# Metabolic Network Reconstructions

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## Contents

## Short Description

Metabolic network reconstructions are biochemically, genetically, and genomically (BiGG) structured knowledge bases that seek to formally represent the known metabolic activities of an organism. Network reconstructions also exist for other types of biological networks, including transcription/translation and signaling networks. Genome-scale metabolic networks have been reconstructed for over 60 organisms so far, including *E. coli*. These reconstructions are useful because they can be converted into constraint-based models, allowing useful predictive calculations like flux balance analysis to be performed. Constraint-based models of *E. coli* have existed for nearly twenty years ^{[1]}. The first genome-scale model of *E. coli* metabolism was released in 2000, and this model continues to be expanded and updated today.

## Constraint-Based Modeling

Constraint-based models are a way of mathematically encoding a metabolic network reconstruction. Networks can be encoded as stoichiometric matrices (**S**), in which each row represents a unique metabolite and each column represents a biochemical reaction. The entries in each column of this matrix are the stoichiometric coefficients of the metabolites in the reaction. Metabolites that are consumed have a negative coefficient and metabolites that are produced have a positive coefficient. Since most reactions involve only a few metabolites, **S** is a sparse matrix. The size of **S** is *m***n* for a network with *m* metabolites and *n* reactions. The vector **x** with length *m* can then be defined as the concentrations of all the metabolites and the vector **v** with length *n* contains the fluxes through each reaction. A mass balance equation can then be written:

d**x**/dt = **Sv**

or at steady state:

**0** = **Sv**

This equation defines the space of possible flux distributions (**v**) allowed by the network. These flux distributions can be further constrained by imposing upper and lower bounds on the flux through each reaction, based on known biochemical data. Flux balance analysis is a method for identifying a particular **v**^{[2]}. To perform flux balance analysis, an objective function such as maximum growth must be defined. Linear programming is then used to quickly identify a **v** that optimizes this objective, given the constraints of the model. Flux balance analysis and related computational methods can be used along with constraint-based models to predict growth rates in different conditions or with different genetic perturbations^{[3]}, identify missing genes or reactions in a network reconstruction^{[4]}, or produce metabolic engineering strain designs^{[5]}.

## Constraint-Based Models of *E. coli*

*i*JE660

The first genome-scale metabolic model of *E. coli*, *i*JE660, was published in 2000^{[6]}. This model accounts for the products of 660 metabolic genes, and has 627 reactions and 438 metabolites. It includes a biomass reaction based on the measured components of *E. coli* biomass that can be used to simulate growth. This model was built using information from textbooks, databases, and extensive literature searches. Reactions were manually curated to ensure correct stoichiometry and use of realistic cofactors.

Model versions:
The original paper described a model with 436 metabolites and 720 reactions. *i*JE660 is listed as GSMN006 at the GSMNDB [[1]], with 627 reactions and 438 reactions. A third version with 739 reactions, called iJE660a (Formerly Version 1.01), was also available previously from http://systemsbiology.ucsd.edu/InSilicoOrganisms/Ecoli/EcoliSBML but now appears to be unavailable.

Model details:

- Proton balancing: Only external protons associated with the proton motive force are accounted for.

*i*JR904

In 2003, the *i*JE660 network was updated to form *i*JR904^{[7]}. This model is significantly expanded, containing 904 genes, 931 compartments, and 625 metabolites. *i*JR904 contains explicit gene-protein-reaction interactions, Boolean rules that define which genes are required for each reaction. Reactions were checked for proper charge balancing, and gaps in the model were identified and filled when possible.

*i*AF1260

The next update to the *E. coli* genome-scale metabolic model was *i*AF1260, published in 2007^{[8]}. The total number of genes increased to 1260, along with increases to 2077 reactions and 1039 unique metabolites. The scope of the network was expanded, explicitly accounting for periplasmic reactions and metabolites. The model was reconciled with the lastest version of the EcoCyc database, and thermodynamic analysis was performed to predict the reversibility of reactions. *i*AF1260 and its predecessors have been used in studies of metabolic engineering, biological discovery, phenotypic behavior, network analysis, and bacterial evolution^{[9]}.

*i*JO1366

The latest version of the *E. coli* metabolic network model was published in 2011 and named *i*JO1366 ^{[10]}. The model was expanded again, this time containing 2251 reactions, 1136 unique metabolites, and accounting for 1366 genes. Newly characterized reactions and pathways were added, and the scope of the model was increased to include biosynthetic pathways for for cofactors such as iron-sulfur clusters and molybdenum cofactors. The biomass reaction was updated and the growth and non-growth associated maintenance parameters were recalculated. As the latest version of the *E. coli* metabolic model, *i*JO1366 continues to be updated as new discoveries are made.

*E. coli* core model

The core *E. coli* model is a small-scale model of the central metabolism of *E. coli*. It is a modified subset of the *i*AF1260 model, and contains 134 genes, 95 reactions, and 72 metabolites. This model is used for educational purposes, since the results of most constraint-based calculations are easier to interpret on this smaller scale. It is also useful for testing new constraint-based analysis methods.

## Links

*i*JR904 and *i*AF1260 are available at http://systemsbiology.ucsd.edu/InSilicoOrganisms/Ecoli/EcoliSBML

*i*JO1366 is available at the BioModels database (accession: MODEL1108160000).

The core *E. coli* model is available here.

The COBRA Toolbox, a Matlab toolbox for analyzing constraint-based models, is available here.

## References

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- ↑ Varma, A et al. (1993) Biochemical production capabilities of Escherichia coli. Biotechnol. Bioeng. 42 59-73 PubMed
- ↑ Orth, JD et al. (2010) What is flux balance analysis? Nat. Biotechnol. 28 245-8 PubMed
- ↑ Joyce, AR & Palsson, BØ (2008) Predicting gene essentiality using genome-scale in silico models. Methods Mol. Biol. 416 433-57 PubMed
- ↑ Reed, JL et al. (2006) Systems approach to refining genome annotation. Proc. Natl. Acad. Sci. U.S.A. 103 17480-4 PubMed
- ↑ Burgard, AP et al. (2003) Optknock: a bilevel programming framework for identifying gene knockout strategies for microbial strain optimization. Biotechnol. Bioeng. 84 647-57 PubMed
- ↑ Edwards, JS & Palsson, BO (2000) The Escherichia coli MG1655 in silico metabolic genotype: its definition, characteristics, and capabilities. Proc. Natl. Acad. Sci. U.S.A. 97 5528-33 PubMed
- ↑ Reed, JL et al. (2003) An expanded genome-scale model of Escherichia coli K-12 (iJR904 GSM/GPR). Genome Biol. 4 R54 PubMed
- ↑ Feist, AM et al. (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information. Mol. Syst. Biol. 3 121 PubMed
- ↑ Feist, AM & Palsson, BØ (2008) The growing scope of applications of genome-scale metabolic reconstructions using Escherichia coli. Nat. Biotechnol. 26 659-67 PubMed
- ↑ Orth, JD et al. (2011) A comprehensive genome-scale reconstruction of Escherichia coli metabolism--2011. Mol. Syst. Biol. 7 535 PubMed