Supplementary material from "Microbial material cycling, energetic constraints and ecosystem expansion in subsurface ecosystems"

To harvest energy from chemical reactions, microbes engage in diverse catabolic interactions that drive material cycles in the environment. Here, we consider a simple mathematical model for cycling reactions between alternative forms of an element (A and A_e), where reaction 1 converts A to A_e and reaction 2 converts A_e to A. There are two types of microbes: type 1 microbes harness reaction 1, and type 2 microbes harness reaction 2. Each type receives its own catabolic resources from the other type and provides the other type with the by-products as the catabolic resources. Analyses of the model show that each type increases its steady-state abundance in the presence of the other type. The flux of material flow becomes faster in the presence of microbes. By coupling two catabolic reactions, types 1 and 2 can also expand their realized niches through the abundant resource premium, the effect of relative quantities of products and reactants on the available chemical energy, which is especially important for microbes under strong energetic limitations. The plausibility of mutually beneficial interactions is controlled by the available chemical energy (Gibbs energy) of the system. We conclude that mutualistic catabolic interactions can be an important factor that enables microbes in subsurface ecosystems to increase ecosystem productivity and expand the ecosystem.