Reactor scale modeling of quorum sensing induced biofilm dispersal

Abstract

We present a simple reactor-scale mathematical model of active biofilm dispersal that is controlled by a quorum sensing system. The model is cast as a system of three ordinary differential equations for the dependent variables biofilm thickness, quorum sensing signal concentration in the reactor, and concentration of the growth limiting substrate in the reactor. The model is investigated with analytical and numerical techniques. We find that a single QS dispersal mechanism, depending on parameters, can lead to (i) continuous cell loss at a signal level at which the biofilm is entirely up-regulated, (ii) periodically repeating almost instantaneous cell loss with the biofilm switching between down- and up-regulated states, (iii) continuous cell loss at a signal level at which the biofilm is entirely down-regulated, or (iv) complete washout. We contrast this with a simple model of starvation induced dispersal, which is cast in the same modeling framework, but shows entirely different dynamic behavior, in that it only permits washout or asymptotic convergence to a steady state at break-even concentration, depending on parameters.