Modelling antibiotic- and anti-quorum sensing treatment of a spatially-structured Pseudomonas aeruginosa population

Abstract

The bacterial cell to cell signalling system known as quorum sensing (QS) is essential for the regulation of virulence in many pathogens and offers a specific biochemical target for novel antibacterial therapies. Expanding on earlier work, in which consideration was given to the primary QS system (lasR system) in a homogeneous population of the common human pathogen Pseudomonas aeruginosa, we build a simple spatial model of an early-stage P. aeruginosa biofilm subject to treatment with topically applied anti-QS drugs (of two specific kinds) and conventional antibiotics. In the case of a slowly growing biofilm we show that both kinds of anti-quorum sensing drug are effective in reducing the level of the relevant signal molecule (3-oxo-C12-homoserine lactone; henceforth AHL), in each case obtaining an explicit bound on the steady-state AHL profile in terms of a prescribed surface drug concentration. Using numerical methods, we are also able to reproduce the hysteretic phenomena exhibited by the homogeneous model, in particular showing that for each kind of anti-QS drug there is a parameter regime in which a catastrophic collapse occurs in the steady-state AHL concentration as the surface drug concentration passes some critical value; an alternative way of interpreting this result is to say that, for a prescribed surface drug concentration, there is a critical biofilm depth such that treatment is successful until this depth is reached, but fails thereafter. In the thick-biofilm limit we show that the critical concentration of each drug increases exponentially with the biofilm thickness (or, conversely, that the critical depth increases logarithmically with surface drug concentration); this is dramatically different to the behaviour observed in the corresponding homogeneous model, where the critical concentrations grow linearly with bacterial carrying capacity, and thus highlights the relative difficulty of treating a large, spatially-structured population with diffusing antibacterials.

Mathematical Modelling of Bacterial Quorum Sensing: A Review

“…They found that sufficient doses of the anti-QS agent can reduce the AHL concentration, but the treatment success depends heavily on the rest of the parameters. Anguige et al (2005) extended this work to include well-mixed spatially structured planktonic P. aeruginosa populations. Viretta and Fussenegger (2004) developed a deterministic model of the P. aeruginosa QS network (at the transcriptional and translational levels) including the interactions between its three known QS systems las, rhl and mvfR-PQS.…”

“…The biofilm is viewed as a multiphase fluid whose growth is governed by nutrients that diffuse from the surrounding fluid. They extended Anguige's series of papers (Anguige et al 2004(Anguige et al , 2005(Anguige et al , 2006 on QS inhibitors, which are based on Ward et al (2001Ward et al ( , 2004. The model is for the LasRI QS System of P. aeruginosa.…”

“…Anguige et al (2006) used a multiphase approach to model biofilm formation of P. aeruginosa. It is an extension of Anguige et al (2005) to include EPS production control by QS, this generates a watery ECM surrounding the bacteria. Their model incorporates four phases: live cells, dead cells, EPS, and extracellular watery fluid.…”

“…It is also, however, a great source of debate with many publications (Hense et al 2007;Platt and Fuqua 2010;Redfield 2002;Stacy et al 2012;West et al 2012) dedicated to questioning the current understanding of the process which underlays the term quorum sensing, introduced by Fuqua et al (1994). Anguige et al (2004Anguige et al ( , 2005 Bioluminescence Vibrio fischeri James et al (2000), Kuttler and Hense (2008), Romero-Campero and Pérez-Jiménez (2008), Perez et al (2011), Müller et al (2008) AHL…”

Resistance to Quorum-Quenching Compounds

“…Most of these models describe the effect of classical antibiotics and antivirulence compounds and suggest a narrow therapeutic concentration range for the QQ agent to be effective in biofilms. For example, Anguige et al (20) found that there is a critical biofilm depth in which the QQ treatment is successful; hence, the biofilm penetrability of QQ drugs is a critical parameter to take into account for the design of antivirulence compounds. Therefore, perhaps resistance to QQ in biofilms may develop by restricting the permeability of the QQ drugs by overproducing extracellular matrix components that sequester the QQ agent, such as the ndvB-encoded glucans that sequester aminoglucosides (21).…”