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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

PSEUDO predictions as a function of the near-optimal growth threshold. Values derived using PSEUDO (black) are compared to values derived from FBA (red) and MOMA (blue). The PSEUDO method accepts a growth threshold input parameter that has no analogy in the other methods. This threshold defines a near-optimal flux space, and mutant flux profiles are determined that minimize the distance to this space. Biologically, this growth threshold could be interpreted as a region of relaxed regulation, within which selection for increased growth is balanced by other metabolic demands or by noise. The growth threshold parameter was allowed to vary from 80% to 99% WT maximal growth. (A, B) Pearson and Spearman correlation coefficients as a function of the near-optimal growth threshold. PSEUDO predictions reached a maximum using a growth threshold of 90%, but were generally robust to parameter variation. Error bars represent one standard error of the mean, calculated with Fisher's z transformation. (C, D, E, F) Mean flux prediction errors from each of the three methods as a function of the growth threshold parameter. Errors were calculated for all 320 fluxes curated from the Tomita data set, and for subsets of reactions belonging to glycolysis, the PPP, or the TCA cycle. Flux errors were generally insensitive to the chosen threshold. TCA cycle fluxes were both the most error-prone, and the most improved by PSEUDO. Error bars represent one standard error of the mean.
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Figure 6: PSEUDO predictions as a function of the near-optimal growth threshold. Values derived using PSEUDO (black) are compared to values derived from FBA (red) and MOMA (blue). The PSEUDO method accepts a growth threshold input parameter that has no analogy in the other methods. This threshold defines a near-optimal flux space, and mutant flux profiles are determined that minimize the distance to this space. Biologically, this growth threshold could be interpreted as a region of relaxed regulation, within which selection for increased growth is balanced by other metabolic demands or by noise. The growth threshold parameter was allowed to vary from 80% to 99% WT maximal growth. (A, B) Pearson and Spearman correlation coefficients as a function of the near-optimal growth threshold. PSEUDO predictions reached a maximum using a growth threshold of 90%, but were generally robust to parameter variation. Error bars represent one standard error of the mean, calculated with Fisher's z transformation. (C, D, E, F) Mean flux prediction errors from each of the three methods as a function of the growth threshold parameter. Errors were calculated for all 320 fluxes curated from the Tomita data set, and for subsets of reactions belonging to glycolysis, the PPP, or the TCA cycle. Flux errors were generally insensitive to the chosen threshold. TCA cycle fluxes were both the most error-prone, and the most improved by PSEUDO. Error bars represent one standard error of the mean.

Mentions: We found that PSEUDO predictions were remarkably stable as the near-optimal growth threshold was varied from 80-99%, as shown in Figure 6. Both Pearson and Spearman correlation values for PSEUDO predictions reached a maximum with the growth threshold set to 90%, and declined as near-optimal growth converged to maximum theoretical growth (Figure 6AB). We observed no qualitative differences in model behavior across this parameter range (Figure 6CDEF). This behavior is consistent with the convex shape of flux space. In a convex space, variability tends to increase rapidly for small deviations from optimality, then decelerate and plateau at moderate deviations [30-32]. Robustness with respect to the selected threshold is an important feature of the PSEUDO model, as this parameter may be difficult to measure in practice.


An objective function exploiting suboptimal solutions in metabolic networks.

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

PSEUDO predictions as a function of the near-optimal growth threshold. Values derived using PSEUDO (black) are compared to values derived from FBA (red) and MOMA (blue). The PSEUDO method accepts a growth threshold input parameter that has no analogy in the other methods. This threshold defines a near-optimal flux space, and mutant flux profiles are determined that minimize the distance to this space. Biologically, this growth threshold could be interpreted as a region of relaxed regulation, within which selection for increased growth is balanced by other metabolic demands or by noise. The growth threshold parameter was allowed to vary from 80% to 99% WT maximal growth. (A, B) Pearson and Spearman correlation coefficients as a function of the near-optimal growth threshold. PSEUDO predictions reached a maximum using a growth threshold of 90%, but were generally robust to parameter variation. Error bars represent one standard error of the mean, calculated with Fisher's z transformation. (C, D, E, F) Mean flux prediction errors from each of the three methods as a function of the growth threshold parameter. Errors were calculated for all 320 fluxes curated from the Tomita data set, and for subsets of reactions belonging to glycolysis, the PPP, or the TCA cycle. Flux errors were generally insensitive to the chosen threshold. TCA cycle fluxes were both the most error-prone, and the most improved by PSEUDO. Error bars represent one standard error of the mean.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 6: PSEUDO predictions as a function of the near-optimal growth threshold. Values derived using PSEUDO (black) are compared to values derived from FBA (red) and MOMA (blue). The PSEUDO method accepts a growth threshold input parameter that has no analogy in the other methods. This threshold defines a near-optimal flux space, and mutant flux profiles are determined that minimize the distance to this space. Biologically, this growth threshold could be interpreted as a region of relaxed regulation, within which selection for increased growth is balanced by other metabolic demands or by noise. The growth threshold parameter was allowed to vary from 80% to 99% WT maximal growth. (A, B) Pearson and Spearman correlation coefficients as a function of the near-optimal growth threshold. PSEUDO predictions reached a maximum using a growth threshold of 90%, but were generally robust to parameter variation. Error bars represent one standard error of the mean, calculated with Fisher's z transformation. (C, D, E, F) Mean flux prediction errors from each of the three methods as a function of the growth threshold parameter. Errors were calculated for all 320 fluxes curated from the Tomita data set, and for subsets of reactions belonging to glycolysis, the PPP, or the TCA cycle. Flux errors were generally insensitive to the chosen threshold. TCA cycle fluxes were both the most error-prone, and the most improved by PSEUDO. Error bars represent one standard error of the mean.
Mentions: We found that PSEUDO predictions were remarkably stable as the near-optimal growth threshold was varied from 80-99%, as shown in Figure 6. Both Pearson and Spearman correlation values for PSEUDO predictions reached a maximum with the growth threshold set to 90%, and declined as near-optimal growth converged to maximum theoretical growth (Figure 6AB). We observed no qualitative differences in model behavior across this parameter range (Figure 6CDEF). This behavior is consistent with the convex shape of flux space. In a convex space, variability tends to increase rapidly for small deviations from optimality, then decelerate and plateau at moderate deviations [30-32]. Robustness with respect to the selected threshold is an important feature of the PSEUDO model, as this parameter may be difficult to measure in practice.

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