Mathematical modelling of therapies targeted at bacterial quorum sensing

Bacteria commonly use diffusible signal molecules to synchronise their behaviour by facilitating population dependent co-ordination. This cell-to-cell signalling mechanism is known as quorum sensing (QS) and provides a way of ensuring that certain genes are ‘switched on’ only when a certain signal concentration (typically corresponding to a large population density) has been reached. In this paper we focus on the QS system of the human pathogen Pseudomonas aeruginosa, which employs a complex hierarchy of QS signalling systems, which regulate the formation of multiple exoproducts, swarming and biofilm differentiation. In P. aeruginosa, the signal molecules are N-acylated homoserine lactones (AHLs; e.g., N-(3-oxododecanoyl)-homoserine lactone [3-oxo-C12-HSL]), which bind to transcriptional regulator proteins (LasR in the case of 3-oxo-C12-HSL) to activate the expression of target genes including lasI, which codes for the 3-oxo-C12-HSL synthase. Since the virulence of P. aeruginosa is controlled by QS, agents (QSBs) designed to block this cell-to-cell communication have potential as novel antibacterials. By drawing on existing models for the reaction kinetics of this system, we model a growing population subject to treatment with two kinds of QSB, together with a conventional antibiotic. The first kind of QSB is assumed to act by diffusing through the cell membrane and then destabilising/sequestering LasR, while the second kind remains outside the cell and degrades the AHL signal molecule itself. Numerical and mathematical analysis of the resulting systems of ordinary differential equations reveals in particular that, while a sufficiently high dose of QSB is, in all cases considered, able to reduce the AHL concentration (and hence virulence) to a negligible level, the qualitative response to treatment is sensitive to parameter values.