How to write a stoichiometric matrix for a part of the Pentose phosphate pathway

maybe this is more bioengineering than biology but I didn't find any such group.

So I got the following photo:

And I was asked to do the following for the network inside the red area.
1) Write the stoichiometric matrix for the network
2) Draw a pathway map for the network
3) Draw primary metabolite connectivity maps
4) Write the mass balance equations for primary metabolites

I know that for the first one the columns are the reactions taking place and the lines are the "chemicals". Should the markings on the columns be the same as the numbers that are written on each reaction? (like "") Almost every reaction can go in both direction, is there anything that says which chemical should get minus and which one gets plus? My attempt at the matrix was:

As for the pathway map, isn't that basically the photo is given?
And finally what would be a "primary metabolite" in this case?

All help and hints very well appreciated!

This is not a particularly well written homework question. I'll try to give some hints based on how I interpret it.

1) The stoichiometric matrix. You have exactly the right idea. I would write the reactions as enzyme names or gene names instead of the EC numbers (e.g. G6PD or G6P dehydrogenase instead of For the reversible reactions, there's no a priori reason to write them in one direction or another, but convention would be to make glucose consumption the positive direction. I would not include "glycolysis" as a separate reaction. I would also consider including cofactors and byproducts in the molecules affected by the reaction (e.g. CO2, NADP+, NADPH, (maybe ADP, ATP, NAD+, NADH also if those come up)).

2) Yes, it's basically what you already have. It's not a particularly great diagram, so you could draw it in a clearer way.

3) I have no idea what this means, but perhaps the next point will help.

4) Primary metabolite is not a super well-defined term, but I think in this context, I would say that the way they're intending the question, they're looking for a "total pathway reaction" that describes the net inputs and outputs of the pathway.

Something like this:

$$ X_1 G6P + X_2 NADP+ implies X_3 GAP + X_4 FBP + X_5 CO_2 + X_6 NADPH $$ (G6P=Glucose-6-phosphate, GAP=Glyceraldehyde-3-phosphate, FBP=Fructose-bis-phosphate)

I'll leave it to you to figure out what the X's are or whether I left anything out (since it's a homework assignment after all.)

Understanding the Causes and Implications of Endothelial Metabolic Variation in Cardiovascular Disease through Genome-Scale Metabolic Modeling

High-throughput biochemical profiling has led to a requirement for advanced data interpretation techniques capable of integrating the analysis of gene, protein, and metabolic profiles to shed light on genotype–phenotype relationships. Herein, we consider the current state of knowledge of endothelial cell (EC) metabolism and its connections to cardiovascular disease (CVD) and explore the use of genome-scale metabolic models (GEMs) for integrating metabolic and genomic data. GEMs combine gene expression and metabolic data acting as frameworks for their analysis and, ultimately, afford mechanistic understanding of how genetic variation impacts metabolism. We demonstrate how GEMs can be used to investigate CVD-related genetic variation, drug resistance mechanisms, and novel metabolic pathways in ECs. The application of GEMs in personalized medicine is also highlighted. Particularly, we focus on the potential of GEMs to identify metabolic biomarkers of endothelial dysfunction and to discover methods of stratifying treatments for CVDs based on individual genetic markers. Recent advances in systems biology methodology, and how these methodologies can be applied to understand EC metabolism in both health and disease, are thus highlighted.


The modern broiler (meat) chicken is the product of more than 60 years of artificial selection for commercially desirable traits, resulting in both improved feed efficiency and breast muscle yield. Currently, broilers reach market weight in ¾ the time it took in the 1950s, yet they weigh nearly twice as much as the 1950s breeds, with the breast muscle representing a greater component of the overall bird mass [1]. Several studies have compared modern lines with unselected lines in terms of growth rate and feed efficiency [2, 3]. In one such study comparing growth of a modern broiler line (Ross 708) with a legacy line of commercial general-purpose birds unselected since the 1950s (UIUC) over the first 5 weeks post hatch, the breast muscle was found to comprise 18 and 9% of total body mass, respectively [4]. Additional changes in growth pattern manifest in liver allometry. In both lines, the relative liver mass reached a similar maximum of approximately 3.8% of body mass and then began declining. However, this peak occurred a week earlier in the modern broiler. This finding provided part of the basis for this study, including selection of the liver and first 3 weeks post hatch, as it was hypothesized the earlier onset of this peak arose due to selection for rapid growth and the liver’s important role in nutrient metabolism.

Chicks undergo drastic physiological changes as a consequence of hatching. The developing embryo relies entirely on nutrients from the yolk [5,6,7]. During late embryonic development, much of the yolk lipid is absorbed and stored in the liver, predominately as cholesteryl esters [8]. At day 18 of incubation, 3 days prior to hatch, lipids make up 10% of the liver’s mass due to absorption and storage of yolk nutrients [9]. This stored lipid, along with the yolk remnant, provides the chick with a nutrients following hatch, but by day 5 post-hatch 90% of the yolk lipid has been absorbed [10]. Chicks are provided with a carbohydrate-rich diet at hatch because fasting during this period stunts the early muscle growth potential of chicks [11]. These early changes in nutrient source, coupled with rapid growth, mean maintaining metabolic homeorhesis is a major challenge facing the liver in the early weeks following hatch.

High-throughput transcriptome analyses provide snapshots of transcribed RNAs at any given time and are useful to identify differentially regulated genes between conditions or time points. Combining transcriptomics with untargeted metabolomics is a powerful means to infer hypotheses about the interactions between the transcriptome and metabolome. For example, integrating these two high throughput methods identified metabolic and signaling pathways responding to heat stress in the liver of modern broilers [12]. Previous studies have described the hepatic transcriptome of the modern broiler [13,14,15,16]. One study compared the hepatic transcriptome over six time points during the embryo to hatchling transition, from 16-day embryos to 9-day old chicks [17]. They identified many metabolic pathways consistent with the nutrient source transition the chicks undergo in the first week post hatch, especially some affecting lipid metabolism. Another recent study examined changes in the hepatic transcriptome resulting from immediate post-hatch fasting and re-feeding, identifying genes regulated by lipogenic transcription factor THRSPA and switching between lipolytic and lipogenic states [18].

There have been no integrated high-throughput studies of the modern broiler liver under normal conditions in the critical first 3 weeks post-hatch. Thus, the molecular changes that are occurring during this time period – the metabolic drivers of rapid muscle growth and feed efficiency – are poorly understood. Exploring these in a data-driven fashion can elucidate new knowledge about the liver’s functions during early post-hatch growth of the chick, and also how the liver itself is developing. In this work, by integrating the hepatic transcriptome and metabolome, we compare the core metabolic pathways of the liver at two time points: Day 4 (D4) and Day 20 (D20) post-hatch. These were selected to capture the metabolic reprogramming required to support the transition from relying on stored yolk to orally consumed feed that underlies the growth rate and phenotype of the modern broiler.

Results and Discussion

We compared our FIA algorithm to the widely used MFA software 13CFLUX [17], which relies on the cumomer approach, and to the more recent Open-FLUX [15] software, which is based on the EMU [14] approach. In order to compare the methods, we conducted flux estimations for various well-studied metabolic pathways. Our first example is based upon the tutorial which Wiechert et al. provide with their 13CFLUX software: the Embden-Meyerhof and Pentose Phosphate metabolic pathways of Escherichia coli[17]. This example compares the running time and robustness of both algorithms in response to input noise. Our second example compares the results and performance of FIA to both an adhoc method and the OpenFLUX algorithm for the analysis of lysine production by C. glutamicum, as described by Becker et al. [18] and Quek et al. [15].

FIA vs. 13CFLUX Comparison: Embden-Meyerhof and Pentose Phosphate Pathways

In this section we examine a network representing the Embden-Meyerhof and Pentose Phosphate pathways of E. coli, which is based upon the tutorial supplied by Wiechert et al. as part of their 13CFLUX software package. Since our FIA implementation natively supports 13CFLUX input files (i.e. "FTBL" files), the same input files can be used for both algorithms. (Note, however, that FIA does not require definition of free fluxes nor initial values, and thus these are simply ignored when imported). Figure 1 shows the simple network used along with the nomenclature used in previous publications. In addition to the network structure, the models are provided with flux and isotopic measurements as shown in Table 1.

E.Coli EMP and PPP Metabolic Pathways. The Embden-Meyerhof and Pentose Phosphate metabolic pathways of Escherichia coli.

First, we examined the output of the two algorithms for the traditional "noiseless" input file. In order to run the analysis, 13CFLUX requires the user to define a set of "free fluxes" along with their associated initial values [7]. Note that a bad choice of free fluxes or their associated values can result in poor algorithmic performance (both in computation time and accuracy). In fact, under various initial guesses the algorithm did not converge at all. As for FIA, none of the above is required. Since the network along with the given measurements are well defined, in the noiseless case the two algorithms returned similar values for unidirectional fluxes, as can be seen in Table 2. Some slight disagreements were observed for the bi-directional fluxes, which are more poorly identified.

We next compared the algorithms' sensitivities to noise. In a series of 10 experiments, white Gaussian noise was added to all of the measured isotopomer values, and the outputs and computation times for both algorithms were recorded. As can be seen in Figure 2, unidirectional fluxes remain quite constant and hardly suffer from the added experimental error (for both algorithms). However, the bi-directional fluxes are affected by the added noise. 13CFLUX suffers from a higher variance spread of the estimated values than FIA (thus is more sensitive to the added measurement noise). Note that the difference arises not only due to the mathematical model used, but also due to the stability properties of the optimization method chosen.

Measured fluxes values. Bidirectional fluxes calculated using FIA and 13CFLUX for noisy measurement set.

We next examined the computational performance of the two methods. Table 3 shows the algorithm running time for convergence (in seconds). The average running time for 13CFLUX was 133 seconds, while for FIA this time was 7 seconds. The running time ratio (13CFLUX/FIA) for individual experiments varied between ×9 to ×75.

FIA vs. OpenFLUX Comparison: Lysine Production by C. glutamicum

In this section we examine the analysis of the central metabolism of two lysine-overproducing strains of Corynebacterium glutamicum: ATCC 13032 (lysC fbr ) and its PEFTUfbp mutant. Both express feedback-resistant isoforms of the aspartokinase enzyme lysC, while the latter is additionally engineered to overexpress the glycolytic enzyme fructose-1,6-bisphosphatase. The example is based upon the measurements provided by Becker et al. [18], who implemented an ad-hoc program to estimate the values of various metabolic fluxes. In their more recent article introducing the OpenFLUX software package [15], Quek et al. chose to compare their results to those of Becker et al. Therefore, we will expand upon their comparison using our FIA implementation. The input file for FIA was constructed using the measurements and pathway structure given in [18] and [15]. As described in [15], the published mass isotopomer fractions were modified for mass interference from non-carbon backbone isotopes using the molecular formula of the amino acid fragments. FIA supports automatic generation of the naturally occurring isotopes correction matrix when the measured molecular formulas are supplied. This adjusts the measured fluxomers vector appearing in the objective function during the process of optimization. If necessary, it is possible not to use this feature but instead to directly supply the algorithm with the corrected measurement values.

When comparing the running times of FIA with OpenFLUX, the different algorithmic approaches of the two must be kept in mind. While OpenFLUX requires the user to supply it with sets of free fluxes, FIA requires no free fluxes nor initial values. Open-FLUX rapidly evaluates dozens of different optimization cycles with random initial values and seeks the best fitting result among them, while FIA uses only one single (longer) run. As such, the convergence probability of OpenFLUX depends on the number of attempts and random values generated during its operation, while the FIA results do not depend on any random value. Furthermore, in its analysis, EMU based algorithms evaluate only the fluxes necessary for measurement comparison, and thus their running time depends both on the metabolic network structure and the amount and location of the given measurements. FIA, on the other hand, can supply the entire set of metabolic fluxes at any given time, with no additional computation requirement (which depends mainly on the network structure).

Measured fluxes as constants

First, we ran the exact same simulation as Quek et al. performed in their article. They supply very accurate (mean error in the order of 0.15 mol%) values for the label measurements, and used the given measured fluxes as if they were noiseless measurements (thus as constants). We start by comparing the simulation time for this simple case. According to [15] and as validated by us using our computer, OpenFLUX required 50 iterations of about 16 seconds each in order to find a decent minimal point, hence about 800 seconds in total. While so, the FIA analysis took 60 seconds for initial analysis and matrices creation, and 300 further seconds for convergence, thus 360 seconds as a whole. Regarding the simulation results, as one can see in Table 4 and Table 5 the fluxes are very close to those calculated before, and the estimated fluxes FIA returned had the lowest residual value compared to the other methods.

Measured fluxes as measurements

We can also run the same optimization, but weight the given flux measurements by their variances. When running this optimization using OpenFLUX (again using 50 iterations), the amount of time was greatly increased, and ended in around 48 minutes. For FIA, on the other hand, the running time was the same as before, thus about 6 minutes. Comparing the results of the algorithms, OpenFLUX suffered from severe convergence problems. Most of its iterations ended without converging at all, while those that did converge yielded useless results, far from the measurements. FIA, on the other hand, succeeded in converging for all scenarios. For the wildtype lysine producing pathway, the results were very close to the ones before (since the fluxes and measurements were quite accurate). For the mutant example, which was less accurate, a reduction of the residual value was achieved by small changes to the measured fluxes. fluxes and residual values can be examined in Table 4 and Table 5.

Using non-normalized MS measurements

We now show that FIA can easily use incomplete or non-normalzied measurements by examining its performance in the example above. The supplied MS measurements were normalized to the n +1 backbone carbon atoms of the measured metabolites. Instead of using the supplied normalized data, we multiply each set of metabolite measurements by a random constant number. By doing so, we simulate the case in which only the first 3 (2 for GLY) MS peaks were measured, and had not been normalized. The original and supplied non-normalized measurement values can be found in Table 4. Note that the values were corrected by the molecular formulas of the measured fragments (again, can be automatically performed by FIA). In the absence of normalized data, FIA gave estimated fluxes very close to the previous cases, with very low residual values, as can be seen in Table 5. The running time of the algorithm was not affected by the change.

Application of a dissolved oxygen control strategy to increase the expression of Streptococcus suis glutamate dehydrogenase in Escherichia coli

The accumulation of acetate in Escherichia coli inhibits cell growth and desired protein synthesis, and cell density and protein expression are increased by reduction of acetate excretion. Dissolved oxygen (DO) is an important parameter for acetate synthesis, and the accumulation of acetate is inversely correlated to DO level. In this study, the effect of DO levels on glutamate dehydrogenase (GDH) expression was investigated, and then different DO control strategies were tested for effects on GDH expression. DO control strategy IV (50% 0–9 h, 30% 9–18 h) provided the highest cell density (15.43 g/L) and GDH concentration (3.42 g/L), values 1.59- and 1.99-times higher than those achieved at 10% DO. The accumulation of acetate was 2.24 g/L with DO control strategy IV, a decrease of 40.74% relative to that achieved for growth at 10% DO. Additionally, under DO control strategy IV, there was lower expression of PoxB, a key enzyme for acetate synthesis, at both the transcriptional and translational level. At the same time, higher transcription and protein expression levels were observed for a glyoxylate shunt gene (aceA), an acetate uptake gene (acs), gluconeogensis and anaplerotic pathways genes (pckA, ppsA, ppc, and sfcA), and a TCA cycle gene (gltA). The flux of acetate with DO strategy IV was 8.4%, a decrease of 62.33% compared with the flux at 10% DO. This decrease represents both lower flux for acetate synthesis and increased flux of reused acetate.

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Chemical compounds and reactions

We created a list of chemical compounds with 2, 3 or 4 carbon atoms by generating all possible linear combinations of the 20 ‘building blocks’ shown in Supplementary Table 2. Each of the building blocks was composed of a single carbon atom with associated oxygen, hydroxyl, hydrogen, phoshate and/or amino groups. Building blocks were connected together in linear chains by single or double bonds. This procedure created 1,966 linear molecules, 1,477 of which are electrostatically charged in solution, that is, containing at least one carboxyl or phosphate group. These 1,477 molecules are our internal metabolites. Next, for every possible pair of molecules from this list we checked systematically whether the reactions from Table 1 (see Supplementary Table 3 also for details) could transform one molecule into another, allowing for all possible couplings with the external metabolites. In this way, a network of 7,940 reactions was generated.

Free energies of compounds and reactions

For those internal metabolites that are known biochemical species, standard free energies of formation ΔfG were taken from the literature 24 . For other internal metabolites, for which such data does not exist, we employed a variant of the group contribution method 25,26,27,28 which accounts for the fact that molecules exist in solution as an equilibrium mixture of different ionic species. For each such molecule g1g2gn, composed from building blocks <gi>, we calculated ΔfG using

where E0 is a constant, E1(gj) is the contribution of group gj and E2(gj,gk) is a small correction due to neighbouring group–group interactions. The values of E0, the vector E1 and matrix E2 are determined by performing a least-squares fit to a training set of molecules with known ΔfGs that correspond most closely to the linear CHOPN molecules of our network (see Supplementary Methods for details).

Flux calculation

We used the method mentioned in ref. 7 to calculate the flux carried by a linear pathway. This method assumes that the flux through reaction i is given by 7,30

where kd is the diffusion-controlled rate constant, [Ei] is the enzyme concentration, [Si−1] and [Si] represent substrate and product concentrations and qi is the thermodynamic constant. This expression assumes that the enzyme acts as a perfect catalyst, and is used to derive an expression for pathway flux and metabolite concentrations (see Supplementary Methods for details). We then use Powell’s method 42 to find the set of enzyme concentrations that maximize the flux subject to the constraints that (i) all steady-state intermediate concentrations are within the prescribed range and (ii) the total enzyme concentration is fixed. We also repeat our analysis using reversible Michaelis–Menten kinetics, see Supplementary Methods for details of calculation.

Sampling the parameter space

We randomly selected 10,000 points from the parameter space corresponding to the concentrations of 11 external metabolites and the G3P and pyruvate concentrations. Each parameter was sampled logarithmically over a range covering several orders of magnitude above and below its typical physiological concentrations (see Supplementary Table 4 for details). For each of these points, we calculated the optimized flux Ji of each candidate pathway as detailed above, and computed the CF of path i as CFi=Ji/max<Jk>, by dividing its flux by the highest flux obtained across all pathways at the given point in parameter space.

Robustness of our results to small free energy changes

Using the group contribution method, the typical error in our calculation of the free energy of formation ΔfG for a given molecule is a few kJ mol −1 (see Supplementary Methods for details). To check the robustness of our results to such errors, our entire analysis was repeated using ΔfG values computed using different sets of training molecules, consisting of 80% of the molecules from the original training set, chosen at random. The qualitative results using such networks were identical from those obtained from the full set of training compounds. For example, the top 25 glycolytic pathways obtained from the reduced set contained 23 out of the 25 pathways from the original analysis.

How to write a stoichiometric matrix for a part of the Pentose phosphate pathway - Biology

Maize Maize, rice, sorghum, sugarcane Rice Rice

Saha et al. (2011) de Oliveira Dal’Molin et al. (2010b) Poolman et al. (2013) Lakshmanan et al. (2013)

Minimize total flux Minimize uptake of biomass rate (photon for photosynthesis/photorespiration and sucrose for heterotrophic metabolism) Minimize metabolic adjustment (MOMA) 25 combinations of five objective functions, including minimization of overall flux, maximization of biomass, minimization of glucose consumption, maximization of ATP production, and maximization of NADPH production Minimize total flux Maximize growth (linear optimization) Minimize overall flux (quadratic optimization) Minimize carbon uptake (linear optimization) Minimize overall flux (quadratic optimization) Flux balance: minimize substrate and light uptakes Flux variability: minimize and maximize each reaction while objective function is fixed The actual biomass production based on measurements from the literature Maximize flux of biomass reaction Same as in AraGEM Minimize total flux Flux balance: maximize biomass production Flux variability: minimize and maximize each reaction while objective function is fixed

Therefore, a realistic description of the multiple behaviors of the cells likely will require multiple and more complex objective functions (Collakova et al., 2012). Another obstacle is the current insufficient knowledge regarding the constraints affecting all species and all environmental condition (Allen et al., 2009). A range of different objective functions can be used in FBA, including maximizing ATP yield per unit flux, minimizing energy usage, minimizing substrate uptake (at fixed biomass efflux), minimizing reaction steps or total flux, and maximizing biomass yield per total flux. However, none of these objective functions are consistently successful in predicting growth rates (Chen and Shachar-Hill, 2012). In plant FBA modeling, the most popular constraint is the requirement to synthesize biomass of appropriate proportions and at a certain rate. The objective function is usually based on either minimization of the total reaction fluxes in the network or maximization of the carbon conversion efficiency (Table 3). A problem that arises here is that net biomass synthesis consumes a small proportion of the total energy budget. Therefore, when FBA is constrained solely by biomass synthesis, the fluxes through the energy-transforming pathways are greatly neglected (Sweetlove et al., 2013). Hence, because of the major energetic demand due to transport costs and cell maintenance, the biomass constraint alone is not sufficient to predict realistic fluxes in central heterotrophic metabolism of plant cells (Cheung et al., 2013). Accordingly, when Cheung et al. (2013) studied the effect of different constraints and objective functions on the accuracy of flux prediction by a FBA model of heterotrophic Arabidopsis cells in culture, they found accounting for energy costs (transport

and maintenance costs) in the network system to be more important than the choice of objective function. In this regard, they developed a method to account for both the ATP and reductant costs of cell maintenance on the basis of the measured flux ratio between the oxidative steps of the oxidative pentose phosphate pathway (OPPP) and glycolysis. Another issue is that while FBA is solely constrained by biomass synthesis, flux through the OPPP is absent in the vast majority of plant FBA models. Considering that these models account for the synthesis of biomass in sufficient quantities, this illustrates that the optimizing algorithm chooses other dehydrogenase enzymes to satisfy the NADPH demand of metabolism (Sweetlove et al., 2013). Cheung et al. (2013) show that the presence of thermodynamically implausible transhydrogenase cycles in the models can also lead to the absence of a predicted OPPP flux. Constraining these cycles to zero leads immediately to non-zero OPPP fluxes. Yet, there are studies showing that FBA, in its current standard form, has been very effective in predicting metabolic fluxes in plants. For instance, it was shown that FBA can predict net CO2 evolution in a range of plant tissues and in response to environment (Sweetlove et al., 2013). More interestingly, by applying a set of appropriate constraints, the FBA framework has been used to establish a more representative model of leaf metabolism by solving the two phases of day and night photosynthetic cycles as a single optimization problem (a diel flux balance model). Applying only minimal changes to the constraints of this model enabled it to accurately capture CAM over a diel cycle (Cheung et al., 2014). Other studies have also shown that FBA has the capability to establish a condition-specific

Systems Biology and Metabolism

metabolic model that is predictive under different environmental conditions (Williams et al., 2010 Cheung et al., 2013 Poolman et al., 2013). The extent to which FBA can successfully predict networks fluxes in plant metabolism is surprising as this method makes no reference to enzyme kinetic or regulation. This implies that enzyme regulation (i.e., allosteric regulation and posttranslational modifications) acts in such a way as to maintain metabolic steady state rather than as a key driver of the flux distribution across the network. Instead, it seems that the output demands are the main drivers of the flux distribution in central metabolism (Sweetlove et al., 2014). Nevertheless, continuing efforts have been undertaken to improve the technical and practical aspects of plant FBA. So far, plant FBA models have been based primarily on data averaged across different cell types (Sweetlove and Ratcliffe, 2011). Given that many plant metabolic functions are based on interactions between different subcellular compartments, cells, tissues, and organs, the reconstruction of FBA models at the cell-type, tissue-specific, or even organ specific level is a prerequisite for their use in metabolic engineering (Grafahrend-Belau et al., 2013). A clear shift in this area has occurred with an increasing number of tissue-specific (de Oliveira Dal’Molin et al., 2010b Hay and Schwender, 2011a, 2011b Lakshmanan et al., 2013) and organ-specific (Mintz-Oron et al., 2012) FBA models or a whole-plant scale model (Grafahrend-Belau et al., 2013). A key issue that may arise in the use of constraint-based models is the existence of alternate optimal solutions in which the same objective function can be achieved through different flux distributions. Flux variability analysis (FVA) is an efficient strategy for calculating flux variability that can exist to achieve optimal and suboptimal objectives (Tomar and De, 2013) and has been used to explore the metabolic capabilities of oil metabolism in a model of developing B. napus embryos (Hay and Schwender, 2011a). FVA was also applied to understand how oxygen influences the internal flux distributions in a model of rice, representing two tissue types: germinating seeds and photorespiring leaves (Lakshmanan et al., 2013). Cheung et al. (2014) also applied FVA to determine the feasible range of all fluxes in order to compare the predictions of a diel-modeling framework with the fluxes predicted in a constant light model. Genome-Scale Metabolic Models Over the past decade, genome-scale metabolic modeling has successfully provided unique insights into the metabolism of prokaryotic microorganisms (Toya and Shimizu, 2013 Xu et al., 2013a). Genome-scale models of prokaryotes can be analyzed with a wide range of optimization based tools and algorithms for rational design in metabolic engineering studies. Three of the most popular tools are OptKnock, OptORF, and OptFlux, which are used to simulate the simultaneous up- or downregulation (or knockout) of multiple genes (Lee et al., 2011 Tomar and De, 2013). Yet in plants, the application of genome-scale metabolic modeling is quite new, and it was not until 2009 that the first genome-scale model for Arabidopsis cell suspension culture (Poolman et al., 2009) became available. Since then, genomescale metabolic modeling has been applied to studying the central metabolism of various C4 plants (de Oliveira Dal’Molin

et al., 2010b Saha et al., 2011), Arabidopsis (de Oliveira Dal’Molin et al., 2010a Mintz-Oron et al., 2012), and rice (Poolman et al., 2013). In general, these plant genome-scale metabolic models have proved to be functional, robust, and accurate in predicting qualitative changes in selected aspects of central carbon metabolism (Collakova et al., 2012 de Oliveira Dal’Molin and Nielsen, 2013). However, in the context of metabolic engineering, there are some concerns when it comes to comparing the application of genome-scale metabolic models to plants and microorganisms as unlike microorganisms, plants generally are not grown under a highly controlled environmental regime. Broadly speaking, extending the network flux analysis results of microorganisms to plant metabolic engineering studies will require some caution (Stitt et al., 2010). In this regard, Shachar-Hill (2013) provided an illustrative study using the case of lysine production, which is a metabolic engineering target common to plants and microbes. Mathematical modeling methods have been used successfully to improve lysine production in bacterial fermentation systems of Corynebacterium glutamicum. These tools have helped to identify possible metabolic bottlenecks and significant changes, leading to significant increase in lysine production. However, when the same approach was applied to maize endosperm, the general conclusion was that such limitations might not exist (Shachar-Hill, 2013). Another concern is that although genome-scale metabolic models may have been validated for selected aspects of central metabolism, they do not usually extend to secondary metabolism (Collakova et al., 2012). One exception to this can be found in a model of Arabidopsis, which includes some aspects of secondary metabolism (Mintz-Oron et al., 2012). Other challenges facing plant genomescale metabolic models include uncertainty about the subcellular localization of reactions and the incomplete annotation of plant genomes (Sweetlove and Fernie, 2013). Approaches have been suggested for dealing with these challenges, such as applying subcellular localization prediction software for compartmentalizing metabolic reactions and comparative genomics for annotating undiscovered genomic content (Seaver et al., 2012 Lakshmanan et al., 2013). Integration of genome-scale modeling and transcriptomics or proteomics data sets is another approach that can be used to extend understanding of the complex metabolic behavior of plants (Töpfer et al., 2012, 2013). An integrative approach was used to predict the metabolic response of Arabidopsis to changing conditions, and it was found that including the transcriptomic data improved the predictions even though transcript levels do not relate directly to fluxes (Töpfer et al., 2013). Further analysis has shown that this approach can successfully bridge the gap between flux- and metabolite-centric methods (Töpfer et al., 2014). In general, the fact that plant genome-scale models rely on constraint-based analysis makes them particularly suitable for defining the outer limits of a system’s behavior rather than for making accurate predictions. An ideal progression would be to build a genome-scale kinetic model of a metabolic network, although the determination of kinetic parameters can be expected to be difficult, perhaps even to the point where it becomes too complex for calculation. A first attempt at building a parameterized genome-scale kinetic model of yeast metabolism

has been described by Smallbone et al. (2010). However, this approach still requires extensive development before it can be applied to higher eukaryotic systems. Given the acceleration in the sequencing of diverse plant genomes and the increasing interest in genome-scale metabolic models as a tool for examining plant metabolic networks, there is every reason to expect that with further improvement in available data and accordingly further refinement of the models their application will make an important contribution to plant metabolic engineering. MFA Despite the fact that steady state MFA techniques have addressed important questions, including the role of Rubisco in developing seeds and the regulation of oil seed metabolism (Kruger et al., 2012), their application to higher organisms (such as plants and mammalian systems) faces challenges, such as complex media formulations, subcellular compartmentation, and slow labeling dynamics (Allen et al., 2009). The major application of MFA to date has been on isolated cells or tissues, where typically 50 to 100 reactions are monitored (Allen et al., 2009). Technical difficulties in extending the analysis to plant networks have encouraged the development of alternative techniques (Sweetlove and Ratcliffe, 2011), such as the combinations MFA/EMA (Schwender et al., 2004) and MFA/FVA, which have been applied to study developing B. napus embryos (Hay and Schwender, 2011a, 2011b). Also, to avoid the long time period that MFA requires to achieve isotopic steady state, the isotopically nonstationary MFA (INST-MFA) technique has been developed. INST-MFA analyzes the metabolite labeling patterns obtained during the transient labeling period prior to isotopic steady state. This technique has been successfully applied to human cell studies (Murphy et al., 2013) and has also been used to study photosynthesis (Young et al., 2011 Szecowka et al., 2013). Steady state MFA is inapplicable to photoautotrophic tissues because labeling with 13CO2 leads to uniform labeling of all metabolites in the steady state (Roscher et al., 2000). Therefore, while steady state MFA is a wellestablished technique for studying heterotrophic and mixotrophic plant tissues, it cannot be used to study photosynthesis. Moreover, achieving an isotopic steady state in leaves is in any case unlikely because of complications introduced by the lightdark cycle and the slow turnover of metabolite pools (Sweetlove et al., 2013). To address this problem, Young et al. (2011) applied the INST-MFA technique to the cyanobacterium Synechocystis. They obtained a comprehensive flux map for all the Calvin-Benson cycle reactions and some side reactions, including those catalyzed by Glc-6-phosphate dehydrogenase, malic enzyme, and the photorespiratory pathway. In this analysis, the metabolic pool sizes were fitted as free parameters, whereas in the application of a similar approach, kinetic flux balancing, to Arabidopsis, the model was constrained with measured pool sizes obtained by mass spectrometry, as well as nonaqueous fractionation to provide information on subcellular pool sizes. In this study, Szecowka et al. (2013) deduced a set of intracellular fluxes in intact illuminated Arabidopsis rosettes. They analyzed the dynamic redistribution of label from 13CO2

supplied to leaves, from which a small set of fluxes were calculated. This approach allowed them to determine kinetic changes in isotope patterns of 40 metabolites of primary carbon metabolism and to benchmark them against four classically determined flux signatures of photosynthesis (Szecowka et al., 2013). Kinetic Modeling Where there is enough reliable data a kinetic model can be both comprehensive and predictive (Schallau and Junker, 2010 Wang et al., 2014). An example is the kinetic model of monolignol biosynthesis in Populus trichocarpa (Wang et al., 2014), which was constructed by performing a comprehensive study to obtain the reaction and inhibition kinetic parameters of all the relevant enzymes based on functional recombinant proteins. However, few such comprehensive models have been presented in plant metabolism because of the difficulty in obtaining the required information (Wang et al., 2014). Structural-kinetic modeling could provide a potential way around this deficiency. This method represents a transitional bridge between the stoichiometric approach and the various dynamic kinetic models. Although it does not define actual dynamic behavior, it describes the stability and robustness of a specific metabolic state, and clarifies related interactions and parameters governing the system’s dynamic properties. Detailed mathematical information, as well as the proposed workflow for modeling, have been provided by Steuer et al. (2006). A structural kinetic model consisting of 18 metabolites and 20 reactions was established to analyze the Calvin-Benson cycle. The model successfully extracted dynamic properties of the system without relying on any particular assumption about the functional form of the kinetic rate equations (Steuer et al., 2006). The same approach has been applied to the TCA cycle in plants (Steuer et al., 2007) to detect and quantify the dynamic behavior. A second approach to address the problem has been to assemble the kinetic model in a “top-down” fashion, amounting to fitting the model to the observed metabolite concentrations and fluxes. This approach was used to model the benzenoid network in the petunia (Petunia hybrida) flower, leading to the successful identification of the key flux-controlling steps (Colón et al., 2010). A “bottom-up” kinetic modeling approach has been described in modeling phloem flow in sugarcane (Saccharum officinarum) in the form of an advection-diffusion reaction framework. This pioneering model can probably be adapted to other plant species and perhaps even be extended to study xylem flow. It has been suggested that the same framework could form the basis for creating an integrated kinetic model of whole plant physiological function (Rohwer, 2012).

NEW INSIGHTS INTO METABOLISM AND ENGINEERING PLANT SYSTEMS One of the most important goals of metabolic engineering is the optimization of metabolic pathways for the production of industrially important metabolites. A major challenge is to accurately select the target pathways and then to tune and optimize

Systems Biology and Metabolism

the expression level of each enzyme for the selected pathways (Xu et al., 2013b). Models of plant metabolism have begun to address this challenge by providing a more rigorous basis for future genetic engineering. One such example is the identification of some key regulatory points within the pathway of monoterpene metabolism in peppermint, using a dynamic MFA approach. The model-derived results of this study have been experimentally verified and demonstrated the potential to guide the manipulation of metabolism to enhance monoterpene accumulation (Rios-Estepa et al., 2008). Another example is provided in a study on Arabidopsis seed, where the FBA model was used to computationally design metabolic engineering strategies for vitamin E overproduction (Mintz-Oron et al., 2012). A third example is a kinetic model of monolignol biosynthesis in P. trichocarpa, which revealed mechanisms involved in the regulation of lignin biosynthesis (Wang et al., 2014). This work provides a platform for future engineering of lignin production as well as improvements in other related areas such as the resistance to biotic and abiotic stresses and new biomaterials production (Wang et al., 2014). The compounds synthesized within the plant cell can be classified as either primary metabolites or secondary metabolites (Bu’Lock, 1965 Luckner, 1972 Richter, 1978). Manipulation of secondary metabolic networks typically is less complex than that of primary metabolism, allowing them to be readily broken down into more manageable entities and therefore offering more favorable opportunities for pathway engineering (Sweetlove et al., 2010). Moreover, despite the remarkable diversity of secondary metabolism, they can still be organized into groups of structurally related compounds. This facilitates the categorizing of pathways and even their order to make their modeling more tractable. Grouping metabolites of similar biosynthetic origin forms the logical basis of organization of models of fluxes as well as kinetic models (Morgan and Shanks, 2002 Fernie and Morgan, 2013). Nevertheless, secondary metabolite engineering in plants is less developed than in other organisms, perhaps because of the highly complicated network connections which link primary and secondary metabolisms. For instance, some transcription factors associated with the production of a particular group of secondary metabolites coactivate the expression of genes encoding metabolic enzymes linked with primary pathways that provide precursors to these secondary metabolites (Aharoni and Galili, 2011). Such links have been responsible for frustrating a number of attempts to engineer plant secondary metabolism, producing unanticipated outcomes or trivial alterations to the system (Colón et al., 2010 Stitt et al., 2010). Therefore, studying the central metabolism network may promote the engineering of both primary and secondary metabolism. Photosynthesis Numerous experiments have been conducted to enhance crop productivity by genetic manipulation of photosynthetic electron transport, RuBP regeneration, Rubisco activity, and the associated flow to photorespiration (Peterhansel et al., 2008 Raines, 2011). These results reaffirm the importance of mathematical models for a better understanding of photosynthetic reactions

(Arnold and Nikoloski, 2014). A functional model of photosynthesis should include not only the individual metabolic steps, but also the major regulatory mechanisms affecting these steps. Such comprehensive models ideally would predict the photosynthetic metabolic network response to environmental or genetic perturbations and would have implications for the redirection of carbon to high value natural products and ultimately the improvement of crop yield (Szecowka et al., 2013 Zhu et al., 2013). Although many aspects of photosynthetic networks have been subjected to modeling studies, the Calvin-Benson cycle has become a favored target, as it is the primary pathway in plants, producing starch and sucrose from CO2 (Arnold and Nikoloski, 2014). However, a neglected aspect of the C3 photosynthesis network is the control of flux from the Calvin-Benson cycle to the output pathways of starch, sucrose, isoprenoids, shikimate, and nucleotides. Because of this, it is difficult to predict in a comprehensive fashion the way the relative flux to these pathways changes during development or in response to environmental changes (Raines, 2011). Nevertheless, the existing models potentially provide a good starting point for extending and improving future photosynthesis models. In this regard, Arnold and Nikoloski (2011) compared 15 Calvin-Benson cycle models assembled over the past 30 years and provided a detailed classification on the basis of the model boundaries, the level of cellular organization, the complexity of the kinetics, and the regulatory processes that were included. They ranked the models on several criteria, including sensitivity, stability, robustness, and the residual sum of squares at the resulting steady states. Their target was to identify model candidates that provided quantitatively accurate predictions for use in metabolic engineering. Based on their analysis, they categorized the existing models into two groups: those suitable for carbon fixation and those suitable for metabolic engineering. The most suitable models appear to be those proposed by Farquhar et al. (1980) and Poolman et al. (2000), respectively. The advantage of the model proposed by Farquhar et al. (1980) is that it links Rubisco with in vivo measurements of photosynthetic rate and therefore is capable of predicting net rates of photosynthetic CO2 fixation in response to variable environmental conditions. Because of these advantages, the model has been studied and extensively validated over many years, and derivatives of the model have been established which are currently used in large-scale ecological modeling studies (Sweetlove et al., 2013). The Farquhar model and its derivatives consist exclusively of algebraic equations that can only capture the steady state behavior through restricting assumptions (Arnold and Nikoloski, 2013). However, photosynthesis is rarely at steady state in the natural environment due to fluctuating conditions of environment. Therefore, a highly mechanistic, wellvalidated model is required to study photosynthesis in a more practical approach. In this regard, a kinetic model (e-photosynthesis), which includes each discrete process from light capture to carbohydrate synthesis, has been recently described for C3 photosynthesis. The e-photosynthesis model effectively mimics many typical kinetic of photosynthetic features and provides a workable platform for guiding engineering of improved photosynthetic efficiency (Zhu et al., 2013).

Because of its steady state nature, Farquhar model and its derivatives are incapable of capturing dynamic changes that occur in the relationship between photosynthesis and photorespiration at varying light intensities and concentrations of CO2 and O2. Recent experimental evidence indicates that photorespiration is also involved in nitrate assimilation, energy production of photosynthesis, exchange of redox equivalents between compartments, one-carbon (C1) metabolism, and redox signal transduction (Arnold and Nikoloski, 2013). Accurate quantitative modeling of photorespiration is thus of major importance to understand how the fine tuning of the levels of intermediates and fluxes maintains optimal CO2 assimilation in response to perpetually changing conditions (Fernie et al., 2013). The Farquhar model’s derivatives aside, even kinetic modeling approaches of photorespiration have neglected its complex role and have mostly coupled a far too simplified version with photosynthetic metabolism. However, the e-photosynthesis model (Zhu et al., 2013) has included photorespiration in more detail. A promising approach toward modeling photorespiration could be assembling a complete metabolic network in such a way that the connection of nitrogen metabolism is also taken into account. For instance, through perturbing nitrogen-specific reactions in such a model, the interplay of photorespiration and photosynthesis as well as effects on the whole system could be tested. An extension to such an approach could be undertaken by adding the recent findings regarding regulatory and signaling events of photorespiration into genome-scale models (Arnold and Nikoloski, 2013). While the balance between photosynthesis and respiration is a key determinant of the carbon economy, another flaw in the Farquhar model and its derivatives is that they predict respiration on the basis of its correlation with other processes not as an independent metabolic phenomenon (Sweetlove et al., 2013). To attain the goal of an applicable mechanistic respiration model, several challenges must be addressed. It seems that the term “respiration” should be defined in such a way as to capture the light-independent metabolic networks, which lead to the net CO2 production. In this regard, Sweetlove et al. (2013) suggest substituting the poorly defined term “respiration” with “net CO2 evolution,” which is defined as the sum of all the CO2-producing steps minus the sum of all the CO2-consuming steps, excluding photosynthesis and photorespiration. Concentrating on net CO2 evolution results in the identification of two precise challenges for the modeling process. First, one must identify all the metabolic processes contributing to net CO2 production and this is generally regarded as extremely difficult. Second, any predictive model must allow for differences between tissue types and the impact of a change in conditions on the processes contributing to net CO2 evolution. In addressing these challenges, quantification of biochemical processes leading to net CO2 evolution by MFA shows that the contribution of different processes to the CO2 balance is highly variable. It also shows that the variability in CO2 evolution between species and tissues might be greater than between growth conditions. This finding would indirectly reflect the need for a robust central metabolic network in the face of suboptimal environmental conditions. In addition to MFA, the potential for FBA as a tool to predict net CO2 evolution has been assessed. Although there are relatively few FBA studies

for which experimentally constrained metabolic flux data are available as a point of comparison/validation, the conclusion is that FBA has the potential to predict the metabolic origin of evolved CO2 in different tissues/species and under different conditions (Sweetlove et al., 2013). However, most of these models assume that the organism grows in constant light, which is unlike the natural situation where the interaction between light and dark metabolism is a major feature of metabolism of photosynthetic organisms. To establish a more representative model of leaf metabolism, Cheung et al. (2014) constructed a diel flux balance model that accounted for metabolic fluxes in the light and dark phases of leaf metabolism by simulating them simultaneously in a single optimization problem. The diel model was obtained by applying a specific framework of constraints to an existing genome-scale model of Arabidopsis metabolism (Cheung et al., 2013). The model successfully captured many known features of C3 leaf metabolism including the role of citrate synthesis and accumulation at night (through the mitochondrial tricarboxylic acid cycle) and its export from the vacuole during the day as a precursor for the provision of carbon skeletons for amino acid synthesis. Generally, this model discovered some important features of interactions between light and dark metabolism and successfully predicted the metabolic fluxes in the light in C3 photosynthesis. C4 plants possess a characteristic leaf anatomy, which supercharges photosynthesis by concentrating CO2 in the vicinity of Rubisco and significantly reducing the oxygenation reaction (Wang et al., 2012). A system understanding of the distinctive anatomy and unique physiology is a prerequisite to effective modeling of C4 metabolism. In order to achieve a system-level understanding of spatial regulation of photosynthesis in C4 plants, a genome-scale metabolic model (C4GEM) was developed and applied to investigate the flux distribution between two interacting tissues of bundle sheath and mesophyll during C4 photosynthesis. The model is an extension of an Arabidopsis model (AraGEM) (de Oliveira Dal’Molin et al., 2010a), which represents three different C4 subtypes NADP-ME (NADPdependent malic enzyme), NAD-ME (NAD-dependent malic enzyme), and PEPCK (phosphoenolpyruvate carboxykinase) (de Oliveira Dal’Molin et al., 2010b). In an extension to this study, Wang et al. (2012) simulated the influence of each subtype on biomass synthesis and CO2 fixation and concluded that the PEPCK subtype is superior to NADP-ME and NAD-ME subtypes under sufficient supply of water and nitrogen. Moreover, the C4GEM model highlighted differences in the relative fluxes through photosystem I and photosystem II (PSII) in the different cell types and in each of the three C4 subtypes. The model also predicted that the NAD-ME and PEPCK subtypes have substantial PSII activity in the bundle sheath tissues, while NADPME species have little PSII and more cyclic electron transport (CET) in their bundle sheath cells. While C4 plants require more ATP than C3 plants to assimilate CO2, it has not been elucidated how the extra ATP is produced. Interestingly, simulations have shown that CET occurring in the bundle sheath is an efficient means for supplying the extra ATP needed in the NADPH-ME subtype. The model compared the minimum photon requirement for CET in the mesophyll bundle sheath. The results showed that

Systems Biology and Metabolism

CET in the bundle sheath is energetically more efficient as it requires fewer photons to produce the extra ATP than CET that is active in the mesophyll (de Oliveira Dal’Molin et al., 2010b). A system-level understanding of how C4 photosynthesis operates and differs from C3 plants is also a prerequisite to understanding how carbon shuttling enzymes are tuned by controlling networks (Wang et al., 2012 Weissmann and Brutnell, 2012). The study by Wang et al. (2012) compared a C3 metabolic network (AraGEM, for Arabidopsis) with a C4 metabolic network (C4GEM, for maize). To this end, they first made some improvement to both models and compared them using graph theory analysis (which allows the comparison of important topological parameters). They found out that the C3 network has a denser topology than C4. This is probably a reflection of the anatomical difference between C4 and C3 leaf structure, as the former includes both mesophyll and bundle sheath cells, while the latter consists of single cell types. The simulation of enzyme knockouts (single reaction deletion) showed that more than 86% (where the objective function is biomass maximal) and more than 96% (where the objective function is CO2 fixation) of reactions have no influence when deleted in C4 and C3 networks. This demonstrates the robustness of these networks. Further to this, a comparison of the redundancy of the primary metabolic network between C4 and C3 showed that, regardless of the type of objective function, the C4 plant is more robust to gene mutation or environmental changes (Wang et al., 2012). CAM represents a temporal separation of metabolic events in which CO2 is initially fixed at night in the form of carboxylic acids (mainly malic acid) and then decarboxylated during the day to provide CO2 for conventional photosynthesis (Cheung et al., 2014). CAM maximizes water use efficiency and maintains high biomass productivity by concentrating CO2 around Rubisco, favoring carboxylase activity. CAM also represents a simpler anatomical structure, as its photosynthetic metabolism occurs in a single mesophyll cell instead of in the two separate cells as in C4 photosynthesis. Modeling could provide a key approach for comprehensive systemic understanding of the enzymatic and temporal regulatory events that control the carboxylationdecarboxylation of carboxylic acids and the concurrent metabolic fluxes through glycolysis-gluconeogenesis (Borland et al., 2014). Relatively little effort has been made toward studying CAM in a systems level. To address this, Cheung et al. (2014) used an innovative technical approach by making some changes to the constraints of the original diel C3 model in order to capture the classical CAM cycle of a mature leaf and to predict the metabolic flux over a diel cycle. While the model successfully predicted metabolic fluxes consistent with the well-known CAM cycle, it also showed that despite the potential for suppression of photorespiration through CO2 concentration, there are unlikely to be significant energetic benefits in CAM photosynthesis over C3. The model predicted that the energetic savings of enzymatic machinery, which have been achieved by suppression of photorespiration, are probably offset by the higher flux demand of the CAM cycle. In addition to Rubisco, which is the carboxylating enzyme operating in the Calvin-Benson cycle, nature employs several other carbon fixation pathways. This diversity of natural solutions

offers the chance of utilizing a combination of modeling together with synthetic biology, to assemble fully innovative CO2 fixation pathways that may be more efficient than the C3 cycle. With the aim of designing synthetic metabolic pathways for improved carbon fixation, growth, and yield, Bar-Even et al. (2010) considered the entire range of 5000 metabolic enzymes known to occur in nature as components and used an FBA to systemically discover all possibilities that can be devised with these enzymes as building blocks. This led to several promising synthetic carbon fixation pathways, which then they compared with the natural pathways using physiochemical criteria. The comparison suggested that some of proposed synthetic pathways could have a significant quantitative advantage over the natural ones. Besides the Calvin-Benson cycle, which supports most of the global carbon fixation, there are currently five known naturally occurring carbon fixation pathways: the reductive TCA cycle, the 3-hydroxypropionate/malyl-CoA cycle, the reductive acetylCoA pathway, the 3-hydroxypropionate/4-hydroxybutyrate cycle, and the dicarboxylate/4-hydroxybutyrate cycle. Boyle and Morgan (2011) compared the thermodynamics and efficiency of these six pathways using FBA. Based on comparisons of either the energy demand or photon requirement for conversion of photoassimilate into biomass, it was shown that the reductive TCA cycle is the most efficient way of generating biomass from solar energy. However, the reductive TCA cycle is only trivially more efficient than Calvin-Benson cycle. Overall, this study emphasizes the role of the Calvin-Benson cycle, which has evolved to operate in the current oxidative environment of the earth (Boyle and Morgan, 2011). TCA Cycle In microorganisms, in silico pathway analysis has suggested a significant potential for TCA cycle optimization (Kjeldsen and Nielsen, 2009) hence, efforts have been initiated to engineer it (Becker et al., 2009). Engineering the TCA cycle in plants could also be useful because of the high value metabolites derived from carbon skeletons provided by this pathway, including amino acids, fatty acids, flavonoids, pigments, alkaloids, and isoprenoids. In plants, there are significant hurdles in advancing engineering of the TCA cycle, perhaps because of the overall complexity of the system. However, almost all the genes encoding the enzymes involved in TCA cycle have been cloned from different plant species, and many of the encoded proteins have been biochemically characterized. Efforts have also been intensified to understand the modular organization of TCA cycle (Carrari et al., 2003). These achievements have provided the basis for efforts to genetically modify TCA cycle and to enhance the organic acid content in plants (Morgan et al., 2013). Genetic and metabolic experiments have shown that the conventional TCA cycle is not the only pathway through which TCA flux passes (Sweetlove et al., 2010), raising numerous as yet unanswered questions concerning the balance between the cyclic and the noncyclic flux modes. Answers to these questions could help to efficiently engineer the plant TCA cycle. To this end, modeling experiments have been of great benefit in showing that when the demand for ATP is low, the cyclic flux

mode is not necessarily maintained (Sweetlove et al., 2010). Similarly, a large-scale model of cellular metabolism in developing embryos of the B. napus developing seed demonstrated that cyclic TCA activity is reduced as the photosynthetic output of NADPH and ATP rises (Hay and Schwender, 2011a, 2011b), while an FBA-based model of heterotrophic Arabidopsis metabolism demonstrated that cyclic TCA flux is only required when there is a high demand for ATP (Poolman et al., 2009). In the barley endosperm, FBA has been used to show that the gradual switch from cyclic TCA (in aerobic tissue) to noncyclic TCA (in hypoxic tissue) occurs during the process of grain maturation, probably because succinate dehydrogenase (which connects the TCA cycle with the mitochondrial electron transport chain) is associated with only a minor flux (GrafahrendBelau et al., 2009a). In agreement with this report, in silico flux maps of seed-derived suspension culture rice cells grown under anoxic conditions showed a truncated TCA cycle operation between fumarate and oxaloacetate while a fully operational TCA cycle was characterized under aerobic conditions. This difference was mainly due to the limited regeneration of redox cofactors since mitochondrial respiration was impaired under anoxia. Interestingly, FBA revealed the possible role of g-aminobutyric acid shunt in the conversion of a-ketoglutarate to succinate instead of a-ketoglutarate dehydrogenase and succinate-CoA ligase under anaerobic conditions. Furthermore, in contrast to anaerobic conditions, a significant amount of pyruvate was converted to acetyl-CoA under aerobic conditions, thus enabling its entry into the TCA cycle for energy production (Lakshmanan et al., 2013). The genome-scale metabolic model of a developing leaf cell of rice predicted that the responses of the three neighboring enzymes succinate dehydrogenase, fumarate, and malate dehydrogenase are different under different light intensities. This study pointed out that the TCA cycle has the ability to reconfigure its reactions to fulfill different requirements under different conditions or developmental stages (Poolman et al., 2013). This view of the TCA cycle is supported by experimental evidence from other studies (Studart-Guimarães et al., 2007 Rocha et al., 2010). Sucrose Metabolism Sucrose accumulation in storage tissues is accompanied by recurring cleavage and synthesis, during which ATP is wasted (Schäfer et al., 2004). The genetic inhibition of this futile cycle might be expected to increase crop productivity. Identifying the candidate genes for transgenic regulation would require a laborious gene-by-gene approach (Rohwer, 2012), whereas modeling could radically short-cut this process. Applying a combination of EMA and kinetic modeling, 14 elementary modes were detected during sucrose accumulation in sugarcane, five of which were associated with a futile cycle. The model also predicted that the attenuation of neutral invertase and the overexpression of a vacuolar sucrose importer and plasma membrane glucose and fructose transporters would provide an efficient means of reducing futile cycling (Rohwer and Botha, 2001). These predictions were partially validated in an analysis of suspension cell cultures in which neutral invertase activity had been downregulated by RNA interference, since these cells were

more capable of accumulating sucrose compared with the wild type (Rohwer, 2012). MFA of the maize kernel similarly showed that depending on the subcellular location of glyceradehyde 3-phosphate and the identity of the enzymes involved, futile cycling could waste between 18 and 47% of the ATP pool (Alonso et al., 2011). However, Kruger et al. (2007) argue that this value is unlikely to be as high as reported and that reliable 13C MFA measurements of the flux from hexose phosphate to glucose (sucrose cycling), will only be possible if the labeling pattern is known for both the cytosolic and vacuolar glucose pools. Seed Oil Synthesis During seed storage deposition, the biosyntheses of different storage compounds need different proportions of energy cofactors (ATP and NADPH), as well as different proportions of metabolic precursors (Hay and Schwender, 2011b). As a predictive model of oil metabolism is helpful in manipulation of seed composition, many efforts have been conducted in this regard. An important feature influencing the seed oil yield is the average carbon conversion efficiency (CCE), a measure of the efficiency of conversion of substrates into storage product (Alonso et al., 2011). CCE is a straightforward definition of metabolic efficiency and highlights the proportion of resources devoted to accumulation of structural, storage, and reproductive biomass (Chen and Shachar-Hill, 2012). CCE estimates have been obtained for the sunflower (Helianthus annuus) embryo (50%) (Alonso et al., 2007), the maize endosperm (76 to 92%) (Alonso et al., 2011) and embryo (56 to 71%) (Alonso et al., 2010), and the B. napus seed (>80%) (Alonso et al., 2007). Studying the metabolic basis underlying these differences may promote insights into how genetic engineering can be used to increase oil content and to improve its composition. Several models have been established for description of oil production, including in B. napus (Schwender et al., 2004 Schwender, 2008 Hay and Schwender, 2011a, 2011b), maize (Alonso et al., 2010, 2011), and sunflower (Alonso et al., 2007). Modeling storage metabolism in the developing B. napus embryo has highlighted the potential participation of various pathways, including the formation of the lipid precursor pyruvate and the potential role of PEP carboxylation in either nitrogen assimilation or in lipid synthesis. No increased uptake or changed use of amino acids, as possible lipid precursor, was predicted using MFA or FVA (Hay and Schwender, 2011a, 2011b). The same studies also characterized the bypass of glycolytic reactions by Rubisco to lipid synthesis. This “Rubisco bypass” pathway can explain the observed increase in CCE. However, due to the energy requirement of the bypass, this contribution is only predicted to be beneficial if the light intensity is above a certain threshold (Hay and Schwender, 2011a). In an elegant study, an FBA model for cultured B. napus (Hay and Schwender, 2011a, 2011b) was combined with highresolution measurements of in planta developing embryos in order to get an in-depth insight into the spatial variation in metabolic fluxes across different tissues of oilseed. Unlike the FBA model prediction, this study predicted that the Rubisco bypass occurs only in the outer cotyledon, hypocotyl, and radicle, but not in the

Systems Biology and Metabolism

inner cotyledon. This probably happens due to the shape of the seed because as the seed gets bigger, light penetration into the inner tissues gets smaller (Hay and Schwender, 2011a Borisjuk et al., 2013). MFA of the developing maize embryo and endosperm has also revealed that flux through the OPPP is greater in the embryo than in endosperm. Nevertheless, even the carbon amount entering the embryo cannot fully meet the NADPH demand for fatty acid synthesis and may limit oil production, while NADPH is not a limiting factor for lipid synthesis in the endosperm. MFA studies also revealed the key role for plastidic NADP-depended malic enzyme activity in providing reductant and carbon for fatty acid synthesis in developing maize embryo (Alonso et al., 2010, 2011).

Metabolism and the Environment The level of metabolites is dramatically influenced by environmental adversity. However, the connection between environmental conditions and metabolism is hidden by the complex networks linking them. Understanding this connection becomes more important when we try to recognize the role of metabolism in acclimation to abiotic stress. Metabolic modeling has been applied to this issue, seeking answers to questions such as to what extent the functioning of metabolic pathway(s) may be associated with environmental change and whether the network connectivity is conserved or changes between different growth conditions. One of the first attempts at stoichiometric modeling of plant metabolism was performed to analyze the storage pattern of developing barley seed endosperm in response to oxygen depletion (Grafahrend-Belau et al., 2009a). Since then, several modeling investigations of plant-environment interactions have studied the impact of stress (increased temperature and hyperosmotic stress) (Williams et al., 2010 Cheung et al., 2013), carbon and nitrogen availability (Sulpice et al., 2013), light and temperature condition (Töpfer et al., 2013), and nitrogen supply (nitrate or ammonium) (Masakapalli et al., 2013) on heterotrophic metabolism in Arabidopsis. The increasing availability of high throughput data for crop plants is leading to new modeling applications in studies of the interaction between crop plants and their environment. For instance, to elucidate metabolic flux profiles during abiotic stresses (flooding and drought stresses) a metabolic/regulatory network of rice cells was reconstructed for two different rice tissues, germinating seeds and photorespiring leaves (Lakshmanan et al., 2013). In another study, a genome-scale metabolic model of a developing leaf cell of rice was used over a range of photon flux values (Poolman et al., 2013). The breeding of new crop varieties with improved performance under abiotic stress is becoming increasingly important. Therefore, it is expected that metabolic modeling will play a key role in this field in the near future.

CONCLUDING REMARKS Plant computational modeling is evolving rapidly and will soon reach the point where it can begin to make an impact on plant

metabolic engineering practice. However, there is still a need to overcome serious difficulties before plant metabolic models can be routinely incorporated as part of crop systems biology and there is a particular need for multiscale models (Baldazzi et al., 2012). By definition, a multiscale model explicitly integrates mechanisms that occur across multiple spatial or temporal scales and/or functions (Baldazzi et al., 2012 Walpole et al., 2013). Establishing such a model sometimes requires a range of diverse inputs from biochemical or mechanistic mechanisms to biomechanical phenomena, which leads to a hybrid multiscale model (Baldazzi et al., 2012). An excellent example of such a hybrid multiscale model was developed for the heart (Noble, 2011) in which the reaction-diffusion equations (as a description for the electro-mechanical contraction of heart) are coupled to a set of ordinary differential equations (as a description for ions transport at the cellular membrane). Examples in plant biology include models that correlate molecular level processes with plant development/morphogenesis in Arabidopsis (Vernoux et al., 2011 Grieneisen et al., 2012). However, the comprehensive physiological role of the metabolic network can only be fully understood from a whole-body perspective where individual cells, the surrounding tissue, and the whole organism interact continuously at a metabolic level (Krauss et al., 2012 Grafahrend-Belau et al., 2013). Several approaches for combining metabolic models, covering different levels of biological organization in humans have been described (Krauss et al., 2012), while at the time of this review, the only multiscale metabolic model in plants was presented by Grafahrend-Belau et al. (2013). During this study, the multiorgan FBA model was combined with a dynamic wholeplant multiscale functional plant model. Dynamic FBA was performed by partitioning a selected plant growth phase into several time intervals and by computing a static FBA at the beginning of each time interval. To include dynamic processes, exchange fluxes that had been predicted by the functional plant model and are also time dependent were used to constrain the static FBA within each time interval. Establishing a multiscale plant model requires simultaneous modeling of many different cell types in several connected tissues/organs. Considering the large scale of a multiorgan or whole-organism model, stoichiometric modeling, in particular FBA, is the most suitable approach. With the aim of achieving a multiscale metabolic model, first the validated subsystem specific models should be constructed separately, and then the separate parts can be coupled together to construct the multiscale model. This presents several technical and mathematical challenges. The first is that we need to formulate new constraints and/or objective functions, both at the level of subsystems and at the level of the integrated model to describe the behavior of the plant as realistically as possible. The second is the lack of tissue-specific information on metabolite uptake and secretion, which is required for FBA (Shlomi et al., 2008). It is obvious that coupling submodels together redraws the system boundaries. The question that arises during coupling subsystem models is to what extent the interdependencies of fluxes in subsystems will vary with those in the coupled metabolic network. Special mathematical analysis, such as flux-coupling analysis, has been developed to deal with this question (Marashi and Bockmayr, 2011 Marashi et al., 2012).

Plant metabolic engineering will be able to address human needs only when it begins to make meaningful changes on an industrial scale. To achieve this, multiscale modeling is a prerequisite for obtaining an improved understanding of metabolism at a systems level. However, before that, plant metabolic modeling needs to be supported by more advanced bioinformatics platforms and computational toolboxes. There is also a need to gain an improved understanding of the regulatory circuits governing cellular metabolism. Moreover, improved cellular resolution and enhanced sensitivity of metabolomics are also required.

AUTHOR CONTRIBUTIONS All authors contributed to writing the article.

ACKNOWLEDGMENTS We thank R. George Ratcliffe for his invaluable intellectual input and feedback throughout the development of this article.

Received July 25, 2014 revised September 22, 2014 accepted October 2, 2014 published October 24, 2014.

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Plant Metabolic Modeling: Achieving New Insight into Metabolism and Metabolic Engineering Kambiz Baghalian, Mohammad-Reza Hajirezaei and Falk Schreiber Plant Cell originally published online October 24, 2014 DOI 10.1105/tpc.114.130328 This information is current as of October 24, 2014 Permissions

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The Reproducible Research Results (R3) team, in particular, C. Trefois and Y. Jarosz, of the Luxembourg Centre for Systems Biomedicine, is acknowledged for their help in setting up the virtual machine and the Jenkins server. This study was funded by the National Centre of Excellence in Research (NCER) on Parkinson’s disease, the U.S. Department of Energy, Offices of Advanced Scientific Computing Research and the Biological and Environmental Research as part of the Scientific Discovery Through Advanced Computing program, grant no. DE-SC0010429. This project also received funding from the European Union’s HORIZON 2020 Research and Innovation Programme under grant agreement no. 668738 and the Luxembourg National Research Fund (FNR) ATTRACT program (FNR/A12/01) and OPEN (FNR/O16/11402054) grants. N.E.L. was supported by NIGMS (R35 GM119850) and the Novo Nordisk Foundation (NNF10CC1016517). M.A.P.O. was supported by the Luxembourg National Research Fund (FNR) grant AFR/6669348. A.R. was supported by the Lilly Innovation Fellows Award. F.J.P. was supported by the Minister of Economy and Competitiveness of Spain (BIO2016-77998-R) and the ELKARTEK Programme of the Basque Government (KK-2016/00026). I.A. was supported by a Basque Government predoctoral grant (PRE_2016_2_0044). B.Ø.P. was supported by the Novo Nordisk Foundation through the Center for Biosustainability at the Technical University of Denmark (NNF10CC1016517).

7 Summary and Outlook

The profound importance of thiamine to the health of all organisms and the shortcomings of previous thiamine analysis methods have together fueled an ongoing interest in improving methodologies for monitoring thiamine in a variety of matrices. Numerous colorimetric, fluorescence, electrochemical, and biological-based approaches have been developed, each with their own inherent benefits and caveats (Table 1). Although colorimetric approaches were once widely used, owing to the inherently simple detection principle, they have largely fallen out of favor in lieu of more sensitive fluorometric methods, owing to their high limits of detection (μ m ) and risk of interferences, especially when biological samples are considered. As a result, the most commonly employed methodologies have relied on fluorescence detection following chromatographic separation. These established methodologies offer the benefit of sensitive quantification of thiamine in multi-component mixtures and speciation of thiamine phosphates. Advances in HPLC separations and improvements in detection capabilities offer the ability to reach impressive pM levels of detection suited for well-equipped laboratory environments.

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