Mathematical modelling of pattern formation in yeast biofilms

Alex Tam (The University of Queensland, School of Mathematics and Physics)

Approximately 80% of microbial life exists in biofilm colonies, consisting of cells embedded in an extracellular fluid matrix. Biofilms of pathogenic yeast species can colonise indwelling medical devices, making them a leading cause of hospital-acquired infections. Since biofilms are highly resistant to anti-microbial treatment, the mortality rate of these infections can approach 40% for patients in intensive care units. With the objective of better understanding and controlling growth, experimentalists have developed methods to initiate yeast biofilm formation in controlled laboratory environments. In these experiments, biofilms expand radially at an approximately constant speed, and adopt a non-uniform floral pattern consisting of petal-like structures. However, the physical mechanisms underlying this growth remain unknown.

We investigate two hypothesised mechanisms of yeast biofilm expansion. First, we use a reaction--diffusion system with a nonlinear, degenerate diffusion term for cell spread to investigate the hypothesis that biofilms expand by nutrient-limited growth. Using travelling wave and linear stability analysis, we show that the model can explain the approximately constant expansion speed, and predict the petal formation observed in experiments. Second, we consider a more detailed two-phase, thin-film model that incorporates nutrient uptake and the mechanics of extracellular fluid flow in addition to nutrient limitation. We find good agreement between numerical solutions to this model and experimental data for realistic parameter values. From this, we conclude that sliding motility, which describes expansion driven by cell proliferation and weak adhesion to the substratum, is a possible mechanism for biofilm growth.