Singular perturbations in a reaction-diffusion model for yeast biofilm formation
Date:
Abstract: Yeasts often form complex communities of cells and fluid known as biofilms. These commonly form on indwelling medical devices, making yeasts a leading cause of hospital-acquired infections. Despite this, the mechanisms governing biofilm shape are not fully understood. To investigate the extent to which nutrient-limited growth determines morphology, we propose a reaction-diffusion model with non-linear cell diffusion. Unfortunately, the diffusion coefficient cannot be measured experimentally; we can only measure biofilm expansion speed. To address this, we seek travelling wave solutions to our model, giving rise to a singularly perturbed dynamical system. Using a combination of geometric singular perturbation theory and numerics, we demonstrate that there is a unique critical speed for each diffusion coefficient, enabling us to infer this parameter from experimental data. Given this knowledge, 2D linear stability analysis, numerics, and image processing show that our model can explain the floral patterns observed in experiments.