Bridging traditional evolutionary game theory and metabolic models for predicting Nash equilibrium of microbial metabolic interactions
Microbial metabolic interactions impact ecosystems, human health and biotechnological processes profoundly. However, their determination remains elusive, invoking an urgent need for predictive models that seamlessly integrate metabolic details with ecological and evolutionary principles which shape the interactions within microbial communities. Inspired by the evolutionary game theory, we formulated a bi-level optimization framework termed NECom for the prediction of Nash equilibria of microbial community metabolic models with significantly enhanced accuracy. NECom is free of a long hidden forced altruism setup in previous static algorithm while allowing for sensing and responding between microbial members that is missing in dynamic methods. We successfully predicted several classical games in the context of metabolic interactions that were falsely or incompletely predicted by existing methods, including prisoners dilemma, snowdrift game and mutualism. The results provided insights into why mutualism is favorable despite seemingly costly cross-feeding metabolites, and demonstrated the potential to predict heterogeneous phenotypes among the same species. NECom was then applied to a reported algae-yeast co-culture system that shares typical cross-feeding features of lichen, a model system of mutualism. More than 1200 growth conditions were simulated, of which 488 conditions correspond to 3221 experimental data points. Without fitting any ad-hoc parameters, an overall 63.5% and 81.7% reduction in root-mean-square error in predicted growth rates for the two species respectively was achieved when compared with the standard flux balance analysis. The simulation results further show that growth-limiting crossfeeding metabolites can be pinpointed by shadow price analysis to explain the predicted frequency-dependent growth pattern, offering insights into how stabilizing microbial interactions control microbial populations.