We develop mathematical models to examine the formation, growth and quorum sensing activity of bacterial biofilms. The growth aspects of the model are based on the assumption of a continuum of bacterial cells whose growth generates movement, within the developing biofilm, described by a velocity field. A model proposed in Ward et al. (2001) to describe quorum sensing, a process by which bacteria monitor their own population density by the use of quorum sensing molecules (QSMs), is coupled with the growth model. The resulting system of nonlinear partial differential equations is solved numerically, revealing results which are qualitatively consistent with experimental ones. Analytical solutions derived by assuming uniform initial conditions demonstrate that, for large time, a biofilm grows algebraically with time; criteria for linear growth of the biofilm biomass, consistent with experimental data, are established. The analysis reveals, for a biologically realistic limit, the existence of a bifurcation between non-active and active quorum sensing in the biofilm. The model also predicts that travelling waves of quorum sensing behaviour can occur within a certain time frame; while the travelling wave analysis reveals a range of possible travelling wave speeds, numerical solutions suggest that the minimum wave speed, determined by linearisation, is realised for a wide class of initial conditions.

Staphylococcus aureus is a pathogenic bacterium that utilises quorum sensing (QS), a cell-to-cell signalling mechanism, to enhance its ability to cause disease. QS allows the bacteria to monitor their surroundings and the size of their population, and S. aureus makes use of this to regulate the production of virulence factors. Here we describe a mathematical model of this QS system and perform a detailed time-dependent asymptotic analysis in order to clarify the roles of the distinct interactions that make up the QS process, demonstrating which reactions dominate the behaviour of the system at various timepoints. We couple this analysis with numerical simulations and are thus able to gain insight into how a large population of S. aureus shifts from a relatively harmless state to a highly virulent one, focussing on the need for the three distinct phases which form the feedback loop of this particular QS system.

Pseudomonas aeruginosa remains a significant pathogen in burn-wound infection, its pathogenicity being associated with the production of a cocktail of virulence determinants which is regulated by a population-density-dependent mechanism termed quorum sensing. Quorum sensing is effected through the production and binding of signalling molecules. Here we present a mathematical model for the early stages of the infection process by P. aeruginosa in burn wounds which accounts for the quorum sensing system and for the diffusion of signalling molecules in the burn-wound environment. The results of the model and the effects of important parameters are discussed in detail. For example, the effect of the degradation rate of signalling molecules and its significance for anti-signalling therapies is discussed.

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) effect the main timescales for up regulation. Repression was found to play less significant role in a biofilms, but mechanisms (i)-(iii) were nevertheless found to reduce the ulitimate up-regulated cell fraction and mechanisms (i) and (iii) increase the timescale for substantial up regulation and decrease the wave speed of an expanding front of QS activity.

Deterministic and stochastic models describing quorum sensing by Staphylococcus aureus within an endosome, and the subsequent escape via the production of virulence factors, are developed and analysed. Particular attention is given to a biologically-relevant asymptotic limit of the problem, for which the solutions, including the endosome escape time, can be explicitly characterised in terms of the model parameters.