Sample programs of an eco-redox model for the article: Microbial redox cycling enhances ecosystem thermodynamic efficiency and productivity

Microbial life in low-energy ecosystems relies on individual energy conservation, optimizing energy use in response to interspecific competition, and mutualistic interspecific syntrophy. Our study proposes a novel community-level strategy for increasing energy use efficiency. By utilizing an oxidation-reduction (redox) reaction network model that represents microbial redox metabolic interactions, we investigated multiple species-level competition and cooperation within the network. Our results suggest that microbial functional diversity allows for metabolic handoffs, which in turn lead to increased energy use efficiency. Furthermore, the mutualistic division of labor and the resulting complexity of redox pathways actively drive material cycling, further promoting energy exploitation. Our findings reveal the potential of self-organized ecological interactions to develop efficient energy utilization strategies, with important implications for microbial ecosystem functioning and co-evolution of life and Earth.

Methods
All the codes were written in Wolfram Language using Mathematica 12. The Example.nb, a notebook file in Mathematica) is an example file to build a redox network template and perform the simulation of the dynamics of Nreac  Sps and Ntot  chemical species. By running cells (working units within a notebook file) in i – iii, i) the standard chemical potential (or the standard Gibbs energy change of formation) is randomly selected, ii) half-reactions with corresponding standard reduction potentials are formulated (see Table S1 in Supplemental Information), and iii) redox reactions are generated for all of the possible combinations of two-half reactions (see Table S2 in SI). Consequently, the numbers of possible redox reactions, Nreac, were uniquely determined (see Table S3 in SI). By running cells in iv – v in Example.nb, iv) the simultaneous differential equations were formulated, and v) the numerical differentiation was performed using the NDSolve function to obtain numerical solutions for a given number of iterations.

When the execution time of numerical differentiation (NDSolve function) exceeds a given time limit (timeconstth= 5 min. in the default setting), the numerical calculation is interrupted and the error message "The required time exceeded timeconstth." is shown. The sample program to generate the result shown in Fig. 2a is provided as Fig2a.zip along with the csv files including values of parameters and equations expressed by Wolfram Language.