Cell-signalling repression in bacterial quorum sensing.

In this paper we expand on two mathematical models for investigating the role of three distinct repression mechanisms within the so-called quorum sensing (QS) cell-signalling process of bacterial colonies growing (1) in liquid cultures and (2) in biofilms. The repression mechanisms studied are (i) reduction of cell signalling molecule (QSM) production by a constitutively produced agent degrading the messenger RNA of a crucial enzyme (QSE), (ii) lower QSM production rate due to a negative feedback process and (iii) loss of QSMs by binding directly to a constitutively produced agent; the first two mechanisms are known to be employed by the pathogenic bacterium Pseudomonas aeruginosa and the last is relevant to the plant pathogen Agrobacterium tumefaciens. The modelling approach assumes that the bacterial colony consists of two sub-populations, namely down- and up-regulated cells, that differ in the rates at which they produce QSMs, while QSM concentration governs the switching between sub-populations. Parameter estimates are obtained by curve-fitting experimental data (involving P. aeruginosa growth in liquid culture, obtained as part of this study) to solutions of model (1). Asymptotic analysis of the model (1) shows that mechanism (i) is necessary, but not sufficient, to predict the observed saturation of QSM levels in an exponentially growing colony; either mechanism (ii) or (iii) also needs to be incorporated to obtain saturation. Consequently, only a fraction of the population will become up-regulated. Furthermore, only mechanisms (i) and (iii) affect the main timescales for up-regulation. Repression was found to play a less significant role in a biofilms, but mechanisms (i)-(iii) were nevertheless found to reduce the ultimate up-regulated cell fraction and mechanisms (i) and (iii) to increase the timescale for substantial up-regulation and to decrease the wave speed of an expanding front of QS activity.