Subcellular compartmentalization of the plant antioxidant system: an integrated overview

Main features of the antioxidant system components

The mathematical description of biochemical reactions based on the observed physical phenomena performs a clear understanding of underlying biological complexity. This section assembles the available information found concerning various mathematical descriptions for the AOS components. We provide the kinetic laws proposed by different authors in their original researches. Nevertheless, we admit that later, during the integration of our knowledge about systems components into a single mechanism-based model, some kinetic laws might be reconsidered.

Ascorbate peroxidase (APX, EC 1.11.1.11) like an enzyme from 1 heme-peroxidase class, binds hydrogen peroxide to form two intermediate compounds (Welinder, 1992) and is inactivated at low concentrations of ascorbate (Miyake & Asada, 1996). Hydrogen peroxide-mediated inactivation of an enzyme occurs in the absence of ascorbate (Kitajima, 2008). Thus, the kinetics of the enzyme is non-linear and depends on the physiological state of the cell and its redox status.

Glutathione peroxidase (GPX, EC 1.11.1.9), unlike APX, does not contain a heme cofactor and can restore itself by two main types of mechanisms: (i) directly reduction by 1-Cys mechanism or (ii) involving thioredoxin by 2-Cys mechanism (Bela et al., 2015). The catalytic efficiency (Kcat/Km) of the plant GPX is similar to other peroxidases (10³–10⁶ M ^{− 1} s ^{− 1}), but lower than that of APXs, CATs and human GPX (10⁷–10⁸ M ^{− 1} s ^{− 1}) (Bela et al., 2015). Even though the role of GPX in the utilization of peroxide for plants is ambiguous in comparison with animals (due to presence of advanced ascorbate system in the cell), nevertheless, it has a similar number of paralogs as APX in plants, and many copies are highly conservative protein structure Doroshkov & Bobrovskikh (2018). The term “glutathione peroxidase” itself is inaccurate for this enzyme since it has been shown that the enzyme is the 5th group of thioredoxin-dependent thiol peroxidases (Navrot et al., 2006) and uses thioredoxins as a substrate, and not glutathione. Herbette, Roeckel-Drevet & Drevet (2007) also reflected this idea. Therefore, thioredoxin reductases restoring thioredoxins might also be considered as the attendant reducing enzyme for AOS functioning. It is known that thioredoxin systems occur ubiquitously in cell (Gelhaye et al., 2005), and thioredoxin reductases have an impact on stress sensitivity (Serrato et al., 2004). A detailed discussion of the thioredoxin system is beyond the scope of this review; for reference, see the review of Balsera & Buchanan (2019).

Catalase (CAT, EC 1.11.1.6) consists of four subunits, which impose features on its kinetics (Aronoff, 1965). In particular, the entire complex’s assembly is necessary for the activity of the enzyme, which imposes restrictions on the activity of CAT under conditions of low hydrogen peroxide concentrations. Investigations of CAT kinetic revealed intermediates and saturation point of its reactions with hydrogen peroxide (Chance & Oshino, 1971). The mechanism is further analyzed by synthetic mimics of the dimanganese CAT enzymes (Pessiki & Dismukes, 1994). The dismutation mechanism is carried out by two consecutive two-electron steps, which are coupled to redox transformation of the two redox centers of catalyst: Mn${}_2^{III,III}\to$Mn${}_2^{II,II}$.

Kinetics of superoxide dismutase (SOD, EC 1.15.1.1) reaction can be described as first-order (Sawada & Yamazaki, 1973). Beckman et al. (1992) demonstrated that the rate of superoxide neutralization by SOD could be limited by the complicated nature of the substrate rather than the concentration of the enzyme, that is, the reaction proceeds without the formation of a long-lived intermediate complex of superoxide and enzyme.

Enzymes that reduce antioxidants have sophisticated kinetic laws. Glutathione reductase, GR, EC 1.8.1.7 (Vanoni et al., 1990), and monodehydroascorbate reductase, MDHAR, EC 1.6.5.4, (Hossain & Asada, 1985) are described in terms of “ping-pong” reactions kinetics. Dehydroascorbate reductase (DHAR, EC:1.8.5.1) might have a more complex reaction mechanism (Shimaoka, Miyake & Yokota, 2003), the so-called “bi-uni-uni-uni-ping-pong” mechanism, in which binding of DHA to the free reduced form of the DHAR was followed by binding of GSH.

For the normal functioning of the AOS, it is essential to maintain the intracellular concentration of low-molecular antioxidants (ascorbate and glutathione). Ascorbate is a primal antioxidant of the plant cell (Njus & Kelley, 1991). In addition to the fact that ascorbate is a cofactor of the ascorbate peroxidase enzyme, it can directly react with several types of ROS: hydroxyls, singlet oxygen, and superoxides (Buettner & Jurkiewicz, 1996). Ascorbate is present in millimolar concentrations in photosynthetic and non-photosynthetic tissues (Foyer, Rowell & Walker, 1983). Chen et al. (2020) found that adding exogenous ascorbate is increases the regeneration process and induces the development of fruiting bodies in Hypsizygus marmoreus.

Glutathione has many functions in the plant cell, among which the most important is antioxidant activity (Noctor et al., 2012). Most glutathione is synthesized in chloroplasts and transported to the phloem (Mendoza-Cózatl et al., 2008). Adams et al. (2020) emphasizes that remediation of glutathione is crucial for alleviation cesium stress in A. thaliana and that exogenous application of sulfur-containing compounds increases its efficiency.

In addition to antioxidant enzymes and low-molecular antioxidants, such classes of proteins as thioredoxins and glutaredoxins play an essential role in the reduction of oxidized forms of antioxidants in the cytosol, nucleus, peroxisomes, mitochondria, and chloroplasts (Noctor, Reichheld & Foyer, 2018). Thioredoxins are an evolutionarily ancient family of proteins that have high similarity in the primary structure, but different stability and activity between different evolutionary lines (Modi et al., 2018). Peroxiredoxins family plays various roles in different cellular compartments, including antioxidant activity and signaling (Lee et al., 2018); and thioredoxins can serve as electron donors for their reduction.

Experimental data concerning the antioxidant system components

The development of the kinetic basis and biochemical methods allowed studying the kinetic data and enzyme activities in different degrees of freedom. This section arranges studies addressed to measurements of the total activity of AOS enzymes in substrate-specific reactions.

For plant tissues, the protocol for measuring the activity of APX and guaiacol peroxidase was established by Amako, Chen & Asada (1994). Some studies for tomato showed tissue-organelle and stress-dependent differences in the AOS enzyme activity. For example, Mazhoudi et al. (1997) noted that the addition of copper to the soil leads to heavy metal stress for tomato changing the activity of plant antioxidant enzymes; specifically, the activity of APX decreased in stem and whole plants. Investigations of Mittova et al. (2000) focused on measurements of antioxidant enzyme activities (APX, MDHAR, DHAR, GR, SOD) in different organelles in leaf and root for two different contrasting tomato species (cv. Lpa is wild and salt-tolerant cv. Lem is cultivated). The authors stressed out that the activity of MDHAR was one order higher than DHAR, which may indicate a dominant role of MDHAR in ascorbate regeneration. Also, salt-tolerant genotype Lpa had a higher SOD/APX ratio in all organelles, which would correspond to its higher tolerance. Their follow-up studies (Mittova et al., 2002; Mittova et al., 2004) showed different regulation of AOS enzyme activity for plastids, mitochondria, and peroxisomes in roots of Lpa and Lem tomatoes. A study of ROS, AOS activities, and expression patterns for bluegrass (Bian & Jiang, 2009) showed that the production of ROS (mainly superoxide) and AOS enzymes activity increased during drought stress. Surprisingly, the expression of most genes that correspond to AOS enzymes was decreased both in leaves and roots. Taufikurahman & Widiyanto (2016) studied the overall expression of CAT and APX in control and under different chromium concentration treatments for Musa acuminata. The CAT and APX expression levels in roots increase 9 and 3 times under chromium stress of 200 ppm, respectively. However, for shoot tissues, authors revealed weaker upregulation than in roots, which strongly support the tissue-specific and enzyme-specific regulation of the antioxidant response besides the differences in the compartmental organization of the AOS, biochemical features of tissues impact AOS properties. New methods for measurements of antioxidant content are still finding out, for example, ferric-bipyridine assay (Naji et al., 2020). The subcellular distribution of ROS was localized by methods of the transmission electron microscope in organelles of leaves (Zhuang et al., 2019). Also, for the technique of RT-PCR to expression studies, it is crucial to use the correct reference genes with stable expression under abiotic treatments, as demonstrated for CAT genes of Cucumis melo by Kong et al. (2014). The authors revealed that levels of CAT were up-regulated after 3 days of inoculation with Fusarium wilt in roots, and were significantly overestimated when using the wrong reference gene for normalization. In addition, various methods for calculating the stability of reference genes and using them in combination is fruitful for accurate quantification of the expression levels of antioxidant genes (Petriccione et al., 2015). Unfortunately, nowadays, there are no precise tools for counting ROS in cellular compartments.

Recent studies describe the stress reaction of the AOS system more comprehensively considering other biological aspects and great importance of this system to stress response. Hippler et al. (2016) established the role of citrus rootstocks in the up-regulation of antioxidant enzymes (Cu/Zn SOD, CAT, APX) in leaves and nutritional status during long-time copper treatment. Additional investigations on two citrus genotypes showed a direct relationship between an increased antioxidant activity and stress tolerance (Zandalinas et al., 2017). Also, there is evidence of a connection between the expression of plastid antioxidant genes and cold-acclimations (Juszczak et al., 2016). Investigation of drought stress effect to photosystems and AOS (Guo et al., 2018) revealed that photosystem I (PSI) is more sensitive to stress than photosystem II (PSII) and process of photoinhibition related to ROS accumulation. Also, drought-resistant plants of sorghum genotype M81E had a significantly higher activity of APX and SOD during stress. Bhuyan et al. (2019) studied AOS components and glyoxalase systems for different wheat genotypes in order to detect its resistance. Study of the effect of salinity on tomato (Parvin et al., 2019) showed a strong increase of SOD, APX, GPX, and DHAR activity proportionally to NaCl concentration during salt stress. Riffat & Ahmad (2020) showed for Zea mays L. that under salt-stress treatment, amounts of ascorbate and tocopherols decreased and production of SOD, CAT, POX, and some compounds (i.e., phenolics, carotenoids, MDA) increased. The authors emphasized the role of exogenous sulfur as an inductor of salt tolerance because of enhancement of SOD, POX, CAT, increasing of AsA, tocopherol, phenolics, and decreasing carotenoids and MDA during sulfur supply. The large-scale meta-transcriptome and complementary experimental analysis of antioxidant genes regulation in response to cold and water deficiency for rice and bread wheat were carried out (Ermakov et al., 2019). As a result, patterns of regulation of different gene copies of AOS in response to stress were described, and cold response turned out to be more stable and homogeneous than salinity, perhaps due to peculiarities of used methods for stress conditions.

Several studies were devoted to estimations for the quantification of antioxidants. Measurements of dynamical concentrations of ascorbate and glutathione in response to ozone exposure (Castillo & Greppin, 1988) showed that the total amount of antioxidants is maintained at approximately the same level, even so, under stress exposure, the number of oxidized forms and the activity of DHAR restoring ascorbate increases. Glutathione concentrations are approximately 1–3.5 mmol in chloroplasts and 0.1–0.7 mmol in other compartments (Rennenberg, 1980). The highest concentrations of AsA were detected in cytosol and nuclei (Zechmann, Stumpe & Mauch, 2011), while levels of AsA in plastids and mitochondria were about half of cytosolic AsA. However, the most definite increase of ascorbate was detected in the vacuole (fourfold) and chloroplasts (twofold). It was shown that concentrations of the thylakoid APX and Cu-Zn SOD reach 1 mmol (Asada, 2006) nearby of PSI in the chloroplast, but stromal APX has a much lower ratio of concentration. Generation ratios of hydrogen peroxide vary by three orders between organelles (Foyer & Noctor, 2003) from 100 in mitochondria to 10,000 nmol m ^{− 2} leaf surface s ^{− 1} in the peroxisome.

Methods of metabolomics also might give a better understanding of the processes related to AOS. For instance, increased amounts of phenolic acids and flavonoids detected on 120 h germination stage compared with the 36-h stage (Chu et al., 2020). Also, the publicly available data of gene expression levels, such as Gene Expression Omnibus (Clough & Barrett, 2016), Expression Atlas (Petryszak et al., 2016) can help to analyze dynamics of the AOS.

All this heterogeneous data can help to understand the complex properties of AOS in normal conditions (ratio of reduced/oxidized forms of antioxidants, units of enzyme activity, expression levels of individual genes, generation of ROS). Still, it seems that the stress response of the AOS is much more complicated and includes changing the activity of AOS enzymes, amounts of antioxidants, and unambiguous transcriptional regulation of the coding genes of antioxidant enzymes either cellular ROS and antioxidant interplay. Also, it seems like the chloroplastic antioxidant system has a unique role in whole-cell ROS metabolism. For example, chloroplasts have the highest hydrogen peroxide generation (Foyer & Noctor, 2003), and strong increasing of AsA concentrations under high-light stress (Zechmann, Stumpe & Mauch, 2011). Besides that, under high-light stress conditions, modulation of the chloroplast antioxidant system by exogenous spermidine is enhanced tolerance to salinity-alkalinity stress for tomato (Li et al., 2015).

Stress-response of the antioxidant system components

The complex nature of the AOS results in diversified regulating inductors of this system on multiscale levels. ROS signaling pathways are involved in systemic acquired acclimation to stresses, and in a non-specific way they may be integrated into other acclimation pathways (Gilroy et al., 2016). Hormones, such as salicylic acid (Wang et al., 2015b), brassinosteroids (Vardhini & Anjum, 2015), and combination of the latter with kinetin (Ahanger et al., 2020) enhance the activity of the AOS enzymes and low-molecular antioxidants. A similar effect is also observed for ethylenediaminetetraacetic acid (EDTA) (Habiba et al., 2015). It was also found that some of the organic chemicals, that is, ferulic acid (Yildiztugay et al., 2019), and trehalose (Mostofa, Hossain & Fujita, 2015) induce the AOS response to stresses (boron and salt, respectively). Alpha-lipoic acid (Terzi et al., 2018) had a similar effect: the activity of SOD, CAT, GPX, GR, and MDHAR increased in osmotic stress but decreased the activity of the APX. Treatment with important inorganic substances, such as calcium (Rahman et al., 2016), silicon (Kim et al., 2017), sulfur (Adams et al., 2020) and selenium (Alyemeni et al., 2018) also can enhance AOS characteristics. Exogenous hydrogen peroxide (Guler & Pehlivan, 2016) can improve drought tolerance by enhancing AOS activity. This fact suggests that there is a cross-talk in the regulation of the system to different inductors.

The AOS has a versatile regulation during abiotic and biotic stresses. Abiotic stress is characterized mainly by the increasing activity of antioxidant enzymes and reducing the growing number of radicals, up to depletion of the system’s capacity. Abiotic stresses usually induce the AOS to enhance the work on the fight against radicals. The antioxidant enzymes (APX, SOD, GPX, GR, CAT) up-regulates during various abiotic stresses (Ahmad et al., 2010). The other two enzymes, DHAR (Yoshida et al., 2006) and MDHAR (Eltayeb et al., 2007), also have essential redox functions to protect against abiotic stress. These facts argue in favor of the co-regulation of enzymes of this system in response to stress. Different types of abiotic stress have a common pathway between them. Roychoudhury, Paul & Basu (2013) noted that regulation of abiotic stresses had an ABA-dependent (for drought and salinity) and ABA-independent pathways (drought, salinity, cold). Also, transgenic plant lines with additional copies of AOS genes showed higher resistance to abiotic stresses. For example, it was shown on peanut and apple during drought and salt treatment (Negi et al., 2015; Sun et al., 2018), on cassava in cooling stress conditions (Xu et al., 2014). On the other hand, plant lines with knockouts of individual antioxidant genes are less tolerant of stress (Wu et al., 2015).

Regulation of the AOS during biotic stresses has a common dual pattern. The first pattern involves the activation of the AOS enzymes to protect the cell from ROS. Second, so-called oxidative burst, characterized by a decrease in the antioxidant activity of enzymes and intercellular signaling on the destruction of infected cells. For example, tomato plants infected by Botrytis sineria Pers. demonstrated increased activities of SOD, CAT, and GPX during an early stage of treatment. Still, during the advanced stage of disease activity of the AOS enzymes decreased that may cause programed cell death (Kużniak & Skłodowska, 2005). El-Argawy & Adss (2016) showed that bacterial treatment (Ralstonia solanacearum) causes a genotype-specific changing expression of peroxidases, polyphenol oxidase, and CAT on different varieties of Solanum tuberosum. Interestingly, polyphenol oxidase levels, especially peroxidase, were higher in highly resistant cv. Nicola and medium resistant cv. Kara. Vice versa, the CAT level was highest for susceptible cv. Spunta and lowest for cv. Nicola. It may indicate a more successful oxidative burst strategy and programed cell death with bacterium-resistant genotypes with reduced CAT levels. During the oxidative burst, NADPH oxidases generate a large amount of ROS, which acts as signaling molecules for apoptosis and can trigger cell death programs to prevent the spread of infection throughout the plant (Torres, 2010). A comprehensive scheme of the signal role of ROS in pathogen interactions described by Camejo, Guzmán-Cedeño & Moreno (2016).

The question about the effects of stress combination is still open. A comprehensive review by Suzuki et al. (2014) focused on interactions of abiotic and biotic stresses. The authors revealed unique response patterns of stress combinations that can’t be predicted by the special effects of stress. Atkinson, Lilley & Urwin (2013) investigated the transcriptome response of A. thaliana on drought stress, pathogen infection, and summarizing the result of stress combination using microchip technology. During this study, the authors revealed about 50 multi-stress-regulated genes with a unique pattern of regulation. Also, another study on the A. thaliana transcriptome in response to drought and pathogens individually and in combination (Davila Olivas et al., 2016) showed that clustering of stress combinations was by type of stress in case of early response (different types of stress are clustered separately) and by time in case of late response (different stresses with the same duration are clustered in the same groups). These facts may indicate a higher specificity of regulation of the antioxidant system to stress in the early response than in the late response. Atkinson & Urwin (2012) gave numerous examples showing the breeding of varieties resistant to abiotic stresses can make hybrids more vulnerable to pathogens, and vice versa. Thus, strategies for protecting against abiotic and biotic stresses are different and often opposite. However, common property for abiotic, biotic stress, and development processes is their signaling system, directly related to NADPH oxidase activity and an increase in ROS production (Suzuki et al., 2011). Thus, a delicate balance between the number of radicals and the activity of the components of the antioxidant system occupies a central place in the study of such a complex issue of the interaction of ROS, AOS, and cell homeostasis.

In the AOS, there are individual enzyme-coding genes that have high importance for the functioning system in general, especially in stress conditions. Doroshkov & Bobrovskikh (2018) found the relationship between the evolutionary features of antioxidant enzymes and their expression levels for predicting prospective targets for selection across cereals. The authors identified groups of highly conserved genes with a high level of mRNA expression and a group of less conservative with a low-level expression. However, a group of highly conserved genes was isolated, but the expression under normal conditions was low. These genes may be activated in response to specific effects, such as stress. This method seems to be a prospective approach for isolating general genetic components of this system. The lack of information about the complex regulation of the system in response to stressful effects makes it difficult to identify specific trends and patterns of its behavior. It is mostly because the AOS behavior is associated with multi-copy of system components, subcellular compartmentalization, and a considerable number of freedom degrees in its regulation, including different stages of plant development, specificity of photosynthetic and non-photosynthetic tissues and various types of stress.

Subcellular compartmentalization of the antioxidant system components

The plant cell contains several compartments depending on its type and/or part of a particular tissue, and each compartment has its own source of ROS. The compartmentalization of a plant cell determines the specifics of the metabolism and the set of metabolic reactions that can occur, allowing the different compartments of the cell to perform unique functions. The AOS also is divided into a set of subsystems functioning in different compartments and tissues. In the various cells, compartments differ in the set of enzyme classes of the AOS (Mittler et al., 2004), conditions (pH, metabolite composition, the ratio of reduced and oxidized antioxidants) and various ratios of the activities of individual isoforms of antioxidant enzymes. Also, it is known that ROS generation rates vary widely between compartments (Foyer & Noctor, 2003). Thus, different organelles have various abilities to neutralize radicals. Herein, we proceed to consideration of the different cell compartments in the context of the generation of radicals and systems to combat them. Based on the researches (Palma et al., 1991; Foyer & Noctor, 2003; Rhoads et al., 2006; Cho et al., 2009; Suzuki et al., 2011; Jarvis & López-Juez, 2013) reviewed in this article we propose the following structural model of the interplay between AOS subsystems and components and the underlying metabolic processes producing ROS under oxidative stress conditions Fig. 2. In the model, the generalized plant cell is represented as a membrane and cytosol containing the following compartments: mitochondria, chloroplast, peroxisome, and nucleus. Features of the AOS functioning in these compartments are described below.

Chloroplasts are the main source of ROS in a plant cell (Foyer & Noctor, 2003) and essential organelle for generating energy. The main processes which generate ROS as byproducts in chloroplasts are associated with photosynthesis and activity of the electron-transport chain complexes. The activity of photosystems during the day varies depending on the intensity of sunlight. Due to the special conditions of chloroplast functioning (including variable illumination and electron flow), chloroplasts are required to flexible regulation of metabolic processes. Such versatile control was demonstrated by Jarvis & López-Juez (2013) for the regulation of the electron balance between photosystems. In particular, the redox status of an important component of the electron transport chain, plastoquinone, is controlled by activating the STN7 and CSK gene cascades that affect the expression of genes to alter the electron balance in photosystems. The signal molecule in this process is oxygen, which is produced in high light conditions. Besides, oxygen produced under high light conditions is the signal molecules in this process. Oxygen can induce the expression of genes involving the stress response pathway (mainly antioxidant genes), or cause cell death. In the absence of the plastid EX1 and EX2 genes, the accumulation of oxygen not causes changes in gene expression and the implementation of the cell death program. Hydrogen peroxide, which is generated by chloroplasts under high light conditions, triggers the transcription of APX2 (cytosolic APX) and other genes in vascular cells, usually through an abscisic acid-induced pathway (Galvez-Valdivieso et al., 2009).

Also, chloroplasts have NADPH-thioredoxin reductase (NTRC) (Serrato et al., 2004), which can restore the disulfide bridges of target proteins by using NADPH. Therefore, the NTR/TRX system plays a vital role in chloroplasts and allows maintaining the redox status of the compartment. In chloroplasts, there is Cu-Zn SOD, which transfers superoxides into hydrogen peroxides. The ascorbate-glutathione cycle (Lidon & Henriques, 1993) neutralizes hydrogen peroxides. APX neutralizes hydrogen peroxide, using ascorbate as an electron acceptor. Approximately 50% of APX is found directly in the thylakoids (Polle, 1997). DHAR and GR mediate the reduction of oxidized ascorbate. Since the rate of non-enzymatic reduction of dehydroascorbate by reduced glutathione (GSH) is relatively high (Polle, 1997), enzymatic reduction in chloroplasts appears to be of secondary importance. Unlike other antioxidant enzymes, GR appears to be directly regulated by the redox status, partially inhibited by NADPH, and activated by hydrogen peroxide and oxidized glutathione (GSSG) (Polle, 1997).

The main feature of AOS in peroxisome is the presence of catalase, which plays a significant role in maintaining redox status. For example, transgenic catalase-deficient leaves of tobacco had necrotic lesions during intensive light conditions (Willekens et al., 1997), but not in low-light conditions. Also, these transgenic plants in high-light conditions accumulated a lot of oxidized glutathione and reduced the amount of ascorbate by four times. Plants with defective catalase accumulate hydrogen peroxide (Hu et al., 2010) and have many adverse physiological effects, such as growth suppression and reduced photorespiratory activity (Bueso et al., 2007; Queval et al., 2007). However, works are proving that the ascorbate-glutathione cycle with its components plays an essential role in the peroxisomal fight against ROS. Thus, it has been shown by Ribeiro et al. (2017) that knockout plants by peroxisomal APX show signs of oxidative stress and early aging, while overexpression is associated with increased plant protection against stress (Wang, Zhang & Allen, 1999). Peroxisomes perform multiple catabolic processes of many substances (fatty acids, amino acids, polyamines, etc.), which generate ROS inside them. Also, most plants are characterized by C3 photosynthesis, which forming glycolate. Then glycolate transported from chloroplasts to peroxisomes, where it is oxidized to glyoxylate (Kisaki & Tolbert, 1969). The byproduct of this reaction is hydrogen peroxide, which is released in significant quantities (Foyer & Noctor, 2003). So, it is essential to maintain a balance between the production and scavenging of ROS in peroxisomes, which clearly illustrated by Wang et al. (2015a). Authors showed that redox status regulates peroxisome biogenesis and degradation what plays a role in the maintenance of integral multi-compartmental cell metabolism. A distinctive feature of peroxisomes is their high plasticity in response to various effects. For example, Rodrguez-Serrano et al. (2009) indicate that peroxisomes had significantly increased dynamics and speed of movement during the treatment with CdCl₂. It has been shown that the number of peroxisomes increases during clofibrate treatment (Palma et al., 1991). However, during oxidative stress, the biogenesis of peroxisomes can be repressed, which may be connected with a violation of the peroxisomal protein importers. This hypothesis is supported by evidence that several peroxins, proteins involved in peroxisome biogenesis, are known to be modified or violated by an imbalance of cellular ROS (Ma et al., 2013).

Mitochondria provide the energy for the plant cell and regulate overall metabolism through respiration. The main reactions in this organelle are phosphorylation of ADP and oxidation of various substrates that generate ROS. Review (Noctor, De Paepe & Foyer, 2007) considers the integrative role of mitochondria in the generation of radicals. Due to photosynthetic processes in the plant cell, mitochondria exist in an environment enriched with oxygen and carbohydrates. Mitochondria regulate their redox homeostasis by regulating the flow of electrons through the electron transfer chain and the change in the activity of NADPH-dependent oxidases. However, the absolute levels of radical production during mitochondrial metabolism are relatively small (Foyer & Noctor, 2003). The main sites of superoxide production in mitochondria are complexes I and complexes III in the ETC (Møller, 2001; Rhoads et al., 2006). In mitochondria, superoxides are fixed by manganese SOD, and peroxides are eliminated in the ascorbate-glutathione cycle. The investigation of Fernie, Carrari & Sweetlove (2004) reveals that the activity of the electron transport chain of mitochondria is associated with the activity of the tricarboxylic acid cycle oxidative phosphorylation, the biosynthesis of carboxylic acids and photorespiration.

Hydrogen peroxide (Bolouri-Moghaddam et al., 2010) can easily transport into the vacuole from the cytoplasm. It is also possible that the vacuole is capable of generating ROS using its NADPH oxidase, based on proteomic analysis of the tonoplast membrane (Shi, Wang & Wei, 2006; Whiteman et al., 2008; Pradedova, Isheeva & Salyaev, 2011). It is shown that there are peroxidases of class 3, which eliminate ROS and control the level of hydrogen peroxide (Costa et al., 2008; Fini et al., 2011). However, the non-enzymatic way of utilizing radicals in vacuoles, which includes low-molecular species like flavonoids and antioxidants, seems to be the most important. Vacuoles contain approximately 2 mM of ascorbate (Zechmann, 2018) and approximately 100 μM of glutathione (Pradedova et al., 2018).

Thereby the AOS is the multi-level system, and it has plant-specific patterns of behavior under various stress conditions (Shalata & Tal, 1998; Gossett, Millhollon & Lucas, 1994) and in various cellular compartments (Mittler et al., 2004).

Modeling approaches to study the antioxidant system

Although the first models of metabolic pathways of photosynthesis in chloroplasts were developed more than 30 years ago (Hahn, 1987; Laisk & Walker, 1986), just a few of them describing the components of the AOS in plants. These models refer to various phenomena related to ROS metabolic pathways, with different levels of accuracy.

In the early 2000s, Polle (2001) built the first model for the functioning of the ascorbate-glutathione cycle in chloroplasts. This model described the functioning of redox reactions of this cycle with the possibility of calculating the steady-state of the system components. However, the model implied many assumptions. For example, the model includes a constant NADPH concentration, which leads to the accumulation of NADP+ in chloroplasts. Also, the model used a constant rate of formation of O${}_2^{-}$ and the non-specific kinetic mechanisms of reactions for enzymes of different classes (except SOD).

Later, Valero et al. (2009) improved this model. In their model, real kinetic mechanisms for various enzymatic reactions were used. The model simulates the conditions of oxidative stress and calculates a steady-state for the AOS components. The innovation of this model is the inclusion of a source of electrons, which is competitively distributed between three competitive routes (radical generation, photoreduction of NADP+ to NADPH, photoreduction of monodehydroascorbate to ascorbate). The simulation established a high sensitivity of the system to the number of substances that restore ascorbate and to the NADPH consumption by the Calvin cycle. In stress conditions, the model reflected the depletion of the system’s antioxidant capacity in the sequence of NADPH-glutathione-ascorbate and their reduction in the opposite order. Further, inactivation during the stress effects of GR, APX, and SOD resulted in irreversible inactivation of APX and excessive accumulation of hydrogen peroxide.

Further development of these ideas by the same scientific group (Valero et al., 2015) describes the most up-to-date and advanced mathematical model of the AOS. The model studies the dynamic behavior of the ascorbate-glutathione cycle in the dark and light phases of photosynthesis. The system is described by a competitive flow of electrons in three different routes; the choice of the route depends on the intensity of sunlight during the photoperiod (in the dark phase, the electron flux is equal to zero). Unlike previous models provided only stationary solutions, this model allows simulating daily fluctuations of metabolites, electron fluxes, and enzyme activity in an ascorbate-glutathione cycle. The simulation results reflect the importance of the distribution of electron fluxes through the system to deal efficiently with the radicals in the ascorbate-glutathione cycle. The authors noted that their model could help to isolate the most important enzymes and metabolites in this pathway. This approach can also describe strategies for analyzing the mechanisms of plant protection from radicals and can be extrapolated to other metabolic pathways in the future.

When constructing a mathematical model for the AOS, we should pay special attention to the pathways of ROS generation and ROS-associated signaling and various mechanisms of cell response to oxidative stress and ways of adaptation. The system complexity is so high that it might be challenging to keep in mind all interactions and various factors affecting those interactions. Thus, system biology approaches can help with an overall description of the system. One can describe biochemical interactions in terms of differential equations. For example, every single biochemical reaction can be described with a rate equation based on a specific kinetic law (Michaelis-Menten law, Hill-type kinetics, “ping-pong” mechanisms, etc.). Then the system of differential equations should be solved numerically. Thus, the emergent behavior of a whole system might be reconstructed in silico on the base of knowledge about interactions between systems components.