Predicting Nash equilibria for microbial metabolic interactions

Jingyi Cai; Tianwei Tan; Siu H J Chan

doi:10.1093/bioinformatics/btaa1014

Predicting Nash equilibria for microbial metabolic interactions

Bioinformatics. 2021 Apr 5;36(24):5649-5655. doi: 10.1093/bioinformatics/btaa1014.

Authors

Jingyi Cai^{1

2}, Tianwei Tan¹, Siu H J Chan³

Affiliations

¹ National Energy R&D Center for Biorefinery, Beijing University of Chemical Technology, Beijing 100029, China.
² Biodesign Center, Tianjin Institute of Industrial Biotechnology, Chinese Academy of Sciences, Tianjin 300308, China.
³ Chemical and Biological Engineering, Colorado State University, Fort Collins, CO 80523, USA.

PMID: 33315094
DOI: 10.1093/bioinformatics/btaa1014

Abstract

Motivation: Microbial metabolic interactions impact ecosystems, human health and biotechnology profoundly. However, their determination remains elusive, invoking an urgent need for predictive models seamlessly integrating metabolism with evolutionary principles that shape community interactions.

Results: Inspired by the evolutionary game theory, we formulated a bi-level optimization framework termed NECom for which any feasible solutions are Nash equilibria of microbial community metabolic models with/without an outer-level (community) objective function. Distinct from discrete matrix games, NECom models the continuous interdependent strategy space of metabolic fluxes. We showed that NECom 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 cooperation. The improved capability originates from the novel formulation to prevent 'forced altruism' hidden in previous static algorithms while allowing for sensing all potential metabolite exchanges to determine evolutionarily favorable interactions between members, a feature missing in dynamic methods. The results provided insights into why mutualism is favorable despite seemingly costly cross-feeding metabolites and demonstrated similarities and differences between games in the continuous metabolic flux space and matrix games. 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. 488 growth conditions corresponding to 3221 experimental data points were simulated. Without training any parameters using the data, NECom is more predictive of species' growth rates given uptake rates compared with flux balance analysis with an overall 63.5% and 81.7% reduction in root-mean-square error for the two species respectively.

Availability and implementation: Simulation code and data are available at https://github.com/Jingyi-Cai/NECom.git.

Supplementary information: Supplementary data are available at Bioinformatics online.