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Topological defects promote layer formation in Myxococcus xanthus colonies

Nature Physics volume 17, pages 211–215 (2021)Cite this article

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Abstract

The soil bacterium Myxococcus xanthus lives in densely packed groups that form dynamic three-dimensional patterns in response to environmental changes, such as droplet-like fruiting bodies during starvation1. The development of these multicellular structures begins with the sequential formation of cell layers in a process that is poorly understood2. Here, using confocal three-dimensional imaging, we find that motile, rod-shaped M. xanthus cells are densely packed and aligned in each layer, forming an active nematic liquid crystal. Cell alignment is nearly perfect throughout the population except at point defects that carry half-integer topological charge. We observe that new cell layers preferentially form at the position of +1/2 defects, whereas holes preferentially open at −1/2 defects. To explain these findings, we model the bacterial colony as an extensile active nematic fluid with anisotropic friction. In agreement with our experimental measurements, this model predicts an influx of cells towards the +1/2 defects and an outflux of cells from the −1/2 defects. Our results suggest that cell motility and mechanical cell–cell interactions are sufficient to promote the formation of cell layers at topological defects, thereby seeding fruiting bodies in colonies of M. xanthus.

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Fig. 1: Dense colonies of M. xanthus form layered active nematic liquid crystals.
Fig. 2: Nematic alignment and topological defects in M. xanthus colonies.
Fig. 3: New layers and new holes preferentially form at +1/2 and −1/2 topological defects, respectively.
Fig. 4: Asymmetric cell flows around topological defects explain the formation of new layers and holes.

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Data availability

Source data are provided with this paper. All other data that support the plots and findings of this study are available from the authors upon request.

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All codes are available from the authors upon request.

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Acknowledgements

We thank F. Beroz, M. Black, C. Fei, E. Han, M. C. Marchetti, J. McEnany and C. Yang for discussions. This work was supported in part by the National Science Foundation, through award PHY-1806501 (J.W.S.); the Center for the Physics of Biological Function (PHY-1734030); and by the National Institutes of Health award R01GM082938 (N.S.W.). R.A. acknowledges support from the Human Frontiers of Science Program (LT000475/2018-C). We acknowledge the use of Princeton’s Imaging and Analysis Center, which is partially supported by the Princeton Center for Complex Materials, a National Science Foundation (NSF)-MRSEC program (DMR-1420541).

Author information

Author notes

  1. These authors contributed equally: Katherine Copenhagen, Ricard Alert.

Authors and Affiliations

  1. Lewis-Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, USA

    Katherine Copenhagen, Ricard Alert, Ned S. Wingreen & Joshua W. Shaevitz

  2. Princeton Center for Theoretical Science, Princeton University, Princeton, NJ, USA

    Ricard Alert

  3. Department of Molecular Biology, Princeton University, Princeton, NJ, USA

    Ned S. Wingreen

  4. Joseph Henry Laboratories of Physics, Princeton University, Princeton, NJ, USA

    Joshua W. Shaevitz

Authors
  1. Katherine Copenhagen
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  3. Ned S. Wingreen
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Contributions

K.C. performed the experiments and analysed the data. R.A. developed the theory and fitted the predictions to the experimental data. All authors interpreted the results and designed the experiments. N.S.W. and J.W.S. supervised the study. K.C. and R.A. wrote the manuscript with input from all the authors.

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Correspondence to Ricard Alert.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Daniel Beller, Anupam Sengupta and Yilin Wu for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Statistics of M. xanthus motility.

Histograms of the cell speed (a) and time between velocity reversals (b) of cells migrating in a low-cell-density environment.

Extended Data Fig. 2 Correlation functions.

Spatial correlation functions of (a) the modified director field \({\hat{{\boldsymbol{n}}}}_{2\theta }=(\cos (2\theta ),\sin (2\theta ))\), and (b) of the velocity field v. Error bars are s.e.m. By fitting exponential decays, we obtain the nematic and the velocity correlation lengths: ℓn = 16.0 ± 0.5 μm and ℓv = 3.9 ± 0.1 μm, respectively.

Extended Data Fig. 3 Net inflow around topological defects.

Vnet, defined in Supplementary Eq. 15 in the Supplementary Note, is the average net inflow velocity through a circumference of radius R centered at a topological defect. Points are experimental data obtained from the average flow fields in Fig. 4c,d. Error bars (s.e.m) are barely visible because they are smaller than the point size. Solid curves are the theoretical predictions given in Supplementary Eq. 18 in the Supplementary Note, evaluated using the parameter values in Table I in the Supplementary Note. Vertical dashed lines indicate the radii at which the experimental net inflow magnitude is maximal. This maximal net inflow is presented in Fig. 4e.

Extended Data Fig. 4 Divergence of the flow field.

Theoretically predicted (a,b) and experimentally measured (c,d) divergence fields around topological defects. The defect schematics show the order parameter (color map) and a few director-field lines. The divergence of the two-dimensional flow field, ∇ ⋅ v, shows pronounced cell accumulation (∇ ⋅ v < 0, purple) in front of +1/2 defects, and cell depletion (∇ ⋅ v < 0, green) in three lobes along the axes of symmetry of −1/2 defects. The parameter values used to plot panels a and b are listed in Table I in the Supplementary Note.

Extended Data Fig. 5 Simultaneous fits of the velocity profiles of +1/2 and −1/2 defects.

The black (grey) data points and the red (blue) curve are the experimentally measured and the fitted midline velocity profile of +1/2 (−1/2) defects, respectively. These simultaneous fits to +1/2 and −1/2 defects, with the common set of parameter values given in Table II in the Supplementary Note, are poorer than the separate fits to the +1/2 and −1/2 defects shown in Fig. 4f.

Extended Data Fig. 6 Predicted cell density profile along the midline of +1/2 defects.

The total cell density is ρ(x, 0) = ρ0 + δρ(x, 0), where δρ(x, 0) is given by Supplementary Eq. 31 in the Supplementary Note, with \({v}_{x}^{0}(x,0)\) obtained from the fits (parameter values in Table III in the Supplementary Note), and J=10−4 (μm·min)−1.

Extended Data Fig. 7 Probability distributions of the distance between defects and new layers (a), and between defects and new holes (b).

In Fig. 3f,g, we normalized these distributions with the distribution p0(r) of distances between defects and randomly selected points within the monolayer (excluding holes). Here, as commonly done for radial distribution functions g(r), we normalized the distributions by the area of an annulus of width dr (the histogram bin size), with A the area of the field of view. Both normalizations give similar results. Errors are s.d.

Extended Data Fig. 8 Average flow field around defects separately measured in each of the 8 replicate experiments.

Each of the separate averages includes a different number of defect frames. The total averages in Fig. 4c,d include all the defect frames across the 8 replicate experiments.

Supplementary information

Supplementary Information

Supplementary note including Tables 1–3 and Videos 1–6.

Reporting Summary

Supplementary Video 1

Reflectance field of a thin cell colony with new holes and cell layers appearing and disappearing.

Supplementary Video 2

Height field corresponding to Supplementary Video 1.

Supplementary Video 3

Reflectance field of a thin colony of ΔpilA mutant cells that lack pili. As for the wild-type cells, colonies of pili-lacking cells also produce new holes and new cell layers.

Supplementary Video 4

Colour map of the cell orientation angle, θ, overlaid on a magnified reflectance movie of the colony.

Supplementary Video 5

Nematic alignment field, S, of the colony.

Supplementary Video 6

Red and blue symbols track the positions and orientations of the +1/2 and −1/2 topological defects, respectively, as they spontaneously appear, move and annihilate within the cell colony. The colour map shows the number of layers overlaid on a laser-brightness movie of the colony. The colour code is the same as in Fig. 1d.

Source data

Source Data Fig. 3

Histogram data for Fig. 3f,g.

Source Data Fig. 4

Data for Fig. 4e.

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Copenhagen, K., Alert, R., Wingreen, N.S. et al. Topological defects promote layer formation in Myxococcus xanthus colonies. Nat. Phys. 17, 211–215 (2021). https://doi.org/10.1038/s41567-020-01056-4

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