DOI: 10.5061/dryad.n5tb2rc0m
title: Sample programs of an eco-redox model for the article: Microbial redox cycling enhances ecosystem thermodynamic efficiency and productivity

description: 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.
description: All the codes were written in Wolfram Language
 using Mathematica 12. The <em>Example.nb</em>, a
 notebook file in Mathematica) is an example file
 to build a redox network template and perform the simulation of the
 dynamics of <em>N<sub>reac  </sub></em>Sps and
 <em>N<sub>tot</sub></em>  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,
 <em>N<sub>reac</sub></em>, were uniquely
 determined (see Table S3 in SI). By running cells in iv – v in
 <em>Example.nb</em>, iv) the simultaneous differential
 equations were formulated, and v) the numerical differentiation was performed
 using the <em>NDSolve</em> function to obtain numerical
 solutions for a given number of iterations. When
 the execution time of numerical differentiation
 (<em>NDSolve</em> function) exceeds a given time limit
 (<em>timeconstth</em>= 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.
description: The compressed file "Sample_Programs.zip" contains
 "Example.nb" and "Fig2a.zip". "Fig2a.zip"
 further consists of four files: "Fig2a.nb",
 "comppar.csv", "eqs.csv", and
 "reacmicrobpar.csv". "Example.nb"
 and "Fig2a.nb" are Wolfram Language programs created in
 Mathematica 12. "Example.nb" is a sample program for the
 Eco-redox model and can perform numerical calculations for the Eco-redox
 model independently. Please refer to the Supplementary Information of the
 paper for a description of the programs.
 "Fig2a.nb" is a program that reproduces Figure 2a from
 the paper by calling data from "comppar.csv",
 "eqs.csv", and "reacmicrobpar.csv". For details about
 the csv files, please refer to the README.