Dr. Stephanie Sonner (Dept. of Mathematics, Radboud University, Nijmegen) 

12/01/2022  2:10pm

Abstract: 

Biofilms are dense aggregations of bacterial cells attached to a surface and held together by a self-produced matrix of extracellular polymeric substances. They affect many aspects of human life and play a crucial role in natural, medical and industrial settings. Mathematical models for their growth have been developed for several decades. We consider deterministic continuum models for spatially heterogeneous biofilm communities formulated as quasilinear reaction diffusion systems. Their characteristic and challenging feature is the two-fold degenerate diffusion coefficient for the biomass density comprising a polynomial degeneracy (as known from the porous medium equation) and a singularity as the biomass density approaches its maximum value (fast diffusion effect). The prototype biofilm growth model is discussed as well as several variations and extensions.

In particular, we focus a recent model for cellulolytic biofilms that play an important role in the production of cellulosic ethanol. Different from traditional biofilm models where the biofilm colonies grow into the aqueous phase and nutrients are transported by diffusion, bacteria colonize, consume and degrade a cellulosic substratum that supports them. Hence, the nutrients are immobilized and modeled by an ordinary differential equation.
We show results on the well-posedness of the model and prove the existence of traveling wave solutions. Invading fronts had earlier been observed in biological experiments on cellulolytic biofilms as well as in numerical simulations of the model.