Spatially implicit and spatially explicit models of bacterial cellulose degradation

Hermann Eberl

University of Guelph, Canada

Cellulosic ethanol is a biofuel that is produced from non-edible plants and plant materials, such switchgrass and corn stover. It can have a positive net energy output with a reduction in green house gas emissions that is drastically lower than that of corn based ethanol and fossil fuels. Clostridium thermocellum is a bacteria that is able to directly convert cellulose into ethanol (and other by products). These bacteria colonize cellulose material and degrade cellulose by "chewing" their way through their substrate. In this talk we first present a very simple, spatially implicit reactor scale model for cellulose degradation by C.thermocellum biofilms. This ODE can be studied with elementary techniques and quantitatively compared against experimental data. However, it does not allow for a detailed description of the spatial effects as the bacteria break down their substratum. To address this, we formulate then a spatially explicit model, which consists of a highly degenerate diffusion-reaction equation for bacterial biomass that is coupled with an ordinary differential equation for the growth limiting substrate. We study this model numerically and qualitatively compare simulation results against experimental observations. The simulations suggest the existence of a traveling wave; time permitting we investigate those in a simplified setting in more detail. This is joint work with Gideon Wolfaardt (Stellenbosch) and Alex Dumitrache (Oar Ridge National Labs)

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