Fig 1.
(a) Nine-day-old maize plant (image from [25]). (b) Organization of the two-cell-type metabolic model, showing compartmentalization and exchanges across mesophyll and bundle sheath cell boundaries. (c) Combined 121-compartment model for leaf 3 at the developmental stage shown in (a). Fifteen identical copies of the model shown in (b) represent 1-cm segments from base to tip.
Fig 2.
CO2 assimilation rates (A) predicted by the C4 photosynthesis model of [15], solid lines, and the present nonlinear genome-scale model (markers) maximizing CO2 assimilation with equivalent parameters.
The nonlinear model incorporates the mesophyll CO2 level as a parameter through the constraints in Eqs 5, 6 and 7. Left, A vs mesophyll CO2 levels with varying PEPC levels (top to bottom, vp,max = 110, 90, 70, 50, and 30 μmol m-2 s-1). Right, A vs total maximum activity of all bundle sheath decarboxylase enzymes (equivalent to the maximum PEP regeneration rate Vpr in [15]) at varying Rubisco levels (top to bottom, vc,max = 70, 60, 50, 40, and 30 μmol m-2 s-1). Other parameters as in Table 4.1 of [15], except with nonphotorespiratory respiration rates rd = rm = 0.
Fig 3.
Source-sink transition along the leaf as predicted by optimizing the agreement between fluxes in the nonlinear model and RNA-seq data.
Predicted fluxes are obtained by minimizing the objective function of Eq 3. (a) Predicted rates of exchange of carbon with the atmosphere and phloem along the leaf. (b) Experimental observation of the source-sink transition, reproduced from [25]. Upper image, photograph of leaf 3; middle image, autoradiograph of leaf 3 after feeding 14CO2 to leaf 2; lower image, autoradiograph of leaf 3 after feeding 14CO2 to the tip of leaf 3. (c) Total biomass production in the best-fitting solution. In panels a and c, dotted lines indicate minimum and maximum predicted rates consistent with an objective function value no more than 0.1% greater than the optimal value. Here, the biomass composition is allowed to vary along the leaf; S8 Fig shows corresponding results where the biomass composition is fixed.
Fig 4.
Operation of the C4 system in the best-fitting solution, as determined by minimizing the objective function, Eq 3.
(a) Rates of carboxylation by PEPC in the mesophyll and Rubisco in the mesophyll and bundle sheath. (b) Rates of CO2 release by PEP carboxykinase and chloroplastic NADP-malic enzyme in the bundle sheath. (c) Transport of 3-phosphoglycerate and glyceraldehyde 3-phosphate from bundle sheath to mesophyll (or the reverse, where negative) and glyceraldehyde 3-phosphate dehydrogenation rate in the mesophyll chloroplast, showing the involvement of the mesophyll in the reductive steps of the Calvin cycle throughout the source region. (d) Oxygen and carbon dioxide levels in the bundle sheath. Straight lines show mesophyll levels. Throughout, dotted lines indicate minimum and maximum predicted values consistent with an objective function value no more than 0.1% greater than the optimal value.
Fig 5.
Agreement between RNA-seq data and predicted fluxes.
(a) Contribution of each segment to the objective function (Eq (3), excluding costs associated with scale factors). (b) Cumulative histogram of Pearson correlations between data and predicted fluxes for all reactions. (c) Predicted fluxes versus expression data at the tip of the leaf (blue, raw fluxes; red, after rescaling each flux vi by the optimal factor of Eq (3)). Some outliers with very low predicted flux are not shown. (d) Relationship between RNA-seq and proteomics measurements for 506 proteins in the 14th segment from the base, redrawn from the data of [40]. NSAF, normalized spectral abundance factor.
Fig 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.