Verticalization of bacterial biofilms

Abstract

Biofilms are communities of bacteria adhered to surfaces. Recently, biofilms of rod-shaped bacteria were observed at single-cell resolution and shown to develop from a disordered, two-dimensional layer of founder cells into a three-dimensional structure with a vertically-aligned core. Here, we elucidate the physical mechanism underpinning this transition using a combination of agent-based and continuum modeling. We find that verticalization proceeds through a series of localized mechanical instabilities on the cellular scale. For short cells, these instabilities are primarily triggered by cell division, whereas long cells are more likely to be peeled off the surface by nearby vertical cells, creating an "inverse domino effect". The interplay between cell growth and cell verticalization gives rise to an exotic mechanical state in which the effective surface pressure becomes constant throughout the growing core of the biofilm surface layer. This dynamical isobaricity determines the expansion speed of a biofilm cluster and thereby governs how cells access the third dimension. In particular, theory predicts that a longer average cell length yields more rapidly expanding, flatter biofilms. We experimentally show that such changes in biofilm development occur by exploiting chemicals that modulate cell length.

Figure 1.

Development of experimental and modeled biofilms. (a, b) Top-down and perspective visualizations of the surface layer of (a) experimental and (b) modeled biofilms, showing positions and orientations of horizontal (blue) and vertical (red) surface-adhered cells as spherocylinders of radius R = 0.8 μm, with the surface shown at height z = 0 μm (brown). Cells with n_z < 0.5 (> 0.5) are considered horizontal (vertical), where n̂ is the orientation vector. The upper-left panel of (a) shows a confocal fluorescence microscopy image, and the upper-right panel shows the corresponding reconstructed central cluster using the positions and orientations of surface cells. The upper-left panel of (b) shows a schematic representation of modeled cell-cell (orange) and cell-surface (yellow) interactions, which depend, respectively, on the cell-cell overlap δ_ij (purple) and cell-surface overlap δ_i (red) (see Methods for details). Scale bars: 5 μm. (c, d) 2D growth of biofilm surface layer for (c) experimental biofilm (same as shown in (a)) and (d) modeled biofilms. The color of each spatiotemporal bin indicates the fraction of vertical cells at a given radius from the biofilm center, averaged over the angular coordinates of the biofilm (gray regions contain no cells). In (d), each spatiotemporal bin is averaged over ten simulated biofilms. In (c,d), the horizontal dashed pink lines show the onset of verticalization. The black dashed lines show the edge of the biofilm. Insets show the distribution of cell orientations at time t = 300 minutes, with color highlighting horizontal and vertical orientations.

Figure 2.

Mechanics of cell reorientation in modeled biofilms, (a-b) Properties of individual cells at the time t_r of reorientation, defined as the time of the peak of total force on the cell prior to it becoming vertical. Analyses are shown for all reorientation events among different biofilms simulated for a range of initial cell lengths ℓ₀ (a) Distributions of reorientation “surface pressure” p_r, defined as the total contact force in the xy plane acting on a cell at time t_r, normalized by the cell’s perimeter, versus cell cylinder length ℓ. The white dashed curve shows the average reorientation surface pressure ⟨p_r⟩ as a function of ℓ. The magenta dashed curve shows the threshold surface pressure p_t from linear stability analysis for a modeled cell under uniform pressure, depicted schematically in the inset, (b) Distributions of the logarithm of reorientation torque τ_r, defined as the magnitude of the torque on a cell due to cell-cell contact forces in the z direction at time t_r, for different cell cylinder lengths ℓ. The white dashed curve shows the average values ⟨log τ_r⟩ as a function of ℓ. The orange dashed curve shows the scaling τ_t ~ ℓ² of the threshold torque for peeling from linear stability analysis for a modeled cell, depicted schematically in the inset, (c) Mean reorientation length ⟨ℓ_r⟩ (red), defined as the average value of cell length at t_r, and mean cell cylinder length ⟨ℓ⟩ (gray), defined as the average length of all horizontal cells over all times of biofilm growth, averaged over ten simulated biofilms, each with initial cell cylinder length ℓ₀, plotted versus ℓ₀. The inset shows the distribution of reorientation lengths (red) and horizontal surface-cell lengths (gray) for ℓ₀ = 1 μm. (d) Mean avalanche size ⟨N⟩, defined as the average size of a cluster of reorienting cells that are proximal in space and time (Supplementary Figs. 8-10), versus initial cell length ℓ₀ for the experimental biofilm (red triangle) and the modeled biofilm (red circles). Open gray triangle and circles indicate the corresponding mean avalanche sizes for a null model. Inset shows a side view of cell configurations in the xy plane at times t_r for all reorientation events in a simulated biofilm with ℓ₀ = 2.5 μm. Reorientation events are colored alike if they belong to the same avalanche. Scale bars: 10 μm and 1 hour.

Figure 3.

Two-component fluid model for verticalizing cells in biofilms. (a) Schematic illustration of the two-component continuum model. Horizontal cells (blue) and vertical cells (red) are modeled, respectively, by densities ρ_h and ρ_v in two spatial dimensions. The total cell density ${\tilde{\rho }}_{\text{tot}}$ is defined as ρ_h + ξρ_ν, where ξ is the ratio of vertical to horizontal cell footprints. (b) Radial densities ρ of vertical cells (ρ_v, red), horizontal cells (ρ_h, blue), and total density (${\tilde{\rho }}_{\text{tot}}$, black), versus shifted radial coordinate $\tilde{r}$, defined as the radial position relative to the boundary between the mixed interior and the horizontal cell periphery. Results are shown for the continuum model (left; radial cell density in units of μm⁻²), the experimental biofilm (middle; radial cell density in each μm-sized bin averaged over an observation window of 50 minutes), and the agent-based model biofilm (right; radial cell density in each μm-sized bin averaged for ten biofilms over an observation window of 6 minutes). For the continuum model and the agent-based model biofilms the parameters were chosen to match those obtained from the experiment (Supplementary Figs. 12-13). Inset in the left-most panel shows the fraction of vertical cells in the continuum model at a given radius from the biofilm center (gray regions contain no cells, color scale is the same as in Fig. 1).

Figure 4.

Global morphological properties of experimental and modeled biofilms, (a) Top-down (upper row) and side views (lower row) of experimental biofilms grown with 0.4 μg/mL A22 (magenta), without treatment (yellow), and with 4 μg/mL Cefalexin (cyan), following overnight growth (upper row) and 7 hours after inoculation (lower row). Scale bar: 10 μm. Insets show magnifications of 10 μm²-sized regions of top-down views taken from the peripheries of biofilms. (b) Expansion speed c*, defined as the speed of the biofilm edge along the surface, versus the initial cell cylinder length ℓ₀ for experimental biofilms (A22, magenta; no treatment, yellow; Cefalexin, cyan), agent-based model biofilms (black circles), and continuum model (dashed black curve). Expansion velocities were determined from a linear fit of the basal radius R_B of the biofilm versus time, where R_B is defined at each time point as the radius of a circle with area equal to that of the biofilm base. For experimental biofilms, the boundary was extracted from the normalized fluorescence data (see Methods for details). For each treatment, the vertical error bars show the standard error of the mean of the expansion speed and the horizontal error bars bound the measured initial cell cylinder length (Supplementary Fig. 1). Inset: model cells with lengths and radii corresponding to the averages for different treatments, (c) Biofilm aspect ratio H/R_B for experimental biofilms grown under different treatments, where the biofilm height is defined as $H=3V∕2R_B^2$, the height of a semi-ellipsoid with a circular base of radius R_B and volume V equal to that of the biofilm. Error bars show the standard error of the mean. Inset: overlay of biofilm outlines from bottom row of panel (a). Color designations and treatments same as in panel (a).