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Bridging evolutionary game theory and metabolic models for predicting 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 ecological, evolutionary principles and metabolic details. Recognizing that metabolic interactions form a complex game in which an individuals strategies are a metabolic flux space constrained also by other individuals strategies, we formulated a bi-level optimization framework termed NECom, which is free of a long hidden ‘forced altruism’ setup adopted by previous algorithms, for prediction of Nash equilibria of microbial metabolic interactions with significantly enhanced accuracy. A complementary shadow-price-based iterative algorithm was used to predict state transitions and draw analogy to traditional payoff matrix analysis. 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 and mutualism, providing insights into why mutualism is favorable despite seemingly costly cross-feeding metabolites, and demonstrating NECom’s potential to predict heterogeneous phenotypes among the same species. An in-depth analysis on a reported algae-yeast co-culture showed that NECom can capture and explain experimental trends using a minimal amount of experimental data as inputs without ad-hoc parameters, and that growth limiting crossfeeding metabolites can be pinpointed by shadow price analysis of NECom solutions to explain frequency-dependent growth pattern, shedding light on control of microbial populations.