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Team:WashU StLouis/Modeling

Washington University - Penn State iGEM

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WashU and Penn State   iGEM 2015
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What is a genome-scale metabolic model?

A genome-scale metabolic model (GSM) is a network reconstruction of all known metabolic reactions in an organism and the genes that encode each associated enzyme.1 Through the construction of these networks, we can assess the metabolic capabilities of an organism as well as its potential to produce biologically useful metabolites.

What are the components of a genome-scale model

  • Gene-Protein-Reaction (GPR) relationships
  • Set of known metabolic reactions represented in a stoichiometric matrix. Identifies stoichiometric coefficients and directionality associated with each reaction.
  • Scaled biomass equation. Assumes flux through the biomass equation is equal to the exponential growth rate of the organism. This is made from experimental measurements of biomass components.

You can download our GSM, adapted from a published model of E. coli strain DH10B (Monk et al)[2], of nitrogen-fixing E. coli (strain WM1788) here.

What is flux balance analysis?

Flux balance analysis, or FBA, is the method by which we determine the flow of metabolites, or flux, through the constructed metabolic network of a GSM1. FBA allows us to predict growth rates of an organism under certain media conditions, along with the production levels of targeted metabolites, such as ATP.

E. Coli StrainMaximum BiomassMaximum ATP
K-12 MG1655.8212333.153125
WM1788 (Wild Type) .8212333.153125
WM1788 (Nitrogen-fixing).4545313.155221*

Sample FBA outputs for several E.coli strain models. Values are in mmol/(gram cell dry weight * hour)

*Note that the units for maximum ATP are tied to biomass; therefore the maximum ATP value for nitrogen fixing E. coli is actually much lower, not higher, than the wild type values.

Mass balance constraints are imposed on each metabolite using the stoichiometric coefficients of each metabolic reaction and the assumption that the organism is in the logarithmic growth phase (i.e. its metabolic fluxes are at steady state). This assumes that the total amount of any compound being produced is equal to the total amount being consumed. Upper and lower bounds are also applied to constrain the maximum fluxes based on the directionality of the reactions.

(from Orth et al)[1]

Linear programming is then used to identify the flux distribution throughout the model in order to maximize the flux through the biomass equation, subject to the previously defined constraints.

Our modeling hypothesis:

How can we use genome scale modeling and flux balance analysis to optimize nitrogenase activity in vivo?

The key limiting factors of the nitrogenase reaction are ATP and reduced flavodoxin. Therefore, our analyses focused on ways to either produce or provide more of these essential metabolites to the nitrogen fixing cell.

  • Looking for potential gene overexpressions which lead to increased production of intracellular reduced flavodoxin and ATP
  • Looking for potential gene knockouts which redistribute flux, decreasing ATP consumption or leading to increased production of reduced flavodoxin
  • Determining which supplemental metabolites lead to the largest increases in reduced flavodoxin and ATP production

Problem Formulations:

Where Sij is the stoichiometric coefficient for metabolite i in reaction j, vj,min and vj,max are the minimum and maximum flux values for reaction j, vj is the flux value of reaction j, N is the number of metabolites, and M is the number of reactions.

What we did The math behind it
Maximizing Biomass

In general, FBA can be formulated to maximize the biomass (growth) of an organism.

Maximize vbiomass

Subject to:
Coupling flavodoxin production to biomass production

With the goal of supplying the maximum amount of ATP and reduced flavodoxin to the nitrogenase reaction, a major part of our analysis involved performing all single and double gene knockouts in the model and iteratively retrieving FBA results for each. We aimed to find instances in which flavodoxin production was coupled to biomass.

Maximize vflavodoxin

Subject to:
Performing flux range analysis

While FBA only produces one optimal solution when multiple valid optima may exist, FVA (flux variability analysis) reveals the entire optimal solution space and provides flux ranges for each reaction in the model.3,4 Therefore, analyzing FVA results gives us insight into which metabolic pathways an organism is using, given constraints that we set.

Result: Pyruvate Metabolism

When we compared flux data for our wild type and nitrogen fixing WM1788 models, we found that pyruvate synthase had higher (more positive) flux ranges for the nitrogen fixing strain than for the wild type.

2 flavodoxin (semi-oxidized) + 1 pyruvate +1 coenzyme A ↔ 1 CO2 + 2 reduced flavodoxin + 1 H+ + 1 acetyl-coA

1 pyruvate + 1 coenzyme A + 1 NAD → 1 CO2 + 1 NADH + 1 acetyl-coA

1 pyruvate + 1 coenzyme A → 1 acetyl-co-A + 1 formate

Therefore, we determined that knocking out pyruvate dehydrogenase (see figure above) redistributed more flux through pyruvate synthase, increasing the positive effect and producing more reduced flavodoxin.

However, experimentally, pyruvate dehydrogenase deficiency in E. coli is associated with a buildup of pyruvate[5], which is then converted into lactic acid, and results in compromised cell activity. To bypass this effect, we proposed simultaneous overexpression of pyruvate synthase, which will favorably produce more reduced flavodoxin from excess pyruvate.

Metabolite Exchange Reactions

We wanted to determine if the addition of any one metabolite to cell media could help promote model growth or activity. We specifically looked into the effects on maximum biomass, ATP, and reduced flavodoxin. From a Max Biomass vs. Max ATP scatter plot we generated with our data, we were able to narrow our set of metabolites to 6 sugars, including maltotriose, maltotetraose, maltose, maltopentaose, maltohexaose, and maltoheptaose.

Based on our results, we believe that the addition of any one of these metabolites to lab media can aid cell activity by providing an additional source of energy.

Additional Work: Single and Double Gene Knockouts

When a gene is knocked out in a cell, a metabolic flux redistribution can result.

A wild type cell, with normal flux distribution.

Flux is redistributed in the mutant cell.

Thus, our goal in performing knockouts is to take advantage of flux redistributions, directing metabolic flux through pathways which produce more of the metabolites we desire. Optimally, we aim to couple metabolite production with biomass -- that is, in order to grow at all, the cell will need to produce more of the specified metabolite.

Nitrogen fixing E. coli is already ATP-limited (the cell has already redistributed flux as much as it can to produce the most ATP). Therefore, we focused most on looking for knockouts that couple reduced flavodoxin production to biomass.

The E. coli genome.[6]

By knocking out every gene in our model (there are 1367), as well as performing all non-essential double gene knockouts (a total of 1,236,544 possible combinations), we can comprehensively assess the effect any single or double gene knockout has on intracellular biomass, ATP, and flavodoxin production. Unfortunately, while we did discover knockouts where maximum flavodoxin increased due to compromised biomass, we did not find any instances of coupling between flavodoxin and biomass.

Our Python workflow for assessing single gene knockouts can be found below

  1. Create a list of all genes, constructed from the provided GPRs in the genome scale model.
  2. Create lists of reactions that will be deleted for each gene knockout. This is done by evaluating each reaction GPR for each gene. If a gene is essential to a given GPR, the reaction is added to the list of reactions which will be deleted for that knockout.
  3. Given a list of deleted reactions for each gene, FBA is run iteratively for each gene knockout. Running FBA will determine maximum biomass, max and min ATP values, and max and min flavodoxin values.
  4. The FBA results are collected and outputted for further analysis.


OptKnock outputs a list of potential reaction knockouts to couple a growth function with the production of a specified compound. We were specifically looking at knockouts that couple maximum biomass with reduced flavodoxin. After running potential double and triple reaction knockouts, however, we found that none of the proposed knockouts were coupled with reduced flavodoxin- i.e. the maximum biomass, ATP, and reduced flavodoxin levels were identical to our original nitrogen-fixing figures.

An example wild-type trade-off plot, using acetate production vs. biomass, with a point indicating the OptKnock suggested mutation.[7]

What can we learn in the future?

The remaining questions:

  • How can we search for new ways to couple reduced flavodoxin production to growth? Is it possible to do this?
    • Will require a reexamination of the reactions flavodoxin is involved in, their roles in metabolism, and the essentiality of parallel pathways.
  • How can we extend our analyses of supplemental metabolites, in order to optimize cell energy and growth?
    • A possible approach to this problem involves extending our analysis from simple metabolites to more complex cell media. Given a database of available media, or a way to create our own media, we could provide a comprehensive formula for lab use that is optimized to provide the most energy to the cell.


  1. Orth J.D., Thiele I., and Palsson, B.O. 2010. What is flux balance analysis? Nat. Biotechnol 28: 245-248.
  2. Monk, J. M., P. Charusanti, R. K. Aziz, J. A. Lerman, N. Premyodhin, J. D. Orth, A. M. Feist, and Palsson, B.O. 2013. Genome-scale metabolic reconstructions of multiple Escherichia coli strains highlight strain-specific adaptations to nutritional environments. Proc. Natl. Acad. Sci. USA 110: 20338–20343.
  3. Oberhardt, M.A., Palsson, B.O. and Papin, J.A. 2009. Applications of genome-scale metabolic reconstructions. Mol. Syst. Biol. 5: 320.
  4. Mahadevan, R., Schilling CH. 2003. The effects of alternate optimal solutions in constraint-based genome-scale metabolic models. Metabolic Engineering 5: 264-276.
  5. U.S. National Library of Medicine. Result Filters. National Center for Biotechnology Information. here
  6. E. Coli genomre
  7. Burgard, A.P., Pharkya, P., and Maranas, C.D. 2003. OptoKnock: A Bilevel Programming Framework for Identifying Single Gene Knockout Strategies for Microbial Strain Optimization. Biotechnol. Bioeng 84: 647-657.


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