Dr. Tianyu Zhang (Dept. of Mathematical Sciences, MSU) 

10/14/2021  3:10pm

Abstract: 

We consider a biofilm community of microrganisms (the players), in which individual microorganism tune their own metabolisms (the strate- gies) in response to the local environment, specifically extracellular con- centrations of substrates and other chemicals, and in turn changing those concentrations. We hypothesize that the resulting metabolic choices will approach a Nash equilibrium state. Determination of metabolic strategies is a generalized Nash equilibrium problem (GNEP). Metabolic choices are subject to chemical fluxes in and out of cells, which in turn are constrained by chemical fluxes in and out of the extracellular environment. The result is a PDE-constrained GNEP. We couple flux balance analysis (FBA) with a continuum model at the community (or environmental) scale. FBA is used here to generate metabolic strategy choices from the set of allowable strategies. The coupling with reaction-diffusion equations can be rather stiff: changes of metabolic strategy at one location in the biofilm can cause significant changes in chemical concentrations at distant locations, leading to numerical instability. An overlapping domain decomposition method was introduced to resolve this.