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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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Related in: MedlinePlus

A cloud theory for metabolic regulation. The PSEUDO method hypothesizes the existence of a degenerate optimal region. Fluxes are regulated to approach this region, but allowed to vary freely within it. (A) Variability of fluxes within the degenerate optimal region. As described in the methods, we used Markov chain Monte Carlo sampling to produce 3000 randomly distributed fluxes, each consistent with at least 99% maximal growth. 3 specific fluxes are plotted on these axes, colored to emphasize their value in each dimension. Red, green and blue content corresponds to value in x, y and z respectively. Histograms present overall distributions of individual fluxes. (B) Variation in measured values for 24 fluxes across 91 transcription factor deletion mutants from the Sauer data set. Measured data is plotted similarly to the Monte Carlo generated data. (C, D) Computationally estimated flux variability within the degenerate optimal region correlates well with measured variability in both the Sauer (C) and Tomita (D) data sets. The coefficient of variation (CV) of the distributions is a normalized expression of both measured and predicted flux variability. Marker shapes are used to indicate the metabolic class of each flux. Metabolic fluxes that are only weakly coupled to biomass production can vary widely within the degenerate optimal region. The same fluxes are more likely to vary in under perturbation in published data sets.
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Figure 7: A cloud theory for metabolic regulation. The PSEUDO method hypothesizes the existence of a degenerate optimal region. Fluxes are regulated to approach this region, but allowed to vary freely within it. (A) Variability of fluxes within the degenerate optimal region. As described in the methods, we used Markov chain Monte Carlo sampling to produce 3000 randomly distributed fluxes, each consistent with at least 99% maximal growth. 3 specific fluxes are plotted on these axes, colored to emphasize their value in each dimension. Red, green and blue content corresponds to value in x, y and z respectively. Histograms present overall distributions of individual fluxes. (B) Variation in measured values for 24 fluxes across 91 transcription factor deletion mutants from the Sauer data set. Measured data is plotted similarly to the Monte Carlo generated data. (C, D) Computationally estimated flux variability within the degenerate optimal region correlates well with measured variability in both the Sauer (C) and Tomita (D) data sets. The coefficient of variation (CV) of the distributions is a normalized expression of both measured and predicted flux variability. Marker shapes are used to indicate the metabolic class of each flux. Metabolic fluxes that are only weakly coupled to biomass production can vary widely within the degenerate optimal region. The same fluxes are more likely to vary in under perturbation in published data sets.

Mentions: Figure 7 compares our measures of theoretical and observed variation. For each flux in our data set, we compared the coefficient of variation (CV) derived from computational Monte Carlo sampling (Figure 7A) to the CV from published measurements (Figure 7B). Measured variability in both data sets was well matched by theoretical variability within the degenerate optimal region (Figure 7CD). The Sauer flux measurements produced a rank correlation of 0.72 (p-value: 6.7·10-5). For the Tomita data, Spearman's ρ was 0.87, (p-value: 5.6·10-9). Exact values for the estimated and measured variability of each flux are reported in Additional file 4: Table S2. The observed correlation between predicted degeneracy and measured variation supports a model in which metabolism may adopt many possible flux configurations without compromising growth rate.


An objective function exploiting suboptimal solutions in metabolic networks.

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

A cloud theory for metabolic regulation. The PSEUDO method hypothesizes the existence of a degenerate optimal region. Fluxes are regulated to approach this region, but allowed to vary freely within it. (A) Variability of fluxes within the degenerate optimal region. As described in the methods, we used Markov chain Monte Carlo sampling to produce 3000 randomly distributed fluxes, each consistent with at least 99% maximal growth. 3 specific fluxes are plotted on these axes, colored to emphasize their value in each dimension. Red, green and blue content corresponds to value in x, y and z respectively. Histograms present overall distributions of individual fluxes. (B) Variation in measured values for 24 fluxes across 91 transcription factor deletion mutants from the Sauer data set. Measured data is plotted similarly to the Monte Carlo generated data. (C, D) Computationally estimated flux variability within the degenerate optimal region correlates well with measured variability in both the Sauer (C) and Tomita (D) data sets. The coefficient of variation (CV) of the distributions is a normalized expression of both measured and predicted flux variability. Marker shapes are used to indicate the metabolic class of each flux. Metabolic fluxes that are only weakly coupled to biomass production can vary widely within the degenerate optimal region. The same fluxes are more likely to vary in under perturbation in published data sets.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4016239&req=5

Figure 7: A cloud theory for metabolic regulation. The PSEUDO method hypothesizes the existence of a degenerate optimal region. Fluxes are regulated to approach this region, but allowed to vary freely within it. (A) Variability of fluxes within the degenerate optimal region. As described in the methods, we used Markov chain Monte Carlo sampling to produce 3000 randomly distributed fluxes, each consistent with at least 99% maximal growth. 3 specific fluxes are plotted on these axes, colored to emphasize their value in each dimension. Red, green and blue content corresponds to value in x, y and z respectively. Histograms present overall distributions of individual fluxes. (B) Variation in measured values for 24 fluxes across 91 transcription factor deletion mutants from the Sauer data set. Measured data is plotted similarly to the Monte Carlo generated data. (C, D) Computationally estimated flux variability within the degenerate optimal region correlates well with measured variability in both the Sauer (C) and Tomita (D) data sets. The coefficient of variation (CV) of the distributions is a normalized expression of both measured and predicted flux variability. Marker shapes are used to indicate the metabolic class of each flux. Metabolic fluxes that are only weakly coupled to biomass production can vary widely within the degenerate optimal region. The same fluxes are more likely to vary in under perturbation in published data sets.
Mentions: Figure 7 compares our measures of theoretical and observed variation. For each flux in our data set, we compared the coefficient of variation (CV) derived from computational Monte Carlo sampling (Figure 7A) to the CV from published measurements (Figure 7B). Measured variability in both data sets was well matched by theoretical variability within the degenerate optimal region (Figure 7CD). The Sauer flux measurements produced a rank correlation of 0.72 (p-value: 6.7·10-5). For the Tomita data, Spearman's ρ was 0.87, (p-value: 5.6·10-9). Exact values for the estimated and measured variability of each flux are reported in Additional file 4: Table S2. The observed correlation between predicted degeneracy and measured variation supports a model in which metabolism may adopt many possible flux configurations without compromising growth rate.

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