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An objective function exploiting suboptimal solutions in metabolic networks.

Wintermute EH, Lieberman TD, Silver PA - BMC Syst Biol (2013)

Bottom Line: Near-optimal flux configurations within this region are considered equally plausible and not subject to further optimizing regulation.Consistent with relaxed regulation near optimality, we find that the size of the near-optimal region predicts flux variability under experimental perturbation.Accounting for suboptimal solutions can improve the predictive power of metabolic FBA models.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Systems Biology, Harvard Medical School, Boston, MA 02115, USA. ehwintermute@gmail.com.

ABSTRACT

Background: Flux Balance Analysis is a theoretically elegant, computationally efficient, genome-scale approach to predicting biochemical reaction fluxes. Yet FBA models exhibit persistent mathematical degeneracy that generally limits their predictive power.

Results: We propose a novel objective function for cellular metabolism that accounts for and exploits degeneracy in the metabolic network to improve flux predictions. In our model, regulation drives metabolism toward a region of flux space that allows nearly optimal growth. Metabolic mutants deviate minimally from this region, a function represented mathematically as a convex cone. Near-optimal flux configurations within this region are considered equally plausible and not subject to further optimizing regulation. Consistent with relaxed regulation near optimality, we find that the size of the near-optimal region predicts flux variability under experimental perturbation.

Conclusion: Accounting for suboptimal solutions can improve the predictive power of metabolic FBA models. Because fluctuations of enzyme and metabolite levels are inevitable, tolerance for suboptimality may support a functionally robust metabolic network.

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Increased TCA cycle predictions using PSEUDO are partially explained by decreased growth, organic secretion and PPP fluxes. (A) Carbon consumed as glucose may ultimately be converted into biomass, oxidized to CO2 or secreted as organic metabolites. For the zwf mutant, FBA predicts the most growth, MOMA predicts the most secretion and PSEUDO the most CO2 production. The molar flux is reported in units of mmol carbon gDW-1 hr-1. (B, C) Sensitivty analysis of growth and organic secretion with respect CO2 output. The WT model achieves optimal growth when CO2 output reaches 15 mmol gDW-1 hr-1. The FBA model of the zwf mutant attains 87% WT growth with a slightly higher optimal CO2 output. The MOMA model predicts a CO2 flux output for the zwf mutant similar to WT, with decreased growth and increased secretion. The PSEUDO objective identifies a wide range of CO2 output fluxes consistent with growth near 80% optimal. The high CO2 output selected by PSEUDO coincides with near-zero carbon secretion, similar to the WT. (D) PSEUDO predicts near-zero flux though the oxidative PPP in the zwf mutant, while both FBA and MOMA predict positive flux. Reducing oxidative PPP flux only marginally decreases growth (<1%) for FBA and MOMA predictions, while significantly increasing MOMA growth predictions. Growth is reported as percent WT. (E) Reducing PPP flux reduces organic secretion in the MOMA model, with no effect on secretion in other models. (F, G) Reduced PPP flux leads to increased glycolysis and TCA cycle fluxes. As the PPP flux approaches zero, the FBA, MOMA and WT predictions converge, suggesting this perturbation moves all three methods to PSEUDO-like solutions.
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Figure 5: Increased TCA cycle predictions using PSEUDO are partially explained by decreased growth, organic secretion and PPP fluxes. (A) Carbon consumed as glucose may ultimately be converted into biomass, oxidized to CO2 or secreted as organic metabolites. For the zwf mutant, FBA predicts the most growth, MOMA predicts the most secretion and PSEUDO the most CO2 production. The molar flux is reported in units of mmol carbon gDW-1 hr-1. (B, C) Sensitivty analysis of growth and organic secretion with respect CO2 output. The WT model achieves optimal growth when CO2 output reaches 15 mmol gDW-1 hr-1. The FBA model of the zwf mutant attains 87% WT growth with a slightly higher optimal CO2 output. The MOMA model predicts a CO2 flux output for the zwf mutant similar to WT, with decreased growth and increased secretion. The PSEUDO objective identifies a wide range of CO2 output fluxes consistent with growth near 80% optimal. The high CO2 output selected by PSEUDO coincides with near-zero carbon secretion, similar to the WT. (D) PSEUDO predicts near-zero flux though the oxidative PPP in the zwf mutant, while both FBA and MOMA predict positive flux. Reducing oxidative PPP flux only marginally decreases growth (<1%) for FBA and MOMA predictions, while significantly increasing MOMA growth predictions. Growth is reported as percent WT. (E) Reducing PPP flux reduces organic secretion in the MOMA model, with no effect on secretion in other models. (F, G) Reduced PPP flux leads to increased glycolysis and TCA cycle fluxes. As the PPP flux approaches zero, the FBA, MOMA and WT predictions converge, suggesting this perturbation moves all three methods to PSEUDO-like solutions.

Mentions: To understand why the PSEUDO objective function improves flux predictions for the TCA cycle, we chose to investigate central carbon metabolism in greater detail using the zwf mutant as a case study (Figure 5). Carbon consumed in the form of glucose may be converted to biomass, fully oxidized to CO2 or secreted as reduced organic metabolites. We reasoned that the metabolic strategy used to fulfill a given objective function would be reflected in the way carbon is partitioned among these three final forms.


An objective function exploiting suboptimal solutions in metabolic networks.

Wintermute EH, Lieberman TD, Silver PA - BMC Syst Biol (2013)

Increased TCA cycle predictions using PSEUDO are partially explained by decreased growth, organic secretion and PPP fluxes. (A) Carbon consumed as glucose may ultimately be converted into biomass, oxidized to CO2 or secreted as organic metabolites. For the zwf mutant, FBA predicts the most growth, MOMA predicts the most secretion and PSEUDO the most CO2 production. The molar flux is reported in units of mmol carbon gDW-1 hr-1. (B, C) Sensitivty analysis of growth and organic secretion with respect CO2 output. The WT model achieves optimal growth when CO2 output reaches 15 mmol gDW-1 hr-1. The FBA model of the zwf mutant attains 87% WT growth with a slightly higher optimal CO2 output. The MOMA model predicts a CO2 flux output for the zwf mutant similar to WT, with decreased growth and increased secretion. The PSEUDO objective identifies a wide range of CO2 output fluxes consistent with growth near 80% optimal. The high CO2 output selected by PSEUDO coincides with near-zero carbon secretion, similar to the WT. (D) PSEUDO predicts near-zero flux though the oxidative PPP in the zwf mutant, while both FBA and MOMA predict positive flux. Reducing oxidative PPP flux only marginally decreases growth (<1%) for FBA and MOMA predictions, while significantly increasing MOMA growth predictions. Growth is reported as percent WT. (E) Reducing PPP flux reduces organic secretion in the MOMA model, with no effect on secretion in other models. (F, G) Reduced PPP flux leads to increased glycolysis and TCA cycle fluxes. As the PPP flux approaches zero, the FBA, MOMA and WT predictions converge, suggesting this perturbation moves all three methods to PSEUDO-like solutions.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
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Figure 5: Increased TCA cycle predictions using PSEUDO are partially explained by decreased growth, organic secretion and PPP fluxes. (A) Carbon consumed as glucose may ultimately be converted into biomass, oxidized to CO2 or secreted as organic metabolites. For the zwf mutant, FBA predicts the most growth, MOMA predicts the most secretion and PSEUDO the most CO2 production. The molar flux is reported in units of mmol carbon gDW-1 hr-1. (B, C) Sensitivty analysis of growth and organic secretion with respect CO2 output. The WT model achieves optimal growth when CO2 output reaches 15 mmol gDW-1 hr-1. The FBA model of the zwf mutant attains 87% WT growth with a slightly higher optimal CO2 output. The MOMA model predicts a CO2 flux output for the zwf mutant similar to WT, with decreased growth and increased secretion. The PSEUDO objective identifies a wide range of CO2 output fluxes consistent with growth near 80% optimal. The high CO2 output selected by PSEUDO coincides with near-zero carbon secretion, similar to the WT. (D) PSEUDO predicts near-zero flux though the oxidative PPP in the zwf mutant, while both FBA and MOMA predict positive flux. Reducing oxidative PPP flux only marginally decreases growth (<1%) for FBA and MOMA predictions, while significantly increasing MOMA growth predictions. Growth is reported as percent WT. (E) Reducing PPP flux reduces organic secretion in the MOMA model, with no effect on secretion in other models. (F, G) Reduced PPP flux leads to increased glycolysis and TCA cycle fluxes. As the PPP flux approaches zero, the FBA, MOMA and WT predictions converge, suggesting this perturbation moves all three methods to PSEUDO-like solutions.
Mentions: To understand why the PSEUDO objective function improves flux predictions for the TCA cycle, we chose to investigate central carbon metabolism in greater detail using the zwf mutant as a case study (Figure 5). Carbon consumed in the form of glucose may be converted to biomass, fully oxidized to CO2 or secreted as reduced organic metabolites. We reasoned that the metabolic strategy used to fulfill a given objective function would be reflected in the way carbon is partitioned among these three final forms.

Bottom Line: Near-optimal flux configurations within this region are considered equally plausible and not subject to further optimizing regulation.Consistent with relaxed regulation near optimality, we find that the size of the near-optimal region predicts flux variability under experimental perturbation.Accounting for suboptimal solutions can improve the predictive power of metabolic FBA models.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Systems Biology, Harvard Medical School, Boston, MA 02115, USA. ehwintermute@gmail.com.

ABSTRACT

Background: Flux Balance Analysis is a theoretically elegant, computationally efficient, genome-scale approach to predicting biochemical reaction fluxes. Yet FBA models exhibit persistent mathematical degeneracy that generally limits their predictive power.

Results: We propose a novel objective function for cellular metabolism that accounts for and exploits degeneracy in the metabolic network to improve flux predictions. In our model, regulation drives metabolism toward a region of flux space that allows nearly optimal growth. Metabolic mutants deviate minimally from this region, a function represented mathematically as a convex cone. Near-optimal flux configurations within this region are considered equally plausible and not subject to further optimizing regulation. Consistent with relaxed regulation near optimality, we find that the size of the near-optimal region predicts flux variability under experimental perturbation.

Conclusion: Accounting for suboptimal solutions can improve the predictive power of metabolic FBA models. Because fluctuations of enzyme and metabolite levels are inevitable, tolerance for suboptimality may support a functionally robust metabolic network.

Show MeSH
Related in: MedlinePlus