Mathematical Modeling of Quorum Sensing Inhibitors as Adjuvantsto Antimicrobials in a Chemostat Environment

Many bacterial cells coordinate group behaviour by a mechanism known as QuorumSensing (QS). QS involves the production and secretion of signalling molecules, called au-toinducers. When the concentration of autoinducers exceed a threshold, certain genes areup-regulated, resulting in a change to cell behaviour. Many species of bacteria use QS toregulate genes that promote protection against pathogens. Although antibiotics have beenused to prevent bacterial infections in the past, emerging evidence suggest that antibiotictreatments are becoming increasingly more ineffective. Quorum Sensing Inhibitors (QSIs)have been proposed as adjuvants to antimicrobial therapies with the goal of reducing QSactivity. To understand the relationship between QSIs and antimicrobials, we develop amathematical model consisting of seven ODEs. We investigate the system analytically andnumerically. Our results suggest that the effects of QSIs as adjuvants are minimal. Fur-thermore, the steady-state of the system depend on the cell-division process of up-regulatedcells.