_off) increases with exposure duration τ and asymptotes to constant values. (Online version in colour.)

Figure 6.

(a) (i) Close-up of a region in the unexposed active phase (scale bar 15 μm) illustrating aligned regions. These features are highlighted when analysing this image using the Orientation J plugin in ImageJ. The false colour rendering obtained shown in (ii) shows domains with distinctly co-aligned bacteria. Coloured regions indicate regions with closely matching alignment (orientation). Higher intensity of the same colour indicates a smaller dispersion along the common direction of orientation. Characteristic length scales here are slightly smaller than that obtained from PIV-based velocity correlation length scales shown in figure 1b. (b) Contrast-adjusted images of the quenched region (octagonal aperture, size 120 μm). Image (i) correspond to the structure at time t_off − 40 s while image (ii) is the structure at time t_off just when the light source is turned off. (c) Analysis of these images using the ImageJ plugin Orientation J reveals the presence of distinct regions where quenched bacteria are aligned in a similar manner. Closer examination of the regions highlighted in the white rectangles reveals that domains can have a distribution of sizes and orientations, are tightly packed, and do not undergo significant changes once quenched. At the same time, the slight differences in the size and shape of the domains suggest that slow processes including thermally driven (Brownian motion related) realignment may occur over long time scales (scale bar in black 20 μm). (d) The orientational distribution in degrees (−π/2 ≤ θ ≤ π/2) of structures in the complete region within the octagonal area in (b(ii)) as detected by the ImageJ plugin Directionality (https://imagej.net/Directionality). Images with completely isotropic content yield a flat histogram. We see a distribution of angles and the peak of the Gaussian fit that accounts for periodicity (blue curve) is close to zero (goodness of the fit =0.95). Combined with (c(i),(ii)), these observations support the hypothesis that the quenched region comprises distinct, multiple, tightly packed domains of aligned bacteria. Each domain has a different mean alignment. (Online version in colour.)

Figure 7.

(a) The effective extent of the quenched, passive domain decreases over time t at rates that depend on the exposure duration τ. Longer exposure times prolong erosion by the active swarming bacteria, increasing the time it takes for the passive phase to disappear (at time t₀). For each τ, the effective size r_eff follows $r_{\mathrm{eff}}\approx \sqrt{t_0-t}$ (grey dashed curves) with t₀(τ) being the time for complete dissolution. All the points here correspond to the irreversibly quenched regime. (b) The average initial dissolution velocity 〈v_int〉 decreases significantly with τ. Data are the average calculated from four experiments with standard deviation as error bars (intensity ≈3 W cm⁻²). (c) False colour image of the orientational map of bacterial clusters obtained by analysis with ImageJ plugin Orientation J (https://imagej.net/Directionality). The aperture used is the 60 μm aperture (effective total span-wise size of 120 μm) and exposure time τ = 180 s. The snapshot analysed is the image obtained 10 s after the light source is switched off. Each colour denotes a similarly oriented cluster of bacteria as identified by the Orientation J plugin. We observe clusters in the quenched region (shown overlaid as the translucent region) and penetration of moving (active) bacteria clusters into the previously exposed region. The intensity of the colour is a measure of the closeness of orientation. Structural information on orientation and the size of coherent structures when combined with PIV gives us a complete picture of how the moving active phase erodes the passive quenched region and the evolution of the interface [33]. (Online version in colour.)

Figure 8.

Dynamics of self-propelled and diffusing particles (N = 10⁴) interacting with a constant, unbounded light field (Φ(r) = 1, R_L = ∞). Light exposure modifies the translational and rotational diffusivities, but not the self-propulsion speed. Cells are released at the origin r = 0 and trajectories integrated for a dimensionless time interval T_F = 10 with Δt ∈ (4 × 10⁻⁴, 10⁻³). (a) When the cell speed is held constant, examination of the ensemble averaged MSD(t) shows trajectories becoming denser and compact yielding a plateau in the MSD corresponding to localization and paralysis of the particles. Changes in rotational diffusivities are required for this to happen since the self-propulsion speed is assumed to be constant; this effect is exacerbated as ${\mathcal{A}}_2$ becomes larger. Note that as ${\mathcal{A}}_1$ increases, the longer the particles typically travel before exposure effects dominate. (b) MSD (t = T_F) as a function of ${\mathcal{A}}_2$ for various values of ${\mathcal{A}}_3$ (from top to bottom: 0.1, 0.5, 1 and 2) with ${\mathcal{A}}_1=1$. Consistent with (a), we observe saturation for ${\mathcal{A}}_2>3$. The inset shows the (x, y) locations of the particles for parameters corresponding to points 1, 2 and 3 marked on the plot at T_F = 10. Examination of the corresponding number distribution plots (right tiles) shows the peak shifting to lower values of radial distance r, and significant changes to the tail end of the distribution function. Since the light field is unbounded, all particles are eventually affected. For particles with low Peclet number (low activity), the exposure time determines how far they can travel before becoming deactivated. (Online version in colour.)

Figure 9.

Effects of an imposed (dimensionless) length scale R_L using a finite extent light field $\mathit{\Phi }(\mathbf{r})=1\hspace{0.17em}\mathrm{\forall }r\in (0,R_{\mathrm{L}})$ and zero elsewhere. We integrate trajectories of 10⁴ particles using Δt = 4 × 10⁻⁴ up to final times T_F. (a) First effects of finite light extent. The dimensionless MSD is shown as a function of time for R_L = 100. Solid curves are results for ${\mathcal{A}}_1=5$ while dashed curves are for ${\mathcal{A}}_1=1$. We see that as ${\mathcal{A}}_3$ increases from 0.2 to 1.0, MSD saturates rapidly. Inset: sample trajectories for ${\mathcal{A}}_1=1$ for 0 ≤ t ≤ 20 demonstrating localization for t > 6. (b) Decreasing R_L from 100 to 10 brings out the role of Peclet number in enabling escape. We show cell positions at t = T_F = 10 (note that cells outside of this domain are not shown). (c) The fraction of 10⁴ trajectories that start at r = 0 and are located at r > R_L at T = 10. Note that some of these trajectories reenter the domain in the simulation. Curves are shown as a function of the rotation diffusion parameter ${\mathcal{A}}_3$. (Online version in colour.)

Figure 10.

Histogram and spatio-temporal distributions of 10⁴ test cells that start within the illuminated region of extent R_L = 10. Here ${\mathcal{A}}_1=5$, ${\mathcal{A}}_2=1$ and ${\mathcal{A}}_3=0.2$. The density of cells is constant at t = 0 (top and bottom, red dots) and each cell starts with values F = 1 and G = 1. We track F(t) and G(t) of the ensemble of cells as a function of time and plot the distribution in terms of cell numbers at three time instances T = 2, 6 and 10. These are not ensemble averaged results and represent just one specific realization; nonetheless, we expect these results to be illustrative of the spatial heterogeneities that develop due to light-mediated effects on the diffusion coefficients. (Online version in colour.)

Figure 11.

The relationship between ${\mathcal{A}}_3$, exposure time τ and the escape time for particles that start off-centre. Here the initial conditions are X(0) = 5 and Y(0) = 0 and integrations are conducted for a time window (in dimensionless terms) τ. Whenever a simulated cell reaches the edge of the illuminated region—a circle with radius R_L = 10 centred at the origin—the simulation of that particle ends and the time taken by the cell to reach the edge is noted. Cells that remain within the illuminated region are not considered. The (conditional) escape time is then calculated. Unfilled circles correspond to ${\mathcal{A}}_1=5$ and filled diamonds to ${\mathcal{A}}_1=1$. In terms of colours, blue data points are for τ = 10, red data points are for τ = 20 and yellow data points correspond to τ = 50. N = 10⁴, Δt = 10⁻³, τ = (10, 20, 50) and ${\mathcal{A}}_2=0$. (Online version in colour.)