Viscosity independent diffusion mediated by death and reproduction in biofilms
Bacterial biofilms, surface-attached communities of cells, are in some respects similar to colloidal solids; both are densely packed with non-zero yield stresses. However, unlike non-living materials, bacteria reproduce and die, breaking mechanical equilibrium and inducing collective dynamic responses. We report experiments and theory investigating the motion of immotile Vibrio cholerae, which can kill each other and reproduce in biofilms. We vary viscosity by using bacterial variants that secrete different amounts of extracellular matrix polymers, but are otherwise identical. Unlike thermally-driven diffusion, in which diffusivity decreases with increased viscosity, we find that cellular motion mediated by death and reproduction is independent of viscosity over timescales relevant to bacterial reproduction. To understand this surprising result, we use two separate modeling approaches. First we perform explicitly mechanical simulations of one-dimensional chains of Voigt-Kelvin elements that can die and reproduce. Next, we perform an independent statistical approach, modeling Brownian motion with the classic Langevin equation under an effective temperature that depends on cellular division rate. The diffusion of cells in both approaches agrees quite well, supporting a kinetic interpretation for the effective temperature used here and developed in previous work. As the viscoelastic behavior of biofilms is believed to play a large role in their anomalous biological properties, such as antibiotic resistance, the independence of cellular diffusive motion --- important for biofilm growth and remodeling --- on viscoelastic properties likely holds ecological, medical, and industrial relevance.