Computational analysis of storage synthesis in developing Brassica napus L. (oilseed rape) embryos: flux variability analysis in relation to 13C metabolic flux analysis

Authors


(fax +1 631 344 3407; e-mail jhay@bnl.gov).

Summary

Plant oils are an important renewable resource, and seed oil content is a key agronomical trait that is in part controlled by the metabolic processes within developing seeds. A large-scale model of cellular metabolism in developing embryos of Brassica napus (bna572) was used to predict biomass formation and to analyze metabolic steady states by flux variability analysis under different physiological conditions. Predicted flux patterns are highly correlated with results from prior 13C metabolic flux analysis of B. napus developing embryos. Minor differences from the experimental results arose because bna572 always selected only one sugar and one nitrogen source from the available alternatives, and failed to predict the use of the oxidative pentose phosphate pathway. Flux variability, indicative of alternative optimal solutions, revealed alternative pathways that can provide pyruvate and NADPH to plastidic fatty acid synthesis. The nutritional values of different medium substrates were compared based on the overall carbon conversion efficiency (CCE) for the biosynthesis of biomass. Although bna572 has a functional nitrogen assimilation pathway via glutamate synthase, the simulations predict an unexpected role of glycine decarboxylase operating in the direction of NH4+ assimilation. Analysis of the light-dependent improvement of carbon economy predicted two metabolic phases. At very low light levels small reductions in CO2 efflux can be attributed to enzymes of the tricarboxylic acid cycle (oxoglutarate dehydrogenase, isocitrate dehydrogenase) and glycine decarboxylase. At higher light levels relevant to the 13C flux studies, ribulose-1,5-bisphosphate carboxylase activity is predicted to account fully for the light-dependent changes in carbon balance.

Introduction

Plant oils as an important renewable resource

Plant oils are an important renewable resource with use in food, feed, fuel and industrial chemicals (Dyer et al., 2008). Brassica napus (oilseed rape), like many plants, produces seeds that store oil in the form of triacylglycerol (TAG). One desirable goal to achieve for the improvement of such oil crops is to increase the fraction of TAG relative to other storage compounds in mature seeds (Durrett et al., 2008). Hence storage metabolism in developing seeds is of biotechnological significance. Although the metabolic processes that govern the synthesis of different storage products during seed development have been studied in great detail, e.g. in Arabidopsis thaliana and B. napus (Rawsthorne, 2002; Baud et al., 2008), the inherent network properties that control partitioning of maternal photoassimilates into different storage compounds are still enigmatic.

Central metabolism and carbon partitioning

Efforts to redirect carbon flow in plant storage organs between different storage products often have limited success. Methods of 13C metabolic flux analysis (13C-MFA) (Ratcliffe and Shachar-Hill, 2006; Libourel and Shachar-Hill, 2008; Schwender, 2008) are useful to understand possible barriers, as they allow us to observe in vivo flux in central metabolism. In previous studies the relative use of various alternative routes in central metabolism has been described quantitatively by the use of 13C-MFA with cultured embryos of B. napus (Schwender and Ohlrogge, 2002; Schwender et al., 2003, 2006; Junker et al., 2007), as well as in similar studies for other seeds (Sriram et al., 2004; Ettenhuber et al., 2005; Spielbauer et al., 2006; Alonso et al., 2007; Iyer et al., 2008; Allen et al., 2009). In B. napus, this approach allowed us to characterize the contribution of the oxidative pentose phosphate pathway (OPPP) (Schwender et al., 2003), the tricarboxylic acid (TCA) cycle (Schwender et al., 2006) and the bypass of glycolytic reactions by ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO) (Schwender et al., 2004a) to lipid synthesis. Yet 13C-MFA studies typically resolve simplified networks only, representing a metabolic ‘core’ of central metabolism. This is in part because of the limitation in labeling information accessible by measurements and because of the mathematical complexity involved in the simulation of isotopomer balancing networks in 13C-MFA (Schwender, 2009). As a consequence, analysis of large-scale metabolic networks with fully detailed and compartmentalized representation of all relevant metabolic processes, including the network-wide balancing of energy co-factors, might be a useful additional tool to model seed metabolism in more realistic detail. Also, results obtained from 13C-MFA are certainly not free from modeling artifacts, i.e. the misinterpretation of data can arise from unrealistic assumptions built into the models (Van Winden et al., 2001; Schwender et al., 2004b). Therefore, the prediction of flux states based on principles other than constraining the flux pattern by isotope labeling signatures should be a useful complementary approach.

Modeling of seed metabolism

Analysis of large-scale metabolic networks based on linear optimization (flux balance analysis, FBA) has been widely used in predicting physiological behavior or the essentiality of biochemical reactions for growth (Varma and Palsson, 1994; Bonarius et al., 1997; Pramanik and Keasling, 1997; Kauffman et al., 2003; Becker et al., 2007; Boyle et al., 2009). For plants, large-scale compartmentalized models have been reported (Boyle and Morgan, 2009; Grafahrend-Belau et al., 2009), as well as genome-scale models (Poolman et al., 2009; de Oliveira Dal’Molin et al., 2010a,b; Williams et al., 2010). As described elsewhere (Hay and Schwender, 2011), we constructed a large-scale metabolic network of a B. napus developing embryo (bna572) based on information mined from biochemical literature and databases. Based on linear optimization, metabolic steady states can be simulated under different nutritional conditions. Specifically, four model configurations were defined that are combinations of photoheterotrophic and heterotrophic modes, with amino acids or inorganic nitrogen acting as nitrogen sources (Hay and Schwender, 2011). Flux variability analysis (FVA), an extension of FBA, was used to describe the many possible flux states in the highly compartmentalized network (Hay and Schwender, 2011).

Objectives

Using bna572 (Hay and Schwender, 2011) we first compared FVA simulations with results of former studies using 13C-MFA with developing B. napus embryos grown in culture. Alternative pathways that can supply plastidic fatty acid synthesis with pyruvate are explored, as well as alternatives to supply reductant. For various heterotrophic nutritional cases we predict the theoretical substrate use efficiency for biomass formation based on carbon conversion efficiency (CCE). We finally analyse the light-dependent carbon economy with respect to the contribution of RuBisCO and other carboxylating enzymes.

Results

Large agreement between flux predictions from FVA and from former 13C-MFA

The simulation of bna572 by FVA was performed by the minimization of all substrate uptakes and photon flux (light uptake), followed by the determination of the range of values admissible under optimality for each reaction in the network. As a first approach, to validate the model we compared the photoheterotrophic/organic nitrogen conditions (PO; Figure 1) with 39 net flux values reported in a former study on 13C-MFA with B. napus embryos cultured under photoheterotrophy with Ala and Gln as nitrogen sources (Schwender et al., 2006), referred to hereafter as bna39/2006. This model is considerably smaller than bna572, is only minimally compartmentalized and features only the main carbon transitions of biochemical reactions. The two models are comparable if for each individual reaction in bna39/2006 all reactions are identified in bna572 that connect the same metabolites present in either the same or in different cell compartments. In the secondary optimization of FVA (see Experimental procedures), bna572 was simulated by selecting groups of reactions to be minimized and maximized simultaneously. In each case the minimal and maximal optimal values of the summed reactions were obtained, respectively (see Experimental procedures). The detailed comparison of bna572 and bna39/2006, including units conversion for comparison of fluxes, can be found in Appendix S2. Overall both models were very similar, as judged by a correlation coefficient of 0.98, computed between the 33 non-variable optimal values in the bna572 projection and bna39/2006 (Figure 2a). As both models use very similar biomass composition, the high correlation could simply be a reproduction of biomass fluxes. The comparison includes 14 fluxes that are defined based on biomass composition. For example, the flux of Ser into the biomass is derived based on the fraction of protein in the biomass and the amino acid composition of protein, but is independent from other flux estimation processes in bna572 or bna39/2006. Yet, without consideration of the 14 biomass fluxes, the correlation is still R2 = 0.97. We therefore conclude that the bna572 simulation (PO conditions) is in reasonably good agreement with the former 13C-MFA study (Schwender et al., 2006). Similar good agreement can be found between bna572 (PI condition) and model bna16/2007, which was a 13C-MFA study of B. napus embryos grown under photoheterotropy with NH4NO3 as a nitrogen source (see Appendix S2). The correlation coefficient computed is also 0.98.

Figure 1.

 Schematic overview of the metabolic network of Brassica napus developing seeds, bna572, as described by Hay and Schwender (2011). Indicated in gray are major model constraints. Conditions of photoheterotrophy (P) or heterotrophy (H) in combination with organic (O) or inorganic (I) nutrients are defined as PO, HO, PI and HI conditions. Under each particular condition, specific uptakes are not allowed. Further constraints define the composition of biomass and biomass flux, maintenance energy requirements (ATPdrain_c) and the carbon balance for photoheterotrophy (ratio R). Abbreviations: Fru, fructose; Glc, glucose; Sucr, sucrose; TAG, triacyl glycerol.

Figure 2.

 Comparison between flux values derived in this study (model bna572, condition PO) and 39 fluxes obtained previously by 13C-MFA of cultured Brassica napus embryos under photoheterotrophic conditions (Schwender et al., 2006: bna39/2006). For comparison, the fully compartmentalized bna572 model was optimized by flux variability analysis (FVA), with simultaneous projection onto the smaller 13C-MFA model (see Experimental procedures), whereas the flux values from bna39/2006 were scaled by the retrospective application of the growth rate used in bna572 (see Appendix S2.
(a) Comparison of bna572 with values from the 13C-MFA study (Schwender et al., 2006). For bna572, lower and upper bounds of flux intervals are signified by X and O, respectively. For 33 fluxes the symbols overlap (fixed values), whereas for six fluxes the boundaries are separate (only visible for four fluxes, see Appendix S2 for full details). Linear regression was computed between 33 fixed values of bna572 and bna39/2006.
(b) Part of the reduced network that includes all six reactions for which flux variability was obtained. Cytosolic and plastidic pools of acetyl-CoA are shown as one lumped metabolite pool (AcCoA). The reaction connecting OxA/Mal and PYRp is only present in bna572 (see text). Three alternative pathways to generate PYRp are emphasized using different colors. Arrows signify the reactions of bna39/2006, with bidirectionality indicated by small arrowheads. AcCoA, acetyl coenzyme A; alKG, α-ketoglutarate; Cit, citrate; Icit, lumped pool of isocitrate/aconitate; OxA/Mal, lumped pool of oxaloacetate and malate; PEP, phosphoenol pyruvate; PYR, pyruvate.

For both bna572 (PO conditions) and bna39/2006, TCA cycle reactions operate at relatively small non-variable rates, and in a non-cyclic fashion (Figure 2b). The two models differ in that the conversion between the α-ketoglutarate and the oxaloacetate/malate pools (alKG → Succ → OxA/Mal; Figure 2b) has a small value for bna39/2006 (0.014 μmol h−1), but is zero in bna572, and can therefore be considered to be inactive. Also, bna572 uses only Gln as a nitrogen substrate, whereas bna39/2006 takes up both Ala and Gln (Figure 2b). Accordingly, in bna572 more carbon is transferred into citrate (Cit) by a route leading from Gln via Glu, α-ketoglutarate and isocitrate (alKG, Icit; Figure 2b). The Gln uptake is lower in bna39/2006 because nucleic acids and free Gln are nitrogen-containing biomass components only accounted for in bna572. In both models the TCA cycle intermediate Cit is used to produce the lipid precursor acetyl coenzyme A (AcCoA) via ATP:citrate lyase at similar rates. Yet in the reduced bna572 model the Cit demand is met by both citrate synthase (from PYRm) and isocitrate dehydrogenase flux (from Icit), whereas in the 13C-MFA model mainly citrate synthase is used (Figure 2b).

Both models bna572 (PI) and bna16/2007 show zero or very small fluxes between alKG and OxA/Mal. Both simulations of inorganic nitrogen condition (Appendix S2) show a flux between Cit, alKG, Glu and Gln, which is reversed relative to the organic nitrogen condition shown in Figure 2(b). In bna572 the rates of those reactions are higher by about 0.05 μmol h−1, which can be attributed to the additional efflux of Gln into biomass only present in bna572.

Variability of reactions leading into fatty acid synthesis

For the bna572 projection on bna39/2006, six of the 39 fluxes feature flux variability, with four large intervals visible in Figure 2(a). Figure 2(b) shows all variable reactions in a subnetwork consisting of parts of glycolysis, the TCA cycle and related reactions, plus the conversion OxA/Mal to PYRp, which is shown even though it is only present in bna572 (ME_p; #49; reaction numbers refer to the model documentation described in Hay and Schwender, 2011; reactions discussed in this study are reproduced in Appendix S1). Whereas the 13C-MFA study resolved this part of the network based on information derived from 13C tracer labeling, the reduced bna572 model only allows us to narrow down the solution space to large variability ranges for different pathways converging to plastidic pyruvate (PYRp) (Figure 2b). PYRp can be generated by the import of cytosolic pyruvate (PYRc; Figure 2b), directly from PEP or from malate (OxA/Mal to PYRp; Figure 2b). Those reactions in the reduced network correspond to H_c::PYR_p_sym (#95), PK_p (#58) and ME_p (#49) in bna572, respectively. All three reactions forming PYRp are characterized by the same variability interval of 0–0.812 μmol h−1 (Figure 2b), indicating that each of them can be inactive (zero) or carry the full flux towards fatty acid synthesis (finitely variable, substitutable). This was confirmed by a series of knock-out simulations, with two out of the three pyruvate-forming reactions being constrained to zero each time. Independent of the simulated nutritional conditions (PO, HO, PI or HI; for definitions see Figure 1), the three respective knock-out simulations consistently result in the same optimal value, with the respective unconstrained pyruvate-forming reaction accounting for the required flux towards fatty-acid synthesis. The plastidic malate used by plastidic malic enzyme can be supplied by the carboxylation of phosphoenol pyruvate (PEP) and the reduction of the resulting oxaloacetate to malate (Figure 2b). Notably this carboxylation of PEP is carried out by PEP carboxykinase (PPCK_c; #13), whereas PEP carboxylase (PEPC_c; #12) is not used. For a knock-out of PPCK_c, ME_p can contribute maximally about 2% of the total flux towards fatty acids.

Generation of reductant for fatty acid synthesis

To assess which plastidic reactions are predicted to contribute reductant to fatty acid synthesis, the production or consumption of NADH and NADPH by different plastidic enzymes is reported in Table 1. Fatty acid synthesis in the plastids has a large biosynthetic demand for NADH and NADPH, both at a non-variable rate of 0.686 μmol h−1 (Table 1). The NADH demand is met by the non-variable flux through plastidic pyruvate dehydrogenase. The demand of NADPH equals the NADH demand and, as indicated by their variability intervals, several reactions can potentially produce plastidic NADPH (Table 1). Under light conditions (PI, PO), ferredoxin-NADP reductase (#2) can fully supply NADPH, whereas plastidic malic enzyme (ME_p; #49) can supply NADPH under all four conditions (Table 1). Plastidic malate dehydrogenase (MDH_p; #48), glyceraldehyde-3-phosphate dehydrogenase (NADPGAPDH_p; #59) and isocitrate dehydrogenase (IDH_p; #533) together can fully or to a large part supply NADPH to fatty acid synthesis (Table 1). The OPPP is predicted to be inactive, and glutamate synthase (Glusynth_p; #45) is predicted to only consume NADPH (Table 1).

Table 1.   Rates of production and consumption of NADH and NADPH by various plastidic reactions in relation to fatty acid synthesis
PathwayReaction (number in bna572)Simulated physiological condition
POPIHOHI
  1. Based on flux variabilities taken from Hay and Schwender (2011), the rates of NAD(P)H production (+) or consumption (−) are reported for key reactions (μmol h−1).

  2. aIn flux variability analysis (FVA) reactions #48, #59 and #533 have infinitely variable solutions. The finite range of their combined NADPH production when optimized together is reported.

NADH
 Plastidic fatty acid synthesisPyruvate dehydrogenase (#480–#482)0.7800.7800.7800.780
Enoyl-[acyl-carrier-protein] reductase (#211, #215, #219, #223, #228, #231, #233, #526)−0.686−0.686−0.686−0.686
NADPH
 OPPPGlucose-6-phosphate dehydrogenase (G6PDH_p; #477), phosphogluconate dehydrogenase (#479)0000
 Photosynthetic electron transportFerredoxin-NADP+ reductase (#2)1.4071.319−0.086−0.086
Glutamate synthase (NADPH) (#45)[0, −0.042]0[0, −0.042]0
Glutamate dehydrogenase (#46)[−0.045, −0.003]−0.164[0.217, 0.259]0.0277
Malate dehydrogenase (decarboxylating) (ME_p; #49)[0, 0.812][0, 0.812][0, 0.812][0, 0.812]
Malate dehydrogenase, glyceraldehyde-3-phosphate dehydrogenase, isocitrate dehydrogenase (#48, #59, #533)a[−1.419, −0.607][−1.213, −0.401][−0.189, 0.623][0.001, 0.813]
 Plastidic fatty acid synthesis3-oxoacyl-[acyl-carrier-protein] reductase (#209, #213, #217, #221, #225, #229, #235, #528)−0.686−0.686−0.686−0.686

Nutritional variations and carbon conversion efficiency

The theoretical value of individual nutrients for biomass synthesis was assessed by simulating various combinations of sugar substrates and nitrogen substrates under heterotrophy (Table 2). Subsequently the CCE was calculated, which we defined in a similar way to Goffman et al. (2005) as the quantity of total carbon uptakes (molar percentage) that is recovered in biomass (see Experimental procedures). The higher the CCE value, the more carbon efficient a certain combination of substrates should be. The highest CCE of 69.86% is found if sucrose and NH4+ are combined, whereas the lowest CCE of 61.15% is for the substrate combination of glucose and NO3 (Table 2). More generally, all nutritional cases where only ammonia (NH4+) is allowed result in higher CCEs than if nitrate is allowed instead (Table 2), indicating that the use of NH4+ is more efficient.

Table 2.   Model-predicted carbon conversion efficiency (% carbon uptakes stored in biomass) for biomass of developing Brassica napus embryos
Carbon substrate allowedNitrogen substrate allowed
NH4+NO3All inorganic NAlaGlnAsnGluAll organic NAll N
  1. Substrate uptakes under heterotrophy (photon uptake inactive) were minimized while different combinations of carbon and nitrogen (N) substrates were allowed, as indicated.

Glucose67.5361.1567.5366.6066.5165.5864.9666.5166.51
Fructose67.5961.2067.5966.6666.5665.6465.0266.5666.56
Sucrose69.8663.2669.8668.5868.5467.6466.7168.5468.54
All sugars69.8663.2669.8668.5868.5467.6466.7168.5468.54

Similar consistent relationships hold for the different sugar substrates. Across all nitrogen cases, the CCE values for sucrose are always higher than if only glucose or fructose can be used (Table 2). This general advantage of sucrose over glucose and fructose can be related to a number of different pathway features in the network. The transformation of sucrose uptake into hexose phosphates involves sucrose synthase (#30) and UDP-glucose pyrophosphorylase (#554). Inactivation of sucrose synthase under HO conditions enforces the use of invertase (#29) and results in a decrease of 0.9% in CCE. Additional simulations that manipulate sugar uptake show that further effects on CCE stem from sugar uptakes by proton co-transport (#118, 120, 122) coupled to plasma membrane proton ATPase (#87). These require one proton per sucrose versus two protons per an equivalent number of two hexose molecules taken up. In addition, sucrose is a minor biomass component of bna572 (Hay and Schwender, 2011). If only glucose or fructose are available substrates, sucrose has to be de novo synthesized. In particular the synthesis of sucrose from fructose requires sucrose synthase (#30), whereas the synthesis of sucrose from glucose occurs by a different route via sucrose phosphate synthase (#557, #558). This explains the minimal advantage of fructose over glucose predicted in Table 2.

Contribution of RuBisCO to carbon economy

In bna572 the simulation of photoheterotrophy is based on fixing the CO2 release relative to the lipid deposition rate by the ratio R, with R = 2.9 ± 0.3, the experimental carbon economy formerly reported for a light level of 50 μmol photons m−2 s−1 (Schwender et al., 2004a). A further range of light intensities was simulated by using additional R values (Table 3), formerly reported for other light levels (Schwender et al., 2004a). The resulting RuBisCO fluxes were expressed relatively, i.e. as the relative contribution of 3-phosphoglyceric acid (x3PG) in sugar catabolism by RuBisCO (Table 3). With increasing light levels under organic nitrogen conditions, the relative RuBisCO flux assumes non-variable values, rising from 0.32 to 0.90 (Table 3; model predicted relative RuBisCO flux). Both glycolysis and RuBisCO always have a positive net contribution to the formation of x3PG, and cyclic regeneration of the RuBisCO substrate RuBP from x3PG (the Calvin–Benson–Bassham Cycle) does not take place.

Table 3.   Carbon economy of developing Brassica napus (cv. Reston) embryos grown under different levels of light
Measured photon flux density (μmol m−2 s−1)Measured ratio RModel predicted photon flux (μmol h−1)Model predicted relative RuBisCO flux
  1. The relative RuBisCO and photon flux were predicted based on the experimentally determined ratio of molar carbon converted into oil to molar CO2 released (R). R values (mean ± SD, n = 3) are reproduced from Schwender et al. (2004a): Table 1 and Figure 2. Model predicted photon flux is reaction #6 (Ph_tm_exch). See Experimental procedures for the computation of predicted relative RuBisCO flux.

  2. aBased on 14C tracers instead of infrared gas analyzer and gas chromatography.

142.63 ± 0.175.520.32
503.21 ± 0.596.400.61
502.90 ± 0.30a5.970.47
914.15 ± 1.057.310.90

To further assess the contribution of RuBisCO carboxylase activity to the carbon economy, a continuum of R values was simulated (Figure 3). For R > 1.1 (the R value for HO) the simulated light levels increase while the net CO2 export decreases (Figure 3a). RuBisCO remains inactive but starts to increase above the value R = 2.3, indicating two metabolic phases (Figure 3a). To characterize these two metabolic phases, Figure 3(b) depicts differential changes in different enzymes in the direction of decarboxylation. Negative values indicate an increase of flux in the direction of carboxylation (RuBisCO; isocitrate dehydrogenase, IDH; Figure 3b) or decrease of flux in the direction of decarboxylation (oxoglutarate dehydrogenase, OGDH; Figure 3). The positive values for glycine decarboxylase (GDC; Figure 3) stem from it operating in the direction of carboxylation, but decreasing with increasing R. Below R = 2.3, the changes in the CO2 efflux can be entirely attributed to GDC, OGDH and IDH (Figure 3b), i.e. the differentials of the three enzymes fully add up to account for the differential changes in net CO2 release. Above = 2.3, the adjustments in CO2 balance are entirely attributable to an increase in RuBisCO (Figure 3b), and without the carboxylation of RuBP, biomass synthesis in this phase is infeasible.

Figure 3.

 Adjustments of the total CO2 balance in developing Brassica napus embryos in response to manipulations of R, the ratio of carbon flux into oil to CO2 exchange flux (net CO2 release).
(a) Photon influx (vPh), oxygen efflux (vO2), carbon dioxide efflux (vCO2) and RuBisCO flux (vRuBisC) in μmol h−1.
(b) Differential of flux with respect to R for glycine decarboxylase (GDC; #457–#459), ribulose bisphosphate carboxylase (RuBisC; #57), sum of mitochondrial and plastidic isoforms of isocitrate dehydrogenase (IDH; #540, #533) and oxoglutarate dehydrogenase (OGDH; #453–#455). Negative differentials mean a change in flux towards less CO2 production.

Discussion

bna572 compares well with flux values formerly derived by 13C-MFA

To compare bna572 under PO conditions (Figure 1) with fluxes derived by 13C-MFA in a former study (Schwender et al., 2006: model bna39/2006), the simulation of bna572 was modified to minimize/maximize sums of multiple reactions that parallel single reactions in bna39/2006. Based on a correlation coefficient (Figure 2a) both models compare well. In the modified simulation 73 unique reactions in bna572 (12.8% of all reactions) were projected onto 43 reactions in bna39/2006 (Appendix S2). This means that 499 reactions in bna572 have no counterpart in bna39/2006. Many of those reactions can be organized in linear pathways that are lumped into one reaction in the 13C model. Also, reactions that represent electron transport chains or interconversions of currency metabolites, like ATP or NADP, are not represented in bna39/2006, as it models carbon transitions in central intermediary metabolism based on carbon tracers. Other pathways only present in bna572 are related to photorespiration, β-oxidation and glyoxylate bypass, as well as the GABA shunt, all of which are not predicted to be active in bna572 (Hay and Schwender, 2011). A particular reaction component missing in bna39/2006 is the plastidic malic enzyme, which is produced in #49 in bna572, and has a high flux variability of 0–0.812 μmol h−1. Major differences between the two models relate to the OPPP, as discussed further below, as well as to the uptake fluxes. Also, 13C labeling experiments with cultured developing B. napus embryos showed the simultaneous uptake of sucrose and glucose, as well as of the amino acids Ala and Gln (Schwender and Ohlrogge, 2002; Schwender et al., 2006). Yet, under different nutritional conditions with alternative sugar and nitrogen sources available, bna572 always predicts the uptake of sucrose and one nitrogen source only (Hay and Schwender, 2011). Agreement between bna572 and 13C labeling experiments can only be found with regards to total uptakes of sucrose and glucose (bna39/2006 actually only models the total hexose uptake; see Appendix S2, vuptGlc). Also, total nitrogen uptakes are comparable, if it is noted that in contrast to bna39/2006, bna572 was given an additional nitrogen sink of free Gln (Hay and Schwender, 2011). Because of the missing ability to predict uptakes of alternative substrates, we conclude that, if possible, all substrate uptake rates should be experimentally determined and added as model constraints. This is obvious because FBA in its essence is concerned with exploring intracellular fluxes, which are not directly experimentally accessible.

Similar to the comparison of 13C-MFA and FVA reported here, Williams et al. (2010) compared Arabidopsis cell cultures grown under different physiological conditions. It was concluded that their genome-scale model can be used to predict flux changes in central carbon metabolism under stress conditions. As in our study, the OPPP flux was predicted to be inactive by the FBA approach, whereas substantial activity was found by the 13C-MFA approach. Other comparisons between 13C-determined in vivo fluxes and large-scale models have been reported for Escherichia coli, where flux variability was reported for selected reactions (Schuetz et al., 2007; Chen et al., 2011).

Regarding the strict selectivity among alternative uptake fluxes, as predicted in bna572 simulations, one also has to keep in mind that to date the relevant mechanisms of substrate transport might be far from being comprehensively elucidated, and therefore only poorly represented in bna572. In addition to the sugar uptakes modeled in bna572, developing embryonic tissues have other not fully characterized sugar transport mechanisms (Lichtner and Spanswick, 1981; Hay and Spanswick, 2007). Including a sucrose uniporter reaction in the plasma membrane to model a component of passive transport would make secondary active transport (#122) suboptimal, and raise the CCE because the coupled transport of sucrose and protons depends on the proton ATPase (Spanswick, 2006). However, the relative use of these parallel sucrose movements in vivo would depend on, among other things, the apoplastic sucrose concentration, which FBA does not account for.

Alternative pathways producing precursors for fatty acid synthesis

Based on their variability intervals, three pyruvate-forming reactions were identified as parts of alternative pathways in lipogenesis (Figure 2b), and by knock-out simulations we confirmed that transport of cytosolic pyruvate into the plastid (H_c::PYR_p_sym), plastidic pyruvate kinase (PK_p) and plastidic malic enzyme (ME_p) can each carry the full lipogenetic flux under optimality. In addition, this prediction holds for the four tested nutritional conditions (HO, HI, PO, PI), proving that these three reactions classified by Hay and Schwender (2011) as substitutable are also mutually substitutable. This means that based on the constraints available in FVA, FVA can predict the actual in vivo flux distribution to be found within the limits given by the flux variability intervals. 13C-MFA, in turn, can better constrain the flux space based on experimentally determined 13C-labeling signatures interpreted with a network model of carbon atom transitions. The former 13C-MFA study in B. napus embryos showed that about two-thirds of the plastidic pyruvate derives from plastidic pyruvate kinase, and one-third derives from the import of cytosolic pyruvate (Figure 2b; Schwender et al., 2006). Although the alternative route via plastidic malic enzyme was not considered in this model, significant use of the pathway seems unlikely based on additional observations in labeling signatures of various metabolites made after culture of B. napus embryos with 13C-labeled glucose and unlabeled Asp (Schwender and Ohlrogge, 2002). In a later 13C-MFA study with cultured developing embryos of A. thaliana, the flux through plastidic malic enzyme was modeled and estimated to be about 2% of the flux through plastidic pyruvate dehydrogenase (Lonien and Schwender, 2009), i.e. malic enzyme made a very minor contribution, and as in B. napus, plastidic pyruvate kinase carries most of the lipogenic flux. So, in vivo flux through the alternative route via the plastidic malic enzyme might not be realized in both B. napus and A. thaliana developing embryos, whereas in both plants the route though the plastidic pyruvate kinase appears to predominate. This is not unexpected based on similarities between B. napus and A. thaliana, but it is also notable that in both flux studies the embryo cultures contained Gln as a nitrogen source. Uptake and metabolism of Gln could lead to relatively high internal levels of Glu, which in turn has been shown to strongly inhibit cytosolic PK and PEPC (Smith et al., 2000), i.e. restrict the corresponding alternative pathways predicted by bna572. If this is the case, then the in vivo distribution of fluxes converging to plastidic pyruvate could change if nitrogen sources other than Gln or Glu were used. Unfortunately, related 13C-MFA studies did not resolve the alternative pathways in question (Junker et al., 2007).

Amino acids as possible precursors for lipids

All three alternative routes that potentially transform PEP into plastidic pyruvate (Figure 2b) appear to depend on glycolytic flux. As an alternative to the production of lipid precursors from glycolytic intermediates, malate could be derived from Gln, Glu or Asn, if available as nutrient substrates. Asn uptake could be transformed via deamination (asparaginase; #14), transamination (aspartate transaminase; #15) and malate dehydrogenase (#16) into malate. Yet no increased uptakes or changed use of amino acids were predicted by the double knock-out simulations that enforce the use of malate as a lipid precursor. In agreement with this observation, former 13C-labeling experiments showed that carbon from various medium amino acids can be traced into storage protein, but not into plastid derived fatty acids (Schwender and Ohlrogge, 2002).

PEP carboxylation in bna572

In developing B. napus embryos PEPC_c is present with substantial activity (Junker et al., 2007), and based on its allosteric regulation the enzyme has been associated with nitrogen assimilation and anaplerotic functions of the TCA cycle (Moraes and Plaxton, 2000). Unexpectedly, PEPC is entirely inactive in simulations of bna572 (Hay and Schwender, 2011). Instead, the carboxylation of PEP to OxA is performed by PPCK_c (Hay and Schwender, 2011), which is apparently chosen by the optimization, as it can form the energy co-factor ATP simultaneously with the carboxylation of PEP (#12, #13; Appendix S1). Although literature associates PPCK primarily with gluconeogenesis during seed germination (Chia et al., 2005; Graham, 2008), PPCK_c is represented in bna572, as Chia et al. (2005) showed that PPCK is present during the oil accumulating stage of B. napus embryos, with activity levels comparable with lipid synthesis rates. Therefore, the presence of PPCK in the model might be well justified. However, if the selectivity between the two enzymes in the simulations is only based on a difference in reaction stoichiometry, conclusions on the in vivo function of PPCK versus PEPC should be taken with care. Based on the FVA modeling approach, the difference between the use of PPCK_c and PEPC_c can be quantified. The network-wide effect of forcing the use of PEPC_c for lipid synthesis under HO conditions (triple knock-out of PPCK_c, PK_p and H_c::PYR_p_sym) can be quantified as a reduction of 2% in CCE.

The carboxylation of PEP might be of essential anaplerotic function for the TCA cycle, in particular under inorganic nitrogen conditions where the TCA cycle intermediates OxA and alKG are needed for the synthesis of amino acids (Schwender, 2008). Simulation of a double knock-out of PPCK_c and PEPC_c shows that for inorganic conditions (PI, HI), the loss of anaplerotic PEP carboxylation is compensated by the activation of reactions of β-oxidation, malate synthase (#562) and glycine transaminase (#521), resulting in the formation of malate. Consistent with this observation, Hay and Schwender (2011) reported the essentiality of PPCK_c for PI and HI. Under the same nutritional simulations, PEPC_c changes from inactive to essential when PPCK_c is knocked out.

Generation of reductant for fatty acid synthesis

In bna572 the two reductive steps in plastidic fatty acid synthesis, enoyl-[acyl-carrier-protein] reductase and 3-oxoacyl-[acyl-carrier-protein] reductase (Table 1), are defined to require NADH and NADPH, respectively. This specificity is based on biochemical studies on the B. napus enzymes (Slabas et al., 1986; Sheldon et al., 1992). The model simulations show that plastidic pyruvate dehydrogenase (#480–482) produces AcCoA for fatty acid synthesis, as well as all of the required NADH (Table 1). With regards to the generation of plastidic NADPH, bna572 predicts that the demands of NADPH can be met alternatively by a number of plastidic dehydrogenases (Table 1). For example, plastidic malic enzyme can provide NADPH, and as discussed above the reaction can also provide pyruvate to fatty acid synthesis. Although the oxidation of glucose-6-phosphate in the OPPP is regarded as a key producer of NADPH for biosynthetic processes, in particular in fatty acid synthesis (Eastmond and Rawsthorne, 2000), in bna572 the pathway is never used (Table 1), i.e. its use appears to be generally suboptimal (Table 1) (see also Hay and Schwender, 2011). In a former study, metabolic flux analysis with developing B. napus embryos cultured under comparable photoheterotrophic conditions showed a substantial flux through the OPPP pathway, but its estimated contribution to plastidic fatty acid synthesis was <50% of the required NADPH (Schwender et al., 2003, 2006). Yet, as the OPPP is used in vivo, our FVA simulations suggest that the use of this pathway is suboptimal. To assess the extent of suboptimality when OPPP is active, HO conditions were simulated while the flux through the OPPP (#477, #479) was set to exactly cover the NADPH demand for plastidic fatty acid synthesis (0.343 μmol h−1). Remarkably, if the usage of the OPPP is enforced in this way, the CCE of 68.54% (Table 2) is reduced by only 0.46%. In conclusion, the use of the OPPP in a lipid-producing developing seed appears to be suboptimal, yet the disadvantage against various alternative NADPH producers in terms of carbon economy is only very minor.

Nutrient substrate use and carbon conversion efficiency

As bna572 allows the use of various substrates we asked how alternative substrates differ in their ability to support storage synthesis. Based on simulation of different combinatorial cases of alternative sugar and nitrogen substrates, and heterotrophy, the value of different substrates to produce biomass was predicted as CCE (Table 2). Goffman et al. (2005) reported a CCE value of 60.4% under heterotrophy for B. napus embryos growing on sucrose, glucose, glutamine and alanine, which is similar to the values predicted in Table 2. The following discussion focuses on the interpretation of differences in CCE between substrate combinations. The highest difference of 8.71% arises by comparing the combinations sucrose/NH4+ (69.86%) with glucose/nitrate (61.15%) (Table 2). For each particular sugar carbon substrate, the effect of replacing NH4+ with nitrate is a reduction in CCE between 3.38 and 6.6%. This difference of about 5% in CCE can be explained by the high-energy demand for the reduction of nitrate to NH4+ of eight electrons per NO3 (#123, #125), which is higher than the demand of four electrons to reduce CO2 to carbohydrates in photosynthesis. Under heterotrophy, the reductant has to be generated by oxidation of carbon substrates to CO2, resulting in a reduced CCE value. In conclusion, for developing B. napus embryos the energetic penalty of using nitrate versus NH4+, expressed as the effect on the total carbon balance, is expected to be about 5% in CCE. Developing seeds might avoid this penalty by using further reduced nitrogen sources provided by the mother plant. In fact, literature suggests that developing seeds of various species take up nitrogen primarily in the form of amino acids (Patrick and Offler, 2001; Rossato et al., 2001; Weber et al., 2005). Based on CCE values (Table 2), amino acids are favorable substrates against nitrate, yet NH4+ consistently results in a higher CCE as compared with amino acids (Table 2). In order to understand this behavior of the model we first consider the isolated mass balance for the formation of amino acids from glucose and NH4+. In higher plants NH4+ is considered to be first bound as an amide by glutamine synthethase (#8, #39; EC 6.3.1.2), followed by reductive amination by glutamate synthase (#45; EC 1.4.1.13). This way assimilation of 1 mol NH4+ into Glu requires one ATP and one NAD(P)H. Alternatively, Glu can be formed by glutamate dehydrogenase (#46, #484; EC 1.4.1.2), which only requires one NAD(P)H. Subsequent to the primary assimilation of NH4+ and the formation of Glu, other amino acids can be formed by transamination between Glu and various 2-ketocarboxylic acids. Those are downstream metabolites of glycolysis and TCA cycle intermediates, which are produced from glucose with a net gain of ATP and NAD(P)H. For example, pyruvate, a precursor of Ala, can be formed from glucose by glycolysis, with a net gain of one ATP and one NADH per mol pyruvate. This gain is equal or more than the energy co-factor requirement for primary assimilation of NH4+ into Glu. In consequence, uptake of preformed Ala should have no advantage over internal production of Ala from glucose and NH4+. Based on this isolated assessment of amino acid synthesis from sugars and NH4+, it becomes less unexpected that the network simulations give inorganic NH4+ an advantage over amino acid substrates (Table 2). CCE values based on network simulations account for further effects like energetic cost for substrate uptakes (proton co-transport for sugars and amino acids) or the possible pathways for degradation of amino acids taken up in surplus of the demands for protein synthesis.

Predicted alternative pathway for the assimilation of NH4+

The above consideration of NH4+ assimilation was based on the widely accepted view of the role of glutamate synthase (GOGAT; #45)/glutamine synthase (#39), and alternatively glutamate dehydrogenase (#46), in this process (Lancien et al., 2000). Examination of the simulation results under inorganic nitrogen (Figure 1, HI conditions) reveals that, in contrast to the above assumption on the assimilation of NH4+, glutamate synthase (#45) is inactive and glutamate dehydrogenase (#46) works towards the formation of NH4+ (Hay and Schwender, 2011). Former studies (Robinson et al., 1991; Aubert et al., 2001) demonstrate the possible in vivo operation of glutamate dehydrogenase in the direction of NH4+ formation in plants. Unexpectedly, glycine decarboxylase (GDC_m; #457–459) operates in the direction of assimilation of NH4+ (Hay and Schwender, 2011), consuming 82% of net NH4+ uptake (#128), indicating the existence of a GDC-dependent pathway of NH4+ assimilation. In bna572, GDC was defined reversibly based on biochemical evidence from isolated plant enzyme (Walker and Oliver, 1986). In a 13C metabolic flux analysis study with cultured embryos of A. thaliana, the labeling signatures measured in Gly and Ser could only be explained by the model if GDC was allowed to operate reversibly, and by net fixation of CO2 and NH4+ (Lonien and Schwender, 2009). If GDC_m is knocked out under heterotrophy, NH4+ assimilation takes place mostly via glutamate dehydrogenase. In this case the use of NH4+ still results in a higher CCE (69.47%) than the use of Gln (68.03%), i.e. the above conclusions about NH4+ as the most efficient nitrogen source still hold.

Sucrose is the preferred sugar substrate

Similar to the considerations on alternative nitrogen sources, sucrose can be compared with glucose and fructose as substrates. Based on Table 2, the CCE is higher by 1.69–2.33% if in various cases a hexose is replaced by sucrose. The degradation of sucrose via sucrose synthase and UDP-glucose pyrophosphorylase is known to be more efficient than the use of invertase and hexokinases (Kruger, 1997), but the model simulations predict the cumulative effect of a number of network features to account for the higher nutritional value of sucrose over hexoses. Altogether, the simulations summarized in Table 2 suggest that if developing embryos would preferentially use hexose sugars over sucrose, the inevitable penalty in carbon economy will achieve a CCE that is about 2% lower than is possible with sucrose. 13C-labeling experiments with cultured developing embryos of B. napus showed the simultaneous uptake of unlabeled sucrose and 13C-labeled glucose (Schwender and Ohlrogge, 2002; Schwender et al., 2006).

Photoheterotrophic seed metabolism

The simulations on photoheterotrophy confirm and extend the interpretation of former experimental observations in B. napus embryos (Schwender et al., 2004a). For R = 2.9, the model predicts a non-variable and essential flux through RuBisCO (#57) and a relative RuBisCO flux of 0.47 (Table 3), which falls into the range of 0.37–0.51 formerly estimated based on 13C-labeling experiments (Schwender et al., 2004a). Our large-scale stoichiometric model therefore validates the activity of a RuBisCO bypass of glycolysis (Schwender et al., 2004a). Furthermore, for R values measured at increasing light levels, a substantial increase in the relative RuBisCO flux from 0.32 to 0.9 is predicted (Table 3), indicating flexible adjustment of the RuBisCO bypass to light. It was concluded in the former study that the improvement of the carbon balance under different light levels must be entirely the result of increased CO2 refixation by RuBisCO, without a contribution from other carboxylating enzymes. The analysis shown in Figure 3 refines this finding by predicting two metabolic phases. For the phase characterized by R > 2.3, which includes the three experimental levels of light (Table 3), the change in RuBisCO flux fully accounts for the changes in carbon balance (Figure 3b). For 1.1 < R < 2.3, which relates to experimental light levels below 14 μmol photons m−2 s−1, carboxylating enzymes other than RuBisCO account for changes in the seed carbon balance. Figure 3 also extends the analysis of Hay and Schwender (2011), who make predictions about RuBisCO flux for just two R values of organic nitrogen conditions: inactivity under heterotrophy (R = 1.1) and nonvariable essentiality under photoheterotrophy (R = 2.9). The changes in isocitrate dehydrogenase and oxoglutarate dehydrogenase rates (Figure 3b) indicate that with an increase of photosynthetic production of NADPH and ATP, energy (ATP) producing TCA cycle activity can be reduced, diminishing its contribution to the total CO2 balance. Coupled to this change is a seemingly contradictory change in GDC flux. In the HO/HI models, GDC operates in the direction of carboxylation (glycine formation), but its rate decreases with increasing R (Figure 3b). In particular, for < 2.3, the differential changes in direction of decarboxylation for OGDH, IDH and GDC (Figure 3b) follow the ratios −1 : −1 : 0.5. In other words, if for increasing R the reactions OGDH and IDH each adjust flux towards CO2 fixation by an increment dx, GDC adjusts flux to fix less CO2 by ½ dx. This stoichiometry can be explained by a combination of IDH, OGDH, GDC, isocitrate lyase (ICL; #523) and a transamination between Gly and glyoxylate (Glox) (#521). This feature is corroborated by the observation that all of these reactions except for GDC differ in usage or direction of use between heterotrophy and photoheterotrophy (R = 2.9) (Hay and Schwender, 2011).

Our analysis of diminishing CO2 production by the TCA cycle parallels the observation derived from flux studies in developing seeds of B. napus, Glycine max (soybean) and Helianthus annuus (sunflower) that TCA cycle activity appears to be inversely related to the availability of photosynthetic energy co-factors (Allen et al., 2009). Also, FBA of a Chlamydomonas reinhardtii network simulating photomixotrophic growth on acetate showed similar results (Boyle and Morgan, 2009). Although flux variability was not considered in the Chlamydomonas study, it suggested that under increasing absorbed light flux two metabolic phases exist, similar to those in our analysis.

Conclusions

Simulations of bna572 based on FVA correlate well with flux data from related 13C-MFA studies on B. napus embryos cultured under photoheterotrophic organic and inorganic conditions. Despite notable differences in particular flux predictions, like the use of the OPPP, there is an overall good similarity in flux predictions of both models, which mutually validates the FVA and 13C-MFA models.

Combining FVA with in silico knock-out simulations gave detailed insights into the potential function of alternative pathways, like the different ways to form the lipid precursor pyruvate, or the different potential roles of PEP carboxylation for either nitrogen assimilation under inorganic nitrogen conditions or for lipid synthesis. Also, an unexpected potential role of glycine decarboxylase in NH4+ assimilation was predicted, which deserves further theoretical and experimental research. The model provides theoretical insights into the nutritional value of different substrates for seed storage synthesis. It confirms experimental findings in the case of the RuBisCO bypass, and gives additional predictive insights into mechanisms behind the light-dependent carbon balance under photoheterotrophy.

Both FVA and 13C-MFA investigate cellular steady-state flux, and can complement each other. FVA is a predictive modeling approach, i.e. it can be used to predict in vivo flux under different physiological conditions or the effect of knock-outs. Alternative pathways that are recognized based on flux variability should be interpreted as potential pathways to function efficiently within the context of the whole modeled network and the environmental constraints. Our flux predictions are based on optimality defined by a particular objective function. Regardless of the specific objective function, such optimal predictions are likely to represent an extreme point that is never reached in vivo. Therefore we assessed in several cases, based on CCE, how much the network performance is reduced from optimality if a pathway like the OPPP is assumed to make a substantial contribution to biosynthetic performance.

In contrast to FVA, 13C-MFA is based on isotope labeling signatures as experimental constraints of intracellular fluxes. 13C-MFA is not a predictive modeling approach, and the results of a 13C labeling experiment strictly reflect the specific physiological conditions of the experiment. The validity of flux results of 13C-MFA studies might suffer from limited detail in network representation or an insufficient realization of the metabolic steady state. As an advantage, 13C-MFA quantifies the in vivo reversibility of reactions as flux values independent from net conversion rates, which allows the inclusion of processes that can constitute futile cycles that are excluded by the optimality principle in FVA. Therefore, both FVA and 13C-MFA should be regarded as complementary. In future the reliability of FVA models can be further improved by adding more constraints, like flux ratio constraints derived by 13C-MFA and physiological measurements like oxygen exchange, light absorption and substrate uptake rates (Schuetz et al., 2007).

Experimental Procedures

bna572 is a metabolic reconstruction of storage metabolism in developing embryos of B. napus, as reported in detail elsewhere (Hay and Schwender, 2011). bna572 (Figure 1) features the stoichiometries of 572 enzyme, transport, biomass component assembly and biomass synthesis reactions, including photon uptake and 13 nutrient uptake and exchange reactions with the environment (Figure 1), allowing various different carbon and nitrogen sources to be used according to the physiological potential found in embryo cultures (Schwender and Ohlrogge, 2002; Hill et al., 2003; Junker et al., 2007; Morley-Smith et al., 2008). The model is highly compartmentalized, with nine cellular compartments. bna572 simulates the synthesis and accumulation of seed storage compounds (oil, protein, starch, cell wall polymer, free metabolites, DNA, RNA) based on the biomass composition of B. napus embryos during culture (Hay and Schwender, 2011) under conditions similar as those reported in previous 13C-MFA studies (Schwender and Ohlrogge, 2002; Schwender et al., 2003, 2004a, 2006). The carbon economy of developing cultured B. napus embryos is considered in the model by constraining the carbon balance based on measurements of net CO2 production relative to the accumulation of lipids during growth in culture in light and in darkness (Schwender et al., 2004a; Goffman et al., 2005).

Flux variability analysis

The optimal solution space is explored with FVA by determining the range of flux values of a reaction admissible under optimality (Mahadevan and Schilling, 2003). Simulation of bna572 by linear optimization and FVA was described in detail elsewhere (Hay and Schwender, 2011). In short, linear optimization was used to predict steady-state flux states. In a primary optimization the objective function, sum of all nutrient uptakes and photon uptake was minimized. For flux variability analysis, the value of the objective function resulting from a primary optimization was fixed, and subsequently each reaction in the network was minimized and then maximized.

Carbon balance constraints

For simulation of photoheterotrophy, the carbon balance was constrained as described in Hay and Schwender (2011), according to the constraint equation:

image(1)

In effect this constrains the flux of carbon into TAG in the biomass to be R times the flux of carbon dioxide leaving the network. The coefficient 60.7118 mole carbon per mole TAG (Hay and Schwender, 2011) converts the flux of TAG into biomass (TAG_c::TAG_uni; #399) into carbon molar flux. R can be experimentally determined as CO2 release rates relative to the deposition rates of carbon into lipids. R values experimentally determined for B. napus embryos cultured under continuous light (Schwender et al., 2004a) were used as a model constraint to simulate photoheterotrophy. As described in Hay and Schwender (2011), an R value of 1.1, representing the carbon balance of dark-grown embryos (Goffman et al., 2005), was used to derived the ATP drain flux (#33).

Calculation of relative RuBisCO flux

The predicted relative RuBisCO flux is the rate of production of 3-phosphoglyceric acid by RuBisCO (carboxylase) relative to the total net production by RuBisCO and other reactions in the network (Schwender et al., 2004a). For this computation the network was constrained to organic nitrogen conditions (with amino acids allowed as a nitrogen source; Figure 1), and the carbon balance ratio R varied according experimental values reported previously (Schwender et al., 2004a). Then the rates of formation of 3-phosphoglyceric acid (x3PG) were considered following Schwender et al. (2004a):

image(2)

Specifically, the computation of the flux ratio was defined after assessing all 10 reactions in bna572 that can produce or consume x3PG. Flux variability was computed for different R constraints between 2.63 and 4.15. To resolve compartmentation, enzyme isoforms specific to cytosolic and plastidic 3-phosphoglyceric acid (x3PG_c, x3PG_p) were combined. As a result, three reactions could be excluded from the computation of the ratio because they always consume x3PG. The sum of the two isoforms of d-phosphoglycerate-2,3-phosphomutase (#535, #552) was always non-variably positive. Similarly, 3-phospho-d-glycerate:NAD+ 2-oxidoreductase (#469), the first enzyme of the serine biosynthetic pathway, always non-variably consumed x3PG_p. Among the remaining enzymes, RuBisCO (carboxylase; #57) and the sum of both isoforms of phosphoglycerate kinase (#40, #571) always had non-variable positive values, i.e. non-variably produce x3PG. Therefore, the following flux ratio defines the relative RuBisCO flux based on bna572:

image(3)

Note that d-glyceraldehyde-3-phosphate:NADP+ oxidoreductase (#23), glycerate kinase (#442) and RuBisCO oxygenase (#473) are always inactive, i.e. do not contribute to the ratio. Therefore, it can be stated that the ratio is non-variable because only RuBisCO (#57) and the isoforms of phosphoglycerate kinase (#40, #571) contribute, and all contributing rates are invariable.

Projection of compartmentalized model bna572 onto models used in 13C-MFA studies

For comparison between flux values derived in this study by FVA and values obtained formerly by 13C-MFA of cultured B. napus embryos (Schwender et al., 2006), the compartmentation of reactions in bna572 had to be related to uncompartmented reactions in the former study. The fully compartmentalized model was projected onto the 13C-MFA model with computation of flux variability in the following way. For each pair of metabolites connected in the 13C-MFA model, all reactions in bna572 were determined that interconvert the same two metabolites, including metabolites present in different subcellular compartments. In the secondary optimization those reactions were selected in the objective function. If the directionality in bna572 was defined in the same direction as the parallel reaction in the 13C-MFA network, the objective coefficient was set as ‘1’, otherwise it was ‘−1’. By using the so-defined objective function, this group of fluxes was minimized and then maximized to result in predicted minimum/maximum values of the objective function, which correspond to the 13C-MFA model.

Calculation of carbon conversion efficiency

bna572 was simulated by minimizing the sum of all substrate uptakes under heterotrophy (Ph_tm_exch = 0), allowing the uptake of sugar substrates (sucrose, glucose, fructose) and nitrogen substrates (NO3, NH4+, Ala, Gln, Asn, Glu) in different combinations. Each time the resulting steady-state values of uptake fluxes were used to calculate CCE, defined as:

image(4)

with ‘sum of carbon uptakes’ and ‘CO2 efflux’ (CO2_ap_exch) in units of μmol carbon h−1.

Note that the objective function is defined as minimization of the sum of all substrate uptakes in substrate molar units, whereas for the calculation of CCE, molar substrate uptake rates were converted into carbon molar uptakes. In all cases where combinations of only two substrates were allowed (one sugar with one nitrogen source), the reported CCE value is truly an optimum as if carbon molar uptakes were minimized. However, note that for combinatorial cases with more than two substrate uptakes allowed, minimization of substrate molar uptakes and minimization of carbon molar uptakes can lead to different results. Full exploration of such variation in the objective functions is not possible here because of space limitations. In future, alternative objective functions could be systematically assessed with regards to their ability to better predict experimentally observed uptakes of alternative substrates.

Acknowledgements

This work was funded by the Division of Chemical Sciences, Geosciences, and Biosciences, Office of Basic Energy Sciences of the US Department of Energy through Fieldwork Proposal BO-133. The authors would like to thank the anonymous referees and the editor for their comments and suggestions that helped improve the article.

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