Mathematical Modeling, Analysis and Simulation of Biofilm Processes

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Bacterial biofilms are microbial depositions on submerged surfaces (a.k.a substratum). In the initial reversible step of biofilm formation bacteria attach to the surface. Cells that stay adhered start producing an extracellular polymeric substance in which they are themselves embedded and that protects them against mechanical washout and antimicrobials. In this protective layer, vivid microbial communities develop. Biofilms are important, e.g for the development of technologies for wastewater treatment or soil remediation. On the other hand biofilms are detrimental in a medical context, where they can lead to difficult to eradicate bacterial infections or hygienic problems. Despite their name, biofilms are often not homogeneous films but can develop in highly irregular architectures. Life in biofilm communities is substantially different from life in suspended or planktonic populations, on which experimental and mathematical microbiology have traditionally focused. This is largely due to the spatial organisation of biofilms, which leads to substrate gradients, and, hence, to spatially heterogeneous growth conditions. Therefore, many of the traditional models of microbial ecology, typically formulated as ODEs for batch or continuous cultures, cannot be applied, but an entirely different class of models must be developed. The microbial and physical complexity of biofilms is often reflected in the mathematical complexity of these models. Several mathematical models of biofilms have been proposed in the literature, drawing on very different mathematical concepts and approaches. Our focus will be on density-dependent diffusion-reaction systems, which we have shown can be interpreted both as a spatially structured microbial populations and as a description of biofilms as complex fluids. In its simplest prototype form this model comprises a porous medium degeneracy when the dependent variable vanishes and simultaneously a super-diffusion singularity when the dependent variable reaches maximum cell density. We have developed a solution theory for this protoype system previously, as well as numerical methods for their simulation. Over the duration of this grant new aspects of biofilms will be incorporated in this model framework which lead to additional mathematical challenges and require a substantial extension and re-thinking of these techniques. One focus will be on spatial mixing in multi-species systems. We revise our previous model to show how the problem leads to additional cross-diffusion terms which we have so far neglected. Another emphasis will be on what we vaguely call chemically induced detachment (to distinguish it from shear induced detachment), including detachment controlled by cell-to-cell signaling, or breakdown of the EPS by enzymes. This will require us to consider concurrently motile and sessile bacterial phases and the exchange between these two modes of growth. A third aspect we want to include is the situation where bacteria degrade the substratum on which they grow, which requires us to consider reactive boundary conditions. This is a phenomenon observed for certain biofuel producing biofilms. Some of the biofilm aspects that we will study are of fundamental nature, others are closely tied to specific systems. In all cases they will be motivated by particular biofilm applications. Applications that we consider will include biofuel production by cellulolytic biofilms; wastewater treatment processes; signal based biofilm control strategies; groundwater protection and soil remediation; (bio)control of detrimental biofilms in food safety and industry.