Biofilm Vertical Growth Dynamics Are Captured by An Active Fluid Framework

Bacterial biofilms, surface-attached microbial communities, grow horizontally across surfaces and vertically above them. Although a simple heuristic model for vertical growth was experimentally shown to accurately describe the behavior of diverse microbial species, the biophysical implications and theoretical basis for this empirical model were unclear. Here, we demonstrate that this heuristic model emerges naturally from fundamental principles of active fluid dynamics. By analytically deriving exact solutions for an active fluid model of vertical biofilm growth, we show that the governing equations reduce to the same form as the empirical model in both early- and late-stage growth regimes. Our analysis reveals that cell death and decay rates likely play key roles in determining the characteristic parameters of vertical growth. The active fluid model produces a single, simple equation governing growth at heights above and below the diffusion limit; surprisingly, this "full" expression is simpler than the heuristic. With this theoretical basis, we explain why the vertical growth rate reaches a maximum at a height greater than the previously identified characteristic length scale. These results provide a theoretical foundation for a simple mathematical model of vertical growth, enabling deeper understanding of how biological and biophysical factors interact during biofilm development.