<p align="center">
<img src="https://github.com/charlesrocabert/MetEvolSim/raw/master/pic/metevolsim_logo.png" width=300>
</p>
<p align="center">
<em>Metabolome Evolution Simulator</em>
<br/><br/>
A Python package to simulate the long-term evolution of metabolic levels.
<br/><br/>
<a href="https://badge.fury.io/py/MetEvolSim"><img src="https://badge.fury.io/py/MetEvolSim.svg" alt="PyPI version" height="18"></a>
<a href="https://github.com/charlesrocabert/MetEvolSim/actions"><img src="https://github.com/charlesrocabert/MetEvolSim/workflows/Upload Python Package/badge.svg" /></a>
<a href="https://github.com/charlesrocabert/MetEvolSim/LICENSE.html"><img src="https://img.shields.io/badge/License-GPLv3-blue.svg" /></a>
</p>
-----------------
<p align="justify">
MetEvolSim (<em>Metabolome Evolution Simulator</em>) is a Python package which provides numerical tools to simulate the long-term evolution of metabolic abundances in kinetic models of metabolic network.
To use MetEvolSim, a <a href="http://sbml.org/Main_Page" target="_blank">SBML-formatted</a> metabolic network model is required, along with kinetic parameters and initial metabolic concentrations.
Additionally, the model must reach a stable steady-state, which is computed with <a href="http://copasi.org/" target="_blank">Copasi</a> software.
</p>
<p align="justify">
MetEvolSim is being developed by Charles Rocabert, Gábor Boross, Orsolya Liska and Balázs Papp.
</p>
<p align="justify">
If you are planning to use MetEvolSim for research or have encountered any issues with the software, do not hesitate to contact <a href="mailto:charles[DOT]rocabert[AT]hhu[DOT]de">Charles Rocabert</a>.
</p>
<p align="center">
<img src="https://github.com/charlesrocabert/MetEvolSim/raw/master/pic/BRC_logo.png" height="100px"></a> <img src="https://github.com/charlesrocabert/MetEvolSim/raw/master/pic/MTA_logo.png" height="100px"></a>
</p>
## Table of contents
- [Publications](#publications)
- [Dependencies](#dependencies)
- [Installation](#installation)
- [First usage](#first_usage)
- [Help](#help)
- [Ready-to-use examples](#examples)
- [List of tested metabolic models](#tested_models)
- [Copyright](#copyright)
- [License](#license)
## Publications <a name="publications"></a>
- O. Liska, G. Boross, C. Rocabert, B. Szappanos, R. Tengölics, B. Papp. Principles of metabolome conservation in animals. <em>Proceedings of the National Academy of Sciences</em> 120 (35), e2302147120 (2023) (https://doi.org/10.1073/pnas.2302147120).
## Dependencies <a name="dependencies"></a>
- Python ≥ 3,
- Numpy ≥ 1.21 (automatically installed when using pip),
- Python-libsbml ≥ 5.19 (automatically installed when using pip),
- NetworkX ≥ 2.6 (automatically installed when using pip),
- CopasiSE ≥ 4.27 (to be installed separately),
- pip ≥ 21.3.1 (optional).
## Installation <a name="installation"></a>
• To install Copasi software, visit http://copasi.org/ and download the command line version CopasiSE.
• To install the latest release of MetEvolSim:
```shell
pip install MetEvolSim
```
Alternatively, download the <a href="https://github.com/charlesrocabert/MetEvolSim/releases/latest">latest release</a> in the folder of your choice and unzip it. Then follow the instructions below:
```shell
# Navigate to the MetEvolSim folder
cd /path/to/MetEvolSim
# Install MetEvolSim Python package
python3 setup.py install
```
## First usage <a name="first_usage"></a>
MetEvolSim has been tested with numerous publicly accessible metabolic networks; however, we cannot guarantee that it will be compatible with any model (please refer to the [list of tested metabolic models](#tested_models)).
The package includes the class <code>Model</code> to manipulate SBML models. Additionally, it is necessary to set up an objective function (a list of target reactions and their coefficients) and to provide the path of <a href="http://copasi.org/">CopasiSE</a> software. Please note that objective function coefficients are not operational in the current version of MetEvolSim.
```python
# Import MetEvolSim package
import metevolsim
# Create an objective function
target_fluxes = [['ATPase', 1.0], ['PDC', 1.0]]
# Load the SBML metabolic model
model = metevolsim.Model(sbml_filename='glycolysis.xml',
objective_function=target_fluxes,
copasi_path='/Applications/COPASI/CopasiSE')
# Print some informations on the metabolic model
print(model.get_number_of_species())
print(model.get_wild_type_species_value('Glc'))
# Get a kinetic parameter at random
param = model.get_random_parameter()
print(param)
# Mutate this kinetic parameter with a log-scale mutation size 0.01
model.random_parameter_mutation(param, sigma=0.01)
# Compute wild-type and mutant steady-states
model.compute_wild_type_steady_state()
model.compute_mutant_steady_state()
# Run a metabolic control analysis on the wild-type
model.compute_wild_type_metabolic_control_analysis()
# This function will output two datasets:
# - output/wild_type_MCA_unscaled.txt containing unscaled control coefficients,
# - output/wild_type_MCA_scaled.txt containing scaled control coefficients.
# Compute all pairwise metabolite shortest paths
model.build_species_graph()
model.save_shortest_paths(filename="glycolysis_shortest_paths.txt")
# Compute a flux drop analysis to measure the contribution of each flux to the fitness
# (in this example, each flux is dropped at 1% of its original value)
model.flux_drop_analysis(drop_coefficient=0.01,
filename="flux_drop_analysis.txt",
owerwrite=True)
```
MetEvolSim offers two distinct numerical approaches for assessing the evolution of metabolic abundances:
- <strong>Evolution experiments</strong>, based on a Markov Chain Monte Carlo (MCMC) algorithm,
<strong>Sensitivity analysis</strong>, that can either explore every kinetic parameter in a given range and record changes in associated fluxes and metabolic abundances (One-At-a-Time sensitivity analysis) or randomly explore the kinetic parameter space by randomly mutating a single kinetic parameter multiple times (random sensitivity analysis).
All numerical analysis output files are saved in the <code>output</code> subfolder.
### Evolution experiments:
<p align="center">
<img src="https://github.com/charlesrocabert/MetEvolSim/raw/master/pic/mcmc_algorithm.png">
</p>
<p align="justify">
<strong>Algorithm overview:</strong> <strong>A.</strong> The model of interest is loaded as a wild-type from a SBML file (kinetic equations, kinetic parameter values and initial metabolic concentrations must be specified). <strong>B.</strong> At each iteration <em>t</em>, a single kinetic parameter is selected at random and mutated through a log10-normal distribution of standard deviation σ. <strong>C.</strong> The new steady-state is computed using Copasi software, and the MOMA distance <em>z</em> between the mutant and the wild-type target fluxes is computed. <strong>D.</strong> If <em>z</em> is under a given selection threshold ω, the mutation is accepted. Else, the mutation is discarded. <strong>E.</strong> A new iteration <em>t+1</em> is computed.
</p>
<br/>
There are six types of selection available:
- <code>MUTATION_ACCUMULATION</code>: Run a mutation accumulation experiment by accepting all new mutations without any selection threshold,
- <code>ABSOLUTE_METABOLIC_SUM_SELECTION</code>: Run an evolution experiment by applying a stabilizing selection on the sum of absolute metabolic abundances,
- <code>ABSOLUTE_TARGET_FLUXES_SELECTION</code>: Run an evolution experiment by applying a stabilizing selection on the MOMA distance of absolute target fluxes,
- <code>RELATIVE_TARGET_FLUXES_SELECTION</code>: Run an evolution experiment by applying a stabilizing selection on the MOMA distance of relative target fluxes.
```python
# Load a Markov Chain Monte Carlo (MCMC) instance
mcmc = metevolsim.MCMC(sbml_filename='glycolysis.xml',
objective_function=target_fluxes,
total_iterations=10000,
sigma=0.01,
selection_scheme="MUTATION_ACCUMULATION",
selection_threshold=1e-4,
copasi_path='/Applications/COPASI/CopasiSE')
# Initialize the MCMC instance
mcmc.initialize()
# Compute the successive iterations and write output files
stop_MCMC = False
while not stop_MCMC:
stop_mcmc = mcmc.iterate()
mcmc.write_output_file()
mcmc.write_statistics()
```
### One-At-a-Time (OAT) sensitivity analysis:
For each kinetic parameter p, each metabolic abundance [X<sub>i</sub>] and each flux ν<sub>j</sub>, the algorithm numerically computes relative derivatives and control coefficients.
```python
# Load a sensitivity analysis instance
sa = metevolsim.SensitivityAnalysis(sbml_filename='glycolysis.xml',
copasi_path='/Applications/COPASI/CopasiSE')
# Run the full OAT sensitivity analysis
sa.run_OAT_analysis(factor_range=1.0, factor_step=0.01)
```
### Random sensitivity analysis:
At each iteration, a single kinetic parameter p is mutated at random in a log10-normal distribution of size σ, and relative derivatives and control coefficients are computed.
```python
# Load a sensitivity analysis instance
sa = metevolsim.SensitivityAnalysis(sbml_filename='glycolysis.xml',
copasi_path='/Applications/COPASI/CopasiSE')
# Run the full OAT sensitivity analysis
sa.run_random_analysis(sigma=0.01, nb_iterations=1000)
```
## Help <a name="help"></a>
To get assistance with a MetEvolSim class or method, use the Python help function:
```python
help(metevolsim.Model.set_species_initial_value)
```
To get a brief overview and a list of parameters and outputs:
```
Help on function set_species_initial_value in module metevolsim:
set_species_initial_value(self, species_id, value)
Set the initial concentration of the species 'species_id' in the
mutant model.
Parameters
----------
species_id: str
Species identifier (as defined in the SBML model).
value: float >= 0.0
Species abundance.
Returns
-------
None
(END)
```
## Ready-to-use examples <a name="examples"></a>
Ready-to-use examples come pre-packaged with MetEvolSim package.
They can also be downloaded here: https://github.com/charlesrocabert/MetEvolSim/raw/master/example/example.zip.
## List of tested metabolic models <a name="tested_models"></a>
| **Reference** | **Model** | **Running with MetEvolSim** |
|-------------------------|--------------------------------------|-----------------------------|
| Bakker et al. (1997) | _Trypanosoma brucei_ glycolysis | :x: |
| Curto et al. (1998) | Human purine metabolism | :x: |
| Mulquiney et al. (1999) | Human erythrocyte | :white_check_mark: |
| Jamshidi et al. (2001) | Red blood cell | :x: |
| Bali et al. (2001) | Red blood cell glycolysis | :white_check_mark: |
| Lambeth et al. (2002) | Skeletal muscle glycogenolysis | :white_check_mark: |
| Holzhutter et al. (2004)| Human erythrocyte | :white_check_mark: |
| Beard et al. (2005) | Mitochondrial respiration | :x: |
| Banaji et al. (2005) | Cerebral blood flood control | :white_check_mark: |
| Bertram et al. (2006) | Mitochondrial ATP production | :x: |
| Bruck et al. (2008) | Yeast glycolysis | :white_check_mark: |
| Reed et al. (2008) | Glutathione metabolism | :x: |
| Curien et al. (2009) | Aspartame metabolism | :x: |
| Jerby et al. (2010) | Human liver metabolism | :x: |
| Li et al. (2010) | Yeast glycolysis | :x: |
| Bekaert et al. (2010) | Mouse metabolism reconstruction | :x: |
| Bordbar et al. (2011) | Human multi-tissues | :x: |
| Koenig et al. (2012) | Hepatocyte glucose metabolism | :white_check_mark: |
| Messiha et al. (2013) | Yeast glycolysis + pentose phosphate | :white_check_mark: |
| Mitchell et al. (2013) | Liver iron metabolism | :x: |
| Stanford et al. (2013) | Yeast whole cell model | :x: |
| Bordbar et al. (2015) | Red blood cell | :x: |
| Costa et al. (2016) | _E. coli_ core metabolism | :white_check_mark: |
| Millard et al. (2016) | _E. coli_ core metabolism | :white_check_mark: |
| Bulik et al. (2016) | Hepatic glucose metabolism | :white_check_mark: |
## Copyright <a name="copyright"></a>
Copyright © 2018-2023 Charles Rocabert, Gábor Boross, Orsolya Liska and Balázs Papp.
All rights reserved.
## License <a name="license"></a>
<p align="justify">
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
</p>
<p align="justify">
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
</p>
<p align="justify">
You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.
</p>
Raw data
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"description": "<p align=\"center\">\n <img src=\"https://github.com/charlesrocabert/MetEvolSim/raw/master/pic/metevolsim_logo.png\" width=300>\n</p>\n<p align=\"center\">\n <em>Metabolome Evolution Simulator</em>\n <br/><br/>\n A Python package to simulate the long-term evolution of metabolic levels.\n <br/><br/>\n <a href=\"https://badge.fury.io/py/MetEvolSim\"><img src=\"https://badge.fury.io/py/MetEvolSim.svg\" alt=\"PyPI version\" height=\"18\"></a>\n <a href=\"https://github.com/charlesrocabert/MetEvolSim/actions\"><img src=\"https://github.com/charlesrocabert/MetEvolSim/workflows/Upload Python Package/badge.svg\" /></a> \n <a href=\"https://github.com/charlesrocabert/MetEvolSim/LICENSE.html\"><img src=\"https://img.shields.io/badge/License-GPLv3-blue.svg\" /></a>\n</p>\n\n-----------------\n\n<p align=\"justify\">\nMetEvolSim (<em>Metabolome Evolution Simulator</em>) is a Python package which provides numerical tools to simulate the long-term evolution of metabolic abundances in kinetic models of metabolic network.\nTo use MetEvolSim, a <a href=\"http://sbml.org/Main_Page\" target=\"_blank\">SBML-formatted</a> metabolic network model is required, along with kinetic parameters and initial metabolic concentrations.\nAdditionally, the model must reach a stable steady-state, which is computed with <a href=\"http://copasi.org/\" target=\"_blank\">Copasi</a> software.\n</p>\n\n<p align=\"justify\">\nMetEvolSim is being developed by Charles Rocabert, G\u00e1bor Boross, Orsolya Liska and Bal\u00e1zs Papp.\n</p>\n\n<p align=\"justify\">\nIf you are planning to use MetEvolSim for research or have encountered any issues with the software, do not hesitate to contact <a href=\"mailto:charles[DOT]rocabert[AT]hhu[DOT]de\">Charles Rocabert</a>.\n</p>\n\n<p align=\"center\">\n<img src=\"https://github.com/charlesrocabert/MetEvolSim/raw/master/pic/BRC_logo.png\" height=\"100px\"></a> <img src=\"https://github.com/charlesrocabert/MetEvolSim/raw/master/pic/MTA_logo.png\" height=\"100px\"></a>\n</p>\n\n## Table of contents\n- [Publications](#publications)\n- [Dependencies](#dependencies)\n- [Installation](#installation)\n- [First usage](#first_usage)\n- [Help](#help)\n- [Ready-to-use examples](#examples)\n- [List of tested metabolic models](#tested_models)\n- [Copyright](#copyright)\n- [License](#license)\n\n## Publications <a name=\"publications\"></a>\n- O. Liska, G. Boross, C. Rocabert, B. Szappanos, R. Teng\u00f6lics, B. Papp. Principles of metabolome conservation in animals. <em>Proceedings of the National Academy of Sciences</em> 120 (35), e2302147120 (2023) (https://doi.org/10.1073/pnas.2302147120).\n\n## Dependencies <a name=\"dependencies\"></a>\n- Python ≥ 3,\n- Numpy ≥ 1.21 (automatically installed when using pip),\n- Python-libsbml ≥ 5.19 (automatically installed when using pip),\n- NetworkX ≥ 2.6 (automatically installed when using pip),\n- CopasiSE ≥ 4.27 (to be installed separately),\n- pip ≥ 21.3.1 (optional).\n\n## Installation <a name=\"installation\"></a>\n• To install Copasi software, visit http://copasi.org/ and download the command line version CopasiSE.\n\n• To install the latest release of MetEvolSim:\n```shell\npip install MetEvolSim\n```\n\nAlternatively, download the <a href=\"https://github.com/charlesrocabert/MetEvolSim/releases/latest\">latest release</a> in the folder of your choice and unzip it. Then follow the instructions below:\n```shell\n# Navigate to the MetEvolSim folder\ncd /path/to/MetEvolSim\n\n# Install MetEvolSim Python package\npython3 setup.py install\n```\n\n## First usage <a name=\"first_usage\"></a>\nMetEvolSim has been tested with numerous publicly accessible metabolic networks; however, we cannot guarantee that it will be compatible with any model (please refer to the [list of tested metabolic models](#tested_models)).\nThe package includes the class <code>Model</code> to manipulate SBML models. Additionally, it is necessary to set up an objective function (a list of target reactions and their coefficients) and to provide the path of <a href=\"http://copasi.org/\">CopasiSE</a> software. Please note that objective function coefficients are not operational in the current version of MetEvolSim.\n\n```python\n# Import MetEvolSim package\nimport metevolsim\n\n# Create an objective function\ntarget_fluxes = [['ATPase', 1.0], ['PDC', 1.0]]\n\n# Load the SBML metabolic model\nmodel = metevolsim.Model(sbml_filename='glycolysis.xml',\n objective_function=target_fluxes,\n copasi_path='/Applications/COPASI/CopasiSE')\n\n# Print some informations on the metabolic model\nprint(model.get_number_of_species())\nprint(model.get_wild_type_species_value('Glc'))\n\n# Get a kinetic parameter at random\nparam = model.get_random_parameter()\nprint(param)\n\n# Mutate this kinetic parameter with a log-scale mutation size 0.01\nmodel.random_parameter_mutation(param, sigma=0.01)\n\n# Compute wild-type and mutant steady-states\nmodel.compute_wild_type_steady_state()\nmodel.compute_mutant_steady_state()\n\n# Run a metabolic control analysis on the wild-type\nmodel.compute_wild_type_metabolic_control_analysis()\n# This function will output two datasets:\n# - output/wild_type_MCA_unscaled.txt containing unscaled control coefficients,\n# - output/wild_type_MCA_scaled.txt containing scaled control coefficients.\n\n# Compute all pairwise metabolite shortest paths\nmodel.build_species_graph()\nmodel.save_shortest_paths(filename=\"glycolysis_shortest_paths.txt\")\n\n# Compute a flux drop analysis to measure the contribution of each flux to the fitness\n# (in this example, each flux is dropped at 1% of its original value)\nmodel.flux_drop_analysis(drop_coefficient=0.01,\n filename=\"flux_drop_analysis.txt\",\n owerwrite=True)\n```\n\nMetEvolSim offers two distinct numerical approaches for assessing the evolution of metabolic abundances:\n- <strong>Evolution experiments</strong>, based on a Markov Chain Monte Carlo (MCMC) algorithm,\n <strong>Sensitivity analysis</strong>, that can either explore every kinetic parameter in a given range and record changes in associated fluxes and metabolic abundances (One-At-a-Time sensitivity analysis) or randomly explore the kinetic parameter space by randomly mutating a single kinetic parameter multiple times (random sensitivity analysis).\n\nAll numerical analysis output files are saved in the <code>output</code> subfolder.\n\n### Evolution experiments:\n<p align=\"center\">\n<img src=\"https://github.com/charlesrocabert/MetEvolSim/raw/master/pic/mcmc_algorithm.png\">\n</p>\n<p align=\"justify\">\n<strong>Algorithm overview:</strong> <strong>A.</strong> The model of interest is loaded as a wild-type from a SBML file (kinetic equations, kinetic parameter values and initial metabolic concentrations must be specified). <strong>B.</strong> At each iteration <em>t</em>, a single kinetic parameter is selected at random and mutated through a log10-normal distribution of standard deviation σ. <strong>C.</strong> The new steady-state is computed using Copasi software, and the MOMA distance <em>z</em> between the mutant and the wild-type target fluxes is computed. <strong>D.</strong> If <em>z</em> is under a given selection threshold ω, the mutation is accepted. Else, the mutation is discarded. <strong>E.</strong> A new iteration <em>t+1</em> is computed.\n</p>\n\n<br/>\nThere are six types of selection available:\n\n- <code>MUTATION_ACCUMULATION</code>: Run a mutation accumulation experiment by accepting all new mutations without any selection threshold,\n- <code>ABSOLUTE_METABOLIC_SUM_SELECTION</code>: Run an evolution experiment by applying a stabilizing selection on the sum of absolute metabolic abundances,\n- <code>ABSOLUTE_TARGET_FLUXES_SELECTION</code>: Run an evolution experiment by applying a stabilizing selection on the MOMA distance of absolute target fluxes,\n- <code>RELATIVE_TARGET_FLUXES_SELECTION</code>: Run an evolution experiment by applying a stabilizing selection on the MOMA distance of relative target fluxes.\n\n```python\n# Load a Markov Chain Monte Carlo (MCMC) instance\nmcmc = metevolsim.MCMC(sbml_filename='glycolysis.xml',\n objective_function=target_fluxes,\n total_iterations=10000,\n sigma=0.01,\n selection_scheme=\"MUTATION_ACCUMULATION\",\n selection_threshold=1e-4,\n copasi_path='/Applications/COPASI/CopasiSE')\n\n# Initialize the MCMC instance\nmcmc.initialize()\n\n# Compute the successive iterations and write output files\nstop_MCMC = False\nwhile not stop_MCMC:\n stop_mcmc = mcmc.iterate()\n mcmc.write_output_file()\n mcmc.write_statistics()\n```\n\n### One-At-a-Time (OAT) sensitivity analysis:\nFor each kinetic parameter p, each metabolic abundance [X<sub>i</sub>] and each flux ν<sub>j</sub>, the algorithm numerically computes relative derivatives and control coefficients.\n\n```python\n# Load a sensitivity analysis instance\nsa = metevolsim.SensitivityAnalysis(sbml_filename='glycolysis.xml',\n copasi_path='/Applications/COPASI/CopasiSE')\n\n# Run the full OAT sensitivity analysis\nsa.run_OAT_analysis(factor_range=1.0, factor_step=0.01)\n```\n\n### Random sensitivity analysis:\nAt each iteration, a single kinetic parameter p is mutated at random in a log10-normal distribution of size σ, and relative derivatives and control coefficients are computed.\n\n```python\n# Load a sensitivity analysis instance\nsa = metevolsim.SensitivityAnalysis(sbml_filename='glycolysis.xml',\n copasi_path='/Applications/COPASI/CopasiSE')\n\n# Run the full OAT sensitivity analysis\nsa.run_random_analysis(sigma=0.01, nb_iterations=1000)\n```\n\n## Help <a name=\"help\"></a>\nTo get assistance with a MetEvolSim class or method, use the Python help function:\n```python\nhelp(metevolsim.Model.set_species_initial_value)\n```\nTo get a brief overview and a list of parameters and outputs:\n```\nHelp on function set_species_initial_value in module metevolsim:\n\nset_species_initial_value(self, species_id, value)\n Set the initial concentration of the species 'species_id' in the\n mutant model.\n\n Parameters\n ----------\n species_id: str\n Species identifier (as defined in the SBML model).\n value: float >= 0.0\n Species abundance.\n\n Returns\n -------\n None\n(END)\n```\n\n## Ready-to-use examples <a name=\"examples\"></a>\nReady-to-use examples come pre-packaged with MetEvolSim package.\nThey can also be downloaded here: https://github.com/charlesrocabert/MetEvolSim/raw/master/example/example.zip.\n\n## List of tested metabolic models <a name=\"tested_models\"></a>\n\n| **Reference** | **Model** | **Running with MetEvolSim** |\n|-------------------------|--------------------------------------|-----------------------------|\n| Bakker et al. (1997) | _Trypanosoma brucei_ glycolysis | :x: |\n| Curto et al. (1998) | Human purine metabolism | :x: |\n| Mulquiney et al. (1999) | Human erythrocyte | :white_check_mark: |\n| Jamshidi et al. (2001) | Red blood cell | :x: |\n| Bali et al. (2001) | Red blood cell glycolysis | :white_check_mark: |\n| Lambeth et al. (2002) | Skeletal muscle glycogenolysis | :white_check_mark: |\n| Holzhutter et al. (2004)| Human erythrocyte | :white_check_mark: |\n| Beard et al. (2005) | Mitochondrial respiration | :x: |\n| Banaji et al. (2005) | Cerebral blood flood control | :white_check_mark: |\n| Bertram et al. (2006) | Mitochondrial ATP production | :x: |\n| Bruck et al. (2008) | Yeast glycolysis | :white_check_mark: |\n| Reed et al. (2008) | Glutathione metabolism | :x: |\n| Curien et al. (2009) | Aspartame metabolism | :x: |\n| Jerby et al. (2010) | Human liver metabolism | :x: |\n| Li et al. (2010) | Yeast glycolysis | :x: |\n| Bekaert et al. (2010) | Mouse metabolism reconstruction | :x: |\n| Bordbar et al. (2011) | Human multi-tissues | :x: |\n| Koenig et al. (2012) | Hepatocyte glucose metabolism | :white_check_mark: |\n| Messiha et al. (2013) | Yeast glycolysis + pentose phosphate | :white_check_mark: |\n| Mitchell et al. (2013) | Liver iron metabolism | :x: |\n| Stanford et al. (2013) | Yeast whole cell model | :x: |\n| Bordbar et al. (2015) | Red blood cell | :x: |\n| Costa et al. (2016) | _E. coli_ core metabolism | :white_check_mark: |\n| Millard et al. (2016) | _E. coli_ core metabolism | :white_check_mark: |\n| Bulik et al. (2016) | Hepatic glucose metabolism | :white_check_mark: |\n\n## Copyright <a name=\"copyright\"></a>\nCopyright © 2018-2023 Charles Rocabert, G\u00e1bor Boross, Orsolya Liska and Bal\u00e1zs Papp.\nAll rights reserved.\n\n## License <a name=\"license\"></a>\n<p align=\"justify\">\nThis program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.\n</p>\n\n<p align=\"justify\">\nThis program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.\n</p>\n\n<p align=\"justify\">\nYou should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/.\n</p>\n",
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