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Plant Physiol. Nov 2009; 151(3): 1570–1581.
PMCID: PMC2773075

A Genome-Scale Metabolic Model of Arabidopsis and Some of Its Properties1,[C][W]

Abstract

We describe the construction and analysis of a genome-scale metabolic model of Arabidopsis (Arabidopsis thaliana) primarily derived from the annotations in the Aracyc database. We used techniques based on linear programming to demonstrate the following: (1) that the model is capable of producing biomass components (amino acids, nucleotides, lipid, starch, and cellulose) in the proportions observed experimentally in a heterotrophic suspension culture; (2) that approximately only 15% of the available reactions are needed for this purpose and that the size of this network is comparable to estimates of minimal network size for other organisms; (3) that reactions may be grouped according to the changes in flux resulting from a hypothetical stimulus (in this case demand for ATP) and that this allows the identification of potential metabolic modules; and (4) that total ATP demand for growth and maintenance can be inferred and that this is consistent with previous estimates in prokaryotes and yeast.

Historically, attempts to engineer plant metabolism for increased production of specific useful products have met with mixed success. Problems arise because of considerable metabolic redundancy that allows imposed genetic changes to be circumvented, because of an insufficiently detailed knowledge of the distribution of control of flux, and because the behavior of plant metabolism at the network level is not well described. While increasingly complex metabolic networks are now being characterized with steady-state stable isotope labeling experiments (Libourel and Shachar-Hill, 2008; Schwender, 2008; Kruger and Ratcliffe, 2009), the resulting flux maps still only cover a small percentage of the total metabolic network. The construction of a comprehensive plant metabolic model that includes the complete repertoire of catalyzed transformations represented within a specific genome (a genome-scale metabolic model) would represent a significant step forward in the development of a description of plant metabolic behavior at the network level.

The aim of this work is to describe a genome-scale structural model of Arabidopsis (Arabidopsis thaliana) metabolism and to explore the utility of the model as a tool to characterize possible flux behavior states of the metabolic network. Arabidopsis is the logical choice for this exercise because of its well-annotated genome. Moreover, the translation of the Arabidopsis genome into a curated set of metabolic reactions is already well advanced, and the reaction lists are available through the Aracyc database (Mueller et al., 2003; Zhang et al., 2005). While this is an excellent starting point for metabolic modeling, uncritical use of such reaction lists is likely to generate models exhibiting a number of problems, the most fundamental of which is violation of mass conservation. Thus, considerable effort is required to generate a useful genome-scale metabolic model from these databases (Poolman et al., 2006).

Once a stoichiometrically balanced structural model is achieved, the investigator is then faced with the challenge of how to analyze such a large model. We have previously introduced the concept of the reaction correlation coefficient (Poolman et al., 2007). Briefly, this is the value of Pearson's correlation coefficient between a pair of fluxes over all possible steady states of a system and is calculated from the stoichiometry matrix. If a correlation matrix for all reactions is constructed, then a dendrogram (a metabolic tree) representing the relationship between fluxes in all reactions in the system can be generated. However, a potential drawback to this approach is that it does not take into account any information concerning flux values in a system, nor does it consider thermodynamic constraints. In this work, we describe a refinement of the approach in which all reactions in a model of the system are assigned flux values, respecting reversibility criteria, on the basis of experimental observation and linear programming (LP).

LP is an established method to explore flux states of large metabolic networks (Kauffman et al., 2003; Price et al., 2003), most commonly in microbes (Schilling et al., 2002; Reed and Palsson, 2003) but more recently including primary metabolism in barley (Hordeum vulgare) seeds (Grafahrend-Belau et al., 2009). It is based on the optimization of an objective function, subject to set of given constraints. Here, the objective function is the minimization of total reaction flux, and the constraints are defined by the steady-state assumption and the biomass composition of a heterotrophic Arabidopsis cell suspension culture. This is, in essence, very similar to the commonly used objective of maximizing efficiency of biomass production by Edwards and Palsson (2000) and Reed and Palsson (2003), with the difference that instead of precomputing a vector in the direction of biomass production, we simply specify that all biomass components are produced at a defined rate. As demonstrated later, the solutions thus found are maximally efficient, at least with regard to Glc utilization.

In this contribution, the properties of the solution space are then investigated by varying the demand for ATP in the model, and correlation coefficients between fluxes that vary as a response are used to generate a dendrogram, allowing the identification of groups of reactions with a common, or similar, response to a given metabolic demand. This approach also allows the identification of a minimal set of reactions needed for growth and the indirect estimation of the ATP requirement for growth and maintenance.

The choice of a heterotrophic cell suspension system is a pragmatic one: the cell suspension system allows ready measurement of relevant constraints (growth rate, biomass composition) and avoids the problem of multiple cell types with different metabolic behaviors. Moreover, the Arabidopsis cell culture we use here (May and Leaver, 1993) has proved to be a useful model for the general molecular-biochemical behavior of heterotrophic plant cells. As well as being used to analyze metabolic responses (Baxter et al., 2007), the cell culture has been used as an experimental system for a range of different investigations, including organellar proteomics (Lee et al., 2008), transcriptomic responses (Desikan et al., 2001), and programmed cell death (McCabe and Leaver, 2000). Moreover, central aspects of metabolic behavior are conserved between the cell culture and heterotrophic plant tissues such as roots (Lehmann et al., 2009), although specific differences between differentiated cells types are likely and one should be cautious about generalizing based on the analysis of a single cell type.

RESULTS

Results obtained from the cell culture investigation were used to define the constraints used in the LP analysis of the metabolic model. We first present these experimental data, then the general properties of the model, and finally the results obtained using the experimental observations to analyze the model.

Experimental

Approximately 40% of Glc consumed was converted into biomass, a figure comparable to that found in other plant systems (e.g. in developing sunflower [Helianthus annuus] seeds; Alonso et al., 2007).

The composition of the biomass in Table I reveals that the bulk of biomass is composed of cellulose and protein, with minor contributions from lipid, starch, and nucleic acids. Our measurements account for 65% of the total biomass. It is likely that the missing fraction consists of soluble metabolites and salts that have not been quantified (Williams et al., 2008). The biomass composition is almost identical to independent determinations on the same cell culture, suggesting that there is little variability in biomass composition of this cell culture. The rates of consumption of substrates and production of biomass were linear over the first 96 h of cell growth (data not shown), suggesting that the cells were in a metabolic steady state over this period.

Table I.
Glc consumption, biomass production, and composition of Arabidopsis cell cultures

Modeling

General Model Properties

The final model consisted of a total 1,253 metabolites and 1,406 reactions, as summarized in Table II.

Table II.
Summary of components of the whole model

Internal metabolites involved in only one reaction, and those reactions, were then removed such that all metabolites were capable of being balanced at steady state, reducing the model to 855 reactions. Examination of the null space of the model showed no zero row vectors; the presence of such a row indicates that the corresponding reaction is incapable of carrying steady-state flux (Heinrich and Schuster, 1996). We have recently described a more robust method of identifying these “dead” reactions, based on consideration of reaction correlation coefficients (Poolman et al., 2007), and the application of this showed that in fact 77 reactions were dead. This does not of itself indicate an error in the model but shows that those reactions are not capable of contributing to biomass production from the nutrients specified here.

LP Results

LP solutions showed that all biomass precursors could be synthesized in realistic proportions from Glc, nitrate and/or ammonia, phosphate, and sulfate and that the system was able to accommodate arbitrary changes in ATP demand.

A total of 232 of the 1,406 available reactions in the model were assigned nonzero flux values. The fact that only a relatively small proportion of reactions were utilized springs from the facts that (1) we are only exploring a limited subset of the organism's biosynthetic potential and (2) the LP objective of minimizing total flux in the system also tends to minimize the total number of reactions employed.

Responses to Changing ATP Demand

The results reveal that only 42 reaction fluxes (including those of ATPase and the mitochondrial equivalence reactions) vary in response to changing ATP demand, with the remaining 185 maintaining constant flux. The varying flux values were used to construct a correlation tree, as described in the model analysis section of “Materials and Methods” and presented in Figure 1.

Figure 1.
The correlation tree of reaction fluxes in the LP model. Uppercase reaction names are Biocyc identifiers, which in some cases have been modified to make them compatible with the tree-drawing software. Reactions with the suffix “tx” represent ...

Three main subtrees are discernible in Figure 1, representing groups of reactions with distinct common responses to changes in ATP demand, and these fall, approximately, into three recognizable areas of central metabolism: reversible pentose phosphate reactions, glycolysis and the tricarboxylic acid (TCA) cycle, and oxidative pentose phosphate metabolism.

In addition to these, and correlating most closely with oxidative pentose phosphate metabolism, are the reactions of Ru5Pk and the Rubisco carboxylase reaction (the oxidase reaction of Rubisco was also found in the solution, but it maintained a fixed flux) as well as the NAD- and NADP-dependent variants of icosanoyl-CoA synthase. This pair of reactions act together as a net transhydrogenase, producing NADPH. They form a reaction subset, and there is no production or consumption of other metabolites by these reactions. There are a number of other pairs of reactions capable of providing this function, and the fact that these were “selected” by LP is not thought to be of particular significance (i.e. that this particular pair of reactions was selected could be regarded as an artifact of the algorithm; as long as at least one pair of reactions providing a net transhydrogenase activity is available, other results would be unaffected).

The reactions exhibiting variable flux form a single connected component, as shown in Figure 2. Although the reactions associated with photorespiration carry fixed flux in these results, the initial and final metabolites of this component reside within the block of variable reactions and so have been included in the figure.

Figure 2.
The network composed of reactions exhibiting variable flux in response to changing ATP demand (see also Figs. 1 and and3).3). Colors correspond to the description in Figure 1; reactions shown with broken lines indicate those that at some level ...

Typical responses of the variable reactions to changing ATP demand are shown in Figure 3. This figure also shows the levels of ATP demand at which one or more reactions start or stop carrying flux, as shown in Table III.

Figure 3.
Responses of reaction fluxes in the model to varying ATP demand. Reactions are colored as previously, and dotted lines indicate reactions that at some point carry zero flux. The black impulses represent points at which one or more reactions become active ...
Table III.
Reactions in the LP solution that are activated or inactivated in response to increasing ATP demand (mol L−1 h−1)

It can be seen that these transitions occur at only two points, which results in the system existing in one of three states, corresponding to low, medium, and high ATP demand. Inflections in the flux response curves only occur at these transitions. Furthermore, only a small number of reactions become active or inactive at transitions. At the first transition, one reaction is inactivated and three are activated; at the second transition, three reactions are inactivated and one reaction is activated.

Rubisco carboxylase can be seen to be active only at the lowest of ATP demands, falling to zero flux at the first transition. Ru5Pk follows a parallel course but remains constant after the first transition, this being equal to the flux of the Rubisco oxygenase reaction.

Flux in the oxidative limb of the oxidative pentose phosphate pathway and the icosanoyl-CoA synthase reactions, while being more closely correlated with Ru5Pk/Rubisco, exhibits subtly different behaviors. Flux falls steeply until the first transition and then more gently until the second transition, at which point it becomes constant. The oxidative pentose phosphate pathway flux becomes zero at this point, while the icosanoyl-CoA synthase reactions do not, indicating a constant transhydrogenase flux.

Reversible pentose phosphate reactions all exhibit the same trajectory, remaining constant until the first transition, increasing steeply until the second transition, and becoming constant thereafter.

Fluxes in glycolysis/TCA cycle also show very similar responses, remaining constant (in some cases zero) until the first transition and increasing linearly with ATP demand after that. An exception to this is the generic NADH oxidase: although flux across this reaction is more closely correlated with glycolysis/TCA fluxes, it remains at zero until the second transition and then increases linearly. After the second transition, all of these fluxes increase linearly in response to further increases in ATP demand.

In addition to supplying energy to the rest of metabolism, this variable block of reactions is also the carbon source for all biomass precursors. A number of carbon compounds are also recycled back into this set of reactions, as detailed in Table IV.

Table IV.
Metabolites utilized by the set of reactions exhibiting variable flux in response to changing ATP demand connecting these reactions to those whose flux remains constant, their rate of utilization (mol L−1 h−1), and the number of constant ...

Calculation of ATP Requirements

In the absence of any additional ATP demand, the LP calculates that total ATP requirement for biomass precursors is 8.7 × 10−3 mol g−1 dry weight. Varying ATP demand in the LP (using a bisection search) to determine the level at which Glc uptake in the solution matches the experimentally observed Glc uptake results in a figure for ATPase flux of 7.9 × 10−3 mol L−1 h−1, approximately four times higher than the greatest ATPase flux used in the results shown in Figure 3. Although it is not possible to achieve separate estimates of growth and maintenance demand from our data, if we assume that the growth demand is 65 × 10−3 mol g−1 dry weight (see “Discussion”) and that growth is linear over the observed time, the maintenance demand can be estimated as 7.1 × 10−3 mol g−1 dry weight h−1.

DISCUSSION

Analysis of the model identifies a core of metabolism required for synthesis of the main biomass components (i.e. all monomeric precursors). Only a relatively small subset of reactions (227 out of 1,406) are required to realize this function and can be regarded as a (possibly nonunique) minimal core of metabolism.

Although the model did not include separate compartments for plastid and cytosol (see “Materials and Methods”), the scheme shown in Figure 2 is consistent with a standard view of metabolic compartmentation between plastid and cytosol, given the presence of transporters for hexose and triose phosphate and 2PG in the plastid membrane (Neuhaus and Emes, 2000; Neuhaus and Wagner, 2000). That is, reactions shown in green and blue are those present in the plastid, while those in red (between G6P and PEP) are present in the cytosol. Indeed, there is no reason to assume that the glycolytic reactions between G6P and PGA could not be occurring simultaneously in both the plastidic and cytosolic compartments. Consequently, the lack of a separate plastidic compartment can be seen to be justifiable for heterotrophic plant cells under the conditions described here, although this does not, of course, justify such an assumption under other conditions, especially not autotrophic conditions.

Within the core reactions, only 42 have altered flux when the demand for ATP is varied, and only four of these undergo on-off transitions. While the identity of the reactions that vary is not entirely surprising (they are connected to processes such as glycolysis and TCA cycle that are known to be involved in ATP generation), the fact that the network can accommodate a large range of ATP synthesis rates with minimal disturbance to most fluxes demonstrates the inherent robustness of the metabolic network. Metabolism is known to be robust to gene deletions (Blank et al., 2005; Gerdes et al., 2006; Behre et al., 2008), and steady-state isotope labeling experiments in plants have revealed an inherent robustness to both genetic intervention (Spielbauer et al., 2006) and altered environment (Williams et al., 2008). This work can now extend that observation of robustness from the tens of reactions amenable to quantification from isotope labeling experiments to some 185 reactions of primary metabolism, and this robustness is conferred by the structure of the network, independently of kinetic or genetic control (because these were not included in the model).

The choice of objective function to analyze was based on simplicity and the fact that it minimized the number of a priori assumptions of what the cultured cells were “optimized for.” However, the model solutions can be seen to be operating at the maximum possible efficiency with respect to Glc consumption. At low ATP demand, 100% of the carbon in Glc is recovered as biomass, and as ATP demand increases, the P/O ratio (of the whole model, not just the mitochondrion) asymptotically approaches a value of 2.7 (Fig. 4).

Figure 4.
Response of P/O ratio of the LP solutions of the whole model to larger changes in ATP demand (mol L−1 h−1). [See online article for color version of this figure.]

This compares with a proposed maximum P/O ratio of 2.58 calculated by Brand (1994), whose calculations included some additional transport costs not considered here.

Coordination of Flux in Primary Metabolism and a Novel Role for Rubisco

A surprising aspect of the model was an active Rubisco reaction in a nonphotosynthetic cell suspension. A function for Rubisco in recycling CO2 during lipid synthesis has been shown in certain oilseeds (Schwender et al., 2004), and the reaction scheme described by those authors between G6P and PGA is almost identical to the low-energy-demand solutions described here. Here, in the absence of photosynthesis, Rubisco is active in two contexts. First, at low ATP demands (before the first transition), the carboxylase reaction of Rubisco operates without the Calvin cycle. In this state, the demand for reducing equivalents exceeds the demand for ATP, and this is satisfied by Rubisco acting in conjunction with G6Pdh, lactonase, 6PGdh, and Ru5Pk to catalyze the net oxidation of G6P to two molecules of PGA, reducing two NADPs at the expense of one ATP (reactions shown in green in Figs. 1–3).

After the first transition (note that up to this point Glc consumption remains constant; Fig. 3), more carbon is routed into glycolysis and the TCA cycle (reactions shown in red in Figs. 1–3),), producing concomitantly more reducing equivalents; the contribution from oxidative reactions above is diminished, and some ATP is saved by no longer operating the Rubisco carboxylase reaction. It is at this point that CO2 export starts to increase (data not shown).

At the second transition, demand for ATP and reducing equivalents is exactly balanced, and once ATP demand exceeds this point, excess NADH is simply oxidized by the NADOxid reaction, which, until this point, carries no flux (Fig. 3). It can also be seen that there is a point of inflection in the Glc uptake curve at this point, indicating that in this state the yield of ATP per unit of Glc is slightly lower than previously.

Over all of these states, the Rubisco oxidase reaction carries a constant flux, and variation in demand for Ru5P is accommodated by variation in the fluxes of the reversible reactions of pentose phosphate metabolism (blue reactions in Figs. 1–3).). In these results, the fate of 2PG is the generation of αKG via Gly aminotransferase, the reactions in the TCA cycle from Mal (see the black and solid red reactions in Fig. 2), and the photorespiratory reactions. These are ultimately responsible for supplying approximately 33% of the αKG demand, with the remainder of the demand being made up with relatively minor and approximately equal fluxes from 13 other reactions involved in amino acid metabolism. The only reaction consuming αKG is Glu dehydrogenase; thus, the role for photorespiration in these results is to support NH3 assimilation.

It is relevant to note that both Rubisco and photorespiratory enzymes have been identified in proteomic studies of heterotrophic Arabidopsis cells (Baerenfaller et al., 2008; L. Miguet and L.J. Sweetlove, unpublished data). However, in the absence of further experimental study, it would be somewhat ambitious to propose that the behavior described here is an exact mirror of the in vivo reality. This is especially so given that the fluxes in the Rubisco carboxylase and oxygenase cannot be independent of one another, and given the fact that at high ATP demand there is higher production of CO2 and consumption of oxygen, which would be expected to favor the carboxylase over the oxygenase reaction.

Nonetheless, these results show that fluxes in a reaction network have the potential to respond to changes in demand in surprisingly subtle and elegant ways and that these responses can only be identified when the network is considered as a whole, rather than as a collection of semi-independent and somewhat arbitrarily defined “pathways.” The concept of groups of reactions acting in concert as metabolic “modules” is an attractive one, but there is little agreement as to their constitution or identification (for discussion, see Poolman et al., 2007). It could be argued that the groups of reactions identified here as having a common response also constitute metabolic modules and that by taking variation in fluxes into account these modules are a closer realization of the biological function than those methods that rely on a purely structural analysis of the network.

Energy Cost of Cell Maintenance

Another feature of the flux distribution obtained here is that, in the absence of an additional ATP demand, the cell can generate sufficient ATP and reductant for complete biosynthesis of all of the main biomass precursors with relatively low flux through glycolysis and without a complete oxidative TCA cycle (the reactions between αKG and Fum carry no flux in the absence of an imposed ATP demand). However, it is known from isotope labeling experiments that in the same Arabidopsis cell suspension culture, glycolytic and TCA fluxes are relatively high and a complete TCA cycle operates (Williams et al., 2008). In the model, introduction of an additional ATP demand leads to activation of the reactions between αKG and Fum, such that a full TCA cycle flux operates and the fluxes of glycolysis and TCA cycle increase linearly, bringing the flux distribution into line with what was seen experimentally (Williams et al., 2008).

This implies that a relatively small proportion of the actual ATP consumed by the cell is used to generate biosynthetic precursors and that the combined ATP requirement for polymerization and maintenance is relatively high.

Conventionally, biological ATP demand is assumed to be distributed between growth and maintenance demands (Stephanopoulos et al., 1998):

equation M1

where rATP is total ATP requirement (mol g−1 dry weight h−1), YxATP is ATP required to generate biomass (mol g−1 dry weight), μ is the specific growth rate (h−1), and mATP is the maintenance requirement (mol g−1 dry weight h−1). Estimates of these values have been previously reported by a number of workers, as summarized in Table V. Using the mean value for YxATP in Table V of 65 × 10−3 mol g−1 dry weight, the estimated value of mATP as 7.1 × 10−3 mol g−1 dry weight h−1 compares favorably with the mean value of 6.3 × 10−3 mol g−1 dry weight h−1 for mATP reported in Table V.

Table V.
Experimentally determined YxATP and mATP for various microbes

Minimal Metabolic Network

There is considerable interest in the identification of the minimal set of cellular components required to sustain life (Fraser et al., 1995; Mushegian and Koonin, 1996; Gil et al., 2004; Forster and Church, 2006; Glass et al., 2006). Such work is centered on the analysis of prokaryotic organisms, in particular Mycoplasma genitalium, which has the smallest known genome, the size of which is thus assumed to place an upper limit on that of the minimal genome. Furthermore, such work tends to pay relatively scant attention to metabolism and is predicated on organisms growing in a nutrient-rich environment. The details of techniques used to determine these minimal genomes are beyond the scope of this work (for review, see Gil et al., 2004), but they tend to rely either on gene disruption or the identification of common genes between phylogenetically distant organisms with small genomes. Recently, Suthers et al. (2009) reported a metabolic reconstruction of M. genitalium (but without reference to minimality) that yielded a network of 380 reactions, with 186 internal and 87 external metabolites. The relevant results are summarized in Table VI.

Table VI.
Sizes of previously predicted minimal prokaryotic genomes and metabolisms

Although the goal of our work is not primarily to identify a minimal network for Arabidopsis, the objective function used, minimization of total flux, will also tend to minimize the number of reactions used, so the solution obtained here sets an upper limit in the size of the minimal metabolic network. The size of the core Arabidopsis network is larger than that of proposed minimal prokaryotic networks, although it is smaller than the average network size of 294 reactions required for growth reported in a constraint-based analysis of a metabolic model Escherichia coli (Reed and Palsson, 2004). This is to be expected, given the greatly increased functionality of the Arabidopsis network, but the size is still of a comparable order of magnitude to the minimal prokaryotic networks and directly comparable to the whole M. genitalium network. Furthermore, approximately 400 genes would be required to encode the Arabidopsis core network, a number falling into the range of minimal genomes shown in Table VI.

However, despite these differences, a certain amount of comparison with our work is possible. The original description of M. genitalium (Fraser et al., 1995) proposed 470 genes, of which 64 were associated with metabolism. A subsequent comparative study of M. genitalium and Haemophilus influenzae (Mushegian and Koonin, 1996) suggested a hypothetical minimal genome of 256 genes, to which 80 were ascribed metabolic function.

It is also noteworthy that the LP optimization method employed here generated a demonstrably functional metabolic network, and this was achieved without any a priori assumptions as to which reactions would be present in the solution. Although there is clearly scope to further investigate this aspect of the study, we propose that the metabolic network we have described is likely to be close to the minimal metabolic network for an organism with single carbon and nitrogen sources.

Recently, a hand-built model of primary metabolism in barley seeds has been described (Grafahrend-Belau et al., 2009) that also contains a similar number of reactions. However, the metabolic requirements of the barley seed model and the methods of model construction and analysis were sufficiently different from those of our model to render detailed comparison of the two beyond the scope of this discussion.

CONCLUSION

Construction of a metabolic model of Arabidopsis, based on reactions reported as being present on the basis of genome sequence data, and with scrupulous curation of reaction stoichiometries to ensure conservation of carbon, nitrogen, phosphorus, and sulfur, has resulted in a network demonstrably capable of reproducing, in at least a semiquantitative fashion, the experimentally observed behavior of a heterotrophic culture of Arabidopsis in a minimal medium. Only about 15% of the total network was needed to achieve this, and the sizes of both whole and minimal networks are comparable to those previously proposed for microbial metabolism.

A novel approach to incorporating experimental data with model analysis has enabled the identification of a number of metabolic modules involved in the response to varying energy demand, which, although composed of groups of reactions previously known to be associated on the basis of their biochemistry, suggest new ways in which their activity may be coordinated. This is especially the case for reactions involving pentose phosphate species. The same technique also provides a means of estimating total cellular ATP requirement, and this estimate is consistent with previously published values for microbial species.

A number of refinements to this work suggest themselves. In particular, the assignment of reaction reversibility is somewhat arbitrary, and the recent group assignment method of Jankowski et al. (2008) provides the potential to improve this aspect.

The models and techniques developed here are readily applicable to other situations and are hereby made freely available, and it is hoped that these will prove to be a useful resource for the wider community.

MATERIALS AND METHODS

Nomenclature and Abbreviations

With the exceptions noted here, all metabolite and reaction names (in text and figures) are the Aracyc unique identifiers. 2PG, 2-Phosphoglycolate; 6PGdh, 6-phosphogluconate dehydrogenase; AconDHatase, aconitate dehydratase; αKG, α-ketoglutarate; αKGdh, α-ketoglutarate dehydrogenase; BPGA, glycerate-1,3-bisP; CisAcon, cis-aconitate; Cit, citrate; CitSynth, citrate synthase; DHAP, dihydroxyacetone phosphate; E4P, erythrose-4-P; F6P, Fru-6-P; FBP, Fru-1,6-bisP; Fum, fumarate; G6P, Glc-6-P; G6Pdh, Glc-6-P dehydrogenase; GAP, glyceraldehyde-3-P; IsoCit, isocitrate; IsoCitDH, isocitrate dehydrogenase; Mal, malate; MalDH, malate dehydrogenase; NADOxid, generic NADH oxidase; OAA, oxaloacetate; PEP, phosphoenolpyruvate; PGA, 3-phosphoglycerate; Pi, inorganic phosphate; PyrDH, pyruvate dehydrogenase; R5P, Rib-5-P; Ru5P, ribulose-5-P; Ru5Pk, ribulose-5-P kinase; RuBP, ribulose-1,5-bisP; S7P, sedoheptulose-7-P; Suc, succinate; SucCoA, succinyl-CoA; SucThioK, succinyl thiokinase; X5P, xylulose-5-P.

Transport processes are denoted by the suffix “_tx” appended to the relevant metabolite name (“GLC_tx” is the Glc transporter, etc.).

Experimental

Plant Material

Cell suspensions of Arabidopsis (Arabidopsis thaliana ecotype Landsberg erecta) were maintained and subcultured as described elsewhere (Millar et al., 2001). Briefly, 15 mL of a 168-h-old, light-grown cell culture was transferred into 90 mL of fresh growth medium and grown in the dark at 21°C for 96 h before cells were harvested for biomass measurements.

Biomass Analysis

Growth rate of cell suspensions was determined as the weight of freeze-dried cells harvested at regular intervals during the 96-h growth cycle.

Cell wall was extracted by repeated washing of a known mass of ground lyophilized tissue with a mixture of phenol, acetic acid, and water in the ratio 2:1:2 (Sriram et al., 2006) The remaining insoluble material was washed with distilled water, freeze dried, and weighed.

Starch content was determined by enzymatic digestion and spectrophotometric assay of the resultant Glc.

Lipids were extracted from a known mass of ground lyophilized tissue using hexane and isopropanol according to an established protocol (Hara and Radin, 1978; Mhaske et al., 2005). Solvent was removed by gentle heating, and lipids were quantified by weight.

Soluble protein extracted with phosphate-buffered saline was quantified using the Bradford assay (Bradford, 1976). The amino acid content of protein hydrolysates (6 n HCl, 110°C) was determined by HPLC (Bruckner et al., 1995). Amino acids were derivatized with O-phthaldialdehyde, separated using a reverse-phase C18 column, and quantified by fluorescence using standard curves.

Nucleic acids were extracted and quantified from lyophilized tissue using standard methods (for RNA, TRIzol followed by DNase; for DNA, phenol/chloroform) and quantified spectrophotometrically.

Glc consumption was determined by measuring the Glc content of the growth medium at regular intervals using a spectrophotometric assay, as described by Sweetlove et al. (1996).

Model Construction

Data Sources

A model of Arabidopsis metabolism was constructed from the Aracyc database (version 4.5; Zhang et al., 2005; http://www.arabidopsis.org/biocyc/), using the ScrumPy metabolic modeling package (Poolman, 2006) such that (1) wherever possible, reactions are taken directly from the Aracyc database; (2) all reactions are atomically balanced with respect to carbon, nitrogen, phosphorus, and sulfur; (3) all reactions are capable of carrying steady-state flux; (4) all metabolites are balanceable (i.e. are both consumed and produced by at least one flux-carrying reaction); and (5) the model is capable of producing all amino acids, nucleotide bases, lipid (assuming linoleate to be a “generic lipid”), starch, and cellulose using Glc, NO3 (and/or NH4), SO4, and Pi as sole input material.

ScrumPy has a modular model definition language (i.e., a model can be defined as a nested set of independent submodels) that is particularly convenient when data for a model are drawn from several different sources. The reactions taken from Aracyc were included in a single module that was incorporated with a number of additional modules, described below, to produce the whole model.

The Aracyc Module

The list of all reactions involving small metabolites in Aracyc was extracted and subsequently modified as follows. Reactions were checked for atomic balance with respect to carbon, nitrogen, phosphorus, and sulfur. A small number were found to be unbalanced, but most of these proved relatively easy to correct. For example, an incorrect empirical formula for synapoyl alcohol resulted in a number of reactions of lignin syntheses becoming unbalanced, and UROPORIIIMETHYLTRANSA-RXN (EC 2.1.1.107) was stoichiometrically incorrect with respect to adenosylmethionine. These were submitted to Aracyc and have been incorporated into the current Aracyc release (Pfeifen Zhang, personal communication). The small remaining number of unbalanced reactions are identified as such in Aracyc and were omitted from the model.

The treatment of hydrogen and oxygen is more problematic: protons and water are frequently omitted from reaction stoichiometries, and the atomic proportion of hydrogen in a compound depends upon its pKA and the intracellular pH. A total of 693 reactions were identified as being unbalanced with respect to H+, of which 374 were also unbalanced with respect to oxygen. This was deemed too many to be practical to correct manually, and reactions that were only unbalanced toward H+ or to H+ and water were left unaltered, and H+ and water were defined as external metabolites.

This may appear to be a dangerously laissez faire strategy, with the apparent potential to violate the laws of both conservation of mass and of energy (the latter because oxygen imbalances might lead to the generation of oxidation potential effectively from nothing). Therefore, it was verified that solutions obtained from the LP analysis (see below) had no mass imbalance not attributable to H+ or oxygen and, furthermore, that the overall solutions were not capable of synthesizing ATP or NADH in the absence of an oxidizable carbon source. Consequently, although these assumptions are not desirable, there is no evidence of them leading to undue consequences in the results obtained.

As there is relatively little information concerning reaction reversibility in Aracyc, a conservative approach was taken whereby all reactions were initially assumed to be irreversible and a subset of these was subsequently made reversible. The reversible list includes all isomerases and amino transferases. A number of reactions were also identified as having been defined in the nonphysiological direction; for example, phosphoglycerate kinase was defined in the anabolic, not the catabolic, direction.

A number of reactions are reported as utilizing NAD(P)H. These were replaced with pairs of reactions, one utilizing NADH and the other NADPH.

Metabolites and associated reactions with ambiguous atomic composition were removed. These included generic reactants (e.g. Carboxylates) and those reported as having an R group as part of their chemical formula (e.g. ALDOSE).

Finally, all isostoichiometric reactions were removed, so that each unique stoichiometry was represented exactly once in the model. Although it is debatable whether or not the presence of such reactions represents a biological error, it is certainly undesirable from a modeling point of view, as it increases the complexity of any analysis and subsequent interpretation without generating any new results.

At the end of this process, the Aracyc module was composed of 1,231 metabolites and 1,336 unique reactions.

The Transport Module

A fundamental consideration in the construction of any metabolic model is the identification of those metabolites whose concentrations are to be assumed to be unaffected by the action of the system under investigation (source and sink metabolites). These commonly include species freely available in the environment (e.g. oxygen) and are called the external metabolites, while all others are called internal. Following this logic, any reaction that interconverts internal and external metabolites is deemed to be a transporter.

However, it should be realized that, in this context, the terms internal and external do not necessarily refer to any particular physical location (e.g. cytosol or other subcellular compartment) and that metabolites denoted as external in this sense may nonetheless be physically located in the cell. An important class of such compounds is polymeric species, which cannot be given a meaningful concentration but which can be considered to be sources and/or sinks of their monomeric subunits. Hence, reactions involved with polymers are included in the transport module.

The stoichiometries of these reactions were redefined to ensure that all reactions involved with a given polymeric species are consistent in terms of the monomeric subunit(s). For example, MALTODEXGLUCOSID-RXN (maltase) is recorded in Aracyc as having the stoichiometry

equation M2

This was replaced with

equation M3

whereas RXN0-5181 (EC 3.2.1.1) is reported as having the stoichiometry

equation M4

which was replaced with

equation M5

(i.e. Glc is assumed to be the monomeric subunit of 1-4-ALPHA-d-GLUCAN). Taken together, the two new stoichiometries imply, correctly, that even in the absence of empirical formulae, MALTOHEXAOSE must contain six times as many carbon atoms as ALPHA-GLUCOSE. This is in contrast to the uncorrected stoichiometries, which imply that they would be the same. This is an important consideration as, if not corrected, it can lead to the possibility of sequences of reactions, using a polymeric species as an intermediate, with a net stoichiometry that violates the law of mass conservation.

CO2 and all internal metabolites assumed to be biomass components (point 5 above) were assigned an external counterpart and an explicit transporter. The advantage of this approach is that transport reactions in the model can be maintained separately from those automatically generated from the database, and individual rates of production and consumption of a given metabolite in the model can be determined or assigned by the manipulation of a single transport step. Likewise, media components assumed to be the ultimate biomass precursors (Glc, NH3, NO3, Pi, and SO4) were also assigned external counterparts and transporters.

Stoichiometries of transport reactions were defined in a consistent fashion such that negative flux indicates production (i.e. loss from the system) and positive flux indicates consumption of the external metabolite.

The Mitochondrial Module

Aracyc contains only very sparse information concerning protein location and membrane transport. For this reason, the model is not fully compartmented. Although this certainly represents a significant approximation, subsequent results do not suggest that it is an unreasonable one (see “Discussion”).

The one exception to this approximation concerns mitochondrial metabolism, more specifically the TCA cycle, electron transport chain, and, especially, oxidative phosphorylation, which cannot be validly represented without a proper distinction between cytosolic and mitochondrial H+.

To this end, relevant mitochondrial metabolism was included in a separate module, and the equivalent reactions were removed from the Aracyc module. These reactions were composed of the TCA cycle, electron transport chain, and oxidative phosphorylation. The substrates and products of these reactions were defined as separate species from their cytosolic counterparts, but “pseudoreactions” transporting metabolites between the mitochondria and cytosol were defined to allow mitochondrial species to take part in amphibolic reactions. Mitochondrial protons are treated as distinct from cytosolic and in particular were defined as internal, thus imposing the requirement that mitochondrial protons must be balanced by reactions of the electron transport chain.

This module was examined as an independent model, and when using pyruvate and CO2 as sole carbon source and sink, it had a single elementary mode, producing ATP with a P/O ratio of 2.5.

Other Reactions

In addition to these, the following reactions were added. (1) For convenience, a generic fatty acid synthase, producing linoleate from acetyl-CoA, ATP, and NADPH in stoichiometrically correct ratio (in order to avoid including a large number of reactions that have a single net function and whose intermediates are not used elsewhere). All lipid in biomass was assumed, in this model, to be in the form of linoleate. (2) dATP diphosphatase, needed for the synthesis of deoxy nucleotides (Metacyc reaction RXN0-384), missing from Aracyc. (3) A generic ATPase to allow investigation of the model's response to changing energy demand. (4) A generic NADH oxidase to balance NADH production.

Reaction Reversibility

Once all of these modules were assembled, LP was used to examine the capability of the model to produce each product in turn (a trivial modification of the LP described below). If the model was not capable of producing a particular product, all reactions were made temporarily reversible and the LP was resolved. Reactions that had been previously irreversible and that subsequently carried negative flux were identified as candidates to be defined as reversible. Online databases (nist [http://xpdb.nist.gov/enzyme_thermodynamics/enzyme_thermodynamics_data.html] and brenda [http://www.brenda-enzymes.org/]) were then examined to establish whether or not these candidates could reasonably made reversible. If such a candidate could not be made reversible, this was added as a constraint to the LP, and the process was repeated until all products could be synthesized with a reasonable set of reversible reactions.

In reality, no reaction is truly irreversible, and there may be a good argument to take the exact opposite approach: start with all reactions reversible and eliminate only those carrying a completely unrealistic negative flux. Although attractive, this is not a terribly practical strategy to execute, as it would require examination of many hundreds of reaction fluxes and respective thermodynamics, the latter being particularly hard to determine for such large numbers of reactions. However, the end result of both strategies should be the same: a set of reactions capable of generating all products while respecting thermodynamic constraints.

Model Availability

The complete model, including the model representing the LP solutions described in “Results,” in ScrumPy and SBML format, is available as supplemental data.

Model Analysis

Model analysis was by LP as described below using the Gnu Linear Programming Kit (http://www.gnu.org/software/glpk) and a Python module to act as an interface between the Gnu Linear Programming Kit and ScrumPy. For the purposes of LP, reversible reactions were split into irreversible forward and reverse components.

The linear program was defined with the objective of minimizing the total flux of all reactions, given that the flux in some of these is fixed (assumed or based on observation). It should be noted that this is a purely computational objective and should not be taken as an assumption of a biological objective. Rather, it is a simply defined objective that allows investigation of the behavior of the system under a range of different scenarios. Formally, the linear program was defined as

equation M6

where v is the flux vector, N is the stoichiometry matrix, reactions i and j are the transport steps, t is the vector of these rates, va is the ATPase reaction, and Ja is the (imposed) flux it carries. The first part defines the objective function, the second part imposes the steady-state constraint, the third part specifies that reactions i and j carry fixed flux, and the fourth part defines an imposed ATP demand.

This program was utilized in three ways. First, elements in t corresponding to export of biomass precursors were set to −1 (in this model, negative transport rate indicates export from the system) to ensure that the model represents a system capable of producing all biomass precursors. Second, the same elements of t were set to the molar ratios derived from experimental observation and shown in Table I in order to verify that the system represented by the model was capable of generating biomass precursors in biologically realistic proportions. Third, the second program was solved repeatedly with increasing flux set in the ATPase reaction to investigate the response of the system to varying energy demands.

Secondary Analysis

Here, we refine the metabolic tree approach using the flux evaluations from the linear program as the data from which to calculate a flux correlation matrix. Thus, we explore reaction flux correlations over a smaller flux subspace, all points of which correspond to steady states generating biomass components in the experimentally observed proportions.

Supplemental Data

The following materials are available in the online version of this article.

  • Supplemental Data S1. Compressed archive file containing descriptions of the models associated with this work, in ScrumPy and SBML formats.

Supplementary Material

[Supplemental Data]

Notes

1This work was supported by the Biotechnology and Biological Sciences Research Council (grant nos. BB/E002323/1 [to L.J.S.] and BB/E00203X/1 [to D.A.F.]).

The author responsible for distribution of materials integral to the findings presented in this article in accordance with the policy described in the Instructions for Authors (www.plantphysiol.org) is: Mark G. Poolman (ku.ca.sekoorb@namloopgm).

[C]Some figures in this article are displayed in color online but in black and white in the print edition.

[W]The online version of this article contains Web-only data.

www.plantphysiol.org/cgi/doi/10.1104/pp.109.141267

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