Electrical signaling in three-dimensional bacterial biofilms using an agent-based fire-diffuse-fire model

Agent-based models were used to describe electrical signaling in bacterial biofilms in three dimensions. Specifically, wavefronts of potassium ions in Escherichia coli biofilms subjected to stress from blue light were modeled from experimental data. Electrical signaling occurs only when the biofilms grow beyond a threshold size, which we have shown to vary with the K^{+} ion diffusivity, and the K^{+} ion threshold concentration, which triggered firing in the fire-diffuse-fire model. The transport of the propagating wavefronts shows superdiffusive scaling on time. K^{+} ion diffusivity is the main factor that affects the wavefront velocity. The K^{+} ion diffusivity and the firing threshold also affect the anomalous exponent for the propagation of the wavefront determining whether the wavefront is subdiffusive or superdiffusive. The geometry of the biofilm and its relation to the mean-square displacement (MSD) of the wavefront as a function of time was investigated for spherical, cylindrical, cubical, and mushroom-like structures. The MSD varied significantly with geometry; an additional regime to the kinetics occurred when the potassium wavefront leaves the biofilm. Adding cylindrical defects to the biofilm, which are known to occur in E. coli biofilms, also gave an extra kinetic regime to the wavefront MSD for the propagation through the defect.