A Mathematical Model of Quorum Sensing in Patchy Biofilm Communities with Slow Background Flow

Quorum sensing is a type of cell to cell communication used to coordinate behavior in groups based on population density. We present a mathematical model of this phenomenon in bacterial biofilms, consisting of a nonlinear diffusion reaction system. The model includes production and spatial spreading of biomass, conversion of down-regulated biomass into up-regulated biomass as a consequence of the quorum sensing signalling molecule concentration, and convective and diffusive transport of nutrients and quorum sensing molecules. In numerical experiments, using quantitative parameter data derived from P.putida experiments, we investigate how the hydrodynamic environment and nutrient conditions contribute to biofilm growth and quorum sensing behaviour. Our main findings are the observation of flow-facilitated inter-colony communication, and that at sufficiently high bulk flow rates, biofilm growth and signalling molecule production is enhanced, yet washout of signalling molecules suppresses quorum sensing induction. A discussion of the ecological implications of these results is included.