A (not so) short introduction to Metabolic Modelling

Python

Metabolic Modelling

Systems Biology

Metabolomics

A practical introduction to concepts, methods and tools that will initiate you in systems biology.

Author

Alexandre Areias Castro

Published

April 14, 2025

In this tutorial:

You will learn several concepts and methods within metabolic modelling, including:
- Network reconstruction;
- Single-model simulations and extensions;
- Community modelling.
Use different tools and methodologies for each step;
Give feedback on this tutorial. I intend to publish it soon!

This tutorial is for you if:

You are familiar with some concepts within systems biology and want to know more;
Are looking for tools and methodologies to add to your worflows;
Need some context to what some of these concepts actually mean.

DISCLAIMER: This tutorial is a contextualization of the tutorials in embo_mcd22 and MEWpy/examples, and therefore utlize the code written with them. The majority of the code here presented is therefore not original, and should be creditted to the authors of the previously mentioned works.

Reconstruction and model building

In this section, we will cover:

How a metabolic model originates from a genome;
The main types of reconstruction;
What tools to use.

According to ChatGPT, metabolic network reconstruction is:

“(…) a process where the complete set of metabolic reactions and pathways in a microorganism, tissue, or organism are reconstructed and represented in a computational model based on its genomic data. This model provides a comprehensive framework for understanding the organism’s metabolic network and can be used to simulate its behavior under various conditions.”

This is a fairly accurate answer, but leaves a lot of questions unanswered. Now, let’s look at how we can actually do this.

1 - Introduction

Metabolic reconstructions are achieved through essentially mapping genes, reactions and metabolites into one cohesive and interconnected network known as a Genome-Scale Metabolic Model (GEM). In practical terms, it requires us to obtain as much information from the genomic data so that through it, we can know which reactions are related to each of the genes present in the genome. The way we obtain this information is accomplished using 2 main approaches:

Bottom-up
Top-down

Bottom-up approaches are the most common and most used reconstruction methodologies. They are comprised of a mapping of the genes to some sort of annotation/database that extracts the proteins and reactions they mediate/catalyze. Afterwards, they connect all the available reactions and establish a “mock-up” metabolic network (also known as a scaffold) and afterwards are curated to cover any missing reactions to the pathways. Generally speaking, they are extremely good for generating models in a manual/semi-automated way, but the more you automate them, the more the models tend to lose quality. If you want to maintain quality, the ammount of work needed to curate and fill the gaps exponentially increases. Examples of tools: ModelSEED [1], merlin [2] and gapseq [3] (for gap-filling).

On the other hand, top-down reconstructions use the scaffolds generated in the first step and then compare them against a universal or complete model with all the available reactions in every pathway from a database and then extract the pathways they have. This methodology is much more efficient for generating large numbers of models without compromising on quality and needing manual curation, but bad for generating models for de novo genomes. One example of tools that utilize this approach is CarveMe [4].

**Source:** Machado D, Andrejev S, Tramontano M, et al. Fast automated reconstruction of genome-scale metabolic models for microbial species and communities. Nucleic Acids Research. 2018;46(15):7542–7553.

2 - Model Definition

The file type used to represent metabolic networks as GEMs is the Systems Biology Markup Language (SBML). These are XML files with specific notation and rules that allow the grouping and connection between genes, reactions, metabolites and their respective units. There are a large number of conventions and versions constantly being released to constantly make these models more updated and comprehensive. To see the specifications for each version see here.

Below is the example of a model for the central carbon metabolism of E. coli (called e_coli_core). It is fairly small in size and is the most widely used model for educational purposes.

WARNING: The output of the file is quite long. If you want to, you can go ahead and go through the various parameters and parts of the model. Otherwise, just jump into the next section using the Table of Contents on the right.

<?xml version='1.0' encoding='UTF-8'?>
<sbml xmlns:fbc="http://www.sbml.org/sbml/level3/version1/fbc/version2" xmlns="http://www.sbml.org/sbml/level3/version1/core" level="3" version="1" sboTerm="SBO:0000624" fbc:required="false">
  <model fbc:strict="true" id="e_coli_core">
    <listOfUnitDefinitions>
      <unitDefinition id="mmol_per_gDW_per_hr">
        <listOfUnits>
          <unit kind="mole" scale="-3" multiplier="1" exponent="1"/>
          <unit kind="gram" scale="0" multiplier="1" exponent="-1"/>
          <unit kind="second" scale="0" multiplier="3600" exponent="-1"/>
        </listOfUnits>
      </unitDefinition>
    </listOfUnitDefinitions>
    <fbc:listOfObjectives fbc:activeObjective="obj">
      <fbc:objective fbc:id="obj" fbc:type="maximize">
        <fbc:listOfFluxObjectives>
          <fbc:fluxObjective fbc:reaction="R_BIOMASS_Ecoli_core_w_GAM" fbc:coefficient="1"/>
        </fbc:listOfFluxObjectives>
      </fbc:objective>
    </fbc:listOfObjectives>
    <listOfParameters>
      <parameter value="-1000" id="cobra_default_lb" sboTerm="SBO:0000626" constant="true" units="mmol_per_gDW_per_hr"/>
      <parameter value="1000" id="cobra_default_ub" sboTerm="SBO:0000626" constant="true" units="mmol_per_gDW_per_hr"/>
      <parameter value="0" id="cobra_0_bound" sboTerm="SBO:0000626" constant="true" units="mmol_per_gDW_per_hr"/>
      <parameter id="R_ATPM_lower_bound" value="8.39" sboTerm="SBO:0000625" constant="true" units="mmol_per_gDW_per_hr"/>
      <parameter id="R_EX_glc__D_e_lower_bound" value="-10" sboTerm="SBO:0000625" constant="true" units="mmol_per_gDW_per_hr"/>
    </listOfParameters>
    <listOfCompartments>
      <compartment id="e" name="extracellular space" constant="true"/>
      <compartment id="c" name="cytosol" constant="true"/>
    </listOfCompartments>
    <listOfSpecies>
      <species id="M_glc__D_e" constant="false" boundaryCondition="false" hasOnlySubstanceUnits="false" name="D-Glucose" metaid="M_glc__D_e" sboTerm="SBO:0000247" compartment="e" fbc:charge="0" fbc:chemicalFormula="C6H12O6">
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              <bqbiol:is xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
                <rdf:Bag>
                  <rdf:li rdf:resource="http://identifiers.org/bigg.metabolite/glc__D"/>
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      </species>
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                <rdf:Bag>
                  <rdf:li rdf:resource="http://identifiers.org/bigg.reaction/ME2"/>
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                  <rdf:li rdf:resource="http://identifiers.org/ec-code/1.1.1.40"/>
                  <rdf:li rdf:resource="http://identifiers.org/kegg.reaction/R00216"/>
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        </listOfReactants>
        <listOfProducts>
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          <speciesReference species="M_pyr_c" stoichiometry="1" constant="true"/>
        </listOfProducts>
        <fbc:geneProductAssociation>
          <fbc:geneProductRef fbc:geneProduct="G_b2463"/>
        </fbc:geneProductAssociation>
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        <listOfProducts>
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        <fbc:geneProductAssociation>
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            <fbc:geneProductRef fbc:geneProduct="G_b2276"/>
            <fbc:geneProductRef fbc:geneProduct="G_b2277"/>
            <fbc:geneProductRef fbc:geneProduct="G_b2278"/>
            <fbc:geneProductRef fbc:geneProduct="G_b2279"/>
            <fbc:geneProductRef fbc:geneProduct="G_b2280"/>
            <fbc:geneProductRef fbc:geneProduct="G_b2281"/>
            <fbc:geneProductRef fbc:geneProduct="G_b2282"/>
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            <fbc:geneProductRef fbc:geneProduct="G_b2288"/>
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        </fbc:geneProductAssociation>
      </reaction>
      <reaction id="R_NADTRHD" fast="false" reversible="false" name="NAD transhydrogenase" metaid="R_NADTRHD" sboTerm="SBO:0000176" fbc:upperFluxBound="cobra_default_ub" fbc:lowerFluxBound="cobra_0_bound">
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              <bqbiol:is xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
                <rdf:Bag>
                  <rdf:li rdf:resource="http://identifiers.org/bigg.reaction/NADTRHD"/>
                  <rdf:li rdf:resource="http://identifiers.org/biocyc/META:PYRNUTRANSHYDROGEN-RXN"/>
                  <rdf:li rdf:resource="http://identifiers.org/ec-code/1.6.1.3"/>
                  <rdf:li rdf:resource="http://identifiers.org/ec-code/1.6.1.2"/>
                  <rdf:li rdf:resource="http://identifiers.org/ec-code/1.6.1.1"/>
                  <rdf:li rdf:resource="http://identifiers.org/kegg.reaction/R00112"/>
                  <rdf:li rdf:resource="http://identifiers.org/metanetx.reaction/MNXR101898"/>
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                  <rdf:li rdf:resource="http://identifiers.org/rhea/11693"/>
                  <rdf:li rdf:resource="http://identifiers.org/seed.reaction/rxn00083"/>
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              </bqbiol:is>
            </rdf:Description>
          </rdf:RDF>
        </sbml:annotation>
        <listOfReactants>
          <speciesReference species="M_nad_c" stoichiometry="1" constant="true"/>
          <speciesReference species="M_nadph_c" stoichiometry="1" constant="true"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="M_nadh_c" stoichiometry="1" constant="true"/>
          <speciesReference species="M_nadp_c" stoichiometry="1" constant="true"/>
        </listOfProducts>
        <fbc:geneProductAssociation>
          <fbc:or>
            <fbc:geneProductRef fbc:geneProduct="G_b3962"/>
            <fbc:and>
              <fbc:geneProductRef fbc:geneProduct="G_b1602"/>
              <fbc:geneProductRef fbc:geneProduct="G_b1603"/>
            </fbc:and>
          </fbc:or>
        </fbc:geneProductAssociation>
      </reaction>
      <reaction id="R_NH4t" fast="false" reversible="true" name="Ammonia reversible transport" metaid="R_NH4t" sboTerm="SBO:0000185" fbc:upperFluxBound="cobra_default_ub" fbc:lowerFluxBound="cobra_default_lb">
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            <rdf:Description rdf:about="#R_NH4t">
              <bqbiol:is xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
                <rdf:Bag>
                  <rdf:li rdf:resource="http://identifiers.org/bigg.reaction/NH4t"/>
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                  <rdf:li rdf:resource="http://identifiers.org/biocyc/META:RXN-9615"/>
                  <rdf:li rdf:resource="http://identifiers.org/biocyc/META:TRANS-RXN0-544"/>
                  <rdf:li rdf:resource="http://identifiers.org/metanetx.reaction/MNXR101950"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-CEL-444416"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-SSC-444416"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-DDI-444416"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-MMU-444416"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-DRE-444416"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-GGA-444416"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-CFA-444416"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-HSA-444416"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-XTR-444416"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-BTA-444416"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-RNO-444416"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-TGU-444416"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-DME-444416"/>
                  <rdf:li rdf:resource="http://identifiers.org/rhea/28749"/>
                  <rdf:li rdf:resource="http://identifiers.org/rhea/28748"/>
                  <rdf:li rdf:resource="http://identifiers.org/rhea/28750"/>
                  <rdf:li rdf:resource="http://identifiers.org/rhea/28747"/>
                  <rdf:li rdf:resource="http://identifiers.org/sabiork/11683"/>
                  <rdf:li rdf:resource="http://identifiers.org/seed.reaction/rxn13364"/>
                  <rdf:li rdf:resource="http://identifiers.org/seed.reaction/rxn09835"/>
                  <rdf:li rdf:resource="http://identifiers.org/seed.reaction/rxn05466"/>
                  <rdf:li rdf:resource="http://identifiers.org/seed.reaction/rxn08987"/>
                  <rdf:li rdf:resource="http://identifiers.org/seed.reaction/rxn08986"/>
                  <rdf:li rdf:resource="http://identifiers.org/seed.reaction/rxn09736"/>
                </rdf:Bag>
              </bqbiol:is>
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          </rdf:RDF>
        </sbml:annotation>
        <listOfReactants>
          <speciesReference species="M_nh4_e" stoichiometry="1" constant="true"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="M_nh4_c" stoichiometry="1" constant="true"/>
        </listOfProducts>
        <fbc:geneProductAssociation>
          <fbc:or>
            <fbc:geneProductRef fbc:geneProduct="G_s0001"/>
            <fbc:geneProductRef fbc:geneProduct="G_b0451"/>
          </fbc:or>
        </fbc:geneProductAssociation>
      </reaction>
      <reaction id="R_O2t" fast="false" reversible="true" name="O2 transport  diffusion " metaid="R_O2t" sboTerm="SBO:0000185" fbc:upperFluxBound="cobra_default_ub" fbc:lowerFluxBound="cobra_default_lb">
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              <bqbiol:is xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
                <rdf:Bag>
                  <rdf:li rdf:resource="http://identifiers.org/bigg.reaction/O2t"/>
                  <rdf:li rdf:resource="http://identifiers.org/biocyc/META:TRANS-RXN0-474"/>
                  <rdf:li rdf:resource="http://identifiers.org/metanetx.reaction/MNXR102090"/>
                  <rdf:li rdf:resource="http://identifiers.org/seed.reaction/rxn09641"/>
                  <rdf:li rdf:resource="http://identifiers.org/seed.reaction/rxn05468"/>
                  <rdf:li rdf:resource="http://identifiers.org/seed.reaction/rxn09031"/>
                  <rdf:li rdf:resource="http://identifiers.org/seed.reaction/rxn09032"/>
                  <rdf:li rdf:resource="http://identifiers.org/seed.reaction/rxn09734"/>
                </rdf:Bag>
              </bqbiol:is>
            </rdf:Description>
          </rdf:RDF>
        </sbml:annotation>
        <listOfReactants>
          <speciesReference species="M_o2_e" stoichiometry="1" constant="true"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="M_o2_c" stoichiometry="1" constant="true"/>
        </listOfProducts>
        <fbc:geneProductAssociation>
          <fbc:geneProductRef fbc:geneProduct="G_s0001"/>
        </fbc:geneProductAssociation>
      </reaction>
      <reaction id="R_PDH" fast="false" reversible="false" name="Pyruvate dehydrogenase" metaid="R_PDH" sboTerm="SBO:0000176" fbc:upperFluxBound="cobra_default_ub" fbc:lowerFluxBound="cobra_0_bound">
        <sbml:annotation xmlns:sbml="http://www.sbml.org/sbml/level3/version1/core">
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              <bqbiol:is xmlns:bqbiol="http://biomodels.net/biology-qualifiers/">
                <rdf:Bag>
                  <rdf:li rdf:resource="http://identifiers.org/bigg.reaction/PDH"/>
                  <rdf:li rdf:resource="http://identifiers.org/biocyc/META:PYRUVDEH-RXN"/>
                  <rdf:li rdf:resource="http://identifiers.org/ec-code/1.2.1"/>
                  <rdf:li rdf:resource="http://identifiers.org/ec-code/1.8.1.4"/>
                  <rdf:li rdf:resource="http://identifiers.org/ec-code/1.2.1.51"/>
                  <rdf:li rdf:resource="http://identifiers.org/ec-code/1.2.4.1"/>
                  <rdf:li rdf:resource="http://identifiers.org/ec-code/2.3.1.12"/>
                  <rdf:li rdf:resource="http://identifiers.org/kegg.reaction/R00209"/>
                  <rdf:li rdf:resource="http://identifiers.org/metanetx.reaction/MNXR102425"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-RNO-71397"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-OSA-71397"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-GGA-373177"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-DME-71397"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-TGU-71397"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-XTR-71397"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-CFA-71397"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-BTA-71397"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-HSA-71397"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-GGA-71397"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-SPO-71397"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-CEL-71397"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-DDI-71397"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-DRE-71397"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-SSC-71397"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-SCE-71397"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-ATH-71397"/>
                  <rdf:li rdf:resource="http://identifiers.org/reactome.reaction/R-MMU-71397"/>
                  <rdf:li rdf:resource="http://identifiers.org/rhea/28043"/>
                  <rdf:li rdf:resource="http://identifiers.org/rhea/28045"/>
                  <rdf:li rdf:resource="http://identifiers.org/rhea/28044"/>
                  <rdf:li rdf:resource="http://identifiers.org/rhea/28042"/>
                  <rdf:li rdf:resource="http://identifiers.org/sabiork/523"/>
                  <rdf:li rdf:resource="http://identifiers.org/seed.reaction/rxn00154"/>
                </rdf:Bag>
              </bqbiol:is>
            </rdf:Description>
          </rdf:RDF>
        </sbml:annotation>
        <listOfReactants>
          <speciesReference species="M_coa_c" stoichiometry="1" constant="true"/>
          <speciesReference species="M_nad_c" stoichiometry="1" constant="true"/>
          <speciesReference species="M_pyr_c" stoichiometry="1" constant="true"/>
        </listOfReactants>
        <listOfProducts>
          <speciesReference species="M_accoa_c" stoichiometry="1" constant="true"/>
          <speciesReference species="M_co2_c" stoichiometry="1" constant="true"/>
          <speciesReference species="M_nadh_c" stoichiometry="1" constant="true"/>
        </listOfProducts>
        <fbc:geneProductAssociation>
          <fbc:and>
            <fbc:geneProductRef fbc:geneProduct="G_b0114"/>
            <fbc:geneProductRef fbc:geneProduct="G_b0115"/>
            <fbc:geneProductRef fbc:geneProduct="G_b0116"/>
          </fbc:and>
        </fbc:geneProductAssociation>
      </reaction>
    </listOfReactions>
  </model>
</sbml>

3 - Testing

We will now test the E. coli ED1a model generated by CarveMe generated through the command below. We will start by reading it and then simulating microbial growth using Flux-Balance Analysis (FBA):

!carve --refseq GCF_000026305.1 -o data/models/ecoli_ed1a.xml -g M9 -i M9 -v

Now let’s test the model!

from reframed import load_cbmodel

# Reading the model
model = load_cbmodel('data/models/ecoli_ed1a.xml')

# Summary of the model
model.summary()

Metabolites:
C_c 882
C_e 352
C_p 412

Reactions:
enzymatic 1209
transport 972
exchange 346
sink 0
other 97

Simulation

In this section:

You will learn how to perform flux balance analysis.
You will use the ReFramed Python library for metabolic modeling. You can check their online documentation for more details.

1- Running the simulation

The most simple thing you can do with a constraint-based model is to run a flux balance analysis (FBA) simulation. This simulation method uses a stoichiometric matrix to represent the metabolic network, where each row represents a metabolite and each column represents a reaction. Afterwards, it calculates the flow of metabolites in the network by solving a linear program with an objective function that normally points towards microbial growth or the production of a specific metabolite [5].

INFO: The simulation is using the default objective function (biomass maximization) and environmental conditions (aerobic growth in M9 minimal medium with glucose) that came pre-defined in this model.

from reframed import FBA

solution = FBA(model)
print(solution)

Set parameter Username
Set parameter LicenseID to value 2582980
Academic license - for non-commercial use only - expires 2025-11-13
Objective: 0.6411325820261964
Status: Optimal

solution.show_values(pattern="R_EX", sort=True)

R_EX_glc__D_e -10
R_EX_o2_e    -10
R_EX_nh4_e   -7.1789
R_EX_pi_e    -0.632216
R_EX_so4_e   -0.160684
R_EX_k_e     -0.125145
R_EX_mg2_e   -0.00556183
R_EX_fe3_e   -0.00500596
R_EX_fe2_e   -0.00430521
R_EX_ca2_e   -0.0033371
R_EX_cl_e    -0.0033371
R_EX_cu2_e   -0.000454563
R_EX_mn2_e   -0.000443023
R_EX_zn2_e   -0.000218626
R_EX_cobalt2_e -6.41133e-05
R_EX_mththf_e  6.41133e-05
R_EX_4hba_e   0.000142973
R_EX_h_e      6.21087
R_EX_etoh_e   7.14746
R_EX_co2_e    18.3497
R_EX_h2o_e    29.2975

Questions to explore:

How realistic are these growth values? How can they be more accurate (if possible)?
Is E. coli growing at its maximum growth rate?

2 - Visualizing fluxes

Escher is a really nice tool for displaying fluxes in a metabolic map. It makes your life easier, especially when comparing flux distributions after performing some perturbations (such as gene deletions or changes in the growth medium).

from reframed import fluxes2escher

fluxes2escher(solution.values)

Downloading Map from https://escher.github.io/1-0-0/6/maps/Escherichia%20coli/e_coli_core.Core%20metabolism.json

3 - Environment and growth media

You can change growth conditions either by modifying the flux bounds of the reactions directly in the model or by supplying those constraints as an argument to the FBA simulation method.

Let’s observe what happens if we remove oxygen uptake to simulate anaerobic growth:

solution2 = FBA(model, constraints={'R_EX_o2_e':0})
print(solution2)

Objective: 0.22770643730880022
Status: Optimal

solution2.show_values(pattern="R_EX", sort=True)

R_EX_glc__D_e -10
R_EX_nh4_e   -2.54968
R_EX_pi_e    -0.22454
R_EX_so4_e   -0.0570692
R_EX_k_e     -0.0444467
R_EX_mg2_e   -0.00197535
R_EX_fe3_e   -0.00177793
R_EX_fe2_e   -0.00152905
R_EX_ca2_e   -0.00118521
R_EX_cl_e    -0.00118521
R_EX_cu2_e   -0.000161444
R_EX_mn2_e   -0.000157345
R_EX_zn2_e   -7.76479e-05
R_EX_cobalt2_e -2.27706e-05
R_EX_mththf_e  2.27706e-05
R_EX_4hba_e   5.07785e-05
R_EX_succ_e   0.0758429
R_EX_for_e    0.176941
R_EX_h_e      2.5345
R_EX_h2o_e    6.80319
R_EX_etoh_e   16.5012
R_EX_co2_e    16.8018

As expected, E. coli switched to a fermentation mode, which resulted in the secretion of fermentation products and a decrease in growth rate.

Again, we can see it better by displaying the flux distribution in a metabolic map.

fluxes2escher(solution2.values)

Downloading Map from https://escher.github.io/1-0-0/6/maps/Escherichia%20coli/e_coli_core.Core%20metabolism.json

4 - Comparing with experimental data

In order to validade the relevance of the usage of these methods, let’s compare them with experimentally measured fluxes.

Gerosa and co-workers[6] have measured fluxes in E. coli growing with different carbon sources.

Let’s load the fluxomics data that has been stored as a CSV file…

import pandas as pd
fluxomics = pd.read_csv('data/gerosa2015.csv', index_col=0)

fluxomics.sample(5) # print 5 random entries

	Acetate	Fructose	Galactose	Glucose	Glycerol	Gluconate	Pyruvate	Succinate
R_EX_glcn_e	0.000000	0.000000	0.00000	0.000000	0.000000	-7.283923	0.000000	0.000000
R_TALA	0.839147	1.983808	0.13221	0.820202	1.080746	0.388774	0.247744	1.563851
R_EX_succ_e	0.000000	0.000000	0.00000	0.000000	0.000000	0.000000	0.000000	-15.902000
R_TKT1	0.839147	1.983808	0.13221	0.820202	1.080746	0.388774	0.247744	1.563851
R_EX_pyr_e	0.000000	0.000000	0.00000	0.000000	0.000000	0.000000	-26.714000	0.000000

We will constrain the model using only the respective uptake rate for each substrate and see how well it predicts the growth rate and all the other fluxes.

Unfortunately, our model only contains 5 of the 8 substrates used in the paper.

uptake_reactions = {
    'Glucose': 'R_EX_glc__D_e',
    'Gluconate': 'R_EX_glcn_e',
    'Galactose': 'R_EX_gal_e',
    'Pyruvate': 'R_EX_pyr_e',
    'Glycerol': 'R_EX_glyc_e',
    'Succinate': 'R_EX_succ_e',
    'Acetate': 'R_EX_ac_e',
    'Fructose': 'R_EX_fru_e',
}

growth_rates = {
    'Glucose': 0.65,
    'Gluconate': 0.59,
    'Galactose': 0.18,
    'Pyruvate': 0.39,
    'Glycerol': 0.49,
    'Succinate': 0.51,
    'Acetate': 0.29,
    'Fructose': 0.49,
}

We need to remove glucose from the pre-defined medium, by setting the lower bound of the exchange reaction to zero:

model.reactions.R_EX_glc__D_e.lb = 0

Now let’s run simulations for all the five conditions.

simulated = {}
growth_predicted = {}

for condition, rxn_id in uptake_reactions.items():
    uptake_rate = fluxomics.loc[rxn_id, condition]
    solution = FBA(model, constraints={rxn_id: uptake_rate})
    simulated[f'{condition}_sim'] = solution.values
    growth_predicted[condition] = solution.fobj

combined = pd.concat([fluxomics, pd.DataFrame(simulated)], axis=1, join='inner')

pd.DataFrame({'Growth': growth_rates, 'Predicted': growth_predicted})

	Growth	Predicted
Glucose	0.65	0.633186
Gluconate	0.59	0.547390
Galactose	0.18	0.185570
Pyruvate	0.39	0.363931
Glycerol	0.49	0.523059
Succinate	0.51	0.317904
Acetate	0.29	0.265458
Fructose	0.49	0.602734

It seems that, in general, the model predicted similar growth rates to those that were measured.

Why do you think this happened?

Now let’s look at the same procedure with the e_coli_core model. Before that, we will have to reduce the number of carbon sources from 8 to 5 to accomodate the available exchange reactions in the model.

uptake_reactions = {
    'Glucose': 'R_EX_glc__D_e',
    'Pyruvate': 'R_EX_pyr_e',
    'Succinate': 'R_EX_succ_e',
    'Acetate': 'R_EX_ac_e',
    'Fructose': 'R_EX_fru_e',
}

growth_rates = {
    'Glucose': 0.65,
    'Pyruvate': 0.39,
    'Succinate': 0.51,
    'Acetate': 0.29,
    'Fructose': 0.49,
}

# Reading the model
model = load_cbmodel('data/models/e_coli_core.xml')

model.reactions.R_EX_glc__D_e.lb = 0

simulated = {}
growth_predicted = {}

for condition, rxn_id in uptake_reactions.items():
    uptake_rate = fluxomics.loc[rxn_id, condition]
    solution = FBA(model, constraints={rxn_id: uptake_rate})
    simulated[f'{condition}_sim'] = solution.values
    growth_predicted[condition] = solution.fobj

combined = pd.concat([fluxomics, pd.DataFrame(simulated)], axis=1, join='inner')

pd.DataFrame({'Growth': growth_rates, 'Predicted': growth_predicted})

	Growth	Predicted
Glucose	0.65	0.842206
Pyruvate	0.39	0.844264
Succinate	0.51	0.658769
Acetate	0.29	0.250744
Fructose	0.49	0.720658

Now we observe that overall, the model predicted higher growth rates than what was measured.

How can we explain the differences? What could be the variables at play here?

One of the limitations of FBA is that it does not predict overflow metabolism, unless we explicitly add additional constraints.

So let’s now additionally constrain the acetate secretion rate as well and see if our predictions improve.

simulated = {}
growth_predicted = {}

for condition, rxn_id in uptake_reactions.items():
    constraints = {
        rxn_id: fluxomics.loc[rxn_id, condition],
        'R_EX_ac_e': fluxomics.loc['R_EX_ac_e', condition],
    }
    solution = FBA(model, constraints=constraints)
    simulated[f'{condition}_sim'] = solution.values
    growth_predicted[condition] = solution.fobj

combined2 = pd.concat([fluxomics, pd.DataFrame(simulated)], axis=1, join='inner')

pd.DataFrame({'Growth': growth_rates, 'Predicted': growth_predicted})

	Growth	Predicted
Glucose	0.65	0.685756
Pyruvate	0.39	0.576763
Succinate	0.51	0.583053
Acetate	0.29	0.250744
Fructose	0.49	0.644378

There is some improvement in the prediction of growth rates. But what about the fluxes? How well are they predicted, and does this also improve when we constrain acetate secretion?

The plots below represent the measured vs predicted fluxes, before and after constraining acetate secretion.

import matplotlib.pyplot as plt

fig, axs = plt.subplots(2, 5, figsize=(15, 6))

for i, condition in enumerate(uptake_reactions):
    combined.plot.scatter(condition, f'{condition}_sim', ax=axs[0,i])
    axs[0,i].plot([-20, 20], [-20, 20], 'k--', alpha=0.3)
    
    combined2.plot.scatter(condition, f'{condition}_sim', ax=axs[1,i])
    axs[1,i].plot([-20, 20], [-20, 20], 'k--', alpha=0.3)

fig.tight_layout()

Community Modeling

In this part:

Build models for artificial communities
Use the MEWpy library for metabolic modelling. You can also read the documentation here.
Analyze interactions and results from different simulation methods.

1 - Introduction

Microbial communities are the natural occuring form of micrboes. To that end, if we want accurate predictions of microbial behaviour, it is important to represent them in conditions as close to those observed in nature as possible. To achieve this, we generate community models that include every gene, reaction and metabolite mapped to the each microbe, with a community exchange compartment to enable cross-cross-feeding and interactions, similarly to the observed below.

**Source:** Colarusso AV, Goodchild-Michelman I, Rayle M, et al. Computational modeling of metabolism in microbial communities on a genome-scale. Current Opinion in Systems Biology. 2021;26:46–57.

There are a multitude of tools and libraries that enable us to generate, manipulate and simulate with these models. Some of the most notable include ReFramed, MEWpy[7] and micom[8]. For this part of the tutorial, we will use MEWpy. You can check more of the documentation here

2 - Setting up

We will create a synthetic microbial consortium with two E. coli mutants growing in minimal medium. In one of the mutants we will knockout the glucose transporter and in the other we will knockout the ammonium transporter.

from cobra.io import read_sbml_model
from mewpy import get_simulator

wild= read_sbml_model('data/models/e_coli_core.xml.gz')
wildtype = get_simulator(wild)
solution = wildtype.simulate()
print(solution)
solution.find('EX')

objective: 0.8739215069684301
Status: OPTIMAL
Method:FBA

	Flux rate
Reaction ID
EX_co2_e	22.809833
EX_glc__D_e	-10.000000
EX_h_e	17.530865
EX_h2o_e	29.175827
EX_nh4_e	-4.765319
EX_o2_e	-21.799493
EX_pi_e	-3.214895

Now we create our two mutants (glc_ko and nh4_ko):

glc_ko = wildtype.copy()
glc_ko.id = 'glc_ko'
glc_ko.set_reaction_bounds('GLCpts', 0, 0)

Read LP format model from file /tmp/tmp_18c7wp4.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros

nh4_ko = wildtype.copy()
nh4_ko.id = 'nh4_ko'
nh4_ko.set_reaction_bounds('NH4t', 0, 0)

Read LP format model from file /tmp/tmpxmaicdpm.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros

Comparing models

Community models require that metabolites have the same identifiers across all models. We can verify that by computing the metabolites, reactions and uptakes overlaps between a list models.

from mewpy.com import *
mets, rxns, over = jaccard_similarity_matrices([glc_ko, nh4_ko])

Read LP format model from file /tmp/tmpa_vtgwyc.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmpe_npi0pt.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmpjhz3narh.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmpq6sqk19v.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmp7vle6rzk.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmp_umlvmsw.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmpus7ivupp.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmpg1k8zshc.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros

mets

	glc_ko	nh4_ko
glc_ko	1.0	1.0
nh4_ko	1.0	1.0

rxns

	glc_ko	nh4_ko
glc_ko	1.000000	0.978947
nh4_ko	0.978947	1.000000

over

	glc_ko	nh4_ko
glc_ko	1.0	1.0
nh4_ko	1.0	1.0

Building communities

Let’s initiate the CommunityModel class to create microbial communities from a list of models of individual species:

from mewpy.model import CommunityModel
community1 = CommunityModel([glc_ko, nh4_ko],flavor='cobra')
sim_com = community1.get_community_model()

Read LP format model from file /tmp/tmpuaujnnqp.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmpn090f92o.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros

Organism:   0%|          | 0/2 [00:00<?, ?it/s]Organism:  50%|█████     | 1/2 [00:00<00:00,  5.01it/s]Organism: 100%|██████████| 2/2 [00:00<00:00,  4.83it/s]Organism: 100%|██████████| 2/2 [00:00<00:00,  4.84it/s]

This community model ignores the environmental conditions that were specified in the original models (since these could be very different).

To make our life easier, we will extract the nutrient composition specified in the wild-type model to use later.

from mewpy.simulation import Environment
M9 = Environment.from_model(wildtype)
M9

Read LP format model from file /tmp/tmpuyjx7awb.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros

	lb	ub
EX_ac_e	0.0	1000.0
EX_acald_e	0.0	1000.0
EX_akg_e	0.0	1000.0
EX_co2_e	-1000.0	1000.0
EX_etoh_e	0.0	1000.0
EX_for_e	0.0	1000.0
EX_fru_e	0.0	1000.0
EX_fum_e	0.0	1000.0
EX_glc__D_e	-10.0	1000.0
EX_gln__L_e	0.0	1000.0
EX_glu__L_e	0.0	1000.0
EX_h_e	-1000.0	1000.0
EX_h2o_e	-1000.0	1000.0
EX_lac__D_e	0.0	1000.0
EX_mal__L_e	0.0	1000.0
EX_nh4_e	-1000.0	1000.0
EX_o2_e	-1000.0	1000.0
EX_pi_e	-1000.0	1000.0
EX_pyr_e	0.0	1000.0
EX_succ_e	0.0	1000.0

3 - Simulation using FBA

A very simple way to simulate a microbial community is to merge the individual models into a single model that mimics a “super organism”, where each microbe lives inside its own compartment, and run a (conventional) FBA simulation for this super organism.

sol_com = sim_com.simulate(constraints=M9)

print(sol_com)
sol_com.find('EX')

objective: 0.40757209363986224
Status: OPTIMAL
Method:FBA

	Flux rate
Reaction ID
EX_glc__D_e	-10.000000
EX_h2o_e	31.248968
EX_h_e	16.351792
EX_nh4_e	-4.444818
EX_o2_e	-24.368743
EX_pi_e	-2.998671
EX_co2_e	25.311132
EX_glc__D_e_nh4_ko	-10.000000
EX_glu__L_e_glc_ko	2.222409
EX_glu__L_e_nh4_ko	-2.222409
EX_h2o_e_glc_ko	30.945021
EX_h2o_e_nh4_ko	0.303946
EX_h_e_glc_ko	-5.029965
EX_h_e_nh4_ko	21.381758
EX_lac__D_e_glc_ko	-20.076753
EX_lac__D_e_nh4_ko	20.076753
EX_nh4_e_glc_ko	-4.444818
EX_o2_e_glc_ko	-19.052926
EX_o2_e_nh4_ko	-5.315818
EX_pi_e_glc_ko	-1.499335
EX_pi_e_nh4_ko	-1.499335
EX_pyr_e_glc_ko	17.017435
EX_pyr_e_nh4_ko	-17.017435
EX_ac_e_glc_ko	-7.810667
EX_ac_e_nh4_ko	7.810667
EX_akg_e_glc_ko	-3.390348
EX_akg_e_nh4_ko	3.390348
EX_co2_e_glc_ko	13.294545
EX_co2_e_nh4_ko	12.016587

We can see that the model predicts a growth rate (total biomass per hour) similar to the wild-type, with an efficient consumption of glucose and ammonia that results in respiratory metabolism.

But what is each organism doing, and are both organisms actually growing at the same rate?

sol_com.find(pattern='BIOMASS', sort=True, show_nulls=True)

	Flux rate
Reaction ID
BIOMASS_Ecoli_core_w_GAM_glc_ko	0.407572
BIOMASS_Ecoli_core_w_GAM_nh4_ko	0.407572

Let’s print the all non null fluxes by organism:

sol_com.find(pattern='_glc_ko', sort=True)

	Flux rate
Reaction ID
H2Ot_glc_ko	-30.945021
EX_lac__D_e_glc_ko	-20.076753
EX_o2_e_glc_ko	-19.052926
PYRt2_glc_ko	-17.017435
CO2t_glc_ko	-13.294545
PTAr_glc_ko	-7.810667
EX_ac_e_glc_ko	-7.810667
SUCOAS_glc_ko	-7.011377
EX_h_e_glc_ko	-5.029965
EX_nh4_e_glc_ko	-4.444818
GLUDy_glc_ko	-4.340602
EX_akg_e_glc_ko	-3.390348
GLUt2r_glc_ko	-2.222409
ENO_glc_ko	-1.693177
EX_pi_e_glc_ko	-1.499335
GAPD_glc_ko	-1.083449
FBA_glc_ko	-0.405412
TPI_glc_ko	-0.405412
RPE_glc_ko	-0.292963
RPI_glc_ko	-0.292963
TKT2_glc_ko	-0.220048
PGI_glc_ko	-0.083552
TALA_glc_ko	-0.072915
TKT1_glc_ko	-0.072915
GLNS_glc_ko	0.104216
FBP_glc_ko	0.405412
BIOMASS_Ecoli_core_w_GAM_glc_ko	0.407572
PGK_glc_ko	1.083449
PIt2r_glc_ko	1.499335
PGM_glc_ko	1.693177
ADK1_glc_ko	1.904747
PPS_glc_ko	1.904747
EX_glu__L_e_glc_ko	2.222409
THD2_glc_ko	3.367243
AKGt2r_glc_ko	3.390348
NH4t_glc_ko	4.444818
ACONTa_glc_ko	6.283168
ACONTb_glc_ko	6.283168
CS_glc_ko	6.283168
ICDHyr_glc_ko	6.283168
AKGDH_glc_ko	7.011377
FUM_glc_ko	7.011377
MDH_glc_ko	7.011377
SUCDi_glc_ko	7.011377
ACKr_glc_ko	7.810667
ACt2r_glc_ko	7.810667
ATPM_glc_ko	8.390000
EX_co2_e_glc_ko	13.294545
EX_pyr_e_glc_ko	17.017435
O2t_glc_ko	19.052926
D_LACt2_glc_ko	20.076753
LDH_D_glc_ko	20.076753
EX_h2o_e_glc_ko	30.945021
NADH16_glc_ko	31.094474
CYTBD_glc_ko	38.105851
ATPS4r_glc_ko	38.563336

sol_com.find(pattern='_nh4_ko', sort=True)

	Flux rate
Reaction ID
D_LACt2_nh4_ko	-20.076753
LDH_D_nh4_ko	-20.076753
PGK_nh4_ko	-18.316897
PGM_nh4_ko	-17.707169
EX_pyr_e_nh4_ko	-17.017435
CO2t_nh4_ko	-12.016587
EX_glc__D_e_nh4_ko	-10.000000
ACKr_nh4_ko	-7.810667
ACt2r_nh4_ko	-7.810667
EX_o2_e_nh4_ko	-5.315818
AKGt2r_nh4_ko	-3.390348
EX_glu__L_e_nh4_ko	-2.222409
EX_pi_e_nh4_ko	-1.499335
RPI_nh4_ko	-0.892617
H2Ot_nh4_ko	-0.303946
GLNS_nh4_ko	0.104216
GLUDy_nh4_ko	0.104216
EX_h2o_e_nh4_ko	0.303946
TKT2_nh4_ko	0.379606
BIOMASS_Ecoli_core_w_GAM_nh4_ko	0.407572
TALA_nh4_ko	0.526739
TKT1_nh4_ko	0.526739
RPE_nh4_ko	0.906345
PIt2r_nh4_ko	1.499335
ACONTa_nh4_ko	1.607668
ACONTb_nh4_ko	1.607668
CS_nh4_ko	1.607668
ICDHyr_nh4_ko	1.607668
G6PDH2r_nh4_ko	1.798962
GND_nh4_ko	1.798962
PGL_nh4_ko	1.798962
GLUt2r_nh4_ko	2.222409
PPC_nh4_ko	2.335877
EX_akg_e_nh4_ko	3.390348
PYK_nh4_ko	5.159721
O2t_nh4_ko	5.315818
PTAr_nh4_ko	7.810667
EX_ac_e_nh4_ko	7.810667
PGI_nh4_ko	8.117486
ATPM_nh4_ko	8.390000
FBA_nh4_ko	8.994934
PFK_nh4_ko	8.994934
TPI_nh4_ko	8.994934
GLCpts_nh4_ko	10.000000
ATPS4r_nh4_ko	10.578752
CYTBD_nh4_ko	10.631636
NADH16_nh4_ko	10.631636
PDH_nh4_ko	10.945833
EX_co2_e_nh4_ko	12.016587
PYRt2_nh4_ko	17.017435
ENO_nh4_ko	17.707169
GAPD_nh4_ko	18.316897
EX_lac__D_e_nh4_ko	20.076753
EX_h_e_nh4_ko	21.381758

Do you think this would be a stable consortium ?

4 - Simulation using SteadyCom

SteadyCom[9] is a recent community simulation method that takes into account the fact that to reach a stable composition the organisms need to grow at the same specific growth rate (1/h), which means that the absolute growth rate (gDW/h) of each organism is proportional to its abundance at steady-state (gDW).

Let’s simulate the same community using SteadyCom:

steady= SteadyCom(community1, constraints=M9)

Organism:   0%|          | 0/2 [00:00<?, ?it/s]Organism:  50%|█████     | 1/2 [00:00<00:00,  4.98it/s]Organism: 100%|██████████| 2/2 [00:00<00:00,  4.95it/s]Organism: 100%|██████████| 2/2 [00:00<00:00,  4.94it/s]

Set parameter FeasibilityTol to value 1e-09
Set parameter OptimalityTol to value 1e-09

In this case the solution object shows the overall community growth rate and the relative abundance of each species:

print(steady)

Community growth: 0.027466848121527204
glc_ko  1.0
nh4_ko  30.785477210097053

The solution object for community simulations implements a few additional features, such as enumerating all the cross-feeding interactions:

steady.cross_feeding(as_df=True).dropna().sort_values('rate', ascending=False)

	donor	receiver	compound	rate
6	nh4_ko	glc_ko	lac__D_e	31.460909
12	glc_ko	nh4_ko	pyr_e	31.254737
13	nh4_ko	glc_ko	ac_e	23.866599
4	nh4_ko	glc_ko	h_e	23.679204
18	glc_ko	nh4_ko	etoh_e	9.979772
14	glc_ko	nh4_ko	acald_e	8.736784
15	nh4_ko	glc_ko	akg_e	4.689488
1	glc_ko	nh4_ko	glu__L_e	4.610779
2	glc_ko	nh4_ko	h2o_e	2.254232

We can plot the fluxes of each mutant in a map to help with interpretation of the results:

from mewpy.visualization.escher import build_escher
build_escher(fluxes=steady.internal['glc_ko'])

Downloading Map from https://escher.github.io/1-0-0/6/maps/Escherichia%20coli/e_coli_core.Core%20metabolism.json

build_escher(fluxes=steady.internal['nh4_ko'])

Downloading Map from https://escher.github.io/1-0-0/6/maps/Escherichia%20coli/e_coli_core.Core%20metabolism.json

5 - Explore alternative solutions

Unfortunately, one limitation of SteadyCom, which is exemplified by Chan, et al (2017) is the variability in the solution space when the community is not growing at the maximum (theoretical) growth rate.

Would you expect a synthetic community to grow at its maximum growth rate?

MEWpy implements a variability analysis function for the SteadyCom solution space, let’s see what happens if the community is growing at 90% of the theoretical maximum:

from mewpy.com import SteadyComVA
variability = SteadyComVA(community1, obj_frac=0.9, constraints=M9)

print('Strain\tMin\tMax')
for strain, (lower, upper) in variability.items():
    print(f'{strain}\t{lower:.1%}\t{upper:.1%}')

Set parameter FeasibilityTol to value 1e-09
Set parameter OptimalityTol to value 1e-09
Strain  Min Max
glc_ko  0.0%    99.9%
nh4_ko  0.1%    100.0%

As you can see, there is a really large variability in this solution space. This means that we know in theory the two mutants can cooperate and survive in minimal media, but there is still a lot of uncertainty with regard to how they will achieve a stable consortium.

How do you think we can reduce this uncertainty?

Firstly, lets set the environment conditions:

sim_com.set_environmental_conditions(M9)

We may now impose constraints on each organism growth, such as stating that each organism need to grow at least 0.1/h.

constraints2={community1.organisms_biomass['nh4_ko']:(0.1,1000), 
             community1.organisms_biomass['glc_ko']:(0.1,1000)}
sol_abun = sim_com.simulate(constraints=constraints2)
sol_abun

objective: 0.40757209363986224
Status: OPTIMAL
Method:FBA

sol_abun.find('BIOMASS')

	Flux rate
Reaction ID
BIOMASS_Ecoli_core_w_GAM_glc_ko	0.407572
BIOMASS_Ecoli_core_w_GAM_nh4_ko	0.407572

Alternatively, we might choose to impose relative growth rates for each of the organisms, as a proxy of the community composition:

community2 = CommunityModel([glc_ko, nh4_ko],
                           add_compartments=True,
                           merge_biomasses=True,
                           flavor='cobra')

Read LP format model from file /tmp/tmp7nr4ciek.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmp9vtfdm9s.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros

sim_com2 = community2.get_community_model()
sim_com2.set_environmental_conditions(M9)

Organism:   0%|          | 0/2 [00:00<?, ?it/s]Organism:  50%|█████     | 1/2 [00:00<00:00,  4.63it/s]Organism: 100%|██████████| 2/2 [00:00<00:00,  4.86it/s]Organism: 100%|██████████| 2/2 [00:00<00:00,  4.81it/s]

sol_rel = sim_com2.simulate()
print(sol_rel)
sol_rel.find('BIOMASS')

objective: 0.40757209363986224
Status: OPTIMAL
Method:FBA

	Flux rate
Reaction ID
BIOMASS_Ecoli_core_w_GAM_glc_ko	0.407572
BIOMASS_Ecoli_core_w_GAM_nh4_ko	0.407572

sim_com2.find(community2.biomass)

	name	lb	ub	stoichiometry	gpr	annotations
id
community_growth	Community growth rate	0	inf	{'Biomass_glc_ko': -1, 'Biomass_nh4_ko': -1}		{}

community2.set_abundance({'glc_ko':1,'nh4_ko':2.5})
sim_com2.simulate().find('BIOMASS')

	Flux rate
Reaction ID
BIOMASS_Ecoli_core_w_GAM_glc_ko	0.105388
BIOMASS_Ecoli_core_w_GAM_nh4_ko	0.263471

6 - Interaction Analysis (SMETANA)

SMETANA[10] implements several algorithms to analyse cross-feeding interactions in microbial communities. Please read the paper for a more detailed explanation.

SCS (species coupling score): measures the dependency of one species in the presence of the others to survive

sc_score(community1)

Organism:   0%|          | 0/2 [00:00<?, ?it/s]Organism:  50%|█████     | 1/2 [00:00<00:00,  4.79it/s]Organism: 100%|██████████| 2/2 [00:00<00:00,  4.88it/s]Organism: 100%|██████████| 2/2 [00:00<00:00,  4.85it/s]

Set parameter FeasibilityTol to value 1e-09
Set parameter OptimalityTol to value 1e-09

	Value
Attribute
glc_ko	{'nh4_ko': 1.0}
nh4_ko	{'glc_ko': 1.0}

MUS (metabolite uptake score): measures how frequently a species needs to uptake a metabolite to survive

MUS = mu_score(community1)
MUS

Organism:   0%|          | 0/2 [00:00<?, ?it/s]Organism:  50%|█████     | 1/2 [00:00<00:00,  4.65it/s]Organism: 100%|██████████| 2/2 [00:00<00:00,  4.80it/s]Organism: 100%|██████████| 2/2 [00:00<00:00,  4.76it/s]

Set parameter FeasibilityTol to value 1e-09
Set parameter OptimalityTol to value 1e-09
Read LP format model from file /tmp/tmp47zjz2y0.lp
Reading time = 0.00 seconds
: 166 rows, 426 columns, 1572 nonzeros
Read LP format model from file /tmp/tmploumnd9_.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros

Read LP format model from file /tmp/tmpi4x48yxf.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmpuwu4t963.lp
Reading time = 0.00 seconds
: 166 rows, 426 columns, 1572 nonzeros
Read LP format model from file /tmp/tmptay8lj02.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmp24r3wqno.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros

	Value
Attribute
glc_ko	{'ac_e': 0.056179775280898875, 'acald_e': 0.10...
nh4_ko	{'ac_e': 0.0, 'acald_e': 0.0, 'akg_e': 0.0, 'c...

MUS.glc_ko

{'ac_e': 0.056179775280898875,
 'acald_e': 0.10112359550561797,
 'akg_e': 0.0449438202247191,
 'co2_e': 0.011235955056179775,
 'etoh_e': 0.02247191011235955,
 'for_e': 0.0,
 'fru_e': 0.5730337078651685,
 'fum_e': 0.0,
 'glc__D_e': 0.0,
 'gln__L_e': 0.33707865168539325,
 'glu__L_e': 0.4157303370786517,
 'h_e': 0.02247191011235955,
 'h2o_e': 0.056179775280898875,
 'lac__D_e': 0.06741573033707865,
 'mal__L_e': 0.12359550561797752,
 'nh4_e': 0.2696629213483146,
 'o2_e': 0.39325842696629215,
 'pi_e': 1.0,
 'pyr_e': 0.06741573033707865,
 'succ_e': 0.02247191011235955}

MUS.nh4_ko

{'ac_e': 0.0,
 'acald_e': 0.0,
 'akg_e': 0.0,
 'co2_e': 0.0,
 'etoh_e': 0.0,
 'for_e': 0.0,
 'fru_e': 0.39,
 'fum_e': 0.0,
 'glc__D_e': 0.61,
 'gln__L_e': 0.48,
 'glu__L_e': 0.52,
 'h_e': 0.0,
 'h2o_e': 0.0,
 'lac__D_e': 0.0,
 'mal__L_e': 0.0,
 'nh4_e': 0.0,
 'o2_e': 0.0,
 'pi_e': 1.0,
 'pyr_e': 0.0,
 'succ_e': 0.0}

MPS (metabolite production score): measures the ability of a species to produce a metabolite

MPS = mp_score(community1,environment=M9)
MPS

Read LP format model from file /tmp/tmph93thot9.lp
Reading time = 0.00 seconds
: 166 rows, 426 columns, 1572 nonzeros
Read LP format model from file /tmp/tmpen51ramt.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmputle66wb.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmp84itqtys.lp
Reading time = 0.00 seconds
: 166 rows, 426 columns, 1572 nonzeros
Read LP format model from file /tmp/tmpf7u_cext.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmpi5eb0ml2.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Set parameter FeasibilityTol to value 1e-09
Set parameter OptimalityTol to value 1e-09

	Value
Attribute
glc_ko	{'ac_e': 1, 'co2_e': 1, 'etoh_e': 1, 'for_e': ...
nh4_ko	{'ac_e': 1, 'acald_e': 1, 'co2_e': 1, 'etoh_e'...

MRO (metabolic resource overlap): calculates how much the species compete for the same metabolites.

score, MRO = mro_score(community1,environment=M9)
print(score)
MRO

Read LP format model from file /tmp/tmphnvlmbje.lp
Reading time = 0.00 seconds
: 166 rows, 426 columns, 1572 nonzeros
Read LP format model from file /tmp/tmp92z0jy04.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmphse6jqoa.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmph884y6rd.lp
Reading time = 0.00 seconds
: 166 rows, 426 columns, 1572 nonzeros
Read LP format model from file /tmp/tmp6myjqrw3.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmpbr1yi1pe.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmpcnr8uu4j.lp
Reading time = 0.00 seconds
: 166 rows, 426 columns, 1572 nonzeros
Read LP format model from file /tmp/tmpfx0f27zj.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmpgwc9pai6.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Set parameter FeasibilityTol to value 1e-09
Set parameter OptimalityTol to value 1e-09
Read LP format model from file /tmp/tmpej7ai3c1.lp
Reading time = 0.00 seconds
: 166 rows, 426 columns, 1572 nonzeros
Read LP format model from file /tmp/tmpsauiujbv.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmplsbtapto.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmpc1nt_zf0.lp
Reading time = 0.00 seconds
: 166 rows, 426 columns, 1572 nonzeros
Read LP format model from file /tmp/tmpghgqe_9_.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmpxv2fizj8.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmp3d7z507q.lp
Reading time = 0.00 seconds
: 166 rows, 426 columns, 1572 nonzeros
Read LP format model from file /tmp/tmpv4mejug0.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmphwjgt30l.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Set parameter FeasibilityTol to value 1e-09
Set parameter OptimalityTol to value 1e-09
Read LP format model from file /tmp/tmpo_6yg6pm.lp
Reading time = 0.00 seconds
: 166 rows, 426 columns, 1572 nonzeros
Read LP format model from file /tmp/tmpyc1vf66i.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Read LP format model from file /tmp/tmpgnwib923.lp
Reading time = 0.00 seconds
: 72 rows, 190 columns, 720 nonzeros
Set parameter FeasibilityTol to value 1e-09
Set parameter OptimalityTol to value 1e-09
1.0

	Value
Attribute
community_medium	{fru, pi, gln}
individual_media	{'glc_ko': {'fru', 'pi', 'gln'}, 'nh4_ko': {'f...

MRO.individual_media.glc_ko

{'fru', 'gln', 'pi'}

MRO.individual_media.nh4_ko

{'fru', 'gln', 'pi'}

References

[1]

Seaver SMD, Liu F, Zhang Q, et al. The ModelSEED Biochemistry Database for the integration of metabolic annotations and the reconstruction, comparison and analysis of metabolic models for plants, fungi and microbes. Nucleic Acids Research. 2021;49(D1):D575–D588.

[2]

Capela J, Lagoa D, Rodrigues R, et al. Merlin, an improved framework for the reconstruction of high-quality genome-scale metabolic models. Nucleic Acids Research. 2022;50(11):6052–6066.

[3]

Zimmermann J, Kaleta C, Waschina S. Gapseq: Informed prediction of bacterial metabolic pathways and reconstruction of accurate metabolic models. Genome Biology. 2021;22(1):81.

[4]

Machado D, Andrejev S, Tramontano M, et al. Fast automated reconstruction of genome-scale metabolic models for microbial species and communities. Nucleic Acids Research. 2018;46(15):7542–7553.

[5]

Orth JD, Thiele I, Palsson BØ. What is flux balance analysis? Nature biotechnology. 2010;28(3):245–248.

[6]

Gerosa L, Haverkorn van Rijsewijk BRB, Christodoulou D, et al. Pseudo-transition Analysis Identifies the Key Regulators of Dynamic Metabolic Adaptations from Steady-State Data. Cell Systems. 2015;1(4):270–282.

[7]

Pereira V, Cruz F, Rocha M. MEWpy: A computational strain optimization workbench in Python. Bioinformatics. 2021;37(16):2494–2496.

[8]

Diener C, Gibbons SM, Resendis-Antonio O. MICOM: Metagenome-Scale Modeling To Infer Metabolic Interactions in the Gut Microbiota. mSystems. 2020;5(1):10.1128/msystems.00606–19.

[9]

Chan SHJ, Simons MN, Maranas CD. SteadyCom: Predicting microbial abundances while ensuring community stability. PLOS Computational Biology. 2017;13(5):e1005539.

[10]

Zelezniak A, Andrejev S, Ponomarova O, et al. Metabolic dependencies drive species co-occurrence in diverse microbial communities. Proceedings of the National Academy of Sciences of the United States of America. 2015;112(20):6449–6454.