Mathematical Approaches in Biofilm Research

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Bacterial biofilms are microbial depositions on immersed interfaces that form wherever environmental conditions sustain bacterial life. Many environmental engineering technologies utilise their properties, in areas like wastewater treatment, soil remediation, or more recently biofuel production. On the other hand, in a medical context they are mainly considered detrimental, as a cause of persistent infections that are difficult to treat with antibiotics. In an industrial context they can cause damage, e.g by biofouling or biocorrosion. Mathematical modeling has become an important tool in biofilm research. This research program seeks to contribute to this development. It involves the formulation of mathematical models, their analysis, and their use in numerical simulation experiments. The methods that will be utilised stem from fields of Partial Differential Equations and Scientific Computing. This will involve highly degenerate quasilinear parabolic systems and their numerical solution, as well as multiscale modeling and simulation techniques. Specific problems that will be addressed include models of quorum sensing inhibition and bacterial cross-talk, models of cellulolytic biofilms that are utilised in the production of cellulosic ethanol from non-edible plant material as a transportation fuel, and models of bioremediation processes that are utilised in the clean up of soils. A focus of the program is research training of students, both on the undergraduate and graduate level, in an area in which mathematical sciences, biology, engineering, and computation overlap.