Game-Theoretic Flux Balance Analysis Model for Predicting Stable Community Composition

Models for microbial interactions attempt to understand and predict the steady state network of inter-species relationships in a community, e.g. competition for shared metabolites, and cooperation through cross-feeding. Flux balance analysis (FBA) is an approach that was introduced to model the interaction of a particular microbial species with its environment. This approach has been extended to analyzing interactions in a community of microbes; however, these approaches have two important drawbacks: first, one has to numerically solve a differential equation to identify the steady state, and second, there are no methods available to analyze the stability of the steady state. We propose a game theory based community FBA model wherein species compete to maximize their individual growth rate, and the state of the community is given by the resulting Nash equilibrium. We develop a computationally efficient method for directly computing the steady state biomasses and fluxes without solving a differential equation. We also develop a method to determine the stability of a steady state to perturbations in the biomasses and to invasion by new species. We report the results of applying our proposed framework to a small community of four E. coli mutants that compete for externally supplied glucose, as well as cooperate since the mutants are auxotrophic for metabolites exported by other mutants, and a more realistic model for a gut microbiome consisting of nine species.