Incorporating Cellular Stochasticity in Solid--Fluid Mixture Biofilm Models

TL;DR

The paper addresses the call to capture stochastic cellular responses within biofilm morphogenesis by coupling a two-phase solid–fluid mixture model with a dynamic energy budget–based cellular automata (CA) layer. It develops a hybrid framework where macroscopic fields (biomass fraction $\phi_s$, fluid fraction $\phi_f$, pressures, stresses, and nutrient diffusion) interact with a micro-scale CA description of cellular metabolism and state transitions, including differentiation to EPS producers and surfactin makers via local chemical cues. Key contributions include deriving a comprehensive set of final governing equations for biomass growth, mechanical deformation, osmotic swelling, and nutrient transport, together with a CA–DEB scheme that generates realistic phenomena such as osmosis-driven accelerated spreading, wrinkle formation, and inhomogeneous distributions of differentiated bacteria. The significance lies in providing a unified, extensible platform to study biofilm morphogenesis on interfaces, offering a route to organism-specific parameterization and predictive insights for interventions in biofilm control and treatment.

Abstract

The dynamics of cellular aggregates is driven by the interplay of mechanochemical processes and cellular activity. Although deterministic models may capture mechanical features, local chemical fluctuations trigger random cell responses, which determine the overall evolution. Incorporating stochastic cellular behavior in macroscopic models of biological media is a challenging task. Herein, we propose hybrid models for bacterial biofilm growth, which couple a two phase solid/fluid mixture description of mechanical and chemical fields with a dynamic energy budget-based cellular automata treatment of bacterial activity. Thin film and plate approximations for the relevant interfaces allow us to obtain numerical solutions exhibiting behaviors observed in experiments, such as accelerated spread due to water intake from the environment, wrinkle formation, undulated contour development, and the appearance of inhomogeneous distributions of differentiated bacteria performing varied tasks.

Figures (9)

• Figure 1: Virtual visualization of a biofilm spreading on agar.
• Figure 2: Schematic structure of a biofilm: (a) View of the macroscopic configuration: a biofilm on an agar--air interface. (b) Microstructure formed by biomass (polymeric mesh and cells) and fluid containing dissolved substances (nutrients, waste, and autoinducers).
• Figure 3: Schematic representation of a biofilm slice, with moving air--biofilm interface $h$ and agar--biofilm interface $\xi$. (a) Initial stages: $\xi$ is flat. (b) Later evolution: $\xi$ deviates out of a plane.
• Figure 4: Biofilm height at dimensionless times $0$ (a), $1$ (b), $6$ (c), and $7$ (d) for $K=10^{-5}$ and $h_{\inf}=10^{-3}.$ The dotted red line and the solid blue line depict the numerical solutions of (\ref{['echeightseminara']}) and (\ref{['echeight']}), respectively, with $R$ given by (\ref{['selfsimilarhR']}) and keeping the same data. We can observe the transition from an initial stage in which increase in biofilm height dominates to a stage with faster horizontal spread. The green line is a reference self-similar approximation.
• Figure 5: Wrinkle formation and coarsening in a growing film with residual stresses computed from analytical formulas for the pressures. As the approximation breaks down, the height of the central wrinkles increases much faster than the height of the outer ones, which blur in comparison. Snapshots taken at times (a) $1.8/g$, (b) $2/g$, (c) $2.2/g$, and (d) $2.4/g$, starting from a randomly perturbed biofilm of radius $R_0=10^{-3}$ m and height $h_0=10^{-4}$ m. The radius does not vary significantly during this time, whereas the height becomes of the order of the radius at the end. Parameter values: $1/g=2.3$ hours, $\mu_f=8.9 \times 10^{-4}$ Pa$\cdot$s at $25^o$, $\xi_\infty=70$ nm, $\phi_\infty=0.2$, $h_a=100 h_0$, $\Pi=30$ Pa (taken from seminara), $E=25$ kPa (taken from asally), $\nu=0.4$, $\mu_s= 8.92$ kPa, $\nu_a=0.45$, $\eta_a=1$ kPa$\cdot$s, $\mu_a=0$, $h_{inf}=h_0/10$.