Fig 1.
A futile cycle that consumes energy drawn from a cofactor pool (left) and an energy generating cycle (EGC) (right), which is thermodynamically impossible but occurs in some metabolic network models (figure extended from [12]).
We can convert the type-II pathways to type-III pathways by closing the cycles in the cofactor pools (dashed arrows).
Fig 2.
A simple (hypothetical) example of an energy generating cycle (EGC).
A symporter that exports a metabolite and a proton acts together with a transporter that takes the same metabolite up without a proton. A combination of both reactions builds up a proton gradient that can then be utilized to generate energy (e.g., via an ATP synthase).
Fig 3.
The majority of metabolic network reconstructions in two of the examined databases (ModelSEED and MetaNetX) contain erroneous internal EGCs that generate energy.
In contrast, most models in BiGG do not contain EGCs. Total bar size reflects the number of models contained in each database. Green: models without EGCs; purple: models with EGCs that could be corrected through GlobalFit; orange: models with EGCs that cannot be corrected through reaction removals.
Fig 4.
Most erroneous models can be corrected by making up to 5 originally reversible reactions irreversible.
Purple: histogram of the number of irreversible reactions removed in each model to eliminate EGCs. Orange: histogram of the number of reversible reactions made irreversible to eliminate EGCs.
Fig 5.
Removal of EGCs led to substantially reduced maximal biomass yield in most models.
Histogram of the ratio between maximal biomass production rate before and after EGC removal.
Fig 6.
Examples of EGCs found in published genome-scale models.
Green/red: metabolites; blue: reactions, linking substrates and products; orange: direction of the energy gradient utilized by the energy dissipation reaction. (A) The simplest identified cycle, which links a Na+/proton antiporter (exporting Na+ in exchange for a single proton) and a Malate/proton symporter (importing Malate together with two protons) via a Malate/Na+ symporter. (B) A cycle involving two antiporters and one symporter, driven by a transporter that translocates tartrate from the periplasm to the cytosol. (C) A NADH:menaquinone oxidoreductase, which translocates protons in the process of transferring electrons from NADH to Menaquinone 8, driven by a chain of four enzymes. (D) rxn00379 creates Adenosine 5'-phosphosulfate from ATP and sulfate. The equivalent sulfate adenyltransferase rxn09240 catalyzes the backward reaction, but charges a GTP in addition to the ATP.
Table 1.
Definitions of the variables used in the system of equations that describes the modified GlobalFit algorithm.