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ABSTRACT Complex interactions exist among microorganisms in a community to carry out ecological processes and adapt to changing environments. Here, we constructed a quad-culture consisting of a cellulolytic bacterium ( Ruminiclostridium cellulolyticum ), a hydrogenotrophic methanogen ( Methanospirillum hungatei ), an acetoclastic methanogen ( Methanosaeta concilii ), and a sulfate-reducing bacterium ( Desulfovibrio vulgaris ). The four microorganisms in the quad-culture cooperated via cross-feeding to produce methane using cellulose as the only carbon source and electron donor. The community metabolism of the quad-culture was compared with those of the R. cellulolyticum -containing tri-cultures, bi-cultures, and mono-culture. Methane production was higher in the quad-culture than the sum of the increases in the tri-cultures, which was attributed to a positive synergy of four species. In contrast, cellulose degradation by the quad-culture was lower than the additive effects of the tri-cultures which represented a negative synergy. The community metabolism of the quad-culture was compared between a control condition and a treatment condition with sulfate addition using metaproteomics and metabolic profiling. Sulfate addition enhanced sulfate reduction and decreased methane and CO 2 productions. The cross-feeding fluxes in the quad-culture in the two conditions were modeled using a community stoichiometric model. Sulfate addition strengthened metabolic handoffs from R. cellulolyticum to M. concilii and D. vulgaris and intensified substrate competition between M. hungatei and D. vulgaris . Overall, this study uncovered emergent properties of higher-order microbial interactions using a four-species synthetic community. IMPORTANCE A synthetic community was designed using four microbial species that together performed distinct key metabolic processes in the anaerobic degradation of cellulose to methane and CO 2 . The microorganisms exhibited expected interactions, such as cross-feeding of acetate from a cellulolytic bacterium to an acetoclastic methanogen and competition of H 2 between a sulfate reducing bacterium and a hydrogenotrophic methanogen. This validated our rational design of the interactions between microorganisms based on their metabolic roles. More interestingly, we also found positive and negative synergies as emergent properties of high-order microbial interactions among three or more microorganisms in cocultures. These microbial interactions can be quantitatively measured by adding and removing specific members. A community stoichiometric model was constructed to represent the fluxes in the community metabolic network. This study paved the way toward a more predictive understanding of the impact of environmental perturbations on microbial interactions sustaining geochemically significant processes in natural systems. 

Networks are vital tools for understanding and modeling interactions in complex systems in science and engineering, and direct and indirect interactions are pervasive in all types of networks. However, quantitatively disentangling direct and indirect relationships in networks remains a formidable task. Here, we present a framework, called iDIRECT (Inference of Direct and Indirect Relationships with Effective Copula-based Transitivity), for quantitatively inferring direct dependencies in association networks. Using copula-based transitivity, iDIRECT eliminates/ameliorates several challenging mathematical problems, including ill-conditioning, self-looping, and interaction strength overflow. With simulation data as benchmark examples, iDIRECT showed high prediction accuracies. Application of iDIRECT to reconstruct gene regulatory networks in Escherichia coli also revealed considerably higher prediction power than the best-performing approaches in the DREAM5 (Dialogue on Reverse Engineering Assessment and Methods project, #5) Network Inference Challenge. In addition, applying iDIRECT to highly diverse grassland soil microbial communities in response to climate warming showed that the iDIRECT-processed networks were significantly different from the original networks, with considerably fewer nodes, links, and connectivity, but higher relative modularity. Further analysis revealed that the iDIRECT-processed network was more complex under warming than the control and more robust to both random and target species removal ( P < 0.001). As a general approach, iDIRECT has great advantages for network inference, and it should be widely applicable to infer direct relationships in association networks across diverse disciplines in science and engineering.