Reaction-diffusion model of nutrient uptake in a biofilm: theory and experiment

Microbes in natural settings typically live attached to surfaces in complex communities called biofilms. Despite the many advantages of biofilm formation, communal living forces microbes to compete with one another for resources. Here we combine mathematical models with stable isotope techniques to test a reaction-diffusion model of competition in a photosynthetic biofilm. In this model, a nutrient is transported through the mat by diffusion and is consumed at a rate proportional to its local concentration. When the nutrient is supplied from the surface of the biofilm, the balance between diffusion and consumption gives rise to gradients of nutrient availability, resulting in gradients of nutrient uptake. To test this model, a biofilm was incubated for a fixed amount of time with an isotopically labeled nutrient that was incorporated into cellular biomass. Thus, the concentration of labeled nutrient in a cell is a measure of the mean rate of nutrient incorporation over the course of the experiment. Comparison of this measurement to the solution of the reaction-diffusion model in the biofilm confirms the presence of gradients in nutrient uptake with the predicted shape. The excellent agreement between theory and experiment lends strong support to this one-parameter model of reaction and diffusion of nutrients in a biofilm. Having validated this model empirically, we discuss how these dynamics may arise from diffusion through a reactive heterogeneous medium. More generally, this result identifies stable isotope techniques as a powerful tool to test quantitative models of chemical transport through biofilms.