Metabolic network reconstruction and flux variability analysis of storage synthesis in developing oilseed rape (Brassica napus L.) embryos


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Computational simulation of large-scale biochemical networks can be used to analyze and predict the metabolic behavior of an organism, such as a developing seed. Based on the biochemical literature, pathways databases and decision rules defining reaction directionality we reconstructed bna572, a stoichiometric metabolic network model representing Brassica napus seed storage metabolism. In the highly compartmentalized network about 25% of the 572 reactions are transport reactions interconnecting nine subcellular compartments and the environment. According to known physiological capabilities of developing B. napus embryos, four nutritional conditions were defined to simulate heterotrophy or photoheterotrophy, each in combination with the availability of inorganic nitrogen (ammonia, nitrate) or amino acids as nitrogen sources. Based on mathematical linear optimization the optimal solution space was comprehensively explored by flux variability analysis, thereby identifying for each reaction the range of flux values allowable under optimality. The range and variability of flux values was then categorized into flux variability types. Across the four nutritional conditions, approximately 13% of the reactions have variable flux values and 10–11% are substitutable (can be inactive), both indicating metabolic redundancy given, for example, by isoenzymes, subcellular compartmentalization or the presence of alternative pathways. About one-third of the reactions are never used and are associated with pathways that are suboptimal for storage synthesis. Fifty-seven reactions change flux variability type among the different nutritional conditions, indicating their function in metabolic adjustments. This predictive modeling framework allows analysis and quantitative exploration of storage metabolism of a developing B. napus oilseed.


Supply of photoassimilates to developing seeds of Brassica napus

Brassica napus (oilseed rape) forms oil-storing seeds which are non-endospermic, i.e. the embryo itself is the predominant storage organ of the seed. Brassica seeds store mainly oil and protein (Murphy and Cummins, 1989) with rapeseed containing typically between 40 and 45% oil and about 20–25% protein on a dry weight (DW) basis (Gunstone, 2001) and starch being present only transiently during early seed development (da Silva et al., 1997; Kang and Rawsthorne, 1994; Norton and Harris, 1975). Developing embryos are surrounded and presumably nurtured by the liquid endosperm, where high levels of sucrose, fructose and glucose as well as the amino acids Gln, Glu and Ala have been found (Schwender and Ohlrogge, 2002). While sucrose is often considered the principal carbon source in developing seeds, the in vivo uptake of glucose or fructose by the B. napus embryo has been debated (Hill et al., 2003; Morley-Smith et al., 2008) and the capability to use those substrates has been demonstrated by embryo cultures (Hill et al., 2003; Lonien and Schwender, 2009; Schwender and Ohlrogge, 2002). Cultured B. napus embryos also have the capability to alternatively use reduced forms of nitrogen (amino acids) or inorganic NH4NO3 (Junker et al., 2007). Furthermore, developing embryos have photosynthetic potential (Asokanthan et al., 1997; Eastmond et al., 1996; Goffman et al., 2005; King et al., 1998; Ruuska et al., 2004) and can grow under different light levels (Goffman et al., 2005). In conclusion, storage synthesis in developing B. napus embryos can be supported by a variety of different carbon and nitrogen sources and various levels of light.

Central metabolism and carbon partitioning

While partitioning of carbon resources into storage products can be considered at the organ system (Hay and Spanswick, 2006a), organ (Hay and Spanswick, 2006b) and cell membrane (Hay and Spanswick, 2007) levels of biological organization, we consider here the level of cellular biochemical networks. During seed storage deposition, the biosyntheses of different storage compounds require different proportions of metabolic precursors derived from central metabolism, as well as different proportions of energy cofactors (ATP, NADPH) (Schwender, 2008). Therefore, the manipulation of seed composition should require reorganization of the flux distribution in central metabolism and descriptive and predictive models of seed metabolism should be helpful.

Main characteristics of constraint-based modeling

Constraint-based analysis of stoichiometric networks allows simulation of cellular flux states under strict mass balance of all cellular metabolites. Mathematical constraints like reaction irreversibility or measured substrate uptake rates confine a space of possible flux distributions. In flux balance analysis (FBA), flux states are predicted which are optimal with regard to an assumed cellular objective such as maximal biomass yield (Becker et al., 2007; Bonarius et al., 1997; Boyle et al., 2009; Kauffman et al., 2003; Pramanik and Keasling, 1997; Varma and Palsson, 1994). For microbial organisms FBA was successful in predicting in vivo maximal growth yields, substrate preference and the requirement for particular biochemical reactions for cellular growth (Price et al., 2003). For plants, highly compartmentalized stoichiometric models of central metabolism have been reported for developing barley seeds (Grafahrend-Belau et al., 2009) and Chlamydomonas (Boyle and Morgan, 2009). Also analyses of photoautotrophic (Knoop et al., 2010; Montagud et al., 2010) and photoheterotrophic (Golomysova et al., 2010) bacterial- and genome-scale networks derived from the Arabidopsis genome (de Oliveira Dal’Molin et al., 2010a,b; Poolman et al., 2009; Radrich et al., 2010; Williams et al., 2010) were reported.

For the detailed interpretation of FBA results it is important to keep in mind that intracellar flux patterns predicted by linear optimization are typically not unique, i.e. many alternative possible flux scenarios usually operate with the same optimality. This is mainly due to inherent redundancy in metabolic networks (Mahadevan and Schilling, 2003). The complex solution space can be explored by various methods that describe alternative optimal solutions based on the principles of exhaustive enumeration of alternative pathways, random sampling of alternative solutions or by solving a series of linear programming problems (Lee et al., 2000; Mahadevan and Schilling, 2003; Phalakornkule et al., 2001; Schellenberger and Palsson, 2009; Schilling et al., 2000; Wiback et al., 2004a,b). By flux variability analysis (FVA) (Mahadevan and Schilling, 2003) the range of flux values admissible under optimality is considered. To a limited extent this concept has been applied to an unpublished B. napus seed metabolism network (Schwender, 2008) and will be more comprehensively explored in this study.


We report here the construction of a large-scale metabolic network of a developing B. napus seed based on biochemical literature, database information and experimentally derived model constraints, along with detailed documentation of the model structure. For different nutritional conditions the range of possible solutions is described based on using FVA and categorization of resulting flux values or intervals by flux variability types. More detailed discussion of model predictions follows elsewhere (Hay and Schwender, 2011), along with validation of the model by comparison of FVA simulations with results of former studies using 13C metabolic flux analysis (MFA).

Results and Discussion

Bibliomic reconstruction and informatics of a seed metabolic network

A metabolic model of a B. napus developing embryo with 572 reactions (bna572) was reconstructed based on biochemical and physiological knowledge by surveying literature, mining databases and considering the different nutritional options present in planta and some of the nutritional and physiological conditions that allow growth of embryos in cultures (for details see Experimental Procedures). A large-scale stoichiometric network was obtained which allows simulation of the synthesis of seed biomass at steady state under different nutritional conditions. Figure 1 outlines the model by summarizing the major pathways and metabolite exchanges as related to subcellular compartmentalization and the environment. Bna572 contains 10 different compartments, nine of which represent cellular organelles/compartments. Eight interfaces were used for transport or exchange with the environment. There are 11 nutrient uptakes and one light uptake, while oxygen and CO2 can freely exchange with the environment. The synthesis of eight biomass components is summarized in the biomass reaction. Three hundred and seventy-six different metabolites have associations with 10 different compartments. About 25% of all reactions involve transport between compartments, with uniport transport processes being the largest fraction (Figure 2).

Figure 1.

 Schematic overview of the metabolic network of Brassica napus developing seeds, bna572.
Major reactions categories are listed in blue, key uptake metabolites, biomass constituents and absorbed light (Ph) are shown in red. The different compartments are indicated along with the number of associated reactions. Grey arrows denote reactions across membranes, with number of reactions indicated. Fru, fructose; GABA shunt, 4-butyric acid shunt; Glc, glucose; PS-ET, photosynthetic electron transport; R-ET, respiratory electron transport; Sucr, sucrose; TAG, triacyl glycerol; TCA cycle, tricarboxylic acid cycle.

Figure 2.

 Pie chart showing the distribution of reaction types in the reconstruction of Brassica napus central metabolism.
Reactions were annotated computationally according to the procedure in Appendix S15 and the resulting field ‘Type’ in Appendix S5 was used to generate the pie chart. Each reaction belongs to only one category. The following in order of decreasing dominance was applied for a reaction that received more than one annotation (e.g. #4, ‘exchange, transporter, uniporter’ or #131, ‘transporter, electron transport’): Exchange, Uniporter/Symporter/Antiporter, Transporter, One compartment, Electron transport, Other.

While the corresponding genes in the Arabidopsis genome are documented for many reactions (Appendix S10 in Supporting Information), we consider the network a bibliomic reconstruction, mostly based on collecting literature knowledge on metabolic pathways that are recognized as important for biosynthetic activities and specifically representing metabolism during seed development and storage deposition in B. napus and Arabidopsis thaliana as its closed proxy. Recently published genomic reconstructions of A. thaliana (de Oliveira Dal’Molin et al., 2010a; Poolman et al., 2009) are comprehensive representations of all genes with annotated metabolic functions, assembled into a functional stoichiometric network, with compartmentalization realized only for a limited number of reactions and reaction directionality largely arbitrarily selected. It should be noted that, to the degree of completeness and accuracy of gene annotation in the A. thaliana genome, these networks should represent all possible metabolic reactions occurring in any possible cell type of Arabidopsis. Our bibliomic reconstruction bna572 should more specifically represent the particular embryo metabolism.

With 572 reactions the model is slightly larger than other fully compartmentalized large-scale plant models which include 484 and 257 reactions for Chlamydomonas and a barley seed model, respectively (Boyle and Morgan, 2009; Grafahrend-Belau et al., 2009). The proportion of enzymes in the Chlamydomonas model was reported as 74% (Boyle and Morgan, 2009), which is close to the 75% for the ‘one compartment’ annotation of our network bna572 (Figure 2). About 25% of all reactions in bna572 have transport function (Figure 2), very similar to the numbers we could derive from the Chlamydomonas and barley networks. With regards to nutrient uptakes, the possibility of multiple alternative nitrogen sources distinguishes bna572 from other large-scale plant models.

Biomass formation

To derive the biomass composition and growth rate for bna572, developing embryos of B. napus were cultured in liquid media under conditions very similar to those used in previous 13C-MFA studies. Growth in culture approximates a sigmoid pattern (Figure 3) and the biomass composition after culture durations of 5, 10 and 15 days is relatively constant (Table 1). Seeds matured in plants have a composition similar to that of cultured embryos, with the most pronounced difference in the fraction of cell wall material being larger in mature seeds (Table 1). This might account for the presence of seed coat material. While the biomass composition of cultured embryos is similar to formerly reported values (Schwender et al., 2006), we now also account for the fraction of free polar metabolites (Table 1). All model simulations were referenced to about mid culture stage (10 days) by fixing the per embryo growth rate to 1.74 mg DW day−1 (Figure 3) and using the biomass composition data of this stage (Table 1, Appendix S9) to define the biomass flux.

Figure 3.

 Dry weight accumulation of Brassica napus embryos in culture.
Error bars are the standard deviation of three replicates. The curve DW(t) = −0.0059t3 + 0.1938t2 − 0.3649+ 0.6633 (DW, dry weight) is the third-degree polynomial that best fits the data. The slope dDW(t)/dt at = 10 days after culture was 1.74 mg day−1 and was used to constrain the biomass flux. Embryos were grown at 22°C under continuous light (50 μmol photons m−2 sec−1) in a liquid medium containing sucrose, glucose, Gln and Ala as organic substrates.

Table 1.   Biomass composition of Brassica napus (cv. Reston) embryos developing in planta, in culture and of mature seed [values in % dry weight (DW) ± SD, = 4]. Lipids and polar compounds were extracted and protein, starch and cell wall fractions were determined in the nonsoluble residue (see Experimental Procedures). Compounds not listed are DNA and RNA which were estimated to be 0.1% DW each according to literature estimates for seed tissue (Experimental Procedures). For the model simulations the composition after 10 days of culture and the molecular weights of the biomass components were used to formulate the biomass synthesis equation (Appendix S9)
SourceDW per embryo or seed (mg)LipidPolar compoundscProteinStarchCell walld
  1. aEmbryos isolated directly from developing seeds of plants, about 22 days after flowering.

  2. bEmbryos cultured as described in Experimental Procedures.

  3. cContaining mainly sugars and organic acids, represented in the model to be 50% (w/w) sucrose and 50% (w/w) glutamine.

  4. dAfter extraction of lipid and polar compounds, the residue was analyzed for protein and starch content. The remaining mass fraction is accounted for as cell wall.

  5. n.d., not detectable.

In plantaa1.6 ± 0.248.2 ± 3.515.7 ± 1.320.3 ± 1.06.6 ± 0.98.9 ± 0.9
5 days cultureb3.4 ± 0.336.8 ± 1.021.9 ± 1.414.2 ± 0.817.3 ± 0.59.5 ± 1.0
10 days cultureb8.1 ± 0.537.2 ± 0.921.2 ± 0.713.9 ± 2.018.1 ± 1.29.4 ± 1.5
15 days cultureb20.5 ± 2.543.4 ± 2.419.7 ± 0.613.8 ± 1.513.8 ± 1.19.1 ± 1.1
Mature seed2.8 ± 0.141.8 ± 1.19.2 ± 0.322.0 ± 0.5n.d.26.8 ± 0.6

Model constraints defining different nutritional conditions

Combinations of photoheterotrophy (P), heterotrophy (H), organic nitrogen (O) and inorganic nitrogen (I) were simulated as defined in Table 2, specifying the conditions PO, PI, HO and HI. All network optimizations were performed with fixed biomass flux and with light and all substrate uptakes minimized as an objective. To simulate different nutritional conditions, different combinations of substrate uptakes were selectively disabled according to the constraints listed in Table 2. Also the relation between total carbon uptake, CO2 emission and biomass synthesis was used as a carbon balance constraint. We used carbon balances formerly determined experimentally in cultures of B. napus embryos (Goffman et al., 2005; Schwender et al., 2004). The carbon economy of developing B. napus embryos had been experimentally determined based on detailed quantification of total net carbon uptakes, CO2 production and total carbon incorporated into biomass during growth in culture (Goffman et al., 2005; Schwender et al., 2004). With the same experimental system, essentially the same carbon balance is captured if only CO2 emission and the amount of carbon used in oil synthesis are measured in parallel, expressed as the ratio R of moles of carbon incorporated into seed oil to the molar amount of CO2 produced (Goffman et al., 2005; Schwender et al., 2004).

Table 2.   Definition of four models of developing Brassica napus embryo physiological conditions. The biomass flux (0.0725 mg h−1) corresponds to the growth rate of cultured embryos at 10 days after culture (see Table 1 and Figure 3). For four different conditions the nine different flux equality equations were added to the model in different combinations (‘x’) to define photoheterotrophic (P) or heterotrophic (H) conditions along with organic (O) or inorganic (I) nitrogen sources. For the constraint that defines photoheterotrophy, 60.7118 is the number of carbons per triacylglycerol (TAG) (Appendix S9) and 2.9 is the ratio of carbon into TAG to CO2 released at 50 μmol m−2 sec−1 photon flux density
ConstraintFlux equalitySimulated physiological condition
 11 × Ala_ap_exch = 0 x x
 21 × Asn_ap_exch = 0 x x
 31 × Gln_ap_exch = 0 x x
 41 × Glu_ap_exch = 0 x x
 51 × NH4_ap_exch = 0x x 
 61 × NO3_ap_exch = 0x x 
 760.7118 ×  TAG_c::TAG_uni − 2.9 ×  CO2_ap_exch = 0xx  
 81 × Ph_tm_exch = 0  xx
 91 × Biomass_exch = 0.0725xxxx
101 × ATPdrain_c = 2.79xxxx

Definition of unspecified ATP-consuming processes

In many organisms a significant amount of cellular ATP is expected to be used to sustain cellular functions that are not directly associated with biomass synthesis and growth. To account for maintenance energy requirements, the model was fitted to the carbon balance measured in dark-grown embryos (Goffman et al., 2005) in a way similar to Poolman et al. (2009). A generic ATPase (ATPdrain_c, #33, denoting reaction number 33 in Appendix S5) was implemented causing hydrolysis of cellular ATP, which in heterotrophy has an effect on the carbon balance since ATP has to be replenished by oxidation of cellular substrate to CO2. Without any ATP drain flux, simulation of the HO condition results in = 1.67. Constraining the model to = 1.1, the carbon balance measured for dark-grown embryos (Goffman et al., 2005), the HO condition (Table 2) was simulated and the ATP drain flux was maximized, resulting in a value of 2.79 μmol h−1. This value was then imposed onto the ATP drain flux for all conditions (constraint 10 in Table 2). The fixed ATP drain flux accounts for 44 or 48% of all cellular ATP consumption under conditions HO and PO, respectively. While it can’t be ruled out that this unspecified ATP consumption is associated with growth-related processes, we conclude that non-growth-associated maintenance requirements consume up to about 50% of the total cellular ATP production. Masakapalli et al. (2010) estimated this fraction to be >85% for Arabidopsis cell cultures, while Alonso et al. (2007) reported that 89% of cellular ATP was used for other purposes than biomass production.

Note that in particular for FVA, imposing a fixed value to the ATP drain flux is not necessarily the only way the model can be adjusted to the carbon balance measured for dark-grown embryos (= 1.1) (Goffman et al., 2005). The ATP drain generically represents processes that are unfavorable for the total carbon balance. If R is constrained to 1.1 under heterotrophic organic nitrogen nutrition and the ATP drain is not fixed to its maximum 2.79 μmol h−1, FVA will extend the range of optimal values for multiple other reactions with the same effect. This means that instead of the generic ATPase reaction, FVA can predict various other suboptimal energy-consuming processes that might adjust the model to the observed carbon balance.

Modeling constraints defining photoheterotrophy

Photoheterotrophy was simulated based on an R-value of 2.9 (Schwender et al., 2004) formerly reported for embryos grown under low light (50 μmol photons m−2 sec−1; see constraint Eqn 7 in Table 2). Under this imposed carbon balance and with the biomass flux fixed to a constant value of 0.0725 mg h−1, minimization of light and substrate uptakes predicted a photon influx of 5.97 μmol h−1 (Table 3, condition PO). The predicted photon flux indicates that the imposed carbon balance can only be met if photosynthetic electron transport results in production of energy cofactors which otherwise in darkness had to be produced by oxidative processes that release CO2. In particular, linear electron transport through photosystem II (#131), cytochrome b6/f complex (#462) and photosystem I (#461) is predicted, yielding reduced ferredoxin at a rate of 2.99 μmol h−1. Ferredoxin reduces NADP_p at a rate of 1.41 μmol h−1 (#2) and is also used for sulfite reduction (#238) and fatty acid desaturation (#559). Moreover, the proton gradients generated by photosynthetic electron transport yield ATP_p at a rate of 1.92 μmol h−1 (#92).

Table 3.   Model predicted exchange fluxes for developing Brassica napus embryos. Negative flux values denote influx. Predictions from flux balance analysis under combinations of photoheterotrophy (P) and heterotrophy (H) with organic (O) and inorganic (I) nitrogen sources. See Table 2 for model constraints defining the four conditions. Note that none of the listed exchange fluxes had variable values
Exchange fluxSimulated physiological condition
  1. *Values fixed prior to optimization. All fluxes in μmol h−1, except Biomass (mg h−1).


While currently reliable measurements of the absorbed photosynthetically effective photon flux are not available, we can verify that the light-exposed surface area of an embryo allows this magnitude of light flux to be received. At a photon flux density of 50 μmol m−2 sec−1 a surface area of 33.16 mm2 is required to receive 5.97 μmol photon h−1. Based on microscopic photos the projected surface area of an embryo was estimated to be 4.1 mm2 mg−1 DW, or 43.46 mm2 for a 10.6 mg DW embryo (weight at 10 days of culture; Figure 2). Therefore the embryo surface area should be sufficiently large to receive the predicted photon flux.

Objective function

In FBA, a cellular flux distribution is predicted based on mathematical optimization. An objective function often used for the simulation of microbial cells is the maximization of the biomass flux, which refers to the idea that microbial cells have typically evolved to maximize growth performance (Edwards et al., 2001). Instead, assuming that developing seeds make the most efficient use of their carbon sources, we determined the network flux state based on minimization of substrate and light uptakes as the objective function, while the biomass flux was fixed. Since all organic substrates are defined as inputs and the biomass efflux is fixed, CO2 exchange with the environment strictly correlates with the total carbon uptake. Minimization of the sum of substrate uptakes results in minimal or close to minimal carbon uptake and therefore largely captures the rationale of minimal loss of CO2. This rationale is suggested by former studies describing active mechanisms of light-dependent CO2 recapture in developing B. napus seeds (Goffman et al., 2005; Ruuska et al., 2004; Schwender et al., 2004) as well as by findings that the seed coat surrounding developing B. napus embryos in planta constitutes a barrier to CO2 diffusion (King et al., 1998) such that high rates of oil synthesis might only be sustained if CO2 release is minimized. In an evolutionary sense carbon-efficient biochemical processes should be favored, in particular since the synthesis of storage oils entails massive production of CO2 at the step of the pyruvate dehydrogenase reaction (Schwender et al., 2004).

Flux variability analysis

To describe the metabolic capabilities of bna572, the solution space of linear optimization was thoroughly analyzed by FVA to capture the effect of alternative optimal flux pattern by defining bounds to the individual reactions. For the four nutritional conditions defined in Table 2, the system was optimized (see Experimental Procedures, Eqn 3) and fluxes were minimized/maximized according to Eqn 5 (see Experimental procedures) in order to define for each network reaction the range of values admissible under optimality. All resulting values are tabulated in Appendix S13 while Tables 3–5 provide insights into these data. For selected cases, the second optimization was also carried out for a set of multiple reactions simultaneously (see Experimental Procedures, Eqn 6), in effect giving the flux boundaries for combined reactions like enzyme isoforms present in different subcellular compartments.

Table 4.   Distribution of different flux variability types across four different nutritional conditions simulated in developing seeds of Brassica napus. See Table 2 for constraints defining physiological conditions. Using a controlled symbolic nomenclature, the flux values allowed in the optimal solution space are categorized as zero (‘0’), positive (‘+’), negative (‘−’), infinitely large (‘−Inf’, ‘+Inf’) and intervals are indicated by brackets. The number of reactions is tabulated. See Appendices S13 and S14 for flux variability analysis (FVA) output and the fluxes that differ between simulations.
Flux variability typeSimulated physiological conditionAlways this type
  1. P, photoheterotrophy; H, heterotrophy; O, organic nitrogen; I, inorganic nitrogen.

  2. *Determined before optimization.

  3. a‘+’, ‘+*’,’−’, or ‘−*’; b‘[0 +]’, ‘[− 0]’, or ‘[− +]’; c‘[+ +]’ or ‘[−−]’; d‘[−Inf −]’ or ‘[+ +Inf]’; e‘[−Inf +Inf]’, ‘[−Inf 0]’, or ‘[0 +Inf]’; f‘0’ or ‘0*’.

[+ +Inf]22462
[+ +]33422
[− +Inf]77533
[− +]65564
[− 0]11111
[−Inf +Inf]3232323232
[−Inf +]55322
[−Inf −]33563
[−Inf 0]00000
[0 + Inf]22222
[0 + ]1313131311
Total sum572572572572515
Nonvariable, essentiala288290290292278
Finitely variable, substitutableb2019192016
Finitely variable, essentialc44532
Infinitely variable, essentiald559125
Infinitely variable, substitutablee4646423939
Never usedf209208207206194
Table 5.   Results from flux variability analysis for key reactions of selected central pathways. Abbreviations and reaction numbers refer to the complete output in ppendices S13 and S14. Tabulated fluxes in μmol h−1. Intervals are indicated by brackets
Pathway/reactionsPO (μmol h−1)PI (μmol h−1)HO (μmol h−1)HI (μmol h−1)
  1. P, photoheterotrophy; H, heterotrophy; O, organic nitrogen; I, inorganic nitrogen.

Sucrose catabolism and synthesis
Sucrose synthase (SuSy_c, #30)0.2680.3170.350.391
UDP glucose pyrophosphorylase (UGPase_c, #554)0.2260.2750.3080.349
Invertase (INV_c, #29), sucrose-phosphate synthase (SPS_c, #557), sucrose-phosphate phosphatase (Sucrsynth_c, #558)0000
Pyrophosphate-dependent phosphofructokinase (PFP_c, #27)[−0.878, 0.275][−1.046, 0.295][−0.96, 0.573][−1.12, 0.655]
ATP-dependent phosphofructokinase (PFK_c, #26), (PFK_p, #63)[0, 1.153][0, 1.34][0, 1.533][0, 1.775]
Pyruvate, phosphate dikinase (PPDK_c, #21)[−0.837, 0.316][−0.955, 0.385][−0.837, 0.696][−0.955, 0.82]
Pyruvate kinase (PK_c, #22)[0, 1.153][0, 1.34][0, 1.533][0, 1.775]
Fructokinase (FK_c, #31), (FK_p, #537)[0, 0.268][0, 0.317][0, 0.35][0, 0.391]
Phosphoglycerate kinase (c, #571)[0.574, Inf][0.574, Inf][1.498, Inf][1.592, Inf]
Phosphoglycerate kinase (p, #40)[−Inf, −0.124][−Inf, −0.124][−Inf, −0.387][−Inf, −0.316]
Sum of #571, 400.4490.4491.1111.2767
Pentose phosphate pathway (PPP)
#548–551, 52–56[−Inf, Inf][−Inf, Inf][−Inf, Inf][−Inf, Inf]
Oxidative pentose phosphate pathway (OPPP)
Glucose-6-phosphate dehydrogenase (G6PDH_c, #512), (G6PDH_p, #477)0000
Tricarboxylic acid (TCA) cycle
Pyruvate dehydrogenase (PDH_m, #543–545)0.0180.1370.0180.137
Citrate synthase (CS_m, #37)0.0180.1370.0180.137
Isocitrate dehydrogenase (NADP+) (IDH_c, #17)
Isocitrate dehydrogenase (NADP+) (IDH_p, #533)[−1.419, Inf][−1.213, Inf][−0.189, Inf][0.001, Inf]
Isocitrate dehydrogenase (NAD+) (IDH_m, #540)[−Inf, 1.258][−Inf, 1.17][−Inf, 0.553][−Inf, 0.339]
Sum of #533, 540−0.162−0.0430.3620.4
Succinate dehydrogenase (ubiquinone) (Sdh_m, #1)0000
Oxoglutarate dehydrogenase (OGDH_m, #453–455)000.5260.383
Succinate-CoA ligase (ADP-forming) (SUCLA_m, #456)000.5260.383
Peroxisomal metabolism, β-oxidation
Isocitrate lyase (ICL_x, #523), glycine transaminase (#521), isocitrate/succinate antiport (c_x, #524), malate/ketoglutarate antiport (c_x, #522)00−0.526−0.383
Malate synthase (MS_x, #562)0000
β-Oxidation #400–437, 449–4520000
GABA shunt
Glutamate decarboxylase (#483)0000
Rubisco shunt
Ribulose-bisphosphate carboxylase oxygenase (RuBisC_p, #57), phosphoribulokinase (#41)0.20.31800
Calvin–Bassham–Benson cycle
Sedoheptulose bisphosphate aldolase (SBPALD_p, #42), sedoheptulose-bisphosphatase (SBPase_p, #43), fructose-bisphosphatase (#64)0000
Ribulose-bisphosphate carboxylase oxygenase (RuBisO_p, #473), glycolate oxidase (x, #474)0000
Phosphoenol pyruvate (PEP) carboxylation
Phosphoenolpyruvate carboxylase (PEPC_c, #12)0000
Phosphoenolpyruvate carboxykinase (ATP) (PPCK_c, #13)[−0.812, 0.019][−1.048, −0.099][−0.812, 0.019][−1.048, −0.099]
Plastidic pyruvate formation
Pyruvate kinase (PK_p, #58), malic enzyme (NADP+) (ME_p, #49), pyruvate transport (c_p, #95)[0, 0.812][0, 0.812][0, 0.812][0, 0.812]
Mitochondrial transport
Dicarboxylate carrier, model reaction names: OxA_c:Succ_m_anti (#67), Pi_m:Succ_c_anti (#68), Mal_m:Pi_c_anti (#70), Mal_m:OxA_c_anti (#73)[−Inf, Inf][−Inf, Inf][−Inf, Inf][−Inf, Inf]
Sum of #67, 68, 70, 73[−Inf, Inf][−Inf, Inf][−Inf, Inf][−Inf, Inf]
Phosphate carrier (PiC_c, m, c_m, #93)[2.237, 2.256][2.308, 2.445][3.757, 3.775][3.478, 3.615]
Nitrogen assimilation/metabolism
Glutamine synthase (GS_p, #39)0[0, 0.076]0[0, 0.076]
Glutamine synthase (GS_c, #8)0[0, 0.076]0[0, 0.076]
Glutamate synthase (NADPH) (Glusynth_p, #45)[0, 0.042]0[0, 0.042]0
Glycine decarboxylase (GDC_m, #457–459)−0.003−0.003−0.265−0.194
Glutamate dehydrogenase (GDH_p, #46)[−0.045, −0.003]−0.164[0.217, 0.259]0.028
Glutamate dehydrogenase (GDH_m, #484)0000
Glutaminase (GLS_c, #9)[0, 0.042]0[0, 0.042]0
Light-dependent reactions
Ferredoxin-NADP+ reductase (#2)1.4071.319−0.086−0.086
Ferredoxin plastiquinone oxidoreductase (#3)0000
Photosystem I (#461), photosystem II (#131)1.4931.40500
H+-transporting two-sector ATPase (#92)1.9181.80600
Mitochondrial electron transport and oxidative phosphorylation
NADH_m dehydrogenase (ubiquinone) (#90)0.9690.9991.4511.378
NADH_c dehydrogenase (ubiquinone) (#89)0000
Ubiquinol-cytochrome-c reductase (#463)0.9690.9991.4521.378
Cytochrome-c oxidase (#464)0.9690.9991.4521.378
H+-transporting two-sector ATPase (#91)2.2372.3083.2313.095

Nutritional variations and exchanges with the environment

To demonstrate the ability of bna572 to grow under the various nutritional conditions (Table 2), the predicted exchange fluxes with the environment are shown in Table 3. All exchange fluxes have nonvariable values and, with regard to alternative carbon and nitrogen sources, strict selectivity can be observed. For example, while uptakes of sucrose, glucose and fructose are allowed, sucrose is the only sugar used (Table 3). Similarly, if bna572 is restricted to use organic nitrogen (Table 2, conditions PO, HO), Gln is the only nitrogen source used (Table 3). For inorganic nitrogen availability (conditions PI, HI), inline image is solely used (Table 3). Besides the strict selectivity, the ability of the network to use substrates other than sucrose, Gln and inline image can be demonstrated if the uptakes are constrained accordingly (Hay and Schwender, 2011).

The exchange fluxes shown in Table 3 also demonstrate that the network simulations capture the main features of the physiological conditions they represent. As expected by oxygenic photosynthesis, both photoheterotrophic modes (PO, PI) are characterized by photon uptake and O2 efflux, while under heterotrophy there is O2 influx as expected if respiration takes place (Table 3). Furthermore, the CO2 exchange differs depending on the involvement of light. Photoheterotrophy (PO, PI), defined by imposing an experimentally observed carbon balance R (constraint 7, Table 2), results in a net CO2 efflux (Goffman et al., 2005; Schwender et al., 2004). The photoheterotrophic CO2 effluxes are more than twice as low as those under both heterotrophic conditions (Table 3). In consequence of the reduced CO2 efflux under photoheterotrophy, a lower sucrose uptake is needed than under heterotrophy (Table 3). Hay and Schwender (2011) report further simulations of heterotrophic nutritional conditions, as well as photoheterotrophic modes with various R-values.

Dependence of simulation results on biomass composition

Note that the comparison of nutritional cases is based on a constant biomass efflux. The model was referenced to the dry matter accumulation rate at 10 days in culture under photoheterotrophic/organic nitrogen conditions (Figure 3). Since the actual growth rates under different conditions might vary, care must be taken with comparison of absolute flux values between the nutritional conditions. The interpretations and conclusions below are mostly based on qualitative categories (flux variability types).

While in simulations of bna572 most reaction rates are determined by linear optimization, between 176 and 178 of the reactions are determined prior to optimization. Those reactions are strictly stoichiometrically dependent on other reactions that were assigned fixed values prior to optimization. An asterisk (*) is used to identify this type of reaction. Most reactions of this category relate to biomass formation, i.e. they depend on the accumulation rate of total dry matter (Figure 3), the dry matter composition (Table 1) and the molar composition of dry matter fractions (Appendix S9).

Flux variability analysis and variability types

We compared flux variability across four different nutritional conditions based on qualitative categories (Appendix S13). In Table 4 flux variability for all fluxes is summarized based on categorizing all 572 reactions into 18 different variability types defined by a symbolic nomenclature. For each nutritional condition the frequencies of variability types are tabulated, while the column headed ‘Always this type’ shows how many reactions are of the same variability type across all four conditions. All 18 variability types are further combined into six disjoint sets (classes). The classes consider reactions with nonzero values (‘nonvariable’), variable ranges of values (‘variable’) or the value zero (‘never used’; Table 4). Furthermore, reactions that cannot assume zero under optimality are ‘essential’ for network performance (Table 4). Reactions that can assume either zero or non-zero values are judged to be substitutable by other reactions (‘substitutable’; Table 4). Finite and infinite bounds are also distinguished (Table 4). In addition to Table 4, particular reactions exemplified below are reported with simulated reaction rates in Table 5.

Essential reactions

In total between 297 and 307 reactions (51.9–53.7%) are categorized as essential since under optimality they assume nonzero values (i.e. are nonvariable) or a range of values that does not include zero (Table 4, ‘essential’). This means that if the rate of such an essential reaction is set to zero, the model network would not operate in an optimal fashion. In addition, if reactions that contribute to biomass formation are inactivated, no steady-state flux solution can be found (infeasibility).

Multiple reactions are nonvariable and essential across all nutritional simulations. Examples that fall under type ‘+’ or ‘−’ (Table 4) can be found in the sucrose catabolism pathway (Table 5, sucrose catabolism reactions #30, 554), the TCA cycle (#543–545, 37, 17), mitochondrial electron transport and oxidative phosphorylation (#90, 91, 463, 464) and nitrogen assimilation/metabolism (#457–459) (Table 5). Optimality generally requires these steps of catabolism and mitochondrial respiration to be active, whether the developing embryo cells receive energy solely from oxidation of organic compounds (heterotrophy) or with contribution of photosynthetic processes (photoheterotrophy). The category ‘nonvariable, essential’ also includes reactions closely related to biomass synthesis. Since in our simulations the biomass flux is fixed, many fluxes for the syntheses of the biomass compounds and of their building blocks like amino acids or nucleotides are nonvariable as well because they are linearly dependent on the biomass flux. Accordingly, across all simulations a set of 167 reactions (29% of all fluxes) is always calculable before optimization (Table 4, ‘+*’ and ‘−*’). Examples are the sulfate, phosphate and biomass exchange reactions shown in Table 3.

Essential reactions can also be variable, like the transport of inorganic phosphate across the mitochondrial envelope (‘[+ +]’; #93 Table 5, mitochondrial transport) and isoforms of phosphoglycerate kinase (‘[+ +Inf]’, #571; ‘[−Inf −]’, #40; Table 5, glycolysis).

Inactive reactions

The flux variability type categorization identifies another general type of reaction that has the same value for all alternative optima. Across all four nutritional conditions between 206 and 209 (36–36.5%) of all reactions are inactive and do not carry flux under optimality (Table 4, ‘Never used’). Several reactions are never used (‘0*’) because they are strictly stoichiometric and depend on the knockout constraints imposed to define specific nutritional conditions (Table 2). Type ‘0*’ could also indicate that a reaction can never have a nonzero rate because a metabolite participating in the reaction is a metabolic dead end. Since bna572 does not contain any reactions that have variability type ‘0*’ under any simulated conditions (Table 4), no such dead ends are present.

Reactions of the type ‘0’ could be used, but would render a penalty on the optimal value of the objective function. Several pathways are of type ‘0’ under any simulated nutritional condition, such as the large number of reactions of peroxisomal β-oxidation (Table 5, peroxisomal metabolism), which makes sense for the simulation of a developing embryo with oil deposition. Degradation of fatty acids in parallel with the de novo fatty acid synthesis would constitute a futile cycle. Reactions of the Calvin–Bassham–Benson cycle (Table 5), in particular the hydrolysis of fructose- and sedoheptulose-bisphosphate and a stoichiometrically dependent aldolase (#42, 43, 64), always have zero flux. These steps would be necessary under photoautotrophic conditions for the cyclic regeneration of pentose phosphates from triose phosphates. Not surprisingly, photorespiration (Table 5) is inactive, being generally thought of as a wasteful cycle making carbon fixation less efficient (Douce and Neuburger, 1999). Consistent with the developing embryo being a sink for maternally supplied photoassimilate, sucrose synthase (#30) and UDP glucose pyrophosphorylase (#554) of sucrose catabolism (Table 5) are active, while reactions #557 and 558 of sucrose synthesis (Table 5) are always inactive. Both being active simultaneously would create a wasteful cycle (Geigenberger and Stitt, 1991). Invertase (Table 5, sucrose catabolism, #29) is another enzyme not used as this pathway requires more ATP for sucrose catabolism than the sucrose synthase pathway. Within mitochondrial electron transport (Table 5), the external NADH dehydrogenase (#89) never carries any flux since its participation in the electron transport chain results in smaller proton motive force than if the internal dehydrogenase is used (#90). More unexpectedly, the tricarboxylic acid (TCA) cycle (Table 5) never functions as a full cycle since succinate dehydrogenase (#1) is always zero. Also surprising, in PEP carboxylation (Table 5) phosphoenol pyruvate (PEP) carboxylase (#12), a key enzyme for anaplerosis of the TCA cycle, is not active under any nutritional simulation, while PEP carboxykinase (#13) appears to be used in its place (see also Hay and Schwender, 2011). Cyclic photophosphorylation/electron transport (Table 5, light-dependent reactions, #3) which produces ATP but no NADPH, is always inactive. Physiological studies on B. napus embryos concluded the predominant activity of linear electron transport and photophosphorylation, which supplies both NADPH and ATP to biosynthetic reactions (Asokanthan et al., 1997). The glyoxylate cycle (malate synthase, #562) and the GABA shunt are also never used (Table 5).

Finally the oxidative pentose phosphate pathway (OPPP, Table 5) is never used in cytosol and plastid, i.e. apparently being generally suboptimal. This observation is surprising because the oxidation of glucose 6-phosphate in the OPPP is regarded as a key producer of reductant for biosynthetic processes, in particular fatty acid synthesis (Eastmond and Rawsthorne, 2000; Rawsthorne, 2002). Instead the model predicts a number of other dehydrogenase enzymes as possible producers of NADPH in the plastid (Hay and Schwender, 2011).

The large number of 194 consistently inactive reactions (Table 4) may seem inappropriate to include in bna572. However, the presence of these reactions, e.g. β-oxidation, was justified by biochemical literature on seed storage synthesis. In addition, a large number of unused reactions in simulations of biomass formation is not unusual. Only 232 out of 1406 reactions carried flux in an Arabidopsis genome-scale model (Poolman et al., 2009). Furthermore, even though a reaction is never used, it is important to realize that its degree of suboptimality in terms of the objective function and constraints may be minor, a subject that is explored elsewhere by Hay and Schwender (2011).

Variable reactions

If FVA results in a range of possible values for a reaction rate, the actual in vivo flux rate is predicted to be within this range. Across all four nutritional conditions 23 or 24 reactions (4 or 4.2%) have flux values variable within finite bounds (‘Finitely variable’, Table 4), and 51 reactions (8.9%) are variable with infinite bounds (‘Infinitely variable’, Table 4).

Reactions that are variable can be related to network redundancy and the existence of alternative pathways (Mahadevan and Schilling, 2003). For an Escherichia coli genome-scale network, after elimination of isoenzymes, and simulation of growth on glucose, the fraction of variable reactions was 3.0% (Mahadevan and Schilling, 2003). In our network, across all four conditions, close to 13% of the reactions are variable (Table 4, ‘Finitely variable’ and ‘Infinitely variable’), which includes most parts of intermediary metabolism (see examples in glycolysis, pentose phosphate pathway, TCA cycle, Table 5). Comparing bna572 simulations with a smaller mostly uncompartmentalized model used in 13C-MFA (Hay and Schwender, 2011) also demonstrated that compartmentalization of parallel, redundant pathways contributes a big part to this complexity of the solution space. Therefore, even more than for prokaryotic models, prediction and interpretation of flux scenarios based on single linear optimization could be misleading since the optimal solution space allows many alternative solutions. To avoid this problem, Grafahrend-Belau et al. (2009) used a modified simulation to predict fluxes in a compartmentalized model of developing barley seeds. They first applied optimization by maximization of biomass flux, followed by quadratic minimization of the sum of intracellular fluxes. This second step selects one out of many alternative optimal solutions with the goal of evenly distributing flux load over parallel pathways. Solutions predicted in this way were then interpreted in detail with regard to the usage of specific pathways and directionality of particular enzymes under particular physiological conditions (Grafahrend-Belau et al., 2009). Based on our findings on high flux variability in a compartmentalized plant model, we conclude that such detailed analysis should be done based on consideration of flux variability.

Substitutable reactions

If a variable reaction has a range of possible optimal values that includes zero, it is judged substitutable (Table 4, ‘Substitutable’). The 59–66 (10.3–11.5%) substitutable reactions (Table 4) comprise mostly transport reactions and enzyme reactions for which parallel reactions exist in different subcellular compartments. Accordingly, fructokinase (glycolysis, Table 5) and isocitrate dehydrogenase (TCA cycle, Table 5) each have substitutable isoforms that can replace each other. Furthermore, in glycolysis (Table 5) pyrophosphate-dependent and ATP-dependent glycolytic enzymes can replace each other: pyrophosphate-dependent phosphofructokinase (#27) can replace ATP-phosphofructokinase (#26) and pyruvate phosphate dikinase (#21) can replace pyruvate kinase (#22). The activity of those pyrophosphate-utilizing enzymes was also predicted in a model of the developing barley seed (Grafahrend-Belau et al., 2009). Furthermore, plastidic pyruvate kinase (#58), plastidic malic enzyme (#34) and a plastid pyruvate transporter (#95) represent three substitutable (‘[0 +]’) pathways for the formation of the fatty acid synthesis precursor plastidic pyruvate (Table 5, plastidic pyruvate formation). This prediction is discussed elsewhere (Hay and Schwender, 2011).

Unbounded reactions

Reactions with infinite bounds (infinitely variable and substitutable) can be found among the antiporter reactions in the mitochondrial envelope (mitochondrial transport, Table 5). In particular, summation of the model reaction equations for the dicarboxylate carriers OxA_c:Succ_m_anti (#67), Pi_m:Succ_c_anti (#68), Mal_m:Pi_c_anti (#70) and Mal_m:OxA_c_anti (#73) (reverse direction) shows that these four antiporters can form a substrate cycle without net conversion of metabolites (i.e. a biochemical loop). Across all nutritional simulations the variability type of every reaction in the loop as well as the summary reaction is ‘[−Inf +Inf]’ (Table 5). Any magnitude of flux in either direction around this loop does not affect the system-wide flux balance (i.e. the optimal value of the objective function). The presence of very large flux values certainly has no physiological relevance and is considered thermodynamically infeasible (Mahadevan and Schilling, 2003). Elimination of substrate cycles would therefore be an improvement of the model. For example, adding flux capacity constraints or flux ratio constraints derived from 13C-MFA might eliminate the occurrence of unbounded variabilities and further shrink the solution space.

The function of infinitely variable reactions can be further described if the combined flux, e.g. through enzyme isoforms, is considered during optimization. Groups of reactions with infinite bounds can have finite bounds if the summed reaction is considered. This can be done in the secondary optimization of FVA, by selecting two reactions in the objective function to be optimized in their sum. For example, the two phosphoglycerate kinase isoforms (Table 5, glycolysis, #571, 40) or the two isoforms of isocitrate dehydrogenase (Table 5, TCA cycle, #533, 540) have infinite bounds, but each pair is nonvariable essential in its sum (Table 5). This kind of reaction lumping in FVA is very useful for comparison of bna572 with outcomes of 13C-MFA, e.g. where multiple reactions that connect glyceraldehyde 3-phosphate and 3-phosphoglycerate were modeled as one reaction (Hay and Schwender, 2011).

Few reactions change flux variability type dependent on nutritional conditions

Remarkably, 515 reactions (90%) have the same variability type across all four conditions (Table 4), i.e. for 57 reactions (10%) the variability type differs by condition. Of these, 14 change between ‘0*’ and ‘0’, ‘+’ and ‘+*’ or ‘−’ and ‘−*’, i.e. the difference is whether the value is a result of optimization or already known prior to optimization (see, e.g. alanine exchange for conditions PO and PI, Table 3). Many other reactions that change variability type also have a transport function. Appendix S13 (first column) marks out all the reactions that differ in variability type according to nutritional simulation, and the figure in Appendix S14 depicts this subset of reactions identified by comparative flux variability analysis in a searchable, graphical form.

The difference between heterotrophy and photoheterotrophy is reflected in changes in variability types of many reactions. Photon exchange is ‘0*’ under heterotrophy and becomes an uptake (‘−’) under photoheterotrophy (Table 3). Reactions of photosystems I and II, photophosphosphorylation and the Rubisco shunt change from ‘+’ to ‘0’ between photoheterotrophy and heterotrophy (Table 5, Rubisco shunt, light-dependent reactions). Ferredoxin-NADP+ reductase (#2) reduces NADP for photoheterotrophy (‘+’) consistent with its function in the light-dependent reactions of photosynthesis. Under heterotrophy it works in the direction of ferredoxin reduction (negative flux, Table 5), feeding multiple ferredoxin-dependent plastidic reactions (Hanke et al., 2004). In contrast to photoheterotrophy-specific reactions, some reactions of the TCA cycle (oxoglutarate dehydrogenase, #453–455; succinate-CoA ligase, #456) are used only under heterotrophy (Table 5), indicating reduced activity of the TCA cycle under photoheterotrophy. Similarly, various reactions of peroxisomal metabolism (Table 5) are used only under heterotrophy. The sum of isocitrate dehydrogenase isoforms (#533, 540) switches from decarboxylation in heterotrophy to the reverse in photoheterotrophy (Table 5). The changes in TCA cycle, Rubisco shunt and peroxisomal metabolism in relation to photoheterotrophic seed metabolism are explored in more depth by Hay and Schwender (2011).

There are also reactions with variability type differences between organic and inorganic nitrogen conditions. With regards to reactions of nitrogen assimilation and metabolism (Table 5), condition-dependent differences in variability type are apparent. Yet it is hard to clearly recognize known pathways to be specific to either ammonia assimilation or the use of organic nitrogen sources. As a classical pathway, glutamine synthase and glutamate synthase can be combined to assimilate ammonia into Glu (Lancien et al., 2000). Yet both enzymes are never active together under the same condition (Table 5, nitrogen assimilation, #8, 39, 45). Glutamate dehydrogenase can assimilate ammonia as well, but only the plastidic isoform (#46) is active and assimilates ammonia (negative flux) only under photoheterotrophy (Table 5). In contrast, another enzyme, glycine decarboxylase, always operates in the direction of ammonia fixation (negative flux, Table 5). Suggesting an anaplerotic function in the coordination between nitrogen assimilation/metabolism and carbon metabolism, PEP carboxylation shows a difference between nitrogen nutritional conditions, where flux in the direction of carboxylation is essential only under inorganic nitrogen availability (Table 5). Further reported simulations of nitrogen metabolism and the carboxylation of PEP are found in Hay and Schwender (2011).


Bna572 is a large-scale highly compartmentalized plant metabolic network, representing storage synthesis of a B. napus developing embryo. The construction process has been made highly transparent by detailed documentation, such as the definition of directionality for reactions based on decision rules (Appendix S5) and the association of reactions to primary literature (Appendix S7) and to database information, including web-links to Arabidopsis pathways and gene models (Appendix S10). This makes bna572 readily usable, extendable and adaptable to other plant systems.

We demonstrated that the model allows simulation of various physiological conditions relevant to B. napus developing embryos in particular considering photoheterotrophy, heterotrophy and the availability of different nitrogen sources. The range of possible optimal flux states was described based on FVA within and across the four simulated conditions. To facilitate the interpretation of the resulting large flux datasets we introduced a categorization into flux variability types. Comparative FVA across four nutritional conditions revealed that 10% of all reactions change flux variability type accordingly, one-third of all reactions are never used in the optimal solution space, and approximately 13% of the 572 reactions have flux variability, i.e. a range of possible values exists.

As a result of this study, certain refinements of the model are indicated. A significant fraction of reactions has infinite variability bounds, indicative of biochemical loops. An important refinement of the model will be to identify and eliminate such loops (Beard et al., 2002; Price et al., 2006). Furthermore, the model can be further constrained by measurement of uptake rates of different substrates and based on flux ratio constraints derived from 13C-tracer experiments.

To date probably any kind of biological model must be considered a largely simplified representation of in vivo reality. Constraint-based analysis, like our analysis of bna572, allows us to simulate large-scale stoichiometric networks with a relatively small number of model parameters (Palsson, 2000; Price et al., 2003). While this means that the metabolism of a whole cell can be captured, one always has to be aware of the limitations and the possibility of unrealistic model predictions. What is important here is model validation by experimental data. There is overall good agreement between flux predictions by bna572 and former results from 13C-MFA as described in detail elsewhere (Hay and Schwender, 2011). However, there are disagreements as well. For example, bna572 predicts the OPPP not to be used under all simulated conditions (Table 5) although by 13C-MFA the pathway was found to be active under photoheterotrophy (Schwender et al., 2003). Better predictive fidelity might be possible by the evaluation of various other possible objective functions (Schuetz et al., 2007).

Experimental Procedures

Stoichiometric network reconstruction

A network of metabolic reactions (Appendix S5) of developing Brassica seeds was reconstructed by mining textbooks (Dennis et al., 1997b), primary literature (Appendices S5 and S7) and the databases KEGG (Kanehisa et al., 2006), AraCyc (Mueller et al., 2003; Zhang et al., 2005) and PlantCyc ( See the Supporting Information for how the network was reconstructed and annotated (Appendix S1), how the reconstruction was used to formulate mathematically a flux balance problem (Appendix S2) and how reaction directionality was assigned (Appendix S3). For the actual reconstruction and annotations in various formats, see the MATLAB® file (Appendix S4), spreadsheet (Appendix S5) and SBML (Appendix S6). A metabolite abbreviation dictionary with KEGG compound numbers and hyperlinks is in Appendix S8.

In short, bna572 contains pathways that have been recognized to be common to higher plants. The reactions of plant central metabolism included in the network can be categorized by assimilation of the macronutrients nitrogen, sulfur and phosphorus (Taiz and Zeiger, 2006), uptake of sugars and amino acids, fatty acid and storage oil synthesis and breakdown (Graham, 2008; Mueller et al., 2003), amino acid and storage protein synthesis (Mueller et al., 2003), nucleotide and polynucleotide synthesis (Mueller et al., 2003), starch storage (da Silva et al., 1997), cell wall synthesis, cytosolic and plastidic glycolysis (Dennis et al., 1997a), reactions of glyoxylate cycle and gluconeogenesis (Graham, 2008), anaplerosis and the TCA cycle (Hill, 1997; Huppe and Turpin, 1994), oxidative and reductive pentose phosphate pathways (Hutchings et al., 2005), γ-aminobutyric acid (GABA) shunt (Breitkreuz and Shelp, 1995; Fait et al., 2008), one-carbon metabolism (Hanson and Roje, 2001), the photorespiratory pathway (Douce and Neuburger, 1999), cyclic and noncyclic photophosphorylation (Prezelin and Nelson, 1997) and mitochondrial oxidative phosphorylation (Lambers, 1997). In addition, a wealth of information specific to metabolism and oil synthesis in developing seeds of B. napus and its close relative A. thaliana was used in the reconstruction process (see Appendix S1).

Each reaction in our network was manually curated with regard to reaction stoichiometry, subcellular localization and directionality. Uni- or bidirectionality was defined based on a set of decision rules, representing coarse thermodynamic guidelines about reaction directionality (Appendix S3). By default each particular reaction was defined to be bidirectional, and if one of the particular rules applied, the reaction was defined irreversible. In multiple cases literature information on physiological reversibility was available and differed from the rules decision. In these cases an ‘overruling assumption’ is documented in Appendix S5. In addition, for all reactions with EC numbers, reference data were automatically retrieved from the KEGG database (Appendix S10) and served as validation of reaction stoichiometries.

Various annotations were made to the reactions in Appendix S5. Pathway associations were described in field ‘Category’. The various reaction name fields (e.g. ‘Reaction name’) were assigned according to Appendix S1. Based on a controlled nomenclature, the field ‘Type’ describes the function of a reaction, and was used to generate descriptive statistics of the bna572 reconstruction (Figure 2, Appendices S11 and S12). See Appendices S1 and S15 for more information about ‘Type’.

Exchange reactions and biomass synthesis

Exchange reactions (Appendix S5, Type ‘exchange’) allow metabolites to enter and/or leave the metabolic network and were formulated considering the nutritional physiology of the seed. According to analysis of liquid endosperm surrounding the embryo in planta (Schwender and Ohlrogge, 2002), the network considers glucose, fructose, sucrose, glutamine, glutamate, alanine and asparagine as organic nutrient uptakes, as well as ammonia and nitrate as inorganic nitrogen uptakes. The ability of B. napus embryos to grow on such substrates has been documented (Hill et al., 2003; Junker et al., 2007; Schwender and Ohlrogge, 2002). Photon influx (#6) allows for photoheterotrophic growth while oxygen (#5) and CO2 (#4) can freely exchange with the environment. Biomass leaves the metabolic network (#241) and is composed of triacylglycerol (TAG), storage protein, starch, free sucrose and glutamine, cell wall polymer, DNA and RNA (Appendix S1). Note that exchange fluxes are negative for influx and positive for efflux by definition.

Embryo culture experiments

Brassica napus cv. Reston embryos were dissected aseptically about 15 days after flowering and grown in a liquid medium containing sucrose (80 mm), glucose (40 mm), Gln (35 mm) and Ala (10 mm) (Schwender et al., 2006), at 22°C under continuous light (50 μmol m−2 sec−1). After different culture durations, embryos were harvested and the DW determined. In addition, for cultures grown for 5, 10 and 15 days, embryos were harvested and the fractions of lipid, protein, starch and free metabolites were determined as described before in detail (Lonien and Schwender, 2009). In short, after hot extraction using a biphasic solvent system (CHCl3/methanol/H2O, 8:4:3 v/v; Folch et al., 1957), the DW fractions of lipids, polar compounds and insoluble material (cell pellet) were obtained. Protein determination was based on elemental analysis of the cell pellet using on a conversion factor of 5.64 (g protein/g nitrogen) (Schwender et al., 2006). Starch in the cell pellet was quantified using a starch assay kit (Sigma, SA-20; If the determined amounts of protein and starch were subtracted from the original weight of the cell pellet, the remaining weight was assumed to represent cell wall material and nucleic acids. The RNA and DNA were estimated to have a concentration of 0.1% (w/w), based on similar low amounts found in literature for seeds from different species (Rogers and Bendich, 1985; Suzuki et al., 2004).

Biomass synthesis equation and flux units

In the stoichiometric model the biomass synthesis equation (#368) represents the formula


where Wi is the dry weight fraction and MWi is the molecular weight in g mmol−1 of biomass component i. Using the biomass composition constraints reported in Appendix S9, by Eqn 1 the explicit biomass deposition equation (#368) is


We constrain the flux of this reaction to 0.0725 mg DW h−1 (Figure 3). Hence the biomass synthesis flux (#368) has units of inline image or μmol h−1, the biomass exchange flux (#241) has units of mg DW h−1, and all other fluxes in the network have units of μmol h−1.

Flux balance problem

Appendix S2 should be consulted for a detailed explanation of how we formulate the flux balance problem as a linear program. The linear program is


where x∈ Rn is an optimization variable (flux vector), p′ is an optimal value, A∈ Rm×n is the equality constraint matrix, b∈ Rm is the vector of equality constraint values, lb∈ Rn is the vector of flux lower bounds, ub∈ Rn is the vector of flux upper bounds, cT is the transpose of the vector of objective function coefficients c∈ Rn, m is the number of equality constraints (rows in A), and n is the number of fluxes (columns in A). A is partitioned into A1 and A2. The upper set of equality constraints A1 are steady-state mass balances. Accordingly, A1 is the stoichiometric matrix (S) with columns corresponding to reactions in Appendix S5 (see also Appendix S4, field ‘RN’) and rows corresponding to sorted balanced metabolites (Appendix S4, field ‘M’). A2 contains the simulation-specific constraints specified in Table 2. The objective function is the sum of light, sugar, amino acid, inorganic nitrogen, phosphate and sulfate exchange fluxes times negative one (exchange influxes are defined negative). In practice, A1, lb, ub and c are automatically populated directly from Appendix S5 using an ActiveX server and object-oriented methods in MATLAB®. Both the MATLAB® file (Appendix S4) and the Excel spreadsheet (Appendix S16) contain all coefficient matrices and vectors described above.

Nutritional manipulations

Type of nutrition was manipulated through equality constraint functions in A2 (Table 2). For photoheterotrophy, the flux of carbon into TAG in biomass was calculated as 60.7118 moles carbon per mole TAG and constrained to be 2.9 times the CO2 leaving the network (Schwender et al., 2004). Light exchange was constrained to zero to simulate heterotrophy. In the case of organic nitrogen nutrition, nitrate and ammonia exchanges were blocked. Amino acid exchange reactions were knocked-out for the inorganic nitrogen case.

Carbon balance constraint

In former studies with cultures of B. napus embryos, the carbon balance was experimentally determined and expressed as R, the ratio of carbon incorporated into oil to carbon released as CO2 during culture (Goffman et al., 2005; Schwender et al., 2004). Given a fairly constant increase of all biomass components in culture (Table 1), and based on the biomass composition defined in the model, R effectively defines how much carbon is stored in biomass relative to the amount of carbon released as CO2. The ratio equation is added to the model as follows (see Table 2):


where the coefficient 60.7118 denotes the number of carbon atoms per mol TAG, being defined by the fatty acid composition (Appendix S9).

Linear program solving

We used the revised simplex method of the MATLAB® MEX interface for the GNU Linear Programming Kit (GLPK) library (glpk.m of Simulations were carried out in MATLAB® along the lines of previous toolbox development (Hay and Spanswick, 2006a) but using new object-oriented programming features (MATLAB® version R2009b).

Fluxes determined prior to optimization and other subsets

To find the set of reactions with a flux determined prior to optimization (flux variability types in Table 3 marked ‘*’) a basis for the null space of the equality constraint matrix A was computed with the function null.m (MATLAB®). Rows of the resulting matrix that had a norm <10−7 were identified and used to judge the corresponding reactions as determined before optimization. To find other subsets (Appendix S5) we used Metatool (Pfeiffer et al., 1999) (MATLAB® implementation 5.1, subsets.m and kernel.m).

Flux variability problem and variability type assignment

Flux values resulting from a single linear optimization typically are not unique. This means there is a large set of alternative solutions, with identical value for the objective function. For FVA the optimal value after primary optimization defines an additional model constraint for secondary optimization steps to determine minimum and maximum flux values for each reaction in the network. Accordingly, for each reaction j without an invariable rate determined prior to optimization, two linear programs were solved:


The first linear program gives the minimum value of a flux (pj) and the second one gives the maximum value (− pj). If the number of feasible points approaches positive infinity and the optimal value approaches negative infinity, then pj or pj is assigned ‘−Inf’ (−∞). If reaction j could be determined prior to optimization, then pj = − pj = xj where x is obtained from Eqn 3.

Qualitative flux variability types were assigned by comparing the minimum and maximum flux values of each reaction. The variability types are based on a controlled nomenclature which has both symbolic and textual features. For example, if pj = − pj = 0 then the variability type assigned to reaction j was ‘0’. If the variability type could be determined prior to optimization, then a ‘0*’ was applied (see Table 4 for a complete description of the variability type nomenclature). Flux variability was judged as inline image and flux inactivity as inline image. Decreasing this tolerance by an order of magnitude to 10−8 μmol h−1 did not change the distribution of the annotated flux variability types.

The complete output in Appendix S13 is based on the generation of 2288 variability types and 4576 flux bounds. Of these, 1416 bounds were determined without optimization and 3160 bounds were solved in 3164 optimization problems.

Flux variability analysis of summary reactions

We applied FVA to summary reactions (lumped reactions) according to Eqn 5 after substituting the appropriate sum of reaction rates for xj in the objective function. More formally, in Eqn 5 note that xj = cTx where c is a unit vector with element cj = 1. Accordingly for FVA of summary reactions we replace xj in Eqn 5 with inline image such that inline image if the summary reaction contains reaction j with directionality as written in Appendix S5, inline image if reaction j is flipped, and inline image if reaction j is not in the summary reaction:


where inline image is the minimum flux bound of the summary reaction and inline image is the maximum value. This technique is also used extensively in further studies on bna572 (Hay and Schwender, 2011).

Maintenance respiration requirement

The fraction of the total ATP demand attributed to nongrowth-associated maintenance requirements was calculated as the fraction of the ATP drain flux (ATPdrain_c, #33) divided by the sum of net ATP consumption rates for all reactions in the network. The ATP consumption rate of a reaction was determined by the reaction stoichiometry in A and the flux distribution in x resulting from Eqn 3. Note that a transporter that both consumes and produces ATP has a net consumption rate of zero.


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 Field Work Proposal BO-133. The authors would like to thank Joachim Lonien for technical assistance and the anonymous referees and the editor for their comments and suggestions that helped to improve the manuscript.