Bridging evolutionary game theory and metabolic models for predicting microbial metabolic interactions

Abstract

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. 1/29In nature, microorganisms seldom exist in isolate. Instead, they form communities governed by different types 2 of interactions, which play essential roles in adaptation to environment [1-3] and evolution of species [4][5][6][7][8].3 Beside the theoretical importance, microbial interactions are also key to applications ranging from drug 4 precursor synthesis [9, 10] to remediation of the gut microbiome [11][12][13][14], from degradation of cellulose for 5 biorefinery [15-17] to microbial power generation [18]. Among microbial interactions, exchange of metabolites 6 is especially important and arguably responsible for the fact that more than 99% of bacterial species are 7 not cultivable [3,19,20]. Understanding metabolic interactions is a fundamental task in microbiome science. 8Despite continual progresses in determining metabolite exchanges using experimental approach such as 9 spatially separated apparatus designs [21,22], isotope probing [23,24] and tracing [25] techniques, 16s RNA 10 analysis [26] and metabolome analysis [27], we still need governing principles to predict and understand these 11 metabolic interactions.12 Benefiting from the advancement of genome-scale metabolic models [28], methods of extending constraint-13 based modeling to microbial communities have been proposed since a decade ago [29] while new challenges 14 emerged in the process. ...

Cell Growth Model with Stochastic Gene Expression Helps Understand the Growth Advantage of Metabolic Exchange and Auxotrophy

“…Some studies have pitted genome-scale dynamic flux models of microbes with different auxotrophies and metabolite secretion rates against each other ( 75 , 76 ). Some have additionally used evolutionary game theory to intuit evolutionarily successful microbial combinations ( 77 , 78 ). These models, while useful in understanding the benefits of cooperation, cannot be used to simulate the population dynamics and the evolution of cooperation.…”

Cell growth model with stochastic gene expression helps understand the growth advantage of metabolic exchange and auxotrophy

“…Each of these represents intermediate states towards the evolution of cooperation, and this framework offers an opportunity to study if such an evolution towards cooperation is possible. Some studies have pitted genome-scale dynamic flux models of microbes with different auxotrophies and metabolite secretion rates (or leakiness) against each other (73, 74), some have even used an evolutionary game theory framework to derive intuition about which microbial combinations could be evolutionarily successful (75, 76). However, these models cannot be used to study the real-time emergence and fixation of such cooperative pairs, starting from prototrophs.…”

Integrating Systems and Synthetic Biology to Understand and Engineer Microbiomes

“…In other bi-level optimization strategies, a microbe may be predicted to produce a metabolite that benefits the community but does not necessarily maximize its own growth rate. To avoid imposing this forced altruism, Cai et al (149) developed NECom, which predicts steady-state community fluxes and pairwise interactions by identifying Nash equilibria and removes any influence by the community optimization problem on a microbe's incentive to secrete a metabolite in community GEMs.…”