Systems biology of plant metabolic interactions

Abstract

Metabolism is the key cellular process of plant physiology. Understanding metabolism and its dynamical behavior under different conditions may help plant biotechnologists to design new cultivars with desired goals. Computational systems biochemistry and incorporation of different omics data unravelled active metabolism and its variations in plants. In this review, we mainly focus on the basics of flux balance analysis (FBA), elementary flux mode analysis (EFMA), and some advanced computational tools. We describe some important results that were obtained using these tools. Limitations and challenges are also discussed.

1 Introduction

Metabolism is the key process of any living organism that comprises a series of chemical reactions involved in building up sugars and other molecules by photosynthesis utilizing smaller molecules and producing energy by respiration from those complex biological molecules, such as proteins, lipids, nucleic acids, carbohydrates, etc., to sustain life. In the case of plant systems, the term ‘metabolism’ directly points towards some cellular processes such as glycolysis, the tricarboxylic acid cycle (TCA cycle), the Calvin cycle, the pentose phosphate pathway, the electron transport chain, etc., which take place in the cytosol and other different cellular compartments such as mitochondria, chloroplasts, and peroxisomes. Most of the reactions of metabolic pathways are catalyzed by different enzymes, and therefore, they can be regulated by varying the activities of those enzymes. On the other hand, there are other factors like substrate and product concentrations, as well as ion concentrations, that act as co-factors for different enzymes, pH levels, genomic and transcriptomic variations, and stress conditions which can up- or down-regulate metabolic pathways. Several important pathways of central carbon metabolism occur within plant mitochondria and synthesis the important players. Various shuttle systems and transporters help mitochondria maintain their interactions with the cytosol, chloroplast, peroxisome, etc. In this review, we focus on mitochondrial metabolism and its interactions with other cellular compartments and their regulations. In the following sections, we will elaborate on the computational approaches that can integrate different omics and simulation data to understand metabolic interactions at the cellular level. Flux balance analysis (FBA) (Orth et al. 2010) is one of the important mathematical constraint-based modeling approaches to understand flux distributions in metabolic networks under different cellular conditions. Regulation of metabolism due to differential gene expressions and variations in enzyme concentrations can be analyzed by modifying the classical FBA method. Flux variability analysis (FVA) may indicate new feasible pathways which can be then validated either through proteomics or gene expression data, i.e., whether under different conditions these different sets of metabolic pathways get activated. Furthermore, elementary flux mode analysis (EFMA) (Schuster et al. 1999) gives us alternative modes of different metabolic pathways. The flux coupling finder (FCF) (Burgard et al. 2004) can indicate coupled metabolic reactions, i.e., whether a change in one reaction will result in a corresponding change in a coupled reaction.

2 Biochemical pathways of biomass production in plant leaves

Incident light energy is converted to chemical energy in the form of adenosine triphosphate (ATP) and nicotinamide adenine dinucleotide phosphate hydrogen (NADPH) by the two photosystems – I and II, embedded in the thylakoid membrane of chloroplasts. These reactions, occurring in the presence of light, are called light reactions (Arnon 1971). The ATP and NADPH produced by light reactions enter the Calvin–Benson cycle, which takes place in the stroma of the chloroplast. The main enzyme that works in the Calvin–Benson cycle is ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO) (Sharkey 2023). Three molecules of ribulose-1,5-bisphosphate (RuBP) and three molecules of CO₂ enter the cycle and generate six molecules of glyceraldehyde-3-phosphate (GAP). One molecule is released and gets utilized in the production of glucose, and the remaining are used in regenerating three molecules of RuBP. The sugar produced in the chloroplast enters the glycolytic pathway in the cytosol, where both GAP and glucose are converted to pyruvate as the end product of this pathway. Now, pyruvate leaves the cytosol, and the mitochondrion comes into play. In the next section, we discuss mitochondrial metabolism in detail. Mitochondrial metabolism and its interactions with other organelles are described schematically in figure 1.

Figure 1

Schematic representation of plant metabolism including four compartments: cytosol, mitochondrion, peroxisome, and chloroplast. This includes a brief overview of the following metabolic pathways: (i) mitochondrial tricarboxylic acid cycle (TCA cycle) producing reductants and amino acid precursors, (ii) mitochondrial electron transport chain (ETC) producing ATP, (iii) chloroplastic Calvin–Benson cycle (C₃ cycle) that generates one molecule of the three carbon sugar, glyceraldehyde-3-phosphate, and (iv) photorespiration (C₂ cycle) which spans all the four compartments and is involved in protecting the cell from photoinhibition.

2.1 Mitochondrial metabolism

Mitochondrial metabolism is closely related to cytosolic and chloroplastic metabolisms, and a major part of mitochondrial metabolism is covered by the TCA cycle (also known as the citric acid or Krebs cycle), the electron transport chain (ETC), and ATP synthesis. These metabolic pathways can also be regulated in different ways. A schematic overview of the regulations of mitochondrial metabolism is shown in figure 2.

Figure 2

Different regulations of mitochondrial metabolism.

Either pyruvate, the end product of glycolysis, enters the mitochondrial matrix directly with the help of mitochondrial pyruvate carriers (MPC) present in the inner mitochondrial membrane, or the mitochondrial NAD-malic enzyme (NAD-ME) synthesizes pyruvate inside mitochondria by oxidatively decarboxylated malate, which is derived from phosphoenolpyruvate (PEP) (Rustin et al. 1980). It can also be synthesized from alanine with the help of alanine aminotransferase inside the mitochondrial matrix (Le et al. 2022). Oxaloacetate (OAA) is produced by cytosolic PEP carboxylase, followed by the production of malate, and both metabolites are transported to the mitochondrion to maintain the pyruvate pool inside the mitochondrial matrix (Zoglowek et al. 1988; Hanning et al. 1999). In the mitochondrial matrix, pyruvate is converted to acetyl CoA by oxidative decarboxylation through the action of the mitochondrial pyruvate dehydrogenase complex (PDC), which releases CO₂ and reduces NAD⁺ to NADH (Tovar-Méndez et al. 2003; Araujo et al. 2012). Acetyl CoA is also used in the fatty acid biosynthesis. Acetyl CoA can be derived, depending on the organism and cell type, from β-oxidation of fatty acids or from the degradation of ketogenic amino acids (Sweetlove et al. 2010). Mitochondrial PDC is inhibited by acetyl CoA (Tovar-Méndez et al. 2003) and light (Poolman et al. 2013), and activated by thiamine pyrophosphate (Bocobza et al. 2013).

2.1.1 TCA cycle

The TCA cycle comprises a series of eight oxidative steps that release two carbon atoms as CO₂ and generate NADH and FADH₂, which are further used in the mitochondrial ETC. The condensation of oxaloacetate (OAA) and acetyl CoA by citrate synthase (CS) occurs in the first step of the TCA cycle to produce citrate. The enzyme citrate synthase is regulated by oxidation and reduction of cysteine residues present in the enzyme (Nishio and Mizushima 2020). Thioredoxins (TRX) reduce the intra- and intermolecular disulfide bonds of the enzyme and form the active dimer of the enzyme (Schmidtmann et al. 2014). An increase in enzyme activity is also observed when it gets reduced with dithiothreitol (DTT) (Stevens et al. 1997). In response to light, its activity increases by 1.4-fold (Unger and Vasconcelos 1989) and hydrogen peroxide (Schmidtmann et al. 2014), and diamide (Stevens et al. 1997) can decrease the activity of the enzyme by 54% and 25%, respectively, due to the formation of mixed disulfides by oxidation. This enzyme is again inhibited by higher temperature (50°C) and higher concentration of ATP, NADH, succinyl-CoA, citrate, and 2-oxoglutarate (Alejandre et al. 1979) and activated by ADP (Barbareschi et al. 1974; Siedow and Day 2000).

Citrate is converted to isocitrate by aconitase via the bound intermediate cis-aconitate. The important metabolites of the TCA cycle, fumarate, malate, succinate, and trans-aconitate, have little inhibitory control over the enzyme aconitase. In the presence of light, succinate dehydrogenase gets inhibited, which results in the accumulation of succinate. The increased level of succinate causes inhibition of mitochondrial aconitase, which stimulates the efflux of citrate from mitochondria (Eprintsev et al. 2015). Previous studies have also shown that a few more events, such as the presence of nitric oxide (Gupta et al. 2012) and a plant metabolite, citramalate (Sipari et al. 2020), lack of manganese superoxide dismutase (Morgan et al. 2008), and accumulation of H₂O₂ in mitochondria due to the suppression of the mitochondrial ETC, can inhibit the activity of aconitase (Verniquet et al. 1991; Nunes-Nesi et al. 2013). Its activity gets completely blocked at 50 µM H₂O₂ (Tretter and Adam-Vizi 2000).

In the next step, NAD- or NADP-dependent isocitrate dehydrogenases (NAD-ICDH/NADP-ICDH) oxidatively decarboxylate isocitrate to 2-oxoglutarate and generate CO₂ and NADH or NADPH, respectively. NAD-ICDH found only in mitochondria (Lancien et al. 1998) is inhibited by NADH (in a competitive manner) (McIntosh and Oliver 1992) and high concentration of isocitrate (Popova and de Carvalho 1998). On the other hand, NADP-ICDH found in mitochondria, plastids, peroxisomes, and cytosol (Hodges et al. 2003) is inhibited by NADPH non-competitively (McIntosh and Oliver 1992; Igamberdiev and Gardeström 2003). Citrate regulates the enzyme in a competitive manner: at low isocitrate concentrations, activation occurs by citrate, but at high isocitrate concentrations, citrate appears to be a competitive inhibitor (Cox and Davies 1969). Various organic acids (2-oxoglutarate, citrate, cis- and trans-aconitate, gly-oxylate, and oxaloacetate), ions of metals (Mn²⁺, Mg²⁺, Zn²⁺, etc.), and some nucleoside phosphates such as ATP regulate the activities of NAD-ICDH and NADP-ICDH (McIntosh and Oliver 1992; Popova and de Carvalho 1998). A previous study showed that the activity of NAD-ICDH present in pumpkin cotyledon is increased by 15% at pH 7.2 and by 70% at pH 8.0 at optimal citrate concentration of 0.5 mM (Popova and de Carvalho 1998).

Another oxidative decarboxylation reaction occurs when succinyl CoA is generated from 2-oxoglutarate, generating CO₂ and NADH as by-products. The reaction is catalyzed by the enzyme 2-oxoglutarate dehydrogenase complex (OGDHC), which is regulated by the levels of both its substrates, i.e., 2-oxoglutarate and NADH and products, i.e., succinyl-CoA, and some other factors, such as Ca²⁺, ATP/ADP, NADH/NAD⁺, and thiamine pyrophosphate (Wedding and Black 1971; Strumilo 2005; Bunik and Fernie 2009).

Succinyl-CoA ligase (ScoAL), also called succinate thiokinase or succinyl-CoA synthetase, subsequently catalyzes the synthesis of succinate from succinyl-CoA along with the formation of ATP from ADP and P_i. Low concentration of 2-oxoglutarate activates the enzyme, whereas citrate, isocitrate, succinate, fumarate, malonate, and intermediates of the porphyrin biosynthesis pathway (Palmer and Wedding 1966) inhibit the enzyme at their high concentrations (Studart-Guimarães et al. 2005).

Next, succinate dehydrogenase (SDH) combines two reactions: the oxidation of succinate to fumarate and the reduction of ubiquinone to ubiquinol. The latter is an essential step for transferring electrons from redox equivalents to oxygen during the process of the ETC. SDH is also known as complex II, a major component of the ETC. Both ATP and ADP can activate the enzyme. On the other hand, the activity of the enzyme is negatively affected by potassium (Affourtit et al. 2001), TRX (Daloso et al. 2015), and nitric oxide (NO) (Simonin and Galina 2013).

In the next step, fumarate is reversibly converted to malate by hydration/dehydration. The investigation of regulation of fumarase from pea (Pisum sativum L.), reveals that the alpha-keto acids pyruvate and 2-oxoglutarate at millimolar concentrations and the adenine nucleotides ATP, ADP, and AMP can inhibit the enzyme (Behal and Oliver 1997). However, the enzyme gets activated by Mg²⁺, K⁺, and Ca²⁺ (Eprintsev et al. 2018) and deactivated by TRX (Daloso et al. 2015).

In the last step of the cycle, malate is oxidized to oxaloacetate by a reversible reaction catalyzed by NAD-dependent malate dehydrogenase. It is likely that accumulation of NADH leads to an inhibition of the mitochondrial malate dehydrogenase (Nunes-Nesi et al. 2013). At low malate concentration, this enzyme appears to be most active (Wedding et al. 1976).

The two most important shuttles – malate-aspartate and malate-OAA – use malate (Zoglowek et al. 1988) for the transport of substrate and redox equivalents across the mitochondrial membrane to maintain the redox balance in the cell. The cycle not only generates the reducing equivalents NADH and FADH₂ to synthesize ATP by oxidative phosphorylation through the ETC, but also supplies carbon skeletons for the synthesis of different biological compounds. For example, 2-oxoglutarate acts as a precursor for amino acid biosynthesis.

2.1.2 Electron transport chain and ATP synthesis

Oxidative phosphorylation comprises two important processes, the ETC and ATP synthesis. It generates ATP by using the redox equivalents NADH and FADH₂ from the TCA cycle.

The electron transport chain is made up of four enzyme complexes present within the inner membrane of mitochondria. The high energy electrons are transferred from the reducing equivalents NADH and FADH₂ through a series of reactions to oxygen, the final electron acceptor, by losing its energy, which is used to pump out protons from the matrix into the inter-membrane space. Complex I, also known as NADH dehydrogenase, and complex II, also known as succinate dehydrogenase, accept two electrons from NADH and FADH₂, respectively. They cause the oxidation of NADH and FADH₂, respectively, and pass the electrons to complex III (Q-cytochrome c oxidoreductase), the first cytochrome (cyt) in the pathway, via coenzyme Q (also known as quinone and CoQ). Complex IV passes the electrons to oxygen, which generates water. Complex I, III, and IV release 4H⁺, 4H⁺, and 2H⁺ into the intermembrane space, respectively, while complex II does not directly pump any protons out. Hence, a concentration difference of protons (higher in the intermembrane space than the matrix), i.e., a pH gradient, is developed across the membrane. A voltage gradient is also developed due to the difference of charge. These two collectively constitute an electro-chemical gradient (equivalent to ∼150–200 mV) which exerts a proton motive force (pmf) across the inner mitochondrial membrane and this pmf is used by the enzyme ATP synthase, a multi-protein complex, to generate ATP.

The generation of one ATP molecule requires four protons (three protons go through ATP synthase and one is used for the transport of P_i and ADP into mitochondria). ATP synthase is made up of two components, F_O (rotor), and F₁ (catalytic head and stalk) (Seelert and Dencher 2011). F_O is a transmembrane protein complex, embedded in the inner mitochondrial membrane, which accepts protons and rotates the F₁ head. A complete rotation of ATP synthase transfers ten protons from the intermembrane space to the matrix and generates three ATP molecules. These ATP molecules are utilized for different cellular activities and survival of the cell.

2.1.3 Alternative oxidase

In addition to cytochrome oxidase, mitochondria contain an alternative oxidase (AOX) that directly couples the oxidation of ubiquinol with the reduction of O₂ to H₂O without proton translocation from the matrix to the mitochondrial inter-membrane space (Jacoby et al. 2012). High-energy electrons are partitioned between two paths in the ETC: the cytochrome pathway (complex III, cyt c, complex IV) and AOX. Notably, AOX bypasses the flow of electrons through complexes III and IV, prohibiting the excessive reduction of the downstream complexes of the ETC and thus dissipates the free energy of electrons in the form of heat (Moore and Siedow 1991; Rhoads and Subbaiah 2007). This reduces the level of ATP synthesis. However, if AOX takes electrons from NADH, a diminished amount of ATP is still synthesized as these electrons arise via the proton pumping complex I. Therefore, if FADH₂ provides the electron flow to AOX, the electron flow will be completely uncoupled from ATP turnover since complex II, unlike complex I, is not proton-pumping. Briefly, the mitochondrial ETC can dramatically modulate the production of ATP depending on the components of the path used for electron flow to cope with different physiological conditions (Millar et al. 2011).

The alternative oxidase is located in the inner mitochondrial membrane in a dimeric form. The dimer exists in two different states: an oxidized state, in which the dimer is covalently cross-linked by an intermolecular disulfide bridge, and a reduced state, in which the disulfide bond is reduced to its component sulfhydryls and non-covalent interactions maintain the dimeric structure of AOX (Moore et al. 1995). The oxidized form is four- to five-fold less active than the reduced form, and the two forms are regulated by reversible oxidation-reduction of the cysteine bond between two monomers (Umbach and Siedow 1993). An increase in reducing equivalents (NADH, NADPH) can activate AOX (Sluse and Jarmuszkiewicz 1998). AOX can be activated by pyruvate (Pastore et al. 2001) and succinate (Vanlerberghe and McIntosh 1997; Sluse and Jarmuszkiewicz 1998; Saha et al. 2016). Electron transfer between cyt oxidase and AOX can be affected by the level of ubiquinone concentration. In the absence of ADP or in the presence of cytochrome chain inhibitors such as nitric oxide (NO), carbon monoxide (CO), hydrogen sulfide (H₂S), hydrogen cyanide (HCN), etc., the cytochrome pathway activity becomes low and AOX gets activated (Sluse and Jarmuszkiewicz 1998; Cooper and Brown 2008). AOX activity can be altered in response to stress (Vanlerberghe 2013). Temperature has an effect on AOX activity in plants (Campbell et al. 2007; Armstrong et al. 2008; Searle et al. 2011; Shi et al. 2013). In a study, it was reported that in a callus culture of Arabidopsis, shifting to a chilling temperature in addition to ethylene treatment was required to induce AOX activity (Wang et al. 2012). Furthermore, higher amount of AOX protein was seen in Arabidopsis grown at 12°C than warm grown plants, and knockdown plants with low AOX levels showed no growth in low temperatures (Fiorani et al. 2005). Similarly, when chilling-sensitive maize was given a short-term cold treatment (5 days at 5°C), the respiration shifted its usage from cyt oxidase to AOX in such a way that, in the new condition, 60% of total respiration occurred through AOX (Ribas-Carbo et al. 2000). Furthermore, cyt activity was found to be reduced and AOX activity was increased in tobacco in response to ozone treatment (Ederli et al. 2006). A shift from cyt oxidase to AOX oxidase was observed in response to high light intensity (Poolman et al. 2013).

2.1.4 Interactions of mitochondria with other organelles through photorespiration

Photorespiration is a wasteful but important biological process which includes a light-dependent uptake of O₂ and release of CO₂ and limits plant growth by regulating the photosynthetic electron flow in different light intensities (Huang et al. 2015). It is called a wasteful process because it does not generate ATP or sugar. Ribulose-1,5-bisphosphate carboxylase/oxygenase (RuBisCO), the main enzyme of the Calvin–Benson cycle, is a bifunctional enzyme since it catalyzes carboxylation and oxygenation of ribulose-1,5-bisphosphate (RuBP). One molecule of 2-phosphoglycolate is produced when O₂ interacts with RuBisCO. Phosphoglycolate accumulation in the cell is toxic as it prevents different important steps of the central carbon metabolism by inhibiting two enzymes, triose-phosphate isomerase and sedoheptulose-1,7-bisphosphate phosphatase (Flügel et al. 2017). Phosphoglycolate is recycled by converting to phosphoglycerate through photorespiration, which is also known as the C₂ cycle or glycolate cycle or oxidative photosynthetic carbon cycle (Leegood et al. 1995). It involves a series of enzymatic reactions in the peroxisome, mitochondrion, and chloroplast (Oikawa et al. 2019). 2-Phosphoglycolate is dephosphorylated by glycolate-2-phosphatase within the chloroplast to form glycolate and this reaction recycles P_i within the chloroplast. Glycolate then leaves the chloroplast and gets oxidized by glycolate oxidase inside the peroxisome and generates glyoxylate along with the generation of hydrogen peroxide, which is then decomposed in the peroxisome by catalases. Serine-glyoxylate aminotransferase (SGAT) and glutamate-glyoxylate aminotransferase (GGAT) then convert glyoxylate to glycine. Glycine then moves to the mitochondrion from the peroxisome and is oxidized to ammonia and serine by glycine decarboxylase (GDC) with the help of another enzyme called serine hydroxymethyltransferase 1 (SHMT1) (Neuburger et al. 1986). Regulation of GDC is important, as a previous study showed that the increased activity of the GDC enhances net photosynthesis and growth of Arabidopsis thaliana (Timm et al. 2012). Mitochondrial NADH/NAD⁺ ratios regulate GDC activity in vivo (Bourguignon et al. 1988; Igamberdiev and Gardeström 2003) and mitochondrial thioredoxins (Trx) Trx o1 (Reinholdt et al. 2019) and Trx h2 (da Fonseca-Pereira et al. 2020) regulate photorespiratory carbon flow from chloroplasts to mitochondria by regulating GDC activity (Timm and Hagemann 2020). In the next step, serine is then transported to the peroxisome and is converted to glycerate, and in this form the chloroplast gets its photorespiratory carbon. Glycerate kinase phosphorylates glycerate and generates phosphoglycerate that re-enters the photosynthesis cycle (Ogren 1984).

3 Different simulation techniques to analyze regulations of metabolism

The active metabolism within different cellular compartments and their variations can be analyzed using different approaches of metabolic flux analysis (such as flux balance analysis and elementary flux mode analysis) and flux coupling analysis. The metabolic modeling techniques can be grouped into two categories: (i) kinetic modeling (Rohwer 2012) and (ii) structural modeling (Schuster and Fell 2007). The details of the different kinetic properties of different enzymes involved in a network are required for kinetic modeling. Therefore, these huge requirements limit its application to small systems having small number of reactions. However, only limited experimental data are required for structural modeling, such as the stoichiometry and reversibility of all biochemical reactions that participate in the network, the uptake rates of essential nutrients, and the biomass composition of the cell, tissue, or organism (Lotz et al. 2014). Thus, the structural modeling technique is widely used in genome-scale metabolic modeling and its analysis. Genome-scale metabolic models (GSMs) of different organisms, including bacteria, simple eukaryotes, and plants, are now available.

Researchers have reconstructed several genome-scale metabolic models to analyze both C₃ and C₄ plant metabolisms. This list includes Arabidopsis (Arabidopsis thaliana) (Poolman et al. 2009; de Oliveira Dal’Molin et al. 2010; Mintz-Oron et al. 2012), rice (Oryza sativa) (Poolman et al. 2013), maize (Zea mays) (Saha et al. 2011), tomato (Solanum lycopersicum L.) (Yuan et al. 2016), soybean (Glycine max) (Moreira et al. 2019), and Setaria viridis (Shaw and Cheung 2019). Moreover, there was an earlier effort to reconstruct a genome-scale metabolic model (C4GEM) (de Oliveira Dal’Molin et al. 2010) to study general C₄ plant metabolism using the reactions of maize (Zea mays), sorghum (Shorghum bicolor), and sugarcane (Saccharum officinarum).

3.1 Flux balance analysis

Flux balance analysis (FBA) is a constraint-based modeling approach that allows the identification of optimal flux through the reactions of a metabolic network in a steady state by applying mass balance constraint to the stoichiometric model and maximizing or minimizing the objective function, defined according to the desired objective (Orth et al. 2010; Lotz et al. 2014). The metabolic reactions and the objective are mathematically represented by a system of linear equations, and these equations are solved using linear programming. As this approach does not require the kinetic parameters of the enzymes involved in the system, even for large networks, FBA can be computed very quickly. This method is used to predict all possible flux distributions of a specific system for different environmental and physiological conditions of the system (Orth et al. 2010).

In the first step, reactions of a metabolic network are represented in the form of a stoichiometry matrix, S of size m×n, where m represents the number of metabolites and n represents the number of reactions of the network. The elements of each column represent the stoichiometric coefficients of the substrates and products of the corresponding reaction. A negative value is given to a substrate that is being consumed, a positive value is given to a product that is being produced, and zero represents a metabolite that is absent in that particular reaction.

At steady state, the rate of production and the rate of consumption are equal for each internal metabolite in the model and that can be mathematically represented as

$${\mathbf{Sv}} = 0$$

where the vector v represents the flux through all the n number of reactions and S is the stoichiometry matrix.

The optimization problem can be defined as

$${\text{maximize or minimize }}{\mathbf{z}} = {\mathbf{c}}^{T} {\mathbf{v}}$$

The flux constraints are given as

$${\mathbf{c}}_{l} \le {\mathbf{v}} \le {\mathbf{c}}_{u}$$

where z is the objective function, c^T is the transpose of a vector (c) of weights that indicate how much a reaction contributes to the objective, v is the vector of all fluxes, S is the stoichiometry matrix, and c_l and c_u are the vectors of lower and upper bound of fluxes, respectively. In the case of an irreversible reaction, the lower bound c_l becomes 0 and the allowable flux is limited to be greater than or equal to 0. The method is schematically described in figure 3.

Figure 3

Schematic overview of the method of flux balance analysis: (a) We have considered three reactions (R1, R2, and R3) of a metabolic network, and at the beginning the solution space is unconstrained; (b) reactions are then represented in a form of stoichiometry matrix, S; (c) reactions at steady state are represented in the form of fluxes; (d) allowable solution space after applying constraints; and (e) optimal solution after optimizing the objective function, i.e., minimizing or maximizing it using linear programming.

3.2 Elementary flux mode analysis

Another structural modelling technique is the elementary flux mode analysis (EFMA) (Schuster et al. 1999). It is a mathematical tool in which the metabolic network is decomposed into several elementary modes, which cannot be further broken. By definition, an elementary mode is a set of reactions that cannot be decomposed further. Any feasible route of a metabolic network from a substrate to a product can be represented as a linear combination of elementary modes.

All reactions of the metabolic network and the information whether they are reversible or irreversible can be represented mathematically as a matrix, called a stoichiometry matrix, S, in which the rows represent the reactions and the column represent the internal metabolites. The reactions which always operate together are lumped to reduce the size of the matrix.

The first step to compute elementary modes of the metabolic network is the construction of initial tableau, T⁰, which is a matrix formed by creating a transposed matrix of the stoichiometry matrix S, and augmented by the identity matrix, I.

$${\mathbf{T}}^{0} = \left( {{\mathbf{S}}^{T} |{\mathbf{I}}} \right)$$

In the next step, from T⁰ we compute a second tableau T¹ in which we obtain a null vector for the first column, i.e., all the elements of the first column are 0, by pairwise linear combination of rows. By this process, for all the columns of the transposed stoichiometry matrix, null vectors are obtained consecutively.

In the final tableau there is a null matrix on the left-hand side, and the identity matrix on the right-hand side is now replaced by a matrix of elementary modes. Each row of the matrix represents a specific elementary mode. A linear combination of two or more elementary modes corresponds to a steady state flux distribution of the network.

3.3 Flux coupling analysis

Flux coupling finder (FCF) is a procedure to find the blocked and coupled reactions in the genome-scale metabolic system. Like EFMA, it does not require computation of null-space matrices, which is a problematic task for large networks. Instead, it requires the solution of a sequence of linear programs (LPs) (Burgard et al. 2004).

By solving the linear programming problem, we can easily identify the blocked reactions by identifying the reactions having 0 as maximum flux value. Blocked reactions are those which are incapable of carrying any flux under steady state condition. Here, limitation of the uptake of resources, i.e., carbon, nitrogen, etc., and transport of the metabolites out of the cells are used as constraints (Burgard et al. 2004).

Coupled reactions can be identified by calculating the maximum and minimum flux ratios (F_max and F_min), where F=x₁/x₂ for every pair of metabolites (x₁ and x₂) and F_min and F_max represent minimum x₁/x₂ and maximum x₁/x₂, respectively. Results can infer the following:

• 1. When F_min=0, F_max=C, a finite value, the fluxes are directionally coupled, i.e., a non-zero flux of one reaction (x₁) implies a non-zero for another reaction (x₂) but not the reverse,

• 2. When F_min=c, a finite value, F_max=infinite, the fluxes are directionally coupled but in the opposite direction in comparison with the previous result i.e., the non-zero flux of the second reaction (x₂) implies a non-zero flux for the 1st reaction (x₁).

• 3. If F_min and F_max both are finite but unequal, the fluxes are partially coupled, that is, a non-zero flux for one reaction (x₁) implies a non-zero but variable flux through another reaction (x₂) and vice versa

• 4. If F_min and F_max both are finite and equal, the fluxes are fully coupled, i.e., a non-zero flux for one reaction (x₁) implies a non-zero and a fixed flux through another reaction (x₂) and vice-versa

• 5. If F_min and F_max vary from 0 to infinity, the fluxes are uncoupled.

The equivalent knockouts, i.e., the reactions whose deletion causes the flux of a particular reaction to be 0 and the affected reactions, i.e., the reactions whose fluxes become 0 after deleting a particular reaction, can also be identified by this approach.

4 Application of the previously described approaches for analyzing metabolic interactions

4.1 Application of flux balance analysis (FBA) to analyze the metabolic interactions in plants

4.1.1 Can we identify active metabolic pathways working in different cellular conditions using FBA?

Metabolism can be defined as the combination of a number of metabolic pathways that occur within a cellular system. All the reactions of different pathways of a cell may or may not be acting together at a time. FBA gives us the optimal flux distributions through the reactions in different cellular conditions by solving biochemical networks using linear programming. Different objective functions are used according to the phenotype of interest. For example, biomass production is used as an objective function in predicting growth. Moreover, different cellular conditions can be applied to a model by applying constraints such as changing the bounds of the flux values of the reactions (Orth et al. 2010). In a previous study (Chatterjee et al. 2017) on the genome-scale model of Oryza sativa indica, the effect of gradually increasing photorespiration, which can be represented as high to low ratios of carboxylase and oxygenase activity of RuBisCO, was analyzed by fixing its ratio during model simulations. Here, the objective function used was minimization of total cellular flux while producing biomass components in an experimentally fixed proportion. The result showed that the photon demand for the production of ATP and NADPH to synthesize biomass decreases with a decrease in photorespiration. They also reported that cyclic photophosphorylation is active only when photorespiration is high, whereas non-cyclic photophosphorylation is always active (Chatterjee et al. 2017).

4.1.2 Is it possible to capture the feasible alternative pathways and variations in reactions occurring in different cellular compartments when a reaction is not working completely or partially inside the cell?

The knockout or complete inhibition of a reaction resembles deletion of that reaction from a metabolic model and can be done by fixing its flux value to zero. This in silico reaction deletion strategy has been used along with FBA on a genome-scale metabolic model of rice leaf to identify the essential reactions of the model (Shaw and Kundu 2015). Reactions that are so important for a model that deletions of them inhibit the synthesis of biomass are called essential reactions. For example, the light-dependent non-cyclic reaction has been reported as an essential reaction as it should be active in every condition of cell in order to produce ATP and NADPH, required for the synthesis of biomass. Another essential reaction is the carboxylase reaction of RuBisCO, without which the cell cannot fix CO₂ for the production of biomass. The O₂ and CO₂ transporters are also essential, as they are necessary for plant survival and biomass production.

This study of metabolic plasticity has also successfully identified several alternative pathways and interactions between different compartments (Shaw and Kundu 2015). The term ‘alternative pathways’ basically means the number of ways in which a cell can adjust its metabolism and tolerate a given perturbation in order to synthesize its required energy and biomass. This study has reported the usage of different alternative pathways as a result of reaction deletion. For example, phosphoglycerate kinase, which is a key enzyme of glycolysis, generates ATP from ADP along with the conversion of 1,3-bisphosphoglycerate to 3-phosphoglycertae. Shaw and Kundu (2015) have shown that deletion of this reaction increases the photon demand of the cell by 12.79%. The reason behind this is the readjustment of the cell to fulfil the ATP demand by utilizing other pathways to synthesize biomass. Another example of cellular adaptation in the cellulose biosynthesis pathway is by removing the enzyme phosphoglucomutase that converts glucose-6-phosphate to glucose-1-phosphate. This reaction is followed by the conversion of glucose-1-phosphate and UTP to UDP-glucose and pyrophosphate by the enzyme UDP-glucosepyrophosphorylase. It has been observed that in the absence of phosphoglucomutase, the cell utilizes another pathway for the production of cellulose and the photon demand increased by 6%. Another study (Poolman et al. 2009) on the model plant Arabidopsis thaliana has shown that when a low amount of ATP is needed for a cell, the ATP requirement can be fulfilled by a truncated TCA cycle, glycolysis, and ETC, and alternative modes of the TCA cycle come into play (Poolman et al. 2009).

Moreover, the results of the reaction deletion method (Shaw and Kundu 2015) show that deletion of different reactions in different cellular compartments can activate different biochemical modes in the cell. For example, the deletion of complexes I and V in mitochondria upregulates the malate–oxaloacetate shuttle in the chloroplast and the light-dependent cyclic reaction, and downregulates the light-dependent non-cyclic reaction. This causes variation in the ratio of ATP and NADPH, which are produced by the light-dependent cyclic and non-cyclic reactions. On the other hand, the effects of partial inhibition of a reaction within a metabolic network can be investigated by limiting the flux to a fraction of its wild-type value. A previous study (Chavali et al. 2008) has evaluated the effect of the presence of an inhibitor of a reaction by varying the flux through that reaction from its wild-type value to zero. Variations in growth rate have been observed with the variation in the flux of mitochondrial F₀F₁-ATP synthase. This study on the metabolic network also gives insight into the effect of gene deletion, with the identification of 69 single lethal gene deletions and 56 non-trivial lethal double-gene deletions (Chavali et al. 2008).

4.1.3 Incorporation of different omics data can mimic availability of metabolites and enzymes in a cell

A study (Shaw and Kundu 2013) on the genome-scale metabolic model of rice (Oryza sativa) investigated the effect of different transporters that transport metabolites from one compartment to another on the photon requirement for biomass synthesis and inter-compartmental interactions within a cell, depending on gene expression. They showed that the number of photons needed for biomass synthesis depends on the capacity of intra-cellular transporters. Different modes of the TCA cycle, cyclic or non-cyclic and different interactions between the compartments have also been analyzed in this study. For example, when sufficient amount of ATP is produced by chloroplastic light reactions, the over-production of ATP is prevented by truncating the TCA cycle and downregulating the ETC, whereas when alternative sources do not work, the TCA cycle operates in cyclic mode (Shaw and Kundu 2013). The effect of variations of different enzymatic gene expressions can further be analyzed in future using this method. Another study (Cheung et al. 2015) on a diel genome-scale model of A. thaliana leaf incorporated flux weighting factors to analyze the metabolic flexibility of a network. The cost-weighted FBA revealed several alternative modes of different pathways which were inactive when investigated using conventional FBA. For example, this study has shown the usage of different alternative pathways to dispose of the excess amount of reductants at different light intensities.

In a recent study (Maiti et al. 2023), FBA has been used to study a multi-segment model of a C₄ plant, Setaria viridis. They divided the leaf into four segments from the base, the most immature segment having the most proliferating cells, to the tip, the most immature segment having the most differentiated cells, including two growing segments in between. The different growth rates of each leaf segment of the plant were used as constraints, and transcriptomic data were incorporated in the objective function of the simulation. They observed metabolic variability in different segments of the leaf, and all the biomass components were not produced in each segment. Instead, different segments produced biomass components at different ratios and these components were exchanged according to the need of the leaf segments. The requirement of carbon in a growing tip was fulfilled by the supply from the base of the leaf, whereas the mid-segments provided amino acids such as phenylalanine, glutamate, etc., to the base more than tip. Supply of the protein building blocks from the mid-segments reduces transport cost, as the mid-segments are closer to the base than the tip. Sucrose is the main transport element in the plant through phloem sap. It is observed that in a leaf, the plant prefers sucrose transport from the most mature segment, the tip. However, the dependencies of fatty acids are fulfilled from the neighboring cells (Maiti et al. 2023). A similar computational technique has been used in analyzing maize leaf metabolism at a multi-scale level (Bogart and Myers 2016).

4.1.4 Can we explain regulation of plant hormones by integrating omics data in metabolic network?

It is known that different plant hormones are differentially produced under varied conditions at different parts of a plant. It is expected that the genes of their biosynthetic pathways may be co-regulated. For example, one can determine whether the genes involved in the biosynthetic pathway of hormones (say, auxin, gibberellin, etc.) are transcriptionally regulated by the same set of transcription factors. This can be achieved by integrating gene expression data and quantifying the co-occurrence of cis-regulatory elements present in a set of promoter sequences (Deb and Kundu 2015). Lakshmanan et al. (2015) integrated rice gene expression data under different light treatments with the rice metabolic network to unravel the transcriptional regulation of different phytohormone biosynthesis, to identify differentially regulating metabolic pathways (e.g., upregulation of photosynthesis and secondary metabolism in blue light) and also showed that upregulation of the abscisic acid (ABA) biosynthesis gene is related to the accumulation of ABA that can reduce ethylene biosynthesis inhibiting plant stem growth.

4.1.5 More realistic flux distribution patterns can be predicted by incorporating different constraints to mimic real scenarios in plants

Cheung et al. (2013) predicted a more accurate flux distribution by the incorporation of the energy cost for transportation of different molecules through plasma membranes and membranes of other organelles and the maintenance of cell. They incorporated the ATP requirement as a cost to the transporters of plasma membrane in order to import nutrients to the cell and the cost to the membranes of mitochondrion, peroxisome, and tonoplast as a cost of intracellular metabolite transport. The central metabolic pathways are not only involved in biomass production, but they also provide energy. And this energy is utilized for transporting ions, metabolites, and macromolecules and cell maintenance along with the synthesis of biomass. Thus, incorporating these costs to the model bring about noticeable changes in the flux distribution pattern of the central carbon metabolism. Simulation of this extended model predicted that 67% of the total energy is utilized for producing biomass and the remaining is used for cell maintenance. Glycolysis and the TCA cycle also give more accurate flux distributions, whereas no change of flux is observed in the case of the oxidative pentose phosphate pathway (OPPP). Addition of the ratio of fluxes through OPPP and the glycolysis pathway as another constraint gives more realistic results. They also analyzed the model for elevated temperature and hyperosmotic conditions. When temperature is increased, ATP and NADPH maintenance cost is increased and the carbon conversion coefficient decreases. However, in the case of hyperosmotic conditions, slow growth of Arabidopsis is observed due to restricted glucose uptake.

4.1.6 Interactions between light and dark metabolism can be captured during day–night cycles using FBA

Some analyses of leaf metabolism by FBA have been done on the models exposed to continuous light. In plants, there are different effects of day and night on leaves, and these effects should be incorporated into models in order to have more realistic flux distribution patterns for different objective functions. Cheung et al. (2014) have constructed a diel genome-scale model of Arabidopsis by applying constraints to a pre-existing model of Arabiopsis in such a way that metabolites produced during the day can be used for overnight cellular maintenance and metabolites stored at night can be used for different purposes. In this study, the two models of day and night phases were used as a single optimization problem. The day phase represents autotrophic metabolism where photon influx is allowed, whereas the night phase represents heterotrophic metabolism by restricting the value of photon flux to zero. They observed many differences in the two cases. For example, in the case of the diel model, starch synthesis was observed during the day to supply the carbon source for the night where no fixation of CO₂ is possible, while in the model continuously exposed to light, no starch synthesis is required as there is continuous assimilation of CO₂ occurring in the leaf. Another important difference is observed in the case of usage of citrate for glutamate and glutamine synthesis. In the model with continuous light, citrate is synthesized in the peroxisome by citrate synthase and used in glutamate and glutamine synthesis. However, in the case of the diel model, citrate, synthesized by the mitochondrial TCA cycle at night, is stored in the vacuole and used further for the production of 2-oxoglutarate followed by the production of glutamate synthesis. They also predicted that in a similar way, nitrate is imported to the vacuole from the xylem during the night, and it leaves the vacuole during daytime and is utilized in producing amino acids, which are then released into the phloem during the night. In the light phase, the photosynthetic electron transport pathways and the Calvin–Benson cycle have maximum fluxes through them for the synthesis of sucrose, starch, and amino acids, and the TCA cycle is operated in a non-cyclic fashion. However, in the dark phase, starch is degraded to provide carbon to the cell and large fluxes are observed through glycolysis, OPPP, the TCA cycle, and mitochondrial ETC. In this phase, the TCA is operated in full cyclic mode.

In another study (Tan and Cheung 2020), stomatal opening and closing due to variation in the metabolism of guard cells of C₃ plants during day and night have been analyzed. The authors constructed a model consisting of four phases: opening of stomata at the time of sunrise (1 h), daytime (11 h), closure of stomata at the time of sunset (1 h), and nighttime (11 h). In the four phases all the reactions are same, whereas different constraints are applied depending on the phases. They have observed that in the open phases, K⁺ and malate are accumulated through the import by the K⁺/H⁺ symporter and degradation of starch stored at night, respectively. The conversion of the Calvin–Benson cycle products to phospoenolpyruvate (PEP) by glycolysis and then conversion of PEP to first OAA and then malate is another way in which malate is accumulated. Accumulation of osmolytes and ions is responsible for the opening of stomata in this phase. In the day phase, sucrose is imported for the maintenance of stomatal opening and K⁺ is exported outside the guard cell. This large amount of sucrose is produced from degradation of malate and the rest is provided by the Calvin–Benson cycle. In the closed phase, sucrose is degraded, and hexose phosphate is produced. This hexose phosphate is used in starch synthesis and production of NADPH through OPPP and ATP through the TCA cycle and mitochondrial ETC. In the night phase, the starch produced in the closed phase is used for the production of ATP and NADPH in order to maintain the metabolism of the guard cell. The remaining starch in the night phase is utilized as a source of malate during the open phase for stomatal opening (Tan and Cheung 2020).

4.1.7 Can we investigate the effect of different intensities of light on cellular metabolism?

Poolman et al. (2013) simulated a model of the rice plant with different photon values using FBA and analyzed the results. In this study, it was shown that in low light, ATP is generated by mitochondria in association with oxidation of pyruvate and malate and decreases as light intensity increases. At high light intensity, the model shifts from using cytochrome oxidase to alternative oxidase in mitochondria to protect the plant against harmful effects of excess light (Bartoli et al. 2005). Results also shows that photorespiration increases as photon flux increases, and at high light level, photorespiration is fully active to dissipate the effect of excess energy. The same result has been observed in another study (Chatterjee et al. 2017).

4.1.8 Explaining how redox is balanced in a cell in different levels of photorespiration

Chatterjee et al. (2017) further showed that with increased photorespiration, to meet the requirement of NADH for peroxisomal hydroxy pyruvate reductase (HPR1), different combinations of reactions and transporters are involved in different levels of photorespiration and the cellular energy demand is maintained. As photorespiration increases, the import of malate to mitochondria decreases, and it stops at medium light. As light increases, to supply more NADH to the peroxisome, mitochondrial malate dehydrogenase works in the opposite direction and produces malate. When light is further increased, chloroplastic triose phosphate exchange involving glyceraldehyde-3-phosphate (GAP) and 3-phosphoglycerate (PGA) comes into play. They make available chloroplastic NADH and ATP in the cytosol and supply that NADH to the peroxisome to fulfil the reductant demand of HPR1. In this manner, the dynamic interplay between the four compartments mitochondrion, chloroplast, cytosol, and peroxisome has been observed in order to dissipate the effect of high light through photorespiration. Further, it is analyzed that pyruvate dehydrogenase in mitochondria gets inactivated by light (Poolman et al. 2013). This light scanning can be done for analyzing the activity of other enzymes of metabolic pathways in the presence and absence of light.

4.1.9 Can we study the effect of nutrient availability and other factors on metabolism?

Refinement of the results of FBA can be done by incorporating thermodynamic and biological information of the reactions of the model as constraints. These additional constraints allow the usage of proteomics and metabolomics data along with FBA. The thermodynamic link between flux directions and metabolite concentrations is incorporated in the model in such a way that reaction directionality is always consistent with measured metabolite concentrations and the Gibbs free energy for the reaction (Hoppe et al. 2007). On the other hand, the concentrations of the catalyzing enzymes in the network, represented by weighting coefficients, are used as a set of constraints to the model (De et al. 2008).

The availability of nutrients (such as nitrogen, oxygen, etc.) in the environment also affects the system. Previous studies have shown that maximum cell growth rates under different environmental conditions, such as aerobic or anaerobic environments, various carbon sources, ammonium, or nitrate as nitrogen source, etc., can be accurately predicted using FBA (Varma and Palsson 1994; Mahadevan and Schilling 2003). For example, the maximum growth rate for E. coli on glucose under aerobic conditions predicted by FBA coincides with the experimentally observed growth rates for adaptively evolved E. coli strains (Long et al. 2017), and acetate is secreted as a metabolic by-product at high growth rates, as observed in experimental studies (Varma and Palsson 1994; Mahadevan and Schilling 2003). The maximum rates of nutrient uptake limit the maximum growth rate of the system (Varma and Palsson 1994). Another study examined the growth of the system on glucose and succinate due to changes in the internal conditions of the network (such as the removal of a reaction) and environmental conditions (such as the availability of substrate and oxygen) using a combined application of pathway analysis and flux balance analysis (Schilling et al. 2000).

4.1.10 Metabolic interactions in a symbiotic relationship between bacteria and plants

An interesting study was performed by Pfau et al. (2018) to understand the metabolic interactions between nitrogen-fixing microorganisms and plants. They took the genome-scale model of the plant Medicago truncatula as a model for legumes and linked the model with a model of Sinorhizobium meliloti as the symbiont. The results of FBA showed that the growth of the plant in the presence of its symbiont is reduced as it needs to supply carbon sources to the symbiont. There is growth of the plant even in low levels of nitrogen because of sufficient supply from the symbiont. They have further observed that, since oxidative phosphorylation provides most of the energy required for the fixation of nitrogen by nitrogenase enzyme in bacteroids, the concentration of oxygen is an important factor in controlling nitrogen fixation. A large amount of O₂ irreversibly inhibits the nitrogenase complex. The amount of oxygen present is maintained by the plant by leghemoglobin (Pfau et al. 2018).

4.2 Usage of elementary flux mode analysis (EFMA) for determining various modes of metabolism

The EFMA method was used in a previous study to investigate photorespiration and its interactions with other mitochondrial metabolisms and ATP synthesis (Huma et al. 2018). The authors constructed a model consisting of four compartments: mitochondrion, chloroplast, peroxisome, and cytosol. After simulating the model, they identified 43 essential reactions out of the 74 reactions active in at least one elementary flux mode (EFM), and 56 EFMs have been obtained in the cellular model of C₃ plant metabolism that represent all feasible routes of photorespiration. They classified the EFMs into four major groups. Different combinations of modes are active in different circumstances, depending on the environmental conditions and other factors. For example, in some energy-dissipating modes, they observed that mitochondrial malate dehydrogenase (MalDH) operates in the reverse direction producing oxaloacetate from malate which is produced in and transported from the chloroplast, cytosol, and/or peroxisome. This is called an energy-dissipating mode, as it oxidizes excess NADH. In these modes, excess photons are absorbed by photorespiration, but have no effect on cellular metabolism. In short, these modes are active to protect the photosystem from getting inhibited by excess light, which is called photoinhibition. In some EFMs, MalDH is active in the forward direction, producing malate and excess NADH. In these modes, ATP is generated by both cyclic and non-cyclic photophosphorylations. When cyclic photophosphorylation is limited, to meet the cell’s ATP demand, non-cyclic photophosphorylation produces ATP in such a manner that excess NADPH is produced. However, in EFMs in which mitochondrial MalDH is inactive, excess amount of reductants is produced by the non-cyclic light reaction in order to maintain photorespiration and the evolution of a net amount of O₂ is observed. Photorespiration gets coupled with nitrogen assimilation and the glutathione ascorbate cycle to reoxidize this excess amount of reduction. One of the major findings is that the assimilation quotient, i.e., the amount of CO₂ fixed per O₂ released, does not change with photorespiration unless nitrogen assimilation is associated with it.

Another study (Rohwer and Botha 2001) using elementary mode analysis (EMA) revealed 14 elementary modes in the central carbon metabolism and sucrose accumulation in sugarcane. Flux modes leading from extracellular glucose or fructose to vacuolar sucrose accumulation, leading from extracellular glucose or fructose to glycolysis and respiration, and a set of five futile cycles have been identified in this study (Rohwer and Botha 2001). EMA can also be expanded by introducing the power-law formula into EMA in order to link an enzyme activity profile to a metabolic flux distribution. A method called enzyme control flux (ECF) successfully predicts the changes in flux distribution due to a change in an enzyme profile in E. coli and B. subtilis (Kurata et al. 2007). Thus, we can expect that regulation of mitochondrial metabolism (described earlier) in different environmental, enzymatic, and stressed conditions can be examined using EMA.

5 Challenges

In this review, we have focused on some computational approaches like FBA and EFMA and discussed how they have been used in previous studies to investigate the metabolism of mitochondria, its regulations, and its interactions with other organelles. We have also discussed how over-represented cis-regulatory interactions can be integrated to find potential co-regulation of plant hormones. Below, we briefly discuss a few computational tools which can be used to obtain greater insight into plant metabolism and its interactions.

To analyze different regulations, previous studies have shown that expression data can be incorporated in FBA in two ways: by directly using them to constrain flux through specific reactions in the model or adding various mathematical rules to the model. In the first approach, one can set the fluxes of reactions to zero if their expressions are low, and if they have high expression values, then that value is set to be the upper bound of the particular reaction (Åkesson et al. 2004; Becker and Palsson 2008; Shlomi et al. 2008; Colijn et al. 2009; van Berlo et al. 2009; Jerby et al. 2010; Jensen and Papin 2011; Maiti et al. 2023). In the second approach, different mathematical modifications of FBA have been effected to incorporate expression data (Covert et al. 2004, 2008; Shlomi et al. 2007; Lee et al. 2008).

One of such modifications is known as regulatory flux balance analysis (rFBA), which requires Boolean rules that represent transcriptomic data to be applied over an existing stoichiometric model of metabolism (Covert et al. 2001; Covert and Palsson 2002, 2003). The ‘ON’ and ‘OFF’ states of the gene products (such as proteins) are defined by the Boolean rules to constrain the flux through the corresponding reactions catalyzed by them in the metabolism. For example, in a particular environmental condition, the flux of a reaction catalyzed by a gene product is set to zero if the transcription of the particular gene is turned ‘OFF’. Several studies of rFBA on stoichiometric models of E. coli and S. cerevisiae metabolisms showed consistency with experimental measurements (Covert and Palsson 2003; Herrgård et al. 2006). For example, in a study on genome-scale metabolism of E. coli, FBA without gene regulatory constraints shows only 86% agreement with experimental results, while rFBA shows 91% agreement (Covert et al. 2001; Covert and Palsson 2003).

To overcome the restriction of application of expression data in a binary manner, another approach called probabilistic regulation of metabolism (PROM) has been developed to apply continuous flux restrictions based on gene expression data. This method shows 95% accuracy in E. coli and Mycobacterium tuberculosis metabolisms (Chandrasekaran and Price 2010).

Transcriptionally controlled flux balance analysis (tFBA) (van Berlo et al. 2009) is another extension of FBA to regulate flux through a reaction if the expression of the associated gene changes significantly from one condition to another.

Furthermore, parsimonious flux balance analysis (pFBA) maximizes biomass yield and minimizes total flux through a network instead of using expression data (Lewis et al. 2010). Linear bound FBA (LBFBA) gives greater accuracy than pFBA in predicting fluxes by using expression data. Other expression-based methods that incorporate transcriptomic data have been reviewed in a previous study (Machado and Herrgård 2014). Thus, it is possible to use this vast field of FBA to analyze metabolic and genetic regulations (described earlier) of mitochondrial metabolism.

Furthermore, three stoichiometric models of H. pylori, E. coli, and S. cerevisiae have been analyzed using flux coupling finder (FCF) to provide a detailed analysis of the coupling of their reactions (Burgard et al. 2004). The result showed that 10%, 14%, and 29% of their respective reactions were blocked unconditionally. Moreover, they found that the percentage of blocked reactions depends on the size of the network: the larger the network, the higher is the percentage of blocked reactions. Furthermore, it can be concluded that larger models of E. coli and S. cerevisiae have greater flexibility and redundancy, since the percentage of reactions in coupled sets decreases substantially with model size. Anaerobic conditions also have little impact on the coupling of reactions (Burgard et al. 2004). Similar analysis can be done for the models of different plant species in order to investigate the coupling of reactions in different cellular conditions.

Proper implementation of the above-mentioned tools will help us to further analyze (i) the metabolic interactions by regulating the TCA cycle and other metabolic pathways of plants by incorporating different omics data to the model, (ii) more realistic results by incorporating the enzymatic costs of reactions and different constraints to mimic the different cellular conditions of plants, (iii) how robust a plant system is to maintain its overall metabolism and redox when different cells produce different biomass depending on the availability of light and nutrients, (iv) the change in metabolic interactions with the change in pH, i.e., concentration of H⁺ in the cell, and (v) the coupling of different reactions, i.e., how change in one reaction affects the other reactions of the metabolic pathways of plants using FCF.

Although several computational studies shed light on plant metabolism, its variations and regulations, a large number of cellular events like change in enzymatic activities, interactions of cellular metabolism with signaling pathways, and differential growths of different parts of a plant and its metabolic variations are unexplained even today.