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The bacteria Pseudomonas aeruginosa use the size and density of their colonies to regulate the production of a large variety of substances, including toxins. This phenomenon, called quorum sensing, apparently enables colonies to grow to sufficient size undetected by the immune system of the host organism. In this paper, we present a mathematical model of quorum sensing in P. aeruginosa that is based on the known biochemistry of regulation of the autoinducer that is crucial to this signalling mechanism. Using this model we show that quorum sensing works because of a biochemical switch between two stable steady solutions, one with low levels of autoinducer and one with high levels of autoinducer.

We describe microbial communities denoted biofilms and efforts to model some of their important aspects, including quorum sensing, growth, mechanics, and antimicrobial tolerance mechanisms.

Bacterial biofilms demonstrate adaptive resistance in response to antimicrobial stress more effectively than corresponding planktonic populations. We propose here that, in biofilms, reaction-diffusion limited penetration may result in only low levels of antimicrobial exposure to deeper regions of the biofilm. Sheltered cells are then able to enter an adapted resistant state if the local time scale for adaptation is faster than that for disinfection. This mechanism is not available to a planktonic population. A mathematical model is presented to illustrate. Results indicate that, for a sufficiently thick biofilm, cells in the biofilm implement adaptive responses more effectively than do freely suspended cells. Effective disinfection requires applied biocide concentration that increases quadratically or exponentially with biofilm thickness.

A simple single substrate limiting model of a growing biofilm layer is presented. One-dimensional moving front solutions are analyzed. Under certain conditions these solutions are shown to be linearly unstable to fingering instabilities. Scaling laws for the biofilm growth rate and length scale are derived. The nonlinear evolution of the fingering instabilities is tracked numerically using a level set method, leading to the observation of mushroom-like structures.

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Biofilm structure plays an important role in biofilm function and control. It is thus important to determine the extent to which mechanics may determine structure in biofilms. We consider a generic qualitative constitutive description of biofilm incorporating as assumptions a small number of fundamental physical properties of biofilm viscoelasticity and cohesion. Implications of cohesive energy on biofilm structure are then explored. Steady solutions and energy minima are studied and it is demonstrated that cohesion energy leads naturally to a free surface film state. It is found that in many circumstances, biofilms could be subject to heterogeneity formation via spinodal decomposition. Such material heterogeneity may have important implications for structural stability in biofilms both on short and long time scales.

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