(35e) Predicting Nash Equilibria and Limiting Cross-Feedings for Microbial Metabolic Interactions

Microbial metabolic interactions impact ecosystems, human health and biotechnology profoundly. Understanding metabolic interactions is a fundamental task in microbiome sciences. Despite continual advances in experimental approaches for detecting interactions within microbial communities, we still need governing principles and predictive models to predict and explain microbial community metabolism in the context of ecology and evolution.

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. NECom is free of a long hidden 'forced altruism' formulation in previous static algorithms while allowing for ‘sensing and responding’ between microbial members that are missing in dynamic methods. We showed enhanced predictive accuracy of NECom over existing classes of algorithms. Using NECom, We successfully predicted several classical games in the context of metabolic interactions that were falsely or incompletely predicted by existing methods, including prisoner’s 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. We then applied NECom 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 including conditions corresponding 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 flux balance analysis. Through NECom-enabled shadow price analysis, we identified limiting cross feeding metabolites and explained a predicted frequency-dependent growth pattern, offering insights into population-stabilizing microbial interactions.