Extending the minimal model of metabolic oscillations in Bacillus subtilis biofilms

Biofilms are composed of microorganisms attached to a solid surface or floating on top of a liquid surface. They pose challenges in the field of medicine but can also have useful applications in industry. Regulation of biofilm growth is complex and still largely elusive. Oscillations are thought to be advantageous for biofilms to cope with nutrient starvation and chemical attacks. Recently, a minimal mathematical model has been employed to describe the oscillations in Bacillus subtilis biofilms. In this paper, we investigate four different modifications to that minimal model in order to better understand the oscillations in biofilms. Our first modification is towards making a gradient of metabolites from the center of the biofilm to the periphery. We find that it does not improve the model and is therefore, unnecessary. We then use realistic Michaelis-Menten kinetics to replace the highly simple mass-action kinetics for one of the reactions. Further, we use reversible reactions to mimic the diffusion in biofilms. As the final modification, we check the combined effect of using Michaelis-Menten kinetics and reversible reactions on the model behavior. We find that these two modifications alone or in combination improve the description of the biological scenario.