Mathematical modelling of pattern formation in yeast biofilms
Date:
Abstract: 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. Quantitative understanding of the physical mechanisms underlying this growth remains limited.
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 fluid model that incorporates nutrient uptake, cell proliferation, and extracellular fluid flow. In the extensional flow thin-film regime where biofilm–substratum adhesion is weak, this model describes expansion by sliding motility. We find good agreement between numerical solutions to the model and experimental data, supporting the hypothesis that sliding motility is a possible mechanism for biofilm growth.