INTRODUCTION

TOP ABSTRACT INTRODUCTION CONSTRUCTION OF METABOLIC... RESULTS AND DISCUSSION MATERIALS AND METHODS LITERATURE CITED

Ascorbate (Asc) and glutathione (GSH) are important metabolites in plants. Among numerous physiological roles attributed to them, their most prominent and best established functions are those of crucial antioxidants in the Asc-GSH cycle (Arrigoni, 1994; Cordoba and Gonzales-Reyes, 1994; Noctor and Foyer, 1998; Asada, 1999). The Asc-GSH cycle serves the removal of toxic oxygen species, which are inevitably formed as by-products of the normal metabolism or as a consequence of various exogenous environmental insults. Chloroplasts bear a particular risk of oxygen toxicity because molecular O₂ can be photo-reduced by photosystem I (PS I) yielding O₂^. (Mehler, 1951). Estimates suggest that 2% to 5% of the photosynthetically produced electrons are dissipated by this reaction under normal conditions and up to 30% under stress (Robinson, 1988; Biehler and Fock, 1996).

Superoxide dismutases (SOD, EC 1.15.1.1) are considered to be the first line of defense against O₂^..Their reaction products are H₂O₂ and O₂ (Fig. 1). H₂O₂ is reduced by Asc to water (Fig. 1). In chloroplasts, this reaction is catalyzed by Asc peroxidases (APX, EC 1.11.1.11) and produces monodehydroascorbate radicals (MDA). MDA can be reduced by ferredoxin (Miyake and Asada, 1994) or by NAD(P)H in a reaction catalyzed by MDA reductase (MDAR, EC 1.1.5.4; Hossain and Asada, 1985). Although these mechanisms efficiently recycle Asc, it is inevitable that dehydroascorbate (DHA) is also formed to some extent because of spontaneous disproportionation of MDA radicals to Asc and DHA (Fig. 1). The observation that reduced GSH was capable of reducing DHA to Asc led Foyer and Halliwell (1976) to propose a role of GSH in the regeneration of Asc. Recycling of GSH is achieved by glutathione reductase (GR, EC 1.6.4.2) reducing glutathione disulphide (GSSG) by consumption of NADPH (Fig. 1).

View larger version (32K): [in this window] [in a new window]   Figure 1.   The SOD-Asc-GSH cycle (fat arrows, enzymatic reactions) and nonenzymatic redox reactions (broken arrows).

DHA reductase activity (DAR, EC 1.8.5.1) originally was not found in chloroplasts and it was assumed that DHA was reduced by GSH in a nonenzymatic reaction (Foyer and Halliwell, 1976). In several subsequent studies, however, enzymes displaying DAR activity have been characterized (Foyer and Halliwell, 1977; Anderson et al., 1983; Hossain and Asada, 1984; Kato et al., 1997; Shimaoka et al., 2000). Evidence currently is accumulating that at least some of the previously found proteins with DAR activities may have other or additional functions. The significance of DAR for Asc recycling is under debate (Foyer and Mullineaux, 1998).

Since the discovery of the Asc-GSH cycle in the mid-1970s, the enzyme-catalyzed reactions of this pathway have attracted considerable interest and still are a matter of intensive research (for recent reviews, see Polle, 1997; Noctor and Foyer, 1998; Noctor et al., 1998; Asada, 1999). Besides chloroplasts, the constituents of the Asc-GSH cycle have also been localized other subcellular compartments (Jiminez et al., 1997). Studies with mutants or transgenic plants over- or underexpressing enzymes or metabolites of the Asc-GSH pathway established causal relationships between certain components of the cycle and stress tolerance (Scandalios, 1993; Allen, 1995). The Asc-GSH cycle does not only combat oxidative stress, but has further roles in metabolism, e.g. regulation of photosynthesis in response to light conditions (Foyer and Harbinson, 1994; Asada, 1999). Furthermore, reactive oxygen species act in cellular signaling and the control of gene expression (May et al., 1998; Karpinski et al., 1999). Because of the dual functions of reactive oxygen species, a tight control of their concentrations may be anticipated, which requires a delicate balance of systems involved in their destruction and their generation.

However, by simple analysis of concentrations of antioxidants and activities of defense enzymes in plant tissues, it will not be possible to understand the regulation in the network of interacting redox reactions. In this respect, a theoretical and quantitative understanding of functioning of the cycle will be necessary, which requires knowledge about the fluxes of oxidants and antioxidants. To date, such information is not readily available. In other areas of biological research where complex interactions are to be studied, e.g. in ecology and bioclimatology, computer-assisted simulations have helped considerably to advance the understanding of intrasystem regulation, to define the critical components within a system, and to develop testable hypotheses. It seems useful to adopt this strategy to study metabolic interactions.

The present paper presents for the first time the construction of a metabolic model, which simulates the functioning of the SOD-Asc-GSH cycle. The model connects the oxidants and antioxidants outlined in Figure 1 by fluxes. The fluxes have been composed of enzyme-catalyzed andas appropriatenonenzymatic components. To simulate in situ conditions, the catalytic properties of purified enzymes, their chloroplastic concentrations, and the concentrations of antioxidants have been incorporated into the model. The model was used to explore the effect of increasing oxidative stress on oxidant and reductant fluxes through the SOD-Asc-GSH cycle and to calculate expected steady-state concentrations of oxidants and antioxidants. The model was also applied to predict how the variation of an individual componentantioxidant or enzymewould affect the redox balance of the cycle. Major goals of this study were: (a) to assess the significance of nonenzymatic versus enzyme-catalyzed redox reactions for oxidant detoxification, (b) to estimate the relative contribution of different defense enzymes to the recycling of antioxidants, and (c) to explore the limits of the SOD-Asc-GSH cycle for stress compensation.

	CONSTRUCTION OF METABOLIC MODELS

TOP ABSTRACT INTRODUCTION CONSTRUCTION OF METABOLIC... RESULTS AND DISCUSSION MATERIALS AND METHODS LITERATURE CITED

Software and Hardware

The superoxide-H₂O₂-Asc-GSH-chemical reaction model (SHAG-CHEM) and the enzymatic reaction model (SHAG-ENZ) were developed for the simulation of metabolic redox interactions using the software ModelMaker (Cherwell Scientific Publishing Limited, Oxford). The software provides programming tools denominated with the following technical terms: "compartments," "flows," "influences," and "list of parameters." These terms do not have any biological meaning. "Compartments" can be used to simulate changes in concentrations and "flows" (F) to simulate reaction velocities. To simulate redox reactions two different programming steps are necessary: one to calculate the reduction of the oxidant and formation of the reduced product, and a second to calculate the oxidation of the antioxidative substrate and the formation of the oxidized product. In a biological system, such a composed reaction is catalyzed by one enzyme, which means for model constructions that the two programming steps have to be linked. This is achieved by the programming tool "influence." The "list of parameters" was used to compile reaction constants, enzyme concentrations, K_m values, etc. The values in the "list of parameters" are available for parameterization, which means that they can be automatically varied in a desired range. For a full description of the software and its documentation, see Walker and Crout (1997). The basic principles of the construction of a single enzyme model and the full definition of the programming steps of the models developed in the present investigation are given in "Materials and Methods."

The Model SHAG-CHEM: Boundary Conditions and Algorithms for Nonenzymatic Reactions of Reactive Oxygen Species with Asc and GSH

Figure 2 illustrates the principle components of SHAG-CHEM. The concentrations of oxidants or antioxidants in the "compartments" (square boxes) were computed as the sum of "flows" (F_I..n) entering the compartment and "flows" (F_II..n) leaving the compartment. In model SHAG-CHEM the flows were defined as the reaction velocities of nonenzymatic reactions and calculated according to the following equation:

(1)

where k is the apparent rate constant of a bimolecular reaction (M¹ s¹) and [A] and [B] are the concentrations of the substrates A and B (M). The rate constants used to run model SHAG-CHEM have been compiled in Table III. A constant electron source, PS I, was added to the model (using the ModelMaker component "defined value" indicated by the hexagonal symbol in Fig. 2) and defined as the maximum electron production rate of PSI. The rate limiting step of the linear electron transport chain, the oxidation of plastoquinone (20 ms per 2 electrons), restricts the electron production of PS I to 100 electrons reaction center¹ s¹ (Haehnel, 1984). This yields molar figures of about 2 to 4 mM electrons s¹ depending on chloroplast volume and number of chlorophyll molecules per reaction center. Published data for chloroplast volumes vary over a range from 21 to 113 µL mg¹ chlorophyll (Chl) (Heldt et al., 1973; Winter et al., 1993; Leidreiter et al., 1995). In the present study, an intermediate volume of 50 µL mg¹ Chl was assumed. The number of Chl molecules per reaction center is also variable because of changes in antenna size, but is generally in a range of 500 to 1,000 molecules (Haehnel, 1984). Based on these considerations PS I activity was assessed as 2.4 mM electrons s¹.

View larger version (16K): [in this window] [in a new window]   Figure 2.   SHAG-CHEM, a model to simulate nonenzymatic antioxidative reactions. The graph displays the original presentation of the computer program ModelMaker. Boxes indicate "compartments" (O2_radical, H2O2, H2O, ASC, MDA, DHA, GSH, and GS_radical), which correspond to concentrations of oxidants and antioxidants (defined in Table I). The compartments were connected by "flows" (F1-F7, solid lines with arrows) defined as the nonenzymatic reaction velocities (Table II). The hexagonal symbol indicates the programming tool "unconditional defined value" and was used to define PS I as a constant source of electrons (2,400 µM s1). The superoxide production rate was defined as 0.1 × PS I. The broken arrows indicate "influences," which were used to link dependent reactions. Further explanations are given in the text.

To account for the fact that only a small portion of photosynthetically produced electrons are transferred to oxygen, the production rate of O₂^. was defined as (relative_factor) × PSI. Under "standard conditions" a relative factor of 0.1 was used to yield a superoxide radical production rate of 240 µM s¹, a figure in the range of those discussed by Asada (1999; Asada and Takahashi, 1987).

In the model SHAG-CHEM, the dismutation of MDA was incorporated as a means to regenerate Asc partly. An additional source of reductant was not added. The model was run under conditions where chemical reactions between O₂^. and the antioxidants Asc and GSH were either forbidden or allowed.

The Model SHAG-ENZ: Boundary Conditions and Algorithms for Enzyme-Catalyzed Reactions of the SOD-Asc-GSH Cycle

For the construction of the model SHAG-ENZ (Fig. 3) the nonenzymatic model SHAG-CHEM served as the backbone. The definition of the flows was expanded by adding terms for enzymatic reactions. The velocity of enzymatic reactions, which consume two substrates (A and B) and produce two products, is given by the Ping-Pong Bi Bi reaction mechanism (Bisswanger, 1994). The equation for the forward reaction is:

(2)

(3)

where v = velocity of the reaction (M s¹); V_max = maximum reaction velocity (M s¹); k_cat = turnover number, i.e. the number of molecules of substrate, which are converted (enzyme molecule¹ s¹); [A], [B], and [enzyme] = concentrations of the substrates A and B, and of the enzyme (M); and K_m (A), K_m (B) = Michaelis-Menten constants of the enzyme for the substrates A and B (M), respectively. The concentrations of antioxidative enzymes in chloroplasts and their catalytic properties used to run the model SHAG-ENZ under "standard conditions" have been summarized in Table VII. The data were used to define compartments (Table IV), flows (Table V), and the list of parameters (Table VI) in "Materials and Methods." The compartment "NADPH" was introduced as a source of reductantto catalyze MDA and GSSG reduction by enzyme activities (Fig. 3). NADPH production rates can be estimated from the photosynthetic electron flux (PSI):

(4)

The factor of 0.3 would account for 30% photorespiration and other electron-consuming reactions. However, Equation 4 decelerates the run time of the model and therefore is only useful if competitive reactions for reductant are to be studied. Because the chloroplastic NADPH concentrations change little after adjustment to light (100 µM NADPH and 360 µM NADP⁺, Gerst et al., 1994; 143 µM NADPH and 96 µM NADP⁺, Bielawski and Joy, 1986), even when chloroplasts were stressed with 10 µM paraquat in short-term experiments (120 µM NADPH and 180 µM NADP⁺, Holfgreve et al.; 1997), in most cases a steady concentration of NADPH of 100 µM was assumed (Fig. 3, influence from NADPH to F10 and F11). The model SHAG-ENZ was run under conditions where flows were composed of chemical (Eq. 1) and enzymatic reaction velocities (Eq. 2 and 3 and Eq. 1 for SOD). Chemical reactivities of O₂^. with Asc and GSH were included (according to Table III). The value for the "relative_factor," which defines O₂^. production rates, was added to the "list of parameters" (Table VI) and was varied between 0.05 and 0.3 to simulate the dissipation of 5% to 30% of total photosynthetically produced electrons to O₂. The concentrations of enzymes and antioxidants were parameterized within the indicated ranges to simulate changes in enzymatic activities and antioxidant availability.

View larger version (17K): [in this window] [in a new window]   Figure 3.   SHAG-ENZ, a model to simulate nonenzymatic and enzyme-catalyzed reactions of the SOD-Asc-GSH cycle. The graph displays the original presentation of the computer program ModelMaker. The nonenzymatic model (Fig. 2) was expanded by the addition of algorithms defining enzymatic activities to flow equations and by definition of new flows (Table IV). Additional compartments were defined (GSSG, ASCmdar, NADPH, and NADP). The regeneration of GSH was introduced by the flows F8, F9, and F10 connecting the compartments GSSG, GS  radical, and GSH. The reduction of MDA by MDAR was introduced as a new flow F11 from MDA to ASCmdar. (The introduction of an additional compartment, denominated as ASCmdar, was necessary to account for the different stoichiometries of the dismutation of MDA and the reduction of MDA by NADPH.) ASCmdar was connected with ASC by F12. F12 was set equal to F11. PS I was connected with the "compartment" NADPH by an "influence" to simulate a constant supply with electrons as defined in Table V. NADPH was connected with NADPH-consuming reactions (F10 and F11). To calculate the cumulative consumption of NADPH, a compartment NADP was defined and linked to NADP+-producing reactions (F10 and F11). The compartments and flows have been defined as indicated in Tables IV-VI.

View this table: [in this window] [in a new window]   Table V.   Definition of compartments (unconditional) for SHAG-ENZ (Fig. 3) The initial concentrations were chosen after Asada and Takahashi (1987; ascorbate and GSH), Asada (1994; O, and H2O2), and Gerst et al. (1994; NADPH).

Under "standard conditions" of model SHAG-ENZ, the initial concentrations of Asc and GSH were chosen according to those reported in chloroplasts, i.e. 10,000 and 5,000 µM, respectively (Asada and Takahashi, 1987; Asada, 1999). O₂^. and H₂O₂ concentrations were set to 0.001 and 0.5 µM, respectively, according to their estimated concentrations in chloroplasts (Asada, 1994, 1997). The production rate of O₂^. was set to 240 µM s¹ and the concentrations of antioxidative enzymes and their kinetic properties were used as indicated in Table VII.

View this table: [in this window] [in a new window]   Table VII.   Reactions of the SOD-Asc-GSH cycle and kinetic parameters used to model "standard" conditions The reaction velocities were calculated according to Equation 2, except for SOD. Because of the almost diffusion-controlled reaction rate, the velocity of the SOD reaction was calculated according to Equation 1 using its pseudo-first order rate constant k(SOD) = 2 × 109 M1 s1 (Asada and Takahashi, 1987). To avoid overestimation of MDAR, its catalytic activity with NADPH, which is lower than that determined with NADH, has been used. Relative occurrence refers to the relative activity of an antioxidant enzyme in chloroplasts as compared with its activity in whole-leaf extracts (100%).

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION CONSTRUCTION OF METABOLIC... RESULTS AND DISCUSSION MATERIALS AND METHODS LITERATURE CITED

Steady-State Concentrations and Fluxes of Oxidants and Antioxidants in the Absence of Antioxidative Enzymes

In the first scenario, SHAG-CHEM calculated the dismutation rate of O₂^., the H₂O₂ production rate, the chemical reduction of H₂O₂ by Asc, the dismutation of the resulting MDA, and the "slow" chemical recycling of Asc by oxidation of GSH (Table III, Fig. 4, A and C) without including the reaction of Asc or GSH with superoxide (i.e. their respective reaction constants were set to 0 in the parameter list, Table VI). Under these premises, GSH prevented net Asc oxidation but not H₂O₂ accumulation (Fig. 4A). MDA concentrations increased, whereas GSH was oxidized (Fig. 4C). After depletion of GSH, Asc was oxidized to DHA resulting in a slightly dampened increase in H₂O₂. After complete conversion of Asc into DHA, H₂O₂ increased at the expected rate of 120 µM s¹ (Fig. 4A).

View larger version (30K): [in this window] [in a new window]   Figure 4.   Nonenzymatic consumption of Asc and GSH, production of DHA, GSSG, H2O2 (A and B), and formation of superoxide radicals and MDA (C and D) calculated by SHAG-CHEM for an O2. production rate of 240 µM s1. Further calculations were performed as defined in Table III. The spontaneous reaction of O2. with Asc and GSH was either not included (A and C) or included (B and D).

It should be noted that antioxidants did not affect the steady-state concentration of superoxide radicals (24 µM), if direct interactions of O₂^. with Asc or GSH were not allowed (Fig. 4C). If chemical reactions between the antioxidants and O₂^. were included, several differences became apparent as compared with the absence of such interactions: The depletion of GSH and subsequently that of Asc were accelerated (Fig. 4B versus Fig. 4A), net production of H₂O₂ increased (Fig. 4B versus Fig. 4A), and the concentration of O₂^. was significantly diminished until the antioxidants had been oxidized (40-100 nM, Fig. 4D).

Under the present settings of the model, concentrations of 10 µM H₂O₂ reported to inhibit photosynthesis by 50% (Kaiser, 1979), were exceeded within less than 1 s (Fig. 4, A and B). The chosen chloroplastic antioxidant concentrations of 5 mM GSH and 10 mM Asc were exhausted in little more than 1 min if recycling systems were absent.

The figures used to run SHAG-CHEM just set a general frame but illustrate several important principles: In the absence of enzymatic interactions, GSH maintains Asc in its reduced state; and both antioxidants diminish steady-state O₂^. concentrations but enhance H₂O₂ production. The latter observation is caused by the differences in the stoichiometries of H₂O₂ formation as a result of the dismutation of O₂^. (0.5 H₂O₂ per 1 O₂^.) and the reduction of O₂^. by Asc or GSH (1 H₂O₂ per 1 O₂^.; compare with Table III).

Steady-State Concentrations and Fluxes of Oxidants and Antioxidants in the Presence of Antioxidative Enzymes

Steady-State Concentrations of Oxidants under "Standard Conditions"

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View larger version (23K): [in this window] [in a new window]   Figure 5.   Calculated changes in oxidant concentrations in response to a superoxide production rate of 240 µM s1. The calculation was performed by SHAG-ENZ for "standard conditions" as defined in Tables III and VII. The x axis break shows an expanded view of initial changes (0-0.2 s).

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Parameterization of Superoxide Production Rates

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View larger version (27K): [in this window] [in a new window]   Figure 6.   Calculated effects of increasing O2. production rates on steady-state concentrations of oxidants (A-E) and substrate fluxes (F-J, black symbols: enzyme-driven fluxes, white symbols: nonenzymatic reactions of Asc × O2. [G], MDA × MDA [H], and GSH × O2. [I]) and in the SOD-Asc-GSH system. The O2. production rate was increased from 120 to 720 µM O2. s1 corresponding to 5% to 30% of photosynthetically produced electrons (PS I = 2,400 µM electrons s1). The calculations were performed by SHAG-ENZ according to Tables IV-VI.

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Parameterization of Antioxidant Enzyme Activities

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View larger version (42K): [in this window] [in a new window]   Figure 7.   Calculated effects of increasing concentrations of SOD, APX, MDAR, DAR, and GR on substrate fluxes (A-E) and on steady-state concentrations of oxidants (F-J). The calculations were performed by SHAG-ENZ according to Tables IV-VI. The O2. production rate was set to 240 µM s1.

View larger version (24K): [in this window] [in a new window]   Figure 8.   Calculated effect of increasing concentrations of SOD, APX, MDAR, DAR, and GR on the MDA dismutation rate (A), the nonenzymatic reactions of Asc with O2. (B), and of GSH with O2. (C). The calculations were performed by SHAG-ENZ according to Tables IV-VI. The O2. production rate was set to 240 µM s1.

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Parameterization of Antioxidant Concentrations

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View larger version (39K): [in this window] [in a new window]   Figure 9.   Calculated effect of increasing concentrations of Asc and GSH on substrate fluxes (A-E, black symbols: enzyme-catalyzed reaction, white symbols: nonenzymatic reactions of Asc × O2. [B], MDA × MDA [C], and GSH × O2. [D]) and on steady-state concentrations of oxidants (F-J). The calculations were performed by SHAG-ENZ according to Tables IV-VI. The O2. production rate was set to 240 µM s1.

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Reductant Availability

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View larger version (22K): [in this window] [in a new window]   Figure 10.   Concentrations of oxidants calculated by SHAG-ENZ for "standard conditions" as defined in Tables III and VII in the absence of NADPH supply. The O2. production rate was set to 240 µM s1.

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View larger version (35K): [in this window] [in a new window]   Figure 11.   Simulated effects of increasing chloroplastic concentrations of NADPH (0.1-100 µM s1) on steady-state concentrations of oxidants (A-C) and substrate fluxes (D-F). The calculations were performed by SHAG-ENZ according to Tables IV-VI. The O2. production rate was set to 240 µM s1.

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SYNOPSIS

In the present study a metabolic model (SHAG-ENZ) has been constructed for theoretical analysis of the individual contributions of components of antioxidative systems to the detoxification of reactive oxygen species in chloroplasts. Only those interactions between oxidants and antioxidants, which frequently have been analyzed and discussed in the literature, were incorporated into the model. Validation of the model in future studies may reveal that adjustments and integration of further steps, such as regulatory devices for enzymes, competition for reductant or biosynthesis, or degradation and transport of antioxidants, may become necessary to address more detailed questions. The calculations of the model were based on the assumption that the reactions occurred in an isotropic, aqueous medium. However, the chloroplast stroma is viscous and the enzymes are not distributed uniformly but are locally concentrated on the thylakoid membranes (Ogawa et al., 1995). However, too little is known about the interactions and in situ concentrations of the multienzyme systems to include these factors at present into the model assumptions.

Under the present model running conditions, which had been chosen according to published data, the hypothetical chloroplast was well equipped with antioxidant enzymes and substrates. Significant accumulation of O₂^. and H₂O₂ above levels estimated for healthy tissues (Asada, 1997) were not obtained, even if conditions of severe oxidative stress were tested. Under the premises outlined above, the model data further suggest that the millimolar concentrations of Asc and GSH normally present in chloroplasts are not necessary for an efficient functioning of the Asc-GSH cycle. However, relatively high GSH concentrations were required as redox buffer when the availability of reductant (NADPH) was low. Furthermore, the model highlighted the contribution of antioxidants to the nonenzymatic O₂^. scavenging. This alternative route of O₂^. consumption resulted in additional H₂O₂ production with important implications when SOD activity was low. Via this pathway all subsequent redox couples of the Asc-GSH pathway were shifted toward a higher degree of oxidation. Therefore, one can predict that low SOD activities can partially be compensated by corresponding increases in antioxidants and APX, MDAR, and GR activities, respectively. Attention should be paid to fact that the reverse, compensation of low activities of the Asc-GSH-related enzymes by increased SOD activities, is not possible. The overall balance among the activities of the antioxidative enzymes is important to mediate stress tolerance. Metabolic modeling provides a tool to assess the consequences of changes in the antioxidative equipment for the compensation of oxidative stress.

According to the model calculations, the antioxidative enzymes -except DAR-were important factors controlling the concentrations of their respective substrates. DAR was dispensable because the "slow" chemical reduction of DHA by GSH was completely sufficient to recycle Asc. A function of DAR in plant tissues could be to exert an active control on the concentrations of DHA, which would not be possible in nonenzymatic interactions.

There is also uncertainty about DHA concentrations in plants. In apparent contrast to published data, the model SHAG-ENZ never reached high DHA concentrations. In plant leaves, especially in plants grown under field conditions, considerable fractions of the total Asc pool were oxidized (Schwanz et al., 1996; Polle, 1997; Noctor et al., 1998; Peltzer et al., 1999). It has been suspected that DHA was an extraction artifact (Morell et al., 1997). However, recovery analyses in my laboratory indicated that leaves often contained more DHA than could be explained by unspecific oxidation during extraction (e.g. Schwanz et al., 1996; Peltzer et al., 1999). Because the results of the present model clearly indicate that DHA accumulation is not possible as long as GSH is available, exploration of this point will be necessary. One possibility is that DHA accumulates only in compartments lacking an efficient Asc recycling system such as the apoplast. Another possibility is that further reactions involving Asc, which have not been included in the present model, may be more important for the ratio of DHA to Asc than anticipated. For example, Asc serves as an electron donator to PS II and as a substrate of violaxanthin de-epoxidase in the thylakoid lumen (Neubauer and Yamamoto, 1994; Mano et al., 1997). In both reactions MDA are formed, which will rapidly disproportionate to Asc and DHA at low pH in the thylakoid lumen. Whether these sources produce higher in situ concentrations of DHA than those predicted by the present model needs to be addressed in future studies. Until these points are clear, it will remain doubtful whether the ratio of DHA to Asc is a suitable indicator for oxidative stress.

The model calculations in SHAG-ENZ indicated that low APX activity will result in an accumulation of millimolar concentrations of H₂O₂ together with a highly reduced Asc pool. This is supported by experimental evidence because examples for stress-induced changes in H₂O₂ concentrations, which were not matched by a corresponding shift in the DHA/Asc balance, have been reported (Anderson et al., 1995; Menconi et al., 1995) These observations cast further doubt on the relevance of the redox ratio of DHA to Asc as a stress indicator.

If the model was run in the absence of MDAR activity, the concentration of MDA increased markedly, but the overall redox state of the Asc pool was hardly affected. This suggests, in the context of Asc recycling, that MDAR is apparently important to suppress MDA below potentially toxic levels but would not be required to keep Asc in its reduced state. For a further discussion of this point it would be useful to have information about the tissue concentrations of MDA and their toxicity. However, such data are not available. In an assumed absence of MDAR, the maintenance of GSH by GR activity would have been a prerequisite to keep the Asc pool reduced. However, in its presence, the rate of DHA formation inferred from the model was so low that this slip hypothetically could have been compensated by Asc synthesis (Davey et al., 1999). The rate of in situ DHA formation driven by O₂^. production may even be lower because of the ferredoxin-mediated path of MDA reduction additionally operating in chloroplasts (Miyake and Asada, 1994).

Based on the above considerations, it can be inferred that the connection between the Asc-related redox systems on the one hand and the GSH-related systems on the other hand is only weak. An independent regulation of the redox states of the two pools has been suggested earlier and is compatible with experimental observation (Schwanz and Polle, 2001). In contrast, other studies supported the idea that both antioxidant pools were closely connected (e.g. Foyer et al., 1995). The present model calculations indicate that GSH was always more susceptible to oxidation than Asc and that the major function of GR was to recycle GSH, which had been oxidized by nonenzymatic reactions.

Based on biochemical data, a metabolic model has been constructed as a tool for a theoretical understanding of the functioning of Asc- and GSH-related redox reactions in the chloroplasts. The next step will be to test the validity of the model for quantitative predictions. For this purpose it would be desirable if many laboratories would employ the model in different experiments. SHAG-ENZ can easily be expanded to include further redox interactions or other interactions; for example, competition for reductant in various stress scenarios. Because the interactions in the network of redox reactions are complex, SHAG-ENZ (or more advanced versions) will be useful to develop a working hypothesis as to how certain mutations or transgenes will respond to stress and where limits may be expected.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION CONSTRUCTION OF METABOLIC... RESULTS AND DISCUSSION MATERIALS AND METHODS LITERATURE CITED

Construction of Enzyme Models

The models were constructed with the software ModelMaker (Cherwell Science Publishing). The models were run on an IBM-compatible personal computer (660 MHz, 128 MB SDRAM, 20 GB) with computation time up to several hours.

To illustrate the basic features of the construction of an enzyme model, the simulation of APX activities is described in detail. APX consumes H₂O₂ for the production of water, which means in the language of the model that there is flow from compartment 1 containing H₂O₂ to compartment 2 containing the reduced product water (F1 in Fig. 12). At the same time APX consumes Asc in compartment 3 and delivers the oxidized product MDA to compartment 4 (Fig. 12). Therefore, compartments 3 and 4 are connected by the flow F2 (Fig. 12). The flow F2 must have the same velocity as F1, because it is driven by the same enzyme. To set F2 = F1, the flows have to be connected. This is achieved by linking F2 to F1 by the modeling tool "influence" (broken arrow). The oxidation rate of Asc (F2) is dependent on the availability of H₂O₂. Therefore, compartment 1 needs to linked with F2. This is achieved by connecting the two components by an "influence" (broken arrow). The consumption of H₂O₂ correspondingly is dependent on the availability of Asc. One might expect that a further "influence" connecting compartment 3 with F1 is required. Because F1 = F2, the APX model is already fully defined and the latter "influence" would be redundant. Redundant steps increase computation times and therefore should be avoided.

View larger version (27K): [in this window] [in a new window]   Figure 12.   Model of APX (A) and simulated enzymatic Asc and H2O2 consumption and MDA and water production.

The flow (F) corresponds to the enzyme activity and can be calculated by the Ping-Pong Bi Bi reaction mechanism (Bisswanger, 1994):

(5)

The changes of concentrations of the substrates and products are defined in compartments taking the stoichiometry of the reaction into account:

compartment 1 = [H₂O₂]/t = F1

compartment 2 = [H₂O]/t = +2 × F1 because two molecules of water are produced per one molecule of H₂O₂ consumed

compartment 3 = [Asc]/t = 2 × F2 because two molecules of Asc are consumed, and
compartment 4 = [MDA]/t = +2 × F2 and two molecules of MDA are produced per one molecule of H₂O₂ consumed.

Running the APX model with initial concentrations of 1 mM H₂O₂ and 10 mM Asc shows that H₂O₂ would be completely consumed after 48 ms, yielding 2 mM MDA and 2 mM water at the expense of 2 mM Asc (Fig. 12).

Definition of Programming Steps

Based on the principles outlined above for a reaction catalyzed by one enzyme, more complex models were constructed to simulate the redox reactions for purely nonenzymatic interactions of reactive oxygen species with antioxidants of the Asc-GSH systems (Fig.2) and for combined enzyme-catalyzed and nonenzymatic reactions of this system (Fig.3). The individual reactions were constructed as described above and "influences" were used to link reaction steps, which were dependent on each other.

The programming steps for model SHAG-CHEM have been compiled in Tables I and II and for model SHAG-ENZ in Tables IV and V. Both models also refer to a "list of parameters" (Table VI).