Abstract
Active nematics are the non-equilibrium analogue of passive liquid crystals. They consist of anisotropic units that consume free energy to drive emergent behaviour. As with liquid crystal molecules in displays, ordering and dynamics in active nematics are sensitive to boundary conditions. However, unlike passive liquid crystals, active nematics have the potential to regulate their boundaries through self-generated stresses. Here we show how a three-dimensional, living nematic can actively shape itself and its boundary to regulate its internal architecture through growth-induced stresses, using bacterial biofilms confined by a hydrogel as a model system. We show that biofilms exhibit a sharp transition in shape from domes to lenses in response to changing environmental stiffness or cell–substrate friction, which is explained by a theoretical model that considers the competition between confinement and interfacial forces. The growth mode defines the progression of the boundary, which in turn determines the trajectories and spatial distribution of cell lineages. We further demonstrate that the evolving boundary and corresponding stress anisotropy define the orientational ordering of cells and the emergence of topological defects in the biofilm interior. Our findings may provide strategies for the development of programmed microbial consortia with emergent material properties.
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Data availability
All relevant data supporting the key findings of this study are available in the article and its Supplementary Information files or from the corresponding authors upon reasonable request. Raw image data can be accessed via https://doi.org/10.5061/dryad.9kd51c5nw. Source data are provided with this paper.
Code availability
The ABSs were implemented in the framework of the molecular dynamics simulator LAMMPS and can be retrieved from https://zenodo.org/record/7879038#.ZE0-US_MKJ8. Images were analysed using custom-written Matlab codes (v.2018a) and can be retrieved from https://doi.org/10.5281/zenodo.5570867.
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Acknowledgements
We thank R. Alert, R. Long, R. Zhang and N. Goldenfeld for helpful discussions. Research reported in this publication was supported by the National Institute of General Medical Sciences of the National Institutes of Health under Award Number DP2GM146253 (J.Y.). J.Y. holds a Career Award at the Scientific Interface from the Burroughs Wellcome Fund (1015763.02). This publication was made possible in part with the support of the Charles H. Revson Foundation 22-28 (J.N.). J.-S.B.T. is a Damon Runyon Fellow supported by the Damon Runyon Cancer Research Foundation (grant no. DRG-2446-21). T.C. acknowledges the support of T. B. Bentley, Office of Naval Research Program Manager, under award number N00014-20-1-2561. S. Zhou acknowledges the support of NSF CAREER award, DMR-2239551.
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Contributions
J.N. and C.L. contributed equally to the work. J.N. and J.Y. conceptualized the project. J.N. and Q.Z. performed the experiments, and J.N. and J.-S.B.T. performed the data analysis. J.N., M.K., T.H., S. Zhou, T.C. and J.Y. formulated the theoretical model. C.L. and S. Zhang developed the ABSs. All authors contributed to the writing of the paper. Correspondence and requests for materials should be addressed to J.Y., T.C. or S. Zhang.
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Extended data
Extended Data Fig. 1 Biofilm image segmentation process.
From top to bottom: Raw data, deconvolved data, binarized image, segmented image and reconstructed image. In the bottom two panels, each colour denotes a distinct cell. Slice 1 and slice 2 correspond to two different \((r,z)\) cuts of the same biofilm grown under a 2% gel overnight. Scale bar, 5 µm.
Extended Data Fig. 2 Example biofilm and contour identification.
(a) Raw image showing the basal plane (top) and cross-section (bottom) of a WT* biofilm grown under a 0.5% agarose gel. Scale bar, 10 µm. (b) Three-dimensional reconstruction of the biofilm in (a) with the areal convex hulls overlain (white). (c) Effective radii of the convex hulls as a function of the height of the biofilm. Red line corresponds to a linear fit from which the effective contact angle is calculated.
Extended Data Fig. 3 Contact angle distributions across experiments and mutant strains.
(a) Probability distribution function of different contact angles for biofilms grown under gels of different agarose concentrations. Each line corresponds to a distinct single field of view with at least 10 biofilms. In general, we find that the distributions, including the bimodal distributions at intermediate concentrations, are well preserved across experiments. (b) Violin plot of contact angles calculated for biofilms formed by different mutant strains grown under gels of different agarose concentrations. Each chord represents a probability distribution and the lines connect the median values of the distributions. The grey data correspond to the data in Fig. 1c, the blue data are for a mutant strain that lacks biofilm adhesins Bap1 and RbmC and the orange data are for a mutant strain that also lacks biofilm adhesins Bap1 and RbmC but expresses the cell-cell adhesin RbmA. We note that the cell-cell adhesion seems to minimally affect the shape transition.
Extended Data Fig. 4 Competition between gel stiffness and substrate friction controls biofilm morphogenesis.
(a) Schematic of the theoretical setup. A biofilm with basal radius \({r}_{{\rm{b}}}\) sits at the interface of a rigid bottom substrate and a semi-infinite elastic gel (blue). As the biofilm grows, its expansion is impeded by friction from the substrate; meanwhile, the growth of the biofilm deforms the gel around it, potentially delaminating the gel from the substrate. (b, c) Example solutions showing the evolution of the rescaled volume \(V/{r}_{{\rm{b}}}^{3}\) (b) and contact angle (c) for \(\mu =3{\rm{kPa}}\) and \(\eta ={10}^{11}{\rm{Pa}}\,{\rm{s}}/{\rm{m}}\). Experimentally, the initial regimes are difficult to observe because of errors in defining the shape of a biofilm consisting of tens of cells. (d) Predicted biofilm contact angle as a function of dimensionless substrate friction and gel modulus. Overlain circles denote the experimental results from Extended Data Fig. 3. The two halves of each circle quantify the interquartile range of measured contact angles. The adhesin-less mutant ∆bap1∆rbmC (∆BC) has a negligible dimensionless friction value and is therefore plotted on the x-axis.
Extended Data Fig. 5 Cell trajectories in agent-based simulations also exhibit different patterns in response to gel stiffness.
Trajectories of cells in agent-based simulations with different gel stiffnesses show two different types of patterns: either curving down leading to fountain-like trajectories (top) or curving up (bottom), consistent with experimental observations.
Extended Data Fig. 6 Distinct gel deformation modes for dome- and lens-shaped phenotypes.
Displacement of tracer particles in the axisymmetric coordinates of the biofilm during growth of 6 different biofilms. The colours denote the direction and magnitude of the vertical displacement of the beads at the end of the experiment with respect to their original locations (\(z\left(t\right)-z\left(0\right)\)). Consistent with the interfacial cavitation model for the growth of dome-shaped biofilms, we observed negative values near the boundary, corresponding to gel materials that are compressed and therefore move closer to the glass substrate.
Extended Data Fig. 7 Cell trajectories in mutant biofilms.
(a) Reconstructed puncta trajectories for a WT* biofilm grown under a soft gel (corresponding to averaged data in Fig. 3b). Scale bar, 10 µm. (b, c) 3D reconstructed puncta trajectories (top) and projected and averaged trajectories (bottom) for a biofilm that does not produce the extracellular adhesins Bap1 and RbmC (b) and for bacteria that do not produce any extracellular matrix (ΔvpsL, c) grown under a stiff gel (\(c=2 \%\)). While the Δbap1ΔrbmC mutant (b) follows similar trajectories as the WT* biofilm under a stiff environment (Fig. 3b), trajectories of ΔvpsL cells exhibit the opposite curvature. It has been shown previously that the Δbap1ΔrbmC mutant still retains some adhesion to the top gel surface through the exopolysaccharide, which is critical to create the upward bending of the cell trajectories. In contrast, the ΔvpsL mutant exhibits a trajectory that can be expected if all regions of the biofilm are growing in dimensions proportional to the growing radius and height. These results support the conclusion that biofilm shape and biofilm-gel adhesion jointly dictate the cell trajectories in a biofilm.
Extended Data Fig. 8 Bacteria reproducibly self-organize into the same overall biofilm architecture.
Azimuthally averaged cell orientations for WT* biofilms grown under 2% gels overnight. Colours denote the nematic order parameter and the ovals denote the average director of the cells projected into (\(r,z\)) space. Each panel corresponds to a unique biofilm of different size but yields the same overall cellular ordering. These data were rescaled and averaged to give the prototypical organization shown in Fig. 5b in the main text.
Extended Data Fig. 9 Agent-based simulations for WT* and mutant biofilms grown under a gel with E = 3 × 104 Pa.
Top: azimuthally averaged cell orientations (black oval) and nematic order parameter (color). Middle: first principal stress direction (black oval) and shear stress distribution (color). Bottom: first principal stress direction (black oval) and pressure distribution (color). Results are shown for (a) a biofilm with cell-substrate friction and cell-gel adhesion, corresponding to WT* biofilms in the experiments; (b) a biofilm with cell-gel adhesion only, corresponding to Δbap1ΔrbmC mutant biofilms in the experiments; (c) a colony with neither cell-substrate friction nor cell-gel adhesion, corresponding to ΔvpsL mutant colonies in the experiments.
Extended Data Fig. 10 Collective delamination enables dispersed cells to explore new territories.
(a) Basal layer of a biofilm, with dispersed cells around it (enclosed by the dashed lines). (b) Radially averaged intensity plot corresponding to the biofilm in (a). The green intensity corresponds to the azimuthally averaged signal from the fluorescently labelled bacteria, and the magenta corresponds to the azimuthal maximum intensity projection of the tracer particles. Empty space is observed between the glass and gel beyond the edge of the biofilm, highlighted by the dashed triangle. (c) Displacement \({dz}\) of the agarose gel nearest to the substrate relative to its initial position. The three peaks correspond to three biofilms which have collectively delaminated the gel from the substrate. The white outline corresponds to the 0.5 µm contour of \({dz}\). (d) Evolution of the delaminated region (the 0.5 µm \({dz}\) contour) over time, showing initially local growth before collective delamination. (e) Image of the basal layer of many biofilms, showing collective delamination. The initial inoculation consisted of three differently coloured but otherwise identical WT* strains. The magenta dots correspond to tracer particles embedded in the gel near the basal plane, the absence of which coincides with the absence of agarose gel – this collectively delaminated region is outlined by the dashed line. Scale bar in a,b,c,d, 10 µm; scale bar in e, 100 µm.
Supplementary information
Supplementary Information
Supplementary Notes 1 and 2, Figs. 1 and 2, Table 1 and References.
Supplementary Video 1
A z-scan of a WT* biofilm grown under a 0.2% agarose gel for 13 hours. The total height scanned in the video is 29.64 μm. Scale bar, 10 μm.
Supplementary Video 2
A z-scan of a WT* biofilm grown under a 2% agarose gel for 20 hours. The total height scanned in the video is 10.4 μm. Scale bar, 10 μm.
Supplementary Video 3
An azimuthal scan (each frame shows data projected into the (r,z) plane at a fixed θ) of a WT* biofilm grown under a 0.2% agarose gel. Left to right: raw data, segmented cells, reconstructed biofilm. The total rotation in the video is 360º. Scale bar, 5 μm.
Supplementary Video 4
An azimuthal scan (each frame shows data projected into the (r,z) plane at a fixed θ) of a WT* biofilm grown under a 2% agarose gel. Top to bottom: raw data, segmented cells, reconstructed biofilm. The total rotation in the video is 360º. Scale bar, 5 μm.
Supplementary Video 5
Representative results of the 3D ABSs for biofilms grown under a stiff gel (E = 3 × 104 Pa). The initial configuration starts from a single cell embedded in a coarse-grained gel, and the duration of the simulation is ~13 generations of cell proliferation. The gel particles are not visualized here for clarity. Shown are the oblique (left) and bottom (right) views of the simulated biofilm. Cells are coloured on the basis of the nematic order parameter S.
Supplementary Video 6
Representative results of the 3D ABSs for biofilms grown under a soft gel (E = 1 × 103 Pa). Other simulation settings and the visualization protocol are the same as in Supplementary Video 5. Shown are the oblique (left) and bottom (right) views of the simulated biofilm.
Supplementary Video 7
A time-lapsed cross-sectional view (x,z) of a WT* biofilm grown under a 0.2% gel with mNeonGreen labelled puncta. The total duration of the video is 12 hours. Scale bar, 5 μm.
Supplementary Video 8
A time-lapsed cross-sectional view (x,z) of magenta labelled tracer particles embedded in a 2% gel. Note that the growing WT* biofilm is omitted and fills the empty space. The total duration of the video is 18 hours. Scale bar, 5 μm.
Source data
Source Data
An Excel sheet containing statistical source data for Figs. 1–6 and Extended Data Figs. 2 and 3.
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Nijjer, J., Li, C., Kothari, M. et al. Biofilms as self-shaping growing nematics. Nat. Phys. 19, 1936–1944 (2023). https://doi.org/10.1038/s41567-023-02221-1
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DOI: https://doi.org/10.1038/s41567-023-02221-1
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