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Prediction of metabolic flux distribution from gene expression data based on the flux minimization principle.

Song HS, Reifman J, Wallqvist A - PLoS ONE (2014)

Bottom Line: The proposed algorithm minimizes a weighted sum of flux magnitudes, while biomass production can be bounded to fit an ample range from very low to very high values according to the analyzed context.We have formulated the flux weights as a function of the corresponding enzyme reaction's gene expression value, enabling the creation of context-specific fluxes based on a generic metabolic network.In case studies of wild-type Saccharomyces cerevisiae, and wild-type and mutant Escherichia coli strains, our method achieved high prediction accuracy, as gauged by correlation coefficients and sums of squared error, with respect to the experimentally measured values.

View Article: PubMed Central - PubMed

Affiliation: Department of Defense Biotechnology High Performance Computing Software Applications Institute, Telemedicine and Advanced Technology Research Center, U.S. Army Medical Research and Materiel Command, Fort Detrick, Maryland, United States of America.

ABSTRACT
Prediction of possible flux distributions in a metabolic network provides detailed phenotypic information that links metabolism to cellular physiology. To estimate metabolic steady-state fluxes, the most common approach is to solve a set of macroscopic mass balance equations subjected to stoichiometric constraints while attempting to optimize an assumed optimal objective function. This assumption is justifiable in specific cases but may be invalid when tested across different conditions, cell populations, or other organisms. With an aim to providing a more consistent and reliable prediction of flux distributions over a wide range of conditions, in this article we propose a framework that uses the flux minimization principle to predict active metabolic pathways from mRNA expression data. The proposed algorithm minimizes a weighted sum of flux magnitudes, while biomass production can be bounded to fit an ample range from very low to very high values according to the analyzed context. We have formulated the flux weights as a function of the corresponding enzyme reaction's gene expression value, enabling the creation of context-specific fluxes based on a generic metabolic network. In case studies of wild-type Saccharomyces cerevisiae, and wild-type and mutant Escherichia coli strains, our method achieved high prediction accuracy, as gauged by correlation coefficients and sums of squared error, with respect to the experimentally measured values. In contrast to other approaches, our method was able to provide quantitative predictions for both model organisms under a variety of conditions. Our approach requires no prior knowledge or assumption of a context-specific metabolic functionality and does not require trial-and-error parameter adjustments. Thus, our framework is of general applicability for modeling the transcription-dependent metabolism of bacteria and yeasts.

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Toy example illustrating an implementation of the E-Fmin algorithm.The network model includes nine reactions (r1 to r9) but only five available stoichiometric constraints among the five intracellular metabolites under the steady-state assumption. E-Fmin determines the full flux vector for this undetermined system by solving a linear programming problem such that a weighted sum of flux magnitudes is minimized while biomass production (i.e., r9 in this example) carries nonzero flux. Given two sets of transcriptomic data, E-Fmin generates different flux distributions (denoted by thick arrows). The weight to the ith reaction (wi) is formulated as a decreasing function of the associated gene expression level (gi), i.e., wi = 1 – gi. The weights highlighted in red represent the reactions for which no associated gene expression data are available.
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pone-0112524-g002: Toy example illustrating an implementation of the E-Fmin algorithm.The network model includes nine reactions (r1 to r9) but only five available stoichiometric constraints among the five intracellular metabolites under the steady-state assumption. E-Fmin determines the full flux vector for this undetermined system by solving a linear programming problem such that a weighted sum of flux magnitudes is minimized while biomass production (i.e., r9 in this example) carries nonzero flux. Given two sets of transcriptomic data, E-Fmin generates different flux distributions (denoted by thick arrows). The weight to the ith reaction (wi) is formulated as a decreasing function of the associated gene expression level (gi), i.e., wi = 1 – gi. The weights highlighted in red represent the reactions for which no associated gene expression data are available.

Mentions: Figure 2 shows the application of E-Fmin to a toy metabolic network. The example network contains four major pathway options (P1 to P4) for converting substrate into product and biomass. Path P1 leads to product formation through reactions r1 and r2, whereas paths P2, P3, and P4 lead to biomass formation through reactions (r1, r3, and r9), (r1, r4, r5, and r9), and (r1, r6, r7, r8, and r9), respectively. This metabolic network is underdetermined, as it has nine unknown fluxes, r1 to r9, but only five available equations given by the stoichiometric matrix S in Figure 2. Thus, the determination of a particular flux distribution among infinite solutions requires either additional experimental flux measurements or application of a computational optimization method such as E-Fmin.


Prediction of metabolic flux distribution from gene expression data based on the flux minimization principle.

Song HS, Reifman J, Wallqvist A - PLoS ONE (2014)

Toy example illustrating an implementation of the E-Fmin algorithm.The network model includes nine reactions (r1 to r9) but only five available stoichiometric constraints among the five intracellular metabolites under the steady-state assumption. E-Fmin determines the full flux vector for this undetermined system by solving a linear programming problem such that a weighted sum of flux magnitudes is minimized while biomass production (i.e., r9 in this example) carries nonzero flux. Given two sets of transcriptomic data, E-Fmin generates different flux distributions (denoted by thick arrows). The weight to the ith reaction (wi) is formulated as a decreasing function of the associated gene expression level (gi), i.e., wi = 1 – gi. The weights highlighted in red represent the reactions for which no associated gene expression data are available.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4232356&req=5

pone-0112524-g002: Toy example illustrating an implementation of the E-Fmin algorithm.The network model includes nine reactions (r1 to r9) but only five available stoichiometric constraints among the five intracellular metabolites under the steady-state assumption. E-Fmin determines the full flux vector for this undetermined system by solving a linear programming problem such that a weighted sum of flux magnitudes is minimized while biomass production (i.e., r9 in this example) carries nonzero flux. Given two sets of transcriptomic data, E-Fmin generates different flux distributions (denoted by thick arrows). The weight to the ith reaction (wi) is formulated as a decreasing function of the associated gene expression level (gi), i.e., wi = 1 – gi. The weights highlighted in red represent the reactions for which no associated gene expression data are available.
Mentions: Figure 2 shows the application of E-Fmin to a toy metabolic network. The example network contains four major pathway options (P1 to P4) for converting substrate into product and biomass. Path P1 leads to product formation through reactions r1 and r2, whereas paths P2, P3, and P4 lead to biomass formation through reactions (r1, r3, and r9), (r1, r4, r5, and r9), and (r1, r6, r7, r8, and r9), respectively. This metabolic network is underdetermined, as it has nine unknown fluxes, r1 to r9, but only five available equations given by the stoichiometric matrix S in Figure 2. Thus, the determination of a particular flux distribution among infinite solutions requires either additional experimental flux measurements or application of a computational optimization method such as E-Fmin.

Bottom Line: The proposed algorithm minimizes a weighted sum of flux magnitudes, while biomass production can be bounded to fit an ample range from very low to very high values according to the analyzed context.We have formulated the flux weights as a function of the corresponding enzyme reaction's gene expression value, enabling the creation of context-specific fluxes based on a generic metabolic network.In case studies of wild-type Saccharomyces cerevisiae, and wild-type and mutant Escherichia coli strains, our method achieved high prediction accuracy, as gauged by correlation coefficients and sums of squared error, with respect to the experimentally measured values.

View Article: PubMed Central - PubMed

Affiliation: Department of Defense Biotechnology High Performance Computing Software Applications Institute, Telemedicine and Advanced Technology Research Center, U.S. Army Medical Research and Materiel Command, Fort Detrick, Maryland, United States of America.

ABSTRACT
Prediction of possible flux distributions in a metabolic network provides detailed phenotypic information that links metabolism to cellular physiology. To estimate metabolic steady-state fluxes, the most common approach is to solve a set of macroscopic mass balance equations subjected to stoichiometric constraints while attempting to optimize an assumed optimal objective function. This assumption is justifiable in specific cases but may be invalid when tested across different conditions, cell populations, or other organisms. With an aim to providing a more consistent and reliable prediction of flux distributions over a wide range of conditions, in this article we propose a framework that uses the flux minimization principle to predict active metabolic pathways from mRNA expression data. The proposed algorithm minimizes a weighted sum of flux magnitudes, while biomass production can be bounded to fit an ample range from very low to very high values according to the analyzed context. We have formulated the flux weights as a function of the corresponding enzyme reaction's gene expression value, enabling the creation of context-specific fluxes based on a generic metabolic network. In case studies of wild-type Saccharomyces cerevisiae, and wild-type and mutant Escherichia coli strains, our method achieved high prediction accuracy, as gauged by correlation coefficients and sums of squared error, with respect to the experimentally measured values. In contrast to other approaches, our method was able to provide quantitative predictions for both model organisms under a variety of conditions. Our approach requires no prior knowledge or assumption of a context-specific metabolic functionality and does not require trial-and-error parameter adjustments. Thus, our framework is of general applicability for modeling the transcription-dependent metabolism of bacteria and yeasts.

Show MeSH
Related in: MedlinePlus