Although the initiation, development and control of biofilms has been an area of experimental investigation for more than three decades, the role of extra-cellular polymeric substance (EPS) has not been well studied. We present a mathematical description of the EPS matrix to study the development of heterogeneous biofilm morphology. In developing the model, we assume that the biofilm is a biological gel composed of EPS and water. The bacteria are enmeshed in the network and are the producers of the polymer. In response to external conditions, gels absorb or expel solvent causing swelling or contraction due to osmotic pressure gradients. The physical morphology of the biofilm depends on the temperature, solvent composition, pH and ionic concentrations through osmotic pressure. This gives a physically based mechanism for the redistribution of biomass within the biofilm. Analysis of a reduced model indicates that biomass redistribution, through the mechanism of swelling, may induce the formation of isolated towers or mushroom clusters by spatial variation in EPS production which leads to gradients in osmotic pressure.

Almost all moist surfaces are colonized by microbial biofilms. Biofilms are implicated in cross-contamination of food products, biofouling and various human infections such as dental cavities, ulcerative colitis and chronic respiratory infections. The recalcitrance of biofilms to typical antibiotic and antimicrobial treatments is one focus of current investigations. Neither reaction-diffusion limitation nor heterogeneities in growth-rate explain the observed tolerance. Another hypothesis is that specialized 'persister' cells, which are extremely tolerant of antimicrobials, are the source of resistance.In this investigation, we describe the formation of 'persister' cells which neither grow nor die in the presence of antibiotics. We propose that these cells are of a different phenotype whose expression is regulated by the growth rate and the antibiotic concentration. Based on several experiments describing the dynamics of persister cells, we introduce a mathematical model that is used to describes the effect of a periodic dosing regiment. Results from our analysis indicate that the relative dose/withdrawal times are important in determining the effectiveness of such a treatment. A reduced model is also introduced and the similar behavior is demonstrated analytically.

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The tolerance of bacterial populations to biocidal or antibiotic treatment has been well documented in both biofilm and planktonic settings. However, there is still very little known about the mechanisms that produce this tolerance. Evidence that small, non-mutant subpopulations of bacteria are not affected by antibiotic challenge has been accumulating and provides an attractive explanation for the failure of typical dosing protocols. Although a dosing challenge can kill all the susceptible bacteria, the remaining persister cells can serve as a source of population regrowth. We give a robust condition for the failure of a periodic dosing protocol for a general chemostat model, which supports the mathematical conclusions and simulations of an earlier, more specialized batch model. Our condition implies that the treatment protocol fails globally, in the sense that a mixed bacterial population will ultimately persist above a level that is independent of the initial composition of the population. We also give a sufficient condition for treatment success, at least for initial population compositions near the steady state of interest, corresponding to bacterial washout. Finally, we investigate how the speed at which the bacteria are wiped out depends on the duration of administration of the antibiotic. We find that this dependence is not necessarily monotone, implying that optimal dosing does not necessarily correspond to continuous administration of the antibiotic. Thus, genuine periodic protocols can be more advantageous in treating a wide variety of bacterial infections.

A mathematical model of the action of antimicrobial agents on bacterial biofilms is presented. The model includes the fluid dynamics in and around the biofilm, advective and diffusive transport of two chemical constituents and the mechanism of physiological resistance. Although the mathematical model applies in three dimensions, we present two-dimensional simulations for arbitrary biofilm domains and various dosing strategies. The model allows the prediction of the spatial evolution of bacterial population and chemical constituents as well as different dosing strategies based on the fluid motion. We find that the interaction between the nutrient and the antimicrobial agent can reproduce survival curves which are comparable to other model predictions as well as experimental results. The model predicts that exposing the biofilm to low concentration doses of antimicrobial agent for longer time is more effective than short time dosing with high antimicrobial agent concentration. The effects of flow reversal and the roughness of the fluid/biofilm are also investigated. We find that reversing the flow increases the effectiveness of dosing. In addition, we show that overall survival decreases with increasing surface roughness.