Biofilms as self-shaping growing nematics

Abstract

Active nematics are the nonequilibrium analogue of passive liquid crystals. They consist of anisotropic units that consume free energy to drive emergent behaviour. Like 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 upon 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.

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_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_b³ (b) and contact angle (c) for 𝜇=3kPa and 𝜂=10¹¹Pa s/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(t)−z(0)). 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.

Fig. 1|. Biofilm shape bifurcation in response to environmental stiffness|

(a) Reconstructed biofilms grown under agarose gels with different concentrations. Biofilms consist of $8600\pm 700$ (mean $\pm$ s.d.; range $7245-9420$) cells. (b) Shape of biofilms in (a) in cylindrical coordinates. The contours are reflected about $r=0$. (c) Violin plot of contact angles calculated for biofilms grown under different agarose concentrations. Each chord represents a probability distribution function calculated from $136\pm 53$ (mean $\pm$ s.d.; range $58-269$) mature biofilms. Stars correspond to biofilms shown in (a) and (b). (d) Bifurcation of the biofilm contact angle with agarose concentration. Each point (and error bar) corresponds to the mean (and standard deviation) of a gaussian fit that encompasses all biofilms with contact angles either greater than or less than 75° (underlying data is the same as Fig. 1c). Inset: two examples of mature biofilms with different morphologies grown under 1.5% agarose gels. (e) Plot of the maximum height and maximum radius of biofilms grown under a 0.5% gel (left) and 2% gel (right). Data corresponds to ensembles of 12 and 6 different biofilms imaged over time, respectively. Inset: shape evolution of a single biofilm under each condition. (f) Time-evolution of the contact angle for biofilms grown under gels with different stiffnesses. Scale bars, 10 µm.

Fig. 2|. Environmental stiffness and biofilm-surface adhesion jointly control biofilm shape|

(a) Phase diagram showing the experimental distribution of biofilm shapes for cells producing varying amounts of the surface adhesion protein bap1, controlled by an arabinose-inducible promoter, and grown under different stiffness environments. Each icon corresponds to a violin plot of contact angles with red and blue corresponding to large and small mean contact angles, respectively. Each histogram corresponds to $41\pm 25$ biofilms (mean $\pm$ s.d.; range $6-138$). (b) Phase diagram showing biofilm contact angles from agent-based simulations for different cell-substrate friction coefficients and gel stiffnesses. Each dot corresponds to a single simulation. (c) Phase diagram showing predicted biofilm contact angles calculated from the continuum model (Supplementary Notes 2) for $V={10}^{-13}{\mathrm{m}}^3$. (d) Predicted evolution of the contact angle with growing volume for stiffness $\mu =3\mathrm{k}\mathrm{P}\mathrm{a}$ for different friction coefficients $\eta$ (unit: Pa·s/m).

Fig. 3|. Boundary conditions dictate cell fate in biofilm|

(a) Reconstructed cell trajectories from puncta tracking in a biofilm confined by a stiff gel ($c=2\%$). Colors denote the intensity of the fluorescently labelled puncta. Scale bar, 10 µm. Inset: image of a green-punctum-containing red V. cholerae cell. Scale bar, 1 µm. (b) Puncta trajectories from biofilms grown under two different conditions projected into $(r,z)$ space. Purple lines denote averaged trajectories that end near the edge of the biofilm. (c) Age of the biofilm-gel interface measured by tracking the displacement of tracer particles embedded in the agarose gel. The delamination time, i.e., birth of the local interface, is defined as the time point when the vertical displacement of the corresponding tracer particle exceeds 0.5 μm. Data consists of an ensemble of three different biofilms labelled with three different markers. (d) Basal layer puncta labelled by whether its height has exceeded 3 μm or not during its entire history, corresponding to cells that have transiently left the surface (green) and cells that are always substrate bound (blue), respectively. (e) Schematic representation of the cell trajectories and their coupling to boundary evolution.

Fig. 4|. 3D spatial variation in cell orientations and ordering in dome-shaped biofilms|

(a) Three-dimensional reconstruction of a biofilm grown under soft confinement ($c=0.5\%$). Cells are colored based on the scalar order parameter calculated in each differential volume with $\mathrm{\Delta }r=2\mathrm{\mu }\mathrm{m}$, $\mathrm{\Delta }z=2\mathrm{\mu }\mathrm{m}$, $\mathrm{\Delta }\theta =45°$. (b) Azimuthally averaged cell orientations for biofilms grown in different stiffness environments. Colors denote the scalar order parameter and the ovals denote the average direction of the cells projected into ($r,z$) space. Data is first averaged azimuthally in each biofilm then averaged across 13 $\pm$ 5 (mean $\pm$ s.d.; range 5–18) different biofilms. To account for different sizes of biofilms, $r$ and $z$ were rescaled by $r_{\mathrm{m}\mathrm{a}\mathrm{x}}$ and $z_{\mathrm{m}\mathrm{a}\mathrm{x}}$ prior to averaging and rescaled after averaging such that the aspect ratio (AR) was equal to the mean aspect ratios of the underlying biofilms. Note the data shown are reflected about $r=0$. Grey denotes regions with an insufficient number of cells for averaging. (c) Scalar order parameter averaged as a function of the normalized distance to the origin (mean $\pm$ s.d.). For each condition, data is first averaged in each biofilm and then averaged across biofilms (data corresponds to the same underlying data as b).

Fig. 5|. 3D spatial variation in cell orientations and ordering in lens-shaped biofilms|

(a) Three-dimensional reconstruction of a biofilm grown under stiff confinement ($c=2\%$). Cells are colored based on the scalar order parameter calculated in each differential volume with $\mathrm{\Delta }r=2\mathrm{\mu }\mathrm{m}$, $\mathrm{\Delta }z=2\mathrm{\mu }\mathrm{m}$, $\mathrm{\Delta }\theta =45°$. (b) Azimuthally averaged cell orientations for biofilms grown in different stiffness environments. Colors denote the scalar order parameter and the ovals denote the average direction of the cells projected into ($r,z$) space. Data is first averaged azimuthally in each biofilm then averaged across 11 $\pm$ 4 (mean $\pm$ s.d.; range 6–16) different biofilms. Grey denotes regions with an insufficient number of cells for averaging. (c) Scalar order parameter averaged as a function of the normalized distance to the origin (mean $\pm$ s.d.).

Fig. 6|. Agent-based simulations recapitulate the experimental cellular ordering and reveal stress anisotropy in biofilms.

(a) Oblique, cross-sectional, and bottom view of a representative simulated biofilm grown under stiff confinement (gel modulus E ~ ${10}^4$ Pa). Cells are colored based on the scalar order parameter calculated in each differential volume with $\mathrm{\Delta }r=2\mathrm{\mu }\mathrm{m}$, $\mathrm{\Delta }z=2\mathrm{\mu }\mathrm{m}$, $\mathrm{\Delta }\theta =45°$. (b) Azimuthally averaged cell orientations for the same simulated biofilm in (a). Colors denote the scalar order parameter and the ovals denote the average director of the cells projected into ($r,z$) space. (c) Azimuthally averaged first principal stress direction ${\widehat{\mathit{n}}}_1$, where colors denote the stress anisotropic parameter $\tau /p$. The ovals denote the projected unit orientation vector corresponding to ${\sigma }_1$ into ($r,z$) space. (d) Azimuthally averaged alignment between the cell direction and first principal stress direction, $\left|{\widehat{\mathit{n}}}_1\cdot {\widehat{\mathit{n}}}_i\right|$. The ovals denote the projected unit orientation vector corresponding to ${\sigma }_1$ into ($r,z$) space. (e) Stress anisotropy $\tau /p$ as a function of the gel modulus $E$ for simulations with both cell-substrate friction and cell-gel adhesion, with cell-gel adhesion only, and with neither cell-substrate friction nor cell-gel adhesion, corresponding to WT*, Δbap1ΔrbmC, and ΔvpsL biofilms, respectively. Each data point corresponds to the mean $\pm$ s.d. of 8 unique simulations. (f-g) Azimuthally averaged cell orientations for (f) Δbap1ΔrbmC and (g) ΔvpsL mutant biofilms (experiment) grown under 2% agarose gel where a total of 6 and 7 biofilms were averaged respectively.