Electrical Signalling in Three Dimensional Bacterial Biofilms Using an Agent Based Fire-Diffuse-Fire Model

Abstract

Agent based models were used to describe electrical signalling in bacterial biofilms in three dimensions. Specifically, wavefronts of potassium ions in E. coli biofilms subjected to stress from blue light were modelled from experimental data. Electrical signalling only occurs 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 super-diffusive 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 sub-diffusive or super-diffusive. 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, the wavefront MSD also had an extra kinetic regime for the propagation through the defect.