A MATHEMATICAL MODEL OF QUORUM QUENCHING IN BIOFILMS AND ITS POTENTIAL ROLE AS AN ADJUVANT FOR ANTIBIOTIC TREATMENT

Abstract

We extend a previously presented mesoseopie (i.e. colony scale) mathematical mode] of the reaction of bacterial biofilms to antibiotics. In that earlier model, exposure to antibiotics evokes two responses: inactivation as the antibiotics kill the bacteria, and induction of a quorum sensing based stress response mechanism upon exposure to small sublethal dosages. To this model we add now quorum quenching as an adjuvant to antibiotic therapy. Quorum quenchers are modeled as enzymes that degrade the quorum sensing signal concentration. The resulting model is a quasilinear system of seven reaction-diffusion equations for the following dependent variables: the volume fractions of up-regulated (protected), down-regulated (unprotected) and inert (inactive) biomass [particulate substances], and the concentrations of a growth promoting nutrient, antibiotics, quorum sensing signals, and quorum quenchers [dissolved substances]. The biomass fractions are subject to two nonlinear diffusion effects: (i) degeneracy, as in the porous medium equation, when? biomass vanishes, and (ii) a super-diffusion singularity as it attains its theoretically possible maximum. We study this model in numerical simulations. Our simulations suggest that for maximum efficacy quorum quenchers should be applicxl early on before quorum sensing induction in the biofilm can take place, and that an antibiotic strategy that by itself might not be successful can be notably improved upon if paired with quorum quenchers as an adjuvant.