| DOI:10.1371/journal.pone.0151722 March 18,11 /Multiscale Metabolic Modeling of C4 PlantsFig 6. Comparison of RNA-seq data to predicted fluxes for a linear pathway and around a metabolic branch point. Upper panels, chlorophyllide a synthesis in the mesophyll; lower panels, production of arogenate in the bundle sheath by prephenate transaminase and its consumption by arogenate dehydrogenase and arogenate dehydratase. Left, aggregate RNA-seq data and experimental standard deviations for each reaction rescaled by a uniform factor (see text). Right, same data and errors further rescaled by reaction-specific optimal factors (e-si, in the variables of Eq 3) to best match data with predicted fluxes (solid circles). Fluxes are equal for all MK-8742MedChemExpress MK-8742 reactions of the linear pathway (1, uroporphyrinogen decarboxylase, 2, coproporphyrinogen oxidase, 3, protoporphyrinogen oxidase, 4, magnesium chelatase, 5, magnesium protoporphyrin IX methyltransferase, 6, magnesium protoporphyrin IX monomethyl ester cyclase, 7, divinyl chlorophyllide a 8-vinyl-reductase, 8, protochlorophyllide reductase.) Error bars represent standard deviations of expression measurements across multiple replicates. doi:10.1371/journal.pone.0151722.gwith data from the same experimental system [40], as well as from the different catalytic capabilities of different enzymes, posttranslational regulation, differences in substrate availability, etc. Reconciling expression data and network structure. Fig 6 illustrates the operation of the fitting algorithm in detail, using two regions of the metabolic network with simple structure as examples. In Fig 6a, expression data for eight reactions of the pathway leading to chlorophyllide a are shown. Expression levels fpsyg.2016.01448 for the different reactions at any point on the leaf may span an order of magnitude or more, but the FBA steady-state assumption requires the rates of all reactions in this unbranched pathway to be equal at each point. (The branch leading to heme productionPLOS ONE | DOI:10.1371/journal.pone.0151722 March 18,12 /Multiscale Metabolic Modeling of C4 Plantsis not included in the reconstruction.) Applying the optimal rescaling determined for each reaction’s expression data, shown in panel b, allows the flux prediction for the pathway (solid dots) to achieve reasonable agreement with the data. (Note that data for reaction 4 cannot be further scaled down because of the lower limit exp(-5) on its scale factor exp(s4), imposed for technical reasons.) Fig 6c shows data for a three-reaction branch point in aromatic amino acid synthesis. To balance production and consumption of arogenate, the prephenate transaminase flux must equal the sum of the fluxes through arogenate dehydrogenase (to tyrosine) and arogenate dehydratase (to phenylalanine) but expression is consistently lower for the transaminase than the other enzymes. After rescaling (Fig 6d), the data agree fnhum.2013.00596 well with the stoichiometrically consistent flux predictions (solid dots). The predicted ratio of dehydrogenase to dehydratase flux reflects data for downstream reactions. Comparison to other methods for integrating RNA-seq data. S4 Fig shows predictions that result when the scale factors si of Eq (3) are fixed to zero. The source-sink transition is apparent but the C4 cycle operates at lower levels, the example pathways of Fig 6 (and a number of others) show little or no activity, and predicted fluxes along the leaf are not as tightly correlated with their NVP-AUY922 web associated expression data. S5 F.| DOI:10.1371/journal.pone.0151722 March 18,11 /Multiscale Metabolic Modeling of C4 PlantsFig 6. Comparison of RNA-seq data to predicted fluxes for a linear pathway and around a metabolic branch point. Upper panels, chlorophyllide a synthesis in the mesophyll; lower panels, production of arogenate in the bundle sheath by prephenate transaminase and its consumption by arogenate dehydrogenase and arogenate dehydratase. Left, aggregate RNA-seq data and experimental standard deviations for each reaction rescaled by a uniform factor (see text). Right, same data and errors further rescaled by reaction-specific optimal factors (e-si, in the variables of Eq 3) to best match data with predicted fluxes (solid circles). Fluxes are equal for all reactions of the linear pathway (1, uroporphyrinogen decarboxylase, 2, coproporphyrinogen oxidase, 3, protoporphyrinogen oxidase, 4, magnesium chelatase, 5, magnesium protoporphyrin IX methyltransferase, 6, magnesium protoporphyrin IX monomethyl ester cyclase, 7, divinyl chlorophyllide a 8-vinyl-reductase, 8, protochlorophyllide reductase.) Error bars represent standard deviations of expression measurements across multiple replicates. doi:10.1371/journal.pone.0151722.gwith data from the same experimental system [40], as well as from the different catalytic capabilities of different enzymes, posttranslational regulation, differences in substrate availability, etc. Reconciling expression data and network structure. Fig 6 illustrates the operation of the fitting algorithm in detail, using two regions of the metabolic network with simple structure as examples. In Fig 6a, expression data for eight reactions of the pathway leading to chlorophyllide a are shown. Expression levels fpsyg.2016.01448 for the different reactions at any point on the leaf may span an order of magnitude or more, but the FBA steady-state assumption requires the rates of all reactions in this unbranched pathway to be equal at each point. (The branch leading to heme productionPLOS ONE | DOI:10.1371/journal.pone.0151722 March 18,12 /Multiscale Metabolic Modeling of C4 Plantsis not included in the reconstruction.) Applying the optimal rescaling determined for each reaction’s expression data, shown in panel b, allows the flux prediction for the pathway (solid dots) to achieve reasonable agreement with the data. (Note that data for reaction 4 cannot be further scaled down because of the lower limit exp(-5) on its scale factor exp(s4), imposed for technical reasons.) Fig 6c shows data for a three-reaction branch point in aromatic amino acid synthesis. To balance production and consumption of arogenate, the prephenate transaminase flux must equal the sum of the fluxes through arogenate dehydrogenase (to tyrosine) and arogenate dehydratase (to phenylalanine) but expression is consistently lower for the transaminase than the other enzymes. After rescaling (Fig 6d), the data agree fnhum.2013.00596 well with the stoichiometrically consistent flux predictions (solid dots). The predicted ratio of dehydrogenase to dehydratase flux reflects data for downstream reactions. Comparison to other methods for integrating RNA-seq data. S4 Fig shows predictions that result when the scale factors si of Eq (3) are fixed to zero. The source-sink transition is apparent but the C4 cycle operates at lower levels, the example pathways of Fig 6 (and a number of others) show little or no activity, and predicted fluxes along the leaf are not as tightly correlated with their associated expression data. S5 F.
