Limits...
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.

Show MeSH

Related in: MedlinePlus

PSEUDO growth predictions fall between FBA and MOMA. Predicted and measured yields are both normalized to a maximum of 1, corresponding to wild-type growth in these conditions. (A) Yields are plotted for 41 mutants for which growth predictions differ by more than 5% among the three methods. The diagonal line indicates equal predictions in PSEUDO and other methods. Note that MOMA predictions are consistently above the diagonal, and FBA consistently below. (B) Compared with measured growth rate data, PSEUDO growth predictions produce a rank correlation ρ of 0.63 with yield data, compared to 0.45 for the FBA method and 0.42 for MOMA. (C) PSEUDO predictions show no systematic bias. The error is the difference between prediction and measurement. The mean of the error distribution for PSEUDO was 0.06 with a 95% confidence interval of [0.13, -0.01] by bootstrap resampling. FBA predictions exceeded growth rates by 0.48 on average [0.39, 0.54]. The mean MOMA prediction error was -0.13 [-0.18, -0.08]. While the PSEUDO errors were unbiased, FBA and MOMA predictions were systematic over- and underestimates, respectively.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4016239&req=5

Figure 2: PSEUDO growth predictions fall between FBA and MOMA. Predicted and measured yields are both normalized to a maximum of 1, corresponding to wild-type growth in these conditions. (A) Yields are plotted for 41 mutants for which growth predictions differ by more than 5% among the three methods. The diagonal line indicates equal predictions in PSEUDO and other methods. Note that MOMA predictions are consistently above the diagonal, and FBA consistently below. (B) Compared with measured growth rate data, PSEUDO growth predictions produce a rank correlation ρ of 0.63 with yield data, compared to 0.45 for the FBA method and 0.42 for MOMA. (C) PSEUDO predictions show no systematic bias. The error is the difference between prediction and measurement. The mean of the error distribution for PSEUDO was 0.06 with a 95% confidence interval of [0.13, -0.01] by bootstrap resampling. FBA predictions exceeded growth rates by 0.48 on average [0.39, 0.54]. The mean MOMA prediction error was -0.13 [-0.18, -0.08]. While the PSEUDO errors were unbiased, FBA and MOMA predictions were systematic over- and underestimates, respectively.

Mentions: Genome-scale optimization methods have a well-established utility for predicting growth rates of mutant strains under a variety of conditions. We compared growth rate predictions using the PSEUDO method to predictions from the FBA and MOMA techniques, both of which are commonly used for this purpose [23]. Predictions were compared to growth rates of E. coli deletion mutants from the Keio collection in defined glucose medium [24]. We compiled data for 795 mutant strains that could be represented in our model and for which growth rate data was available. The results of this comparison are shown in Figure 2.


An objective function exploiting suboptimal solutions in metabolic networks.

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

PSEUDO growth predictions fall between FBA and MOMA. Predicted and measured yields are both normalized to a maximum of 1, corresponding to wild-type growth in these conditions. (A) Yields are plotted for 41 mutants for which growth predictions differ by more than 5% among the three methods. The diagonal line indicates equal predictions in PSEUDO and other methods. Note that MOMA predictions are consistently above the diagonal, and FBA consistently below. (B) Compared with measured growth rate data, PSEUDO growth predictions produce a rank correlation ρ of 0.63 with yield data, compared to 0.45 for the FBA method and 0.42 for MOMA. (C) PSEUDO predictions show no systematic bias. The error is the difference between prediction and measurement. The mean of the error distribution for PSEUDO was 0.06 with a 95% confidence interval of [0.13, -0.01] by bootstrap resampling. FBA predictions exceeded growth rates by 0.48 on average [0.39, 0.54]. The mean MOMA prediction error was -0.13 [-0.18, -0.08]. While the PSEUDO errors were unbiased, FBA and MOMA predictions were systematic over- and underestimates, respectively.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 2: PSEUDO growth predictions fall between FBA and MOMA. Predicted and measured yields are both normalized to a maximum of 1, corresponding to wild-type growth in these conditions. (A) Yields are plotted for 41 mutants for which growth predictions differ by more than 5% among the three methods. The diagonal line indicates equal predictions in PSEUDO and other methods. Note that MOMA predictions are consistently above the diagonal, and FBA consistently below. (B) Compared with measured growth rate data, PSEUDO growth predictions produce a rank correlation ρ of 0.63 with yield data, compared to 0.45 for the FBA method and 0.42 for MOMA. (C) PSEUDO predictions show no systematic bias. The error is the difference between prediction and measurement. The mean of the error distribution for PSEUDO was 0.06 with a 95% confidence interval of [0.13, -0.01] by bootstrap resampling. FBA predictions exceeded growth rates by 0.48 on average [0.39, 0.54]. The mean MOMA prediction error was -0.13 [-0.18, -0.08]. While the PSEUDO errors were unbiased, FBA and MOMA predictions were systematic over- and underestimates, respectively.
Mentions: Genome-scale optimization methods have a well-established utility for predicting growth rates of mutant strains under a variety of conditions. We compared growth rate predictions using the PSEUDO method to predictions from the FBA and MOMA techniques, both of which are commonly used for this purpose [23]. Predictions were compared to growth rates of E. coli deletion mutants from the Keio collection in defined glucose medium [24]. We compiled data for 795 mutant strains that could be represented in our model and for which growth rate data was available. The results of this comparison are shown in Figure 2.

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