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Estimating Metabolic Fluxes Using a Maximum Network Flexibility Paradigm.

Megchelenbrink W, Rossell S, Huynen MA, Notebaart RA, Marchiori E - PLoS ONE (2015)

Bottom Line: A small decrease in growth rate is exchanged for a relatively large gain in metabolic capability to adapt to changing environmental conditions.By mapping measured flux data from central metabolism to the genome-scale models of Escherichia coli and Saccharomyces cerevisiae we show that i) indeed, most of the measured fluxes agree with a high adaptability of the network, ii) this result can be used to further reduce the space of feasible solutions iii) this reduced space improves the quantitative predictions made by FBA and contains a significantly larger fraction of the measured fluxes compared to the flux space that was reduced by a uniform sampling approach and iv) MMF can be used to select reactions in the network that contribute most to the steady-state flux space.Our method can be applied to any cell type without requiring prior information.

View Article: PubMed Central - PubMed

Affiliation: Institute for Computing and Information Sciences (ICIS), Radboud University, Nijmegen, the Netherlands; Centre for Molecular and Biomolecular Informatics (CMBI), Radboud University Medical Centre, Nijmegen, the Netherlands; Centre for Systems Biology and Bioenergetics (CSBB), Radboud University Medical Centre, Nijmegen, the Netherlands.

ABSTRACT

Motivation: Genome-scale metabolic networks can be modeled in a constraint-based fashion. Reaction stoichiometry combined with flux capacity constraints determine the space of allowable reaction rates. This space is often large and a central challenge in metabolic modeling is finding the biologically most relevant flux distributions. A widely used method is flux balance analysis (FBA), which optimizes a biologically relevant objective such as growth or ATP production. Although FBA has proven to be highly useful for predicting growth and byproduct secretion, it cannot predict the intracellular fluxes under all environmental conditions. Therefore, alternative strategies have been developed to select flux distributions that are in agreement with experimental "omics" data, or by incorporating experimental flux measurements. The latter, unfortunately can only be applied to a limited set of reactions and is currently not feasible at the genome-scale. On the other hand, it has been observed that micro-organisms favor a suboptimal growth rate, possibly in exchange for a more "flexible" metabolic network. Instead of dedicating the internal network state to an optimal growth rate in one condition, a suboptimal growth rate is used, that allows for an easier switch to other nutrient sources. A small decrease in growth rate is exchanged for a relatively large gain in metabolic capability to adapt to changing environmental conditions.

Results: Here, we propose Maximum Metabolic Flexibility (MMF) a computational method that utilizes this observation to find the most probable intracellular flux distributions. By mapping measured flux data from central metabolism to the genome-scale models of Escherichia coli and Saccharomyces cerevisiae we show that i) indeed, most of the measured fluxes agree with a high adaptability of the network, ii) this result can be used to further reduce the space of feasible solutions iii) this reduced space improves the quantitative predictions made by FBA and contains a significantly larger fraction of the measured fluxes compared to the flux space that was reduced by a uniform sampling approach and iv) MMF can be used to select reactions in the network that contribute most to the steady-state flux space. Constraining the selected reactions improves the quantitative predictions of FBA considerably more than adding an equal amount of flux constraints, selected using a more naïve approach. Our method can be applied to any cell type without requiring prior information.

Availability: MMF is freely available as a MATLAB plugin at: http://cs.ru.nl/~wmegchel/mmf.

No MeSH data available.


Related in: MedlinePlus

TFR reduction and pFBA improvement of MMF compared to random and “MaxSpan” selection on the S. cerevisiae iMM904 model (high oxygen).(A) The MMF method selects flux measurements that provide a larger reduction of the flux ranges compared to the MaxSpan or random measurements. (B) Fluxes predicted by pFBA obtain the smallest errors when the reactions selected by MMF are measured.
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pone.0139665.g005: TFR reduction and pFBA improvement of MMF compared to random and “MaxSpan” selection on the S. cerevisiae iMM904 model (high oxygen).(A) The MMF method selects flux measurements that provide a larger reduction of the flux ranges compared to the MaxSpan or random measurements. (B) Fluxes predicted by pFBA obtain the smallest errors when the reactions selected by MMF are measured.

Mentions: As a proof of concept, we looked specifically for reduction of the flux ranges for reactions inside central metabolism. Since flux data for other pathways was not available, little reduction can be expected within these pathways. Fig 5a shows that indeed, the flux ranges in the S. cerevisiae model are reduced faster when reactions selected by MMF are constrained with measured fluxes compared to the other methods (for all models and scenarios see S4 File). Fig 5b shows that, as expected, the larger reduction obtained after measurement of these reactions also results in better prediction of the fluxes by pFBA (see S5 File for all models and scenarios). Notice that although the TFR decreases with each flux measurement, this does not guarantee a better prediction of pFBA. The reason that the error can increase is that the additional constraint causes pFBA to perform a major flux rerouting, which is actually a worse estimate than the flux routing before imposing the extra constraint. Fig 6 illustrates this behavior for a subset of the reactions from the genome-scale model of S. cerevisiae (those residing in central metabolism). Some reactions in the glycolysis pathway have a large flux range and pFBA actually underestimates the flux through these reactions (Fig 6a). MMF selects the reaction G3P -> PEP for measurement. Due to the increased flux through glycolysis, more pyruvate enters the mitochondria. Apparently, the minimal sum of fluxes constraint drives a large portion of the flux through a shortcut which converts citrate into malate. As a consequence, reactions in the right part of the TCA cycle have underestimated rates and the fluxes in the left part are overestimated. A second measurement constrains the flux from succinyl-coa to succinate, which results in a much more accurate prediction.


Estimating Metabolic Fluxes Using a Maximum Network Flexibility Paradigm.

Megchelenbrink W, Rossell S, Huynen MA, Notebaart RA, Marchiori E - PLoS ONE (2015)

TFR reduction and pFBA improvement of MMF compared to random and “MaxSpan” selection on the S. cerevisiae iMM904 model (high oxygen).(A) The MMF method selects flux measurements that provide a larger reduction of the flux ranges compared to the MaxSpan or random measurements. (B) Fluxes predicted by pFBA obtain the smallest errors when the reactions selected by MMF are measured.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4601694&req=5

pone.0139665.g005: TFR reduction and pFBA improvement of MMF compared to random and “MaxSpan” selection on the S. cerevisiae iMM904 model (high oxygen).(A) The MMF method selects flux measurements that provide a larger reduction of the flux ranges compared to the MaxSpan or random measurements. (B) Fluxes predicted by pFBA obtain the smallest errors when the reactions selected by MMF are measured.
Mentions: As a proof of concept, we looked specifically for reduction of the flux ranges for reactions inside central metabolism. Since flux data for other pathways was not available, little reduction can be expected within these pathways. Fig 5a shows that indeed, the flux ranges in the S. cerevisiae model are reduced faster when reactions selected by MMF are constrained with measured fluxes compared to the other methods (for all models and scenarios see S4 File). Fig 5b shows that, as expected, the larger reduction obtained after measurement of these reactions also results in better prediction of the fluxes by pFBA (see S5 File for all models and scenarios). Notice that although the TFR decreases with each flux measurement, this does not guarantee a better prediction of pFBA. The reason that the error can increase is that the additional constraint causes pFBA to perform a major flux rerouting, which is actually a worse estimate than the flux routing before imposing the extra constraint. Fig 6 illustrates this behavior for a subset of the reactions from the genome-scale model of S. cerevisiae (those residing in central metabolism). Some reactions in the glycolysis pathway have a large flux range and pFBA actually underestimates the flux through these reactions (Fig 6a). MMF selects the reaction G3P -> PEP for measurement. Due to the increased flux through glycolysis, more pyruvate enters the mitochondria. Apparently, the minimal sum of fluxes constraint drives a large portion of the flux through a shortcut which converts citrate into malate. As a consequence, reactions in the right part of the TCA cycle have underestimated rates and the fluxes in the left part are overestimated. A second measurement constrains the flux from succinyl-coa to succinate, which results in a much more accurate prediction.

Bottom Line: A small decrease in growth rate is exchanged for a relatively large gain in metabolic capability to adapt to changing environmental conditions.By mapping measured flux data from central metabolism to the genome-scale models of Escherichia coli and Saccharomyces cerevisiae we show that i) indeed, most of the measured fluxes agree with a high adaptability of the network, ii) this result can be used to further reduce the space of feasible solutions iii) this reduced space improves the quantitative predictions made by FBA and contains a significantly larger fraction of the measured fluxes compared to the flux space that was reduced by a uniform sampling approach and iv) MMF can be used to select reactions in the network that contribute most to the steady-state flux space.Our method can be applied to any cell type without requiring prior information.

View Article: PubMed Central - PubMed

Affiliation: Institute for Computing and Information Sciences (ICIS), Radboud University, Nijmegen, the Netherlands; Centre for Molecular and Biomolecular Informatics (CMBI), Radboud University Medical Centre, Nijmegen, the Netherlands; Centre for Systems Biology and Bioenergetics (CSBB), Radboud University Medical Centre, Nijmegen, the Netherlands.

ABSTRACT

Motivation: Genome-scale metabolic networks can be modeled in a constraint-based fashion. Reaction stoichiometry combined with flux capacity constraints determine the space of allowable reaction rates. This space is often large and a central challenge in metabolic modeling is finding the biologically most relevant flux distributions. A widely used method is flux balance analysis (FBA), which optimizes a biologically relevant objective such as growth or ATP production. Although FBA has proven to be highly useful for predicting growth and byproduct secretion, it cannot predict the intracellular fluxes under all environmental conditions. Therefore, alternative strategies have been developed to select flux distributions that are in agreement with experimental "omics" data, or by incorporating experimental flux measurements. The latter, unfortunately can only be applied to a limited set of reactions and is currently not feasible at the genome-scale. On the other hand, it has been observed that micro-organisms favor a suboptimal growth rate, possibly in exchange for a more "flexible" metabolic network. Instead of dedicating the internal network state to an optimal growth rate in one condition, a suboptimal growth rate is used, that allows for an easier switch to other nutrient sources. A small decrease in growth rate is exchanged for a relatively large gain in metabolic capability to adapt to changing environmental conditions.

Results: Here, we propose Maximum Metabolic Flexibility (MMF) a computational method that utilizes this observation to find the most probable intracellular flux distributions. By mapping measured flux data from central metabolism to the genome-scale models of Escherichia coli and Saccharomyces cerevisiae we show that i) indeed, most of the measured fluxes agree with a high adaptability of the network, ii) this result can be used to further reduce the space of feasible solutions iii) this reduced space improves the quantitative predictions made by FBA and contains a significantly larger fraction of the measured fluxes compared to the flux space that was reduced by a uniform sampling approach and iv) MMF can be used to select reactions in the network that contribute most to the steady-state flux space. Constraining the selected reactions improves the quantitative predictions of FBA considerably more than adding an equal amount of flux constraints, selected using a more naïve approach. Our method can be applied to any cell type without requiring prior information.

Availability: MMF is freely available as a MATLAB plugin at: http://cs.ru.nl/~wmegchel/mmf.

No MeSH data available.


Related in: MedlinePlus