Ig shows the metabolic state predicted by applying the expression data for each reaction as an upper bound on the absolute value of the reaction rate as in the E-Flux method [41] to the fifteen-segment model with the same RNA-seq data. (Here, the objective function maximizes CO2 assimilation.) The C4 system is predicted to operate, but no source-sink transition is apparent, and typical data-predicted flux correlations are poor. Imposing a realistic biomass composition restores the source-sink transition and somewhat improves correlation between data and fluxes (S6 Fig). Fluxes predicted by E-Flux are generally smaller than those predicted by the least-squares method, with or without per-reaction scale factors. S9 Fig compares the fluxes predicted at the tip by optimizing agreement with the data through the non-biological objective function Eq (3), fluxes predicted at the tip with an explicit biological objective function (maximizing CO2 assimilation) constrained by the experimental data in the E-Flux method, and fluxes predicted in an FBA calculation which ignores the data entirely (minimizing total flux while achieving the same CO2 assimilation rate as predicted at the tip by the least-squares method.) Both data-integration methods lead to predictions very different from the unconstrained FBA calculation. S10 Fig shows results obtained when the requirement that predicted fluxes obey the kinetic laws [Eqs (5), (6), (7)] is relaxed. The source-sink transition is still apparent and predictions for most reactions are similar, but quantitative and qualitative changes in predicted rates of several key reactions of the C4 system are observed.Discussion Fitting metabolic fluxes to expression dataThe expression of a gene encoding a metabolic enzyme need not correlate with the SART.S23506 rate of the reaction that enzyme catalyzes. The relationship between transcription and degradation of mRNA and control of flux is indirect, mediated by protein translation, folding, and degradation, complex formation, posttranslational modification, allosteric regulation, and substrate availability. Indeed, as reviewed by [42], experimentally observed correlations among RNA-seq or microarray data (each itself an imperfect proxy for mRNA abundance or transcription rate), protein abundance, enzyme activity, and fluxes are variable and often weak. For example, RNA-seq and quantitative proteomic data obtained from maize leaves at the same developmental stage studied here, j.jebo.2013.04.005 harvested simultaneously from plants grown together,PLOS ONE | DOI:10.1371/journal.pone.0151722 March 18,13 /Multiscale Metabolic Modeling of C4 Plantsshowed Pearson correlation approximately 0.6 across the entire dataset, but some significantly lower values were found when correlations were restricted to genes of particular functional classes, and measured mRNA/protein ratios for individual genes varied up to 10-fold along the gradient [40]. A get Quinagolide (hydrochloride) subset of this data is shown in Fig 5d. The most comprehensive study of the issue in plants so far [43] found so little agreement between RNA-seq and 13C-MFA data from embryos of two Brassica napus accessions that the authors concluded the inference of central metabolic fluxes from transcriptomics is, in general, impossible. In this light, it is not surprising that methods for integrating transcriptomic data with metabolic models to predict reaction rates have met with limited success. APTO-253 site Machado and Herrg d [44] reviewed 18 such methods and assessed the performance of se.Ig shows the metabolic state predicted by applying the expression data for each reaction as an upper bound on the absolute value of the reaction rate as in the E-Flux method [41] to the fifteen-segment model with the same RNA-seq data. (Here, the objective function maximizes CO2 assimilation.) The C4 system is predicted to operate, but no source-sink transition is apparent, and typical data-predicted flux correlations are poor. Imposing a realistic biomass composition restores the source-sink transition and somewhat improves correlation between data and fluxes (S6 Fig). Fluxes predicted by E-Flux are generally smaller than those predicted by the least-squares method, with or without per-reaction scale factors. S9 Fig compares the fluxes predicted at the tip by optimizing agreement with the data through the non-biological objective function Eq (3), fluxes predicted at the tip with an explicit biological objective function (maximizing CO2 assimilation) constrained by the experimental data in the E-Flux method, and fluxes predicted in an FBA calculation which ignores the data entirely (minimizing total flux while achieving the same CO2 assimilation rate as predicted at the tip by the least-squares method.) Both data-integration methods lead to predictions very different from the unconstrained FBA calculation. S10 Fig shows results obtained when the requirement that predicted fluxes obey the kinetic laws [Eqs (5), (6), (7)] is relaxed. The source-sink transition is still apparent and predictions for most reactions are similar, but quantitative and qualitative changes in predicted rates of several key reactions of the C4 system are observed.Discussion Fitting metabolic fluxes to expression dataThe expression of a gene encoding a metabolic enzyme need not correlate with the SART.S23506 rate of the reaction that enzyme catalyzes. The relationship between transcription and degradation of mRNA and control of flux is indirect, mediated by protein translation, folding, and degradation, complex formation, posttranslational modification, allosteric regulation, and substrate availability. Indeed, as reviewed by [42], experimentally observed correlations among RNA-seq or microarray data (each itself an imperfect proxy for mRNA abundance or transcription rate), protein abundance, enzyme activity, and fluxes are variable and often weak. For example, RNA-seq and quantitative proteomic data obtained from maize leaves at the same developmental stage studied here, j.jebo.2013.04.005 harvested simultaneously from plants grown together,PLOS ONE | DOI:10.1371/journal.pone.0151722 March 18,13 /Multiscale Metabolic Modeling of C4 Plantsshowed Pearson correlation approximately 0.6 across the entire dataset, but some significantly lower values were found when correlations were restricted to genes of particular functional classes, and measured mRNA/protein ratios for individual genes varied up to 10-fold along the gradient [40]. A subset of this data is shown in Fig 5d. The most comprehensive study of the issue in plants so far [43] found so little agreement between RNA-seq and 13C-MFA data from embryos of two Brassica napus accessions that the authors concluded the inference of central metabolic fluxes from transcriptomics is, in general, impossible. In this light, it is not surprising that methods for integrating transcriptomic data with metabolic models to predict reaction rates have met with limited success. Machado and Herrg d [44] reviewed 18 such methods and assessed the performance of se.
