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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

FBA, MOMA and PSEUDO approaches to predicting metabolic fluxes. (A) In FBA wild-type flux space is constrained to a polytope defined by thermodynamic and conservation-of-mass requirements. A linear objective describing cell growth, the green arrow, is maximized within this region. If the growth vector is perpendicular to a facet of the constrained polytope then a range of fluxes allow equally optimum growth, indicated by the heavy green edge. However, a linear programming solver can return only a single optimal point, the green target. (B) Mutations are represented as additional linear constraints that reduce the size of the allowed flux polytope. The yellow region represents the subset of wild-type fluxes allowed under a mutation. FBA finds a new optimum within this space as for the wild type. The green face represents a range of equally optimal mutant solutions. The blue target is a single point that a solver might return. (C) MOMA is an alternative approach for predicting mutant fluxes. The point in the mutant region, blue target, is found that minimizes the distance to a wild-type solution, green target. If FBA was used to generate the wild-type solution, then alternative optima may exist along the heavy green edge. (D) The PSEUDO strategy does not use FBA to select a wild-type flux vector. Instead we define a degenerate optimal region that contains all flux distributions capable of supporting near-maximal growth. A solution within the mutant region is found with minimum distance to this degenerate optimal region. Note that PSEUDO may select a point in mutant flux space different from the MOMA solution and closer to the growth-optimal region.
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Figure 1: FBA, MOMA and PSEUDO approaches to predicting metabolic fluxes. (A) In FBA wild-type flux space is constrained to a polytope defined by thermodynamic and conservation-of-mass requirements. A linear objective describing cell growth, the green arrow, is maximized within this region. If the growth vector is perpendicular to a facet of the constrained polytope then a range of fluxes allow equally optimum growth, indicated by the heavy green edge. However, a linear programming solver can return only a single optimal point, the green target. (B) Mutations are represented as additional linear constraints that reduce the size of the allowed flux polytope. The yellow region represents the subset of wild-type fluxes allowed under a mutation. FBA finds a new optimum within this space as for the wild type. The green face represents a range of equally optimal mutant solutions. The blue target is a single point that a solver might return. (C) MOMA is an alternative approach for predicting mutant fluxes. The point in the mutant region, blue target, is found that minimizes the distance to a wild-type solution, green target. If FBA was used to generate the wild-type solution, then alternative optima may exist along the heavy green edge. (D) The PSEUDO strategy does not use FBA to select a wild-type flux vector. Instead we define a degenerate optimal region that contains all flux distributions capable of supporting near-maximal growth. A solution within the mutant region is found with minimum distance to this degenerate optimal region. Note that PSEUDO may select a point in mutant flux space different from the MOMA solution and closer to the growth-optimal region.

Mentions: FigureĀ 1 presents a geometric interpretation of the commonly used FBA and MOMA objective functions, contrasting them with the PSEUDO objective that we will describe below.


An objective function exploiting suboptimal solutions in metabolic networks.

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

FBA, MOMA and PSEUDO approaches to predicting metabolic fluxes. (A) In FBA wild-type flux space is constrained to a polytope defined by thermodynamic and conservation-of-mass requirements. A linear objective describing cell growth, the green arrow, is maximized within this region. If the growth vector is perpendicular to a facet of the constrained polytope then a range of fluxes allow equally optimum growth, indicated by the heavy green edge. However, a linear programming solver can return only a single optimal point, the green target. (B) Mutations are represented as additional linear constraints that reduce the size of the allowed flux polytope. The yellow region represents the subset of wild-type fluxes allowed under a mutation. FBA finds a new optimum within this space as for the wild type. The green face represents a range of equally optimal mutant solutions. The blue target is a single point that a solver might return. (C) MOMA is an alternative approach for predicting mutant fluxes. The point in the mutant region, blue target, is found that minimizes the distance to a wild-type solution, green target. If FBA was used to generate the wild-type solution, then alternative optima may exist along the heavy green edge. (D) The PSEUDO strategy does not use FBA to select a wild-type flux vector. Instead we define a degenerate optimal region that contains all flux distributions capable of supporting near-maximal growth. A solution within the mutant region is found with minimum distance to this degenerate optimal region. Note that PSEUDO may select a point in mutant flux space different from the MOMA solution and closer to the growth-optimal region.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: FBA, MOMA and PSEUDO approaches to predicting metabolic fluxes. (A) In FBA wild-type flux space is constrained to a polytope defined by thermodynamic and conservation-of-mass requirements. A linear objective describing cell growth, the green arrow, is maximized within this region. If the growth vector is perpendicular to a facet of the constrained polytope then a range of fluxes allow equally optimum growth, indicated by the heavy green edge. However, a linear programming solver can return only a single optimal point, the green target. (B) Mutations are represented as additional linear constraints that reduce the size of the allowed flux polytope. The yellow region represents the subset of wild-type fluxes allowed under a mutation. FBA finds a new optimum within this space as for the wild type. The green face represents a range of equally optimal mutant solutions. The blue target is a single point that a solver might return. (C) MOMA is an alternative approach for predicting mutant fluxes. The point in the mutant region, blue target, is found that minimizes the distance to a wild-type solution, green target. If FBA was used to generate the wild-type solution, then alternative optima may exist along the heavy green edge. (D) The PSEUDO strategy does not use FBA to select a wild-type flux vector. Instead we define a degenerate optimal region that contains all flux distributions capable of supporting near-maximal growth. A solution within the mutant region is found with minimum distance to this degenerate optimal region. Note that PSEUDO may select a point in mutant flux space different from the MOMA solution and closer to the growth-optimal region.
Mentions: FigureĀ 1 presents a geometric interpretation of the commonly used FBA and MOMA objective functions, contrasting them with the PSEUDO objective that we will describe below.

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