Continuous versus Arrested Spreading of Biofilms at Solid-Gas Interfaces: The Role of Surface Forces

We introduce and analyze a model for osmotically spreading bacterial colonies at solid-air interfaces that includes wetting phenomena, i.e., surface forces. The model is based on a hydrodynamic description for liquid suspensions which is supplemented by bioactive processes. We show that surface forces determine whether a biofilm can expand laterally over a substrate and provide experimental evidence for the existence of a transition between continuous and arrested spreading for Bacillus subtilis biofilms. In the case of arrested spreading, the lateral expansion of the biofilm is confined, albeit the colony is biologically active. However, a small reduction in the surface tension of the biofilm is sufficient to induce spreading. The incorporation of surface forces into our hydrodynamic model allows us to capture this transition in biofilm spreading behavior.

Figure 1

Experimental observation of the influence of surfactants on the transition between continuous and arrested biofilm spreading. (a) The B. subtilis WT spreads laterally with a velocity of $0.2\mathrm{mm}/\mathrm{h}$ over the agar substrate, whereas (b) for the mutant strain with deficient surfactin production ($\mathrm{\Delta }srfAA$) spreading is arrested. An external addition of the surfactants (c),(d) surfactin or (e),(f) Tween 20 enables the mutant strain to spread but does not affect the WT.

Figure 2

Sketch of the osmotically driven spreading of a biofilm with the height profile $h(\mathbf{x},t)$. Osmotic pressure gradients are generated as bacteria consume water and nutrients to produce biomass via bacterial proliferation and matrix secretion, which is described by the growth term $G(h,\varphi )$. This causes an osmotic influx of nutrient-rich water $\zeta (h,\varphi )$ from the moist agar substrate into the biofilm.

Figure 3

Comparison of continuously spreading biofilms (top row, at $W=8$) and arrested spreading of biofilms (bottom row, at $W=12$). (a) Height profiles taken at equidistant times. (b) Time evolution of the biofilm extension $r(t)$ (solid black line) measured at the inflection point of the height profile and of the maximal film height $h_{\max }(t)$ (solid blue line). (c) Bioactivity and osmotic influx for biofilms at a late time when all transients have decayed. The shading within the film indicates the bioactivity $G(h,\varphi )$. The direction and strength of the effective osmotic flux $\zeta (h,\varphi )$ are represented by the direction and thickness of the blue arrows below the biofilm. Note that a time lapse of $10^6\tau$ corresponds to $\approx 5$  h. Remaining parameters are $\tilde{g}=2\times {10}^{-5}$ and ${\tilde{Q}}_{\mathrm{osm}}=0.01$.

Figure 4

Spreading behavior of the biofilm in the $\tilde{g}\text{−}W$ parameter plane for various values of the osmotic mobility ${\tilde{Q}}_{\mathrm{osm}}$ as indicated in the legend. In the shaded regions, biofilm spreading is arrested; i.e., it reaches a steady profile, while outside of this region, lateral spreading is not limited. The inset gives the dependence of spreading speed $v$ on wettability $W$ for $\tilde{g}=2\times {10}^{-5}$ and ${\tilde{Q}}_{\mathrm{osm}}=0.01$. A speed of $v={10}^{-5}$ corresponds to an actual spreading speed of $0.1–0.2\mathrm{mm}/\mathrm{h}$, comparable to the experiment in Fig. 1 and in Ref. [2] (scale bar, 5 mm).