Abstract
Bacteria commonly live attached to surfaces in dense collectives containing billions of cells1. While it is known that motility allows these groups to expand en masse into new territory2,3,4,5, how bacteria collectively move across surfaces under such tightly packed conditions remains poorly understood. Here we combine experiments, cell tracking and individual-based modelling to study the pathogen Pseudomonas aeruginosa as it collectively migrates across surfaces using grappling-hook-like pili3,6,7. We show that the fast-moving cells of a hyperpilated mutant are overtaken and outcompeted by the slower-moving wild type at high cell densities. Using theory developed to study liquid crystals8,9,10,11,12,13, we demonstrate that this effect is mediated by the physics of topological defects, points where cells with different orientations meet one another. Our analyses reveal that when defects with topological charge +1/2 collide with one another, the fast-moving mutant cells rotate to point vertically and become trapped. By moving more slowly, wild-type cells avoid this trapping mechanism and generate collective behaviour that results in faster migration. In this way, the physics of liquid crystals explains how slow bacteria can outcompete faster cells in the race for new territory.
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Code availability
The FAST cell-tracking package can be accessed at https://doi.org/10.5281/zenodo.3630641, with extensive documentation on its use and functionality available at https://mackdurham.group.shef.ac.uk/FAST_DokuWiki/dokuwiki. The Defector defect detection package is available at https://doi.org/10.5281/zenodo.3974873, while the colEDGE colony composition package can be accessed at https://doi.org/10.5281/zenodo.3974875. The MATLAB-based implementation of the 3D SPR model can be accessed at https://doi.org/10.5281/zenodo.4139459.
Change history
13 February 2021
A Correction to this paper has been published: https://doi.org/10.1038/s41567-021-01181-8
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Acknowledgements
We thank S. Booth, N. Clarke, C. Durham, A. Fenton, E. Granato, J. Guasto, J. Hobbs, T. Meiller-Legrand, W. Smith, A. Morozov and J. Wheeler for providing comments on a previous version of this manuscript, R. Allen and R. Hawkins for helpful discussions, W. Smith for assistance with the SPR model, J. Engel for sharing bacterial strains, and M. Hopkins for assistance with preliminary experiments. O.J.M. was supported by an EPSRC studentship through the Life Sciences Interface Centre for Doctoral Training (EP/F500394/1); A.D. was supported by the Novo Nordisk Foundation (grant number NNF18SA0035142), Villum Fonden (grant number 29476), Danish Council for Independent Research, Natural Sciences (DFF-117155-1001), and the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement number 847523 (INTERACTIONS); K.R.F. was supported by European Research Council grant 787932 and Wellcome Trust Investigator award 209397/Z/17/Z; and W.M.D was supported by a startup grant from the University of Sheffield’s Imagine: Imaging Life initiative, an EPSRC Pump Priming Award (EP/M027430/1) and a BBSRC New Investigator Grant (BB/R018383/1).
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Contributions
O.J.M. performed experiments, implemented the SPR model, analysed data and prepared figures. A.D. and J.M.Y. proposed the mechanism of rosette formation. O.J.M, A.D., K.R.F, J.M.Y. and W.M.D. all contributed to the design of experiments and models, as well as to the interpretation of results. O.J.M, K.R.F. and W.M.D. wrote the paper with input from A.D. and J.M.Y. This collaborative effort was led by W.M.D.
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Extended data
Extended Data Fig. 1 In the subsurface environment, colonies composed of cells lacking flagella expand faster than those of WT cells, while pili-based chemotaxis mutants display little, if any, motility.
a, b, Measurements of the colony radius, rSUB, and colony expansion rate, \(\frac{{{\mathrm{d}}r_{{\mathrm{SUB}}}}}{{{\mathrm{d}}t}}\), for the wild-type (WT, black, n = 5), a non-flagellated mutant (∆flgK, cyan, n = 3) and a mutant previously shown to be incapable of performing pilus-based chemotaxis in microfluidic devices18 (∆pilG, green, n = 3). Thick lines indicate the mean of n different colonies. Comparison of ∆flgK and WT data indicate that flagella actually hinder colony expansion. We speculate this is because flagella actively stick to surfaces18, increasing the cells’ resistance to movement. c, Single-cell speed distributions of WT (n = 347) and ∆pilG cells (n = 483) when mixed together at low cell density. The speed of solitary ∆pilG cells was significantly smaller than that of solitary WT cells (p < 10−68, Mann-Whitney U test), demonstrating that the slow expansion of ∆pilG colonies is caused by a more general defect in their motility, rather than a lack of chemotaxis. ∆pilG cells express few pili17, which likely impedes their ability to move in high friction environments like those found in agar-based subsurface assays.
Extended Data Fig. 2 Cells have similar orientations in both subsurface and surficial colonies.
a, Surficial and subsurface colonies of YFP labelled WT cells were grown for 24 h at room temperature and then imaged using confocal microscopy (Methods). Both subsurficial (upper row) and surficial (lower row) colonies have a ‘monolayer’ of cells lying flat against the surface at their periphery, a ‘dense’ region where most cells are vertically standing up on end at their center, and a ‘transition’ region where some cells are standing up between the colony edge and center (Fig. 1b–d). We note that subsurface colony images shown here are the same as those presented in Fig. 1d, but are reproduced here to facilitate direct comparison. b, Volumetric projections of a confocal image of a surficial colony inoculated with equal fractions of WT-CFP and ∆pilH-YFP cells. In the upper projection, the three-dimensional image is tilted to show the upper air-exposed surface of the colony, while in the lower projection the image is tilted in the opposite direction to show the side of the colony facing the agar. As the thickness of surficial colonies increases over time, we imaged the colony 16 h after inoculation while it was still sufficiently thin to visualise its entire depth using confocal microscopy. Each edge of the imaged region is 170 µm long. A zoomed-in view of the region within the orange boxes (c) shows that nearly all of the vertically oriented cells protruding into the agar below are ∆pilH-YFP cells, while WT-CFP cells tend to remain horizontal along the air-exposed surface. Orthogonal views show cross sections through the colony at the locations marked by the red lines. These images demonstrate that ∆pilH tends to form structures in surficial colonies similar to those observed in subsurface colonies (Fig. 4f).
Extended Data Fig. 3 ∆pilH cells move faster than WT cells.
Cells in the monolayer of ∆pilH colonies move faster than those in WT colonies (Fig. 1e, reproduced in a). However, ∆pilH monolayers are also observed to have a smaller packing fraction than WT monolayers (a, inset). To test if the variation in cell density could confound our analyses, we also performed a separate experiment in which ∆pilH and WT cells were mixed together at low density. Separate fluorescent markers were used to distinguish strains (b, inset). This confirmed that ∆pilH cells move more quickly than WT cells when the two are at equal density (p < 10−17, Mann-Whitney U test). All experiments shown were performed using the subsurface assay.
Extended Data Fig. 4 Automated analysis of defects reveals differences between the collective motility of WT and ∆pilH monolayers.
a, We used automated defect detection to count the number of comets/trefoils in monolayers of both genotypes and normalized these by the area of the field of view (Methods). Averaging over time, we found that WT monolayers contain 79% more defects than ∆pilH monolayers. Fluctuations in the numbers of comets and trefoils closely follow one another, as predicted by the Poincaré–Hopf theorem which requires that the total topological charge of the system must remain fixed9. b, This relationship was quantified further by calculating the normalized cross-correlation between comet and trefoil density. The maximum cross-correlation occurs at a lag time of zero for both strains, indicating that comet/trefoil pairs are created and annihilated instantaneously. This matches predictions made by previous SPR simulations50. c, Timeseries of ∆pilH and WT monolayers were processed to obtain measurements of the average flow of cells around comets and trefoils as for Fig. 3d. While the same characteristic flow structures were observed in both strains, we observed that the magnitude of the flow velocity was larger for the ∆pilH monolayer. This is consistent with ∆pilH monolayers having a larger activity than WT monolayers10.
Extended Data Fig. 5 Rods that propel themselves with larger forces are more likely to become vertically oriented, which disrupts collective movement.
a, Measurements of the average rod speed as a function of time in three different simulations, each of which contains a uniform population of N = 1600 rods with an aspect ratio of a = 4 and a self-propulsive force, F. Although rods with F = 1.5 collectively move faster than rods with F = 0.5, increasing the propulsive force to F = 3 causes collective speed to sharply decline over time. b, Snapshots of simulations shown in a at steady state. Rods are color-coded by their orientation with respect to the surface, ϕ, such that rods lying flat against the surface are shown in red, while those orthogonal to the surface are shown in blue. Rods with larger F are more likely to stand on end, disrupting their capacity to move. c, We then performed independent simulations for different values of F and plotted the average rod speed and proportion of rods oriented orthogonal to the surface at steady state (Methods). This shows that the mean speed of the collective peaks at intermediate F, with larger values of F causing rods to become vertically oriented. We denote the force that generates the maximum mean rod speed as Fv. Values of F for simulations shown in a and b are denoted by coloured arrows. Our results show that out of plane cell rotation places an upper limit on how much propulsive force can be exerted within collectives. Lines and error bars show the mean and standard deviation of three simulations with different (random) initial conditions.
Extended Data Fig. 6 ∆pilH cells are longer than WT cells, which stabilizes them against verticalization but increases their representation in rosettes when mixed with a shorter genotype.
a, Boxplots of lengths of WT (black) and ∆pilH (orange) cells mixed together in a high-density subsurface colony (‘Monolayer’, WT n = 223, ∆pilH n = 218), a low-density subsurface colony (‘Low-density’, WT n = 114, ∆pilH n = 84), and in liquid culture at exponential phase (‘Liquid’, WT n = 60, ∆pilH n = 34) (Methods). The ∆pilH cells were significantly longer than WT cells in all three environments (* = p < 10−3, ** = p < 10−10, Mann-Whitney U test). Boxplots indicate the median (central white rings), interquartile range (box limits), 1.5x interquartile range (whiskers) and outliers (individual circles). b, Average rod speed at steady state in 3D SPR monolayer simulations for rods with different propulsive forces, F, and rod aspect ratio, a. All rods in a given simulation have identical parameters. c, Proportion of rods oriented vertically at the end of simulations shown in b. d, Steady-state velocity and verticalization measurements for simulations in which a ‘mutant’ population of rods that are propelled by a variable force F2 and with a fixed aspect ratio a2 = 5 interacts with a ‘wild-type’ population with F1 = Fv = 1.5 (fixed), a1 = 4 (fixed). These simulations are similar to the ones shown in Fig. 4b, except the two populations of rods also have different aspect ratios. Error bars in b–d indicate the standard deviation of three separate simulations, each with a different random initial configuration. e, A rosette spontaneously generated in co-culture simulation with parameters F1 = Fv = 1.5, a1 = 4, F2 = 5 and a2 = 5 illustrates how the longer length of the mutant enhances its representation in rosettes (compare with Fig. 4c and see Supplementary Notes).
Extended Data Fig. 7 Rosettes drive convergent flow in a mixed WT/∆pilH subsurface colony and have a topological charge of +1.
a, We used particle image velocimetry (PIV) to quantify collective cell movement in a monolayer of cells over a period of 60 min. The divergence and streamlines of the temporally averaged velocity field reveal that cells locally accumulate (indicated by negative divergence) at rosettes (purple stars). b, A timeseries of brightfield images during rosette formation illustrates this process (also shown in Fig. 4d–f and the first part of Supplementary Video 9), with increasing numbers of cells becoming verticalized and trapped within the boundary of the rosette core (white circles) over time. By calculating the director field of these images (Methods), we can calculate the topological charge n around the core of the rosette (c, white circular arrows). At all timepoints, the charge of the rosette is equal to +1. In a, the region shown in the second part of Supplementary Video 9 is indicated with a white dashed box.
Extended Data Fig. 8 Neither labelling cells with constitutively expressed fluorescent proteins nor the deletion of pilH or pilB has an appreciable impact on the intrinsic growth rate of cells.
a, The leading edge of six different subsurface colonies inoculated with equal fractions of CFP labelled and unlabelled strains (left), YFP labelled and unlabelled strains (middle), and CFP labelled and YFP labelled strains (right) after 16 h of incubation at room temperature. WT and ∆pilH colonies are shown on the upper and lower rows respectively. In all six colonies, near equal proportions of each cell type are present at the colony’s leading edge indicating that expression of a fluorescent label has a negligible impact on each strain’s competitive ability. Unlabelled strains are imaged using brightfield and appear grey. b, Relative fitness of three YFP labelled test strains (WT, ∆pilH and ∆pilB) compared to a CFP labelled WT reference strain mixed together in liquid culture. The relative fitness of each test strain was not significantly different from 1 at either 3.5 or 7 h post-inoculation (p > 0.05, one sample t-test, n = 3, Methods). Error bars indicate standard deviation of 3 replicates.
Extended Data Fig. 9 Differences in motility, rather than differences in cell-cell adhesion, drive changes in strain composition at the front of subsurface colonies.
a, Images of the leading edge of a subsurface colony initialised with equal numbers of ∆pilB-YFP and WT-CFP cells at 150, 250, 350 and 450 minutes after the start of imaging, processed as shown in Supplementary Fig. 1i. During colony expansion (b) a small number of non-piliated ∆pilB cells were observed to be dragged along by motile WT cells. However, over time the number of ∆pilB cells near the edge of the colony gradually declined (c). These results are in stark contrast to those of equivalent Neisseria gonorrhea colonies, where non-piliated cells are pushed to the colony edge due to decreased intercellular adhesion24. Thick lines in b and c indicate the mean of three separate colonies. We note that N. gonorrhoeae cells are spherical, a shape which is predicted to produce a jammed state in dense collectives15. In contrast, steric interactions between rod-shaped P. aeruginosa cells produce local nematic alignment, which permits collective motility and likely explains why motility is dominant over adhesion in this system. d, ∆pilH cells are hyperpilated, which has been shown to increase cell-cell adhesion in other systems24,25. We tested for the importance of this effect by measuring the mean speed of previously solitary ∆pilH cells as they came into contact with one another (orange line, n = 41) and the mean speed of ∆pilH cells already in contact with one another as they moved apart (red, n = 47). If cells actively adhered to each other, we would expect them to slow down after contacting one another and increase their speed after moving away from one another (Supplementary Notes). We find that cell speed peaks at t = 0, which corresponds to the time point at which cells either make or break contact. However, in both cases we observed that there was no appreciable change in cell speed before or after either event, indicating that ∆pilH cells do not appreciably adhere to each other.
Extended Data Fig. 10 Stiffer agar suppresses rosettes, increasing the fraction of ∆pilH cells at the front of mixed WT/∆pilH colonies as they expand.
a, Subsurface colonies prepared with 0.8% (red), 1.2% (purple) and 1.6% (blue) agar were inoculated with equal fractions of WT-CFP and ∆pilH-YFP cells. Cells in colonies prepared with 1.6% agar are predicted to experience an approximately four-fold larger stabilizing torque compared to those with 0.8% agar, which acts to resist the formation of vertically oriented rosettes (Supplementary Notes). Here, we plot the packing fraction, ρ, at the front of colonies as they expand across the surface, aligning each by the radius at which the front becomes fully packed with cells, or confluent (rC). This collapses data from all colonies onto a single curve and allows us to control for variation across replicates (Supplementary Notes). b, Measurements of the ∆pilH to total cell fraction, fH, at the colony front shows that stiffer agar allows ∆pilH cells to migrate greater distances. The inset shows fH at rSUB − rC = 1200 µm, the final position for which data is available for all replicates. We find that fH is positively correlated with agar concentration at this position (p < 0.005, n = 9, Spearman’s rank correlation test), demonstrating that stiffer substrates allow ∆pilH cells to migrate further when competed against WT cells. c, The increased persistence of ∆pilH cells can readily be observed in representative images of the front of 0.8% (top), 1.2% (middle) and 1.6% agar (bottom) colonies. Dashed lines indicate the corresponding positions in a and b. d, e, Images of the region behind the front at the confluency time tC and tC + 100 min in colonies prepared with 0.8% (d) and 1.6% (e) agar. With 0.8% agar, ∆pilH cells form numerous discrete, tightly-packed rosettes. With 1.6% agar, ∆pilH cells still form aggregations but remain horizontally oriented, allowing them to escape and form plume-like patterns. To improve clarity, only YFP-expressing ∆pilH cells are shown in d and e. Thick lines in a, b show the mean of three separate colonies.
Supplementary information
Supplementary Information
Supplementary Notes, Methods, video captions, Fig. 1, Table 1 and references.
Supplementary Video 1
P. aeruginosa displays collective motility in surficial colonies. A surficial colony was inoculated with equal proportions of YFP- and CFP-labelled WT cells. Shown here is the monolayer after 48 h of incubation at room temperature. The left image shows both strains imaged using brightfield microscopy. The right panel shows only the YFP-labelled cells. Patterns of collective movement are clearly visible in the right-hand image because only half of the cells are visible. Total duration is 20 min.
Supplementary Video 2
Our custom tracking software (FAST) can follow the movement of individual cells even when very tightly packed together. Cyan dots show cell centroids and orange traces show cell trajectories. Total duration is 2 min.
Supplementary Video 3
Subsurface ∆pilH colonies initially expand more quickly than WT colonies, but are eventually overtaken. Brightfield images were background subtracted, inverted and contrast enhanced (Methods). Four adjacent fields of view were recorded and stitched together to form a single image. The dark vertical lines are caused by subtle variations in focus between adjacent fields of view. A colony of ∆pilB cells, which lack pili-based motility, is shown as a control. Total duration is 15 h.
Supplementary Video 4
Quantification of bacterial competition in subsurface colonies using automated image analysis. WT and ∆pilH cells were mixed together in equal fractions and used to inoculate a subsurface colony. Automated routines were then used to resolve the location of both the ‘front’ (green boxes) and ‘homeland’ (purple boxes), which were then used in subsequent analyses (Fig. 2d–f). While these datasets also include fluorescent images (Fig. 2g), shown here is the brightfield channel, which is processed as described in Methods. Total duration is 8 h.
Supplementary Video 5
Rosettes in mixed WT and ∆pilH colonies are primarily composed of ∆pilH cells. The left panel shows the monolayer of a subsurface colony inoculated with an equal proportion of CFP-labelled WT cells (grey) and YFP-labelled ∆pilH cells (yellow). The right panel shows an analogous experiment, but with the opposite labelling, that is, with ∆pilH cells in grey and WT cells in yellow. The first half of this video shows an overlay of brightfield and YFP channels (showing both cell types), while the latter half shows only the YFP-labelled cells. ∆pilH cells in both experiments become preferentially trapped in rosettes, which appear as yellow patches and dark patches in the left and right panels, respectively. To minimize phototoxicity, we did not image the CFP channel in these experiments. Total duration is 3 h.
Supplementary Video 6
Automated detection of topological defects in WT and ∆pilH monolayers. Red circles indicate locations of comet defects (+1/2 charge) and blue triangles trefoil defects (−1/2 charge). Orange arrows and cyan lines indicate the orientation of comets and trefoils, respectively. Total duration is 5 min.
Supplementary Video 7
The collision of comets generates stable rosettes only if the force exerted by self-propelled rods exceeds a critical threshold. We initialized our 3D SPR model with two comets (red circles, orange arrows) directed towards one another. The initial static image shows the initial configuration of rods. The trefoils (blue triangles) ensure the total topological charge of the system is zero. Rods that propel themselves with a relatively small force (F = 1, left) remain horizontally oriented after an initial transient, whereas rods that propel themselves with a larger force (F = 3, right) form stable rosettes. Snapshots from these simulations are presented in Fig. 4a.
Supplementary Video 8
Increased propulsive force causes rosettes to form in a monolayer of rods initialized in a random configuration. Three separate 3D SPR simulations are shown. Rods propel themselves with F = 0.5, F = 1.5 and F = 3 in the left, middle, and right simulations, respectively. All other parameters were kept constant between simulations. Data from these simulations are shown in Extended Data Fig. 5a,b.
Supplementary Video 9
The collision of comets triggers rosette formation in a monolayer composed of both WT and ∆pilH cells. This video shows the formation of two different rosettes, in turn. The initial static image in each sequence shows the position of comets (red circles, orange arrows) and trefoils (blue triangles, cyan spokes) before rosette formation. In both cases, rosettes are initiated by the collision of two comets. The flow field generated during the formation of both rosettes is shown in Extended Data Fig. 7a. The first half of the video shows the formation of the rosette presented in Fig. 4d–f; subsequent confocal imaging revealed this rosette was nearly wholly composed of vertically oriented ∆pilH cells. Duration of each sequence is 60 min.
Source data
Source Data Fig. 1
WT/∆pilH monolayer cell speed histogram source data (panel e), with WT, ∆pilH, ∆pilB colony edge positions (panel f) and expansion rates (panel g).
Source Data Fig. 2
WT/∆pilH surficial competition source data (panel b), with measurements of WT/∆pilH subsurficial competitions in the front and homeland regions (panels d–f).
Source Data Fig. 3
RMSD measurements of comet and trefoil movement in WT and ∆pilH monolayers.
Source Data Fig. 4
Source data for plot of average rod speed and verticalization fraction for co-culture simulations.
Source Data Extended Data Fig. 1
WT, ∆pilG and ∆flgK colony edge positions (panel a) and expansion rates (panel b), along with low-density WT/∆pilG speed histogram source data (panel c).
Source Data Extended Data Fig. 3
WT/∆pilH speed histogram source data from separate monolayer (panel a) and low-density co-culture (panel b) experiments.
Source Data Extended Data Fig. 4
Comet and trefoil defect density timecourses for WT and ∆pilH monolayers (panel a) and normalized cross-correlation values between comet and trefoil density timecourses (panel b).
Source Data Extended Data Fig. 5
Average rod speed timecourses from SPR simulations with differing values of F (panel a), source data for plot of rod speed and verticalization fraction for different values of F (panel c).
Source Data Extended Data Fig. 6
Source data for cell length boxplot (panel a), with source data for plots of rod speed and verticalization fraction for monoculture (panels b and c) and co-culture (panel d) simulations.
Source Data Extended Data Fig. 8
Liquid culture relative fitness source data.
Source Data Extended Data Fig. 9
Colony edge positions (panel b) and fraction of ∆pilB in front region (panel c) for ∆pilB/WT co-culture colony expansions, with event-averaged cell velocities around cell–cell touching and untouching events for low-density ∆pilH cells (panel d).
Source Data Extended Data Fig. 10
Front packing fraction (panel a) and ∆pilH fraction in front (panel b) for ∆pilH/WT co-culture colony expansions under pads containing different agar concentrations.
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Meacock, O.J., Doostmohammadi, A., Foster, K.R. et al. Bacteria solve the problem of crowding by moving slowly. Nat. Phys. 17, 205–210 (2021). https://doi.org/10.1038/s41567-020-01070-6
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DOI: https://doi.org/10.1038/s41567-020-01070-6
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