Computationally modeling mammalian succinate dehydrogenase kinetics identifies the origins and primary determinants of ROS production

Abstract

Succinate dehydrogenase (SDH) is an inner mitochondrial membrane protein complex that links the Krebs cycle to the electron transport system. It can produce significant amounts of superoxide (${\text{O}}_2^{\overline{·}}$) and hydrogen peroxide (H₂O₂); however, the precise mechanisms are unknown. This fact hinders the development of next-generation antioxidant therapies targeting mitochondria. To help address this problem, we developed a computational model to analyze and identify the kinetic mechanism of ${\text{O}}_2^{\overline{·}}$ and H₂O₂ production by SDH. Our model includes the major redox centers in the complex, namely FAD, three iron-sulfur clusters, and a transiently bound semiquinone. Oxidation state transitions involve a one- or two-electron redox reaction, each being thermodynamically constrained. Model parameters were simultaneously fit to many data sets using a variety of succinate oxidation and free radical production data. In the absence of respiratory chain inhibitors, model analysis revealed the 3Fe-4S iron-sulfur cluster as the primary ${\text{O}}_2^{\overline{·}}$ source. However, when the quinone reductase site is inhibited or the quinone pool is highly reduced, ${\text{O}}_2^{\overline{·}}$ is generated primarily by the FAD. In addition, H₂O₂ production is only significant when the enzyme is fully reduced, and fumarate is absent. Our simulations also reveal that the redox state of the quinone pool is the primary determinant of free radical production by SDH. In this study, we showed the importance of analyzing enzyme kinetics and associated side reactions in a consistent, quantitative, and biophysically detailed manner using a diverse set of experimental data to interpret and explain experimental observations from a unified perspective.

Succinate dehydrogenase (SDH) is a heterotetrametric protein attached to the mitochondrial inner membrane of eukaryotes and many bacteria. It is both a Krebs cycle enzyme and a member of the mitochondrial electron transport system (ETS) (1, 2). Similar to other ETS members, SDH houses several major redox centers. The flavoprotein subunit SDHA contains a flavin adenine dinucleotide (FAD) covalently bound to one of the active sites. The SDHB subunit contains three iron-sulfur clusters (ISCs): [2Fe-2S], [4Fe-4S], and [3Fe-4S]. In mammals, subunits C and D (SDHC and SDHD) contain a single transmembrane cytochrome b heme (3, 4). These subunits along with the interface of SDHB form the ubiquinone (Q) binding site (Q site) (4, 5). SDH couples the oxidation of succinate to fumarate with the reduction of Q to ubiquinol (QH₂). The oxidation of each succinate molecule provides two electrons that fully reduce the flavin (FAD to FADH₂). Electrons are subsequently shuttled through the ISCs one at a time. The first electron is transferred to the [2Fe-2S] iron-sulfur center from FADH₂, producing a flavin radical (FADH^•). When the [2Fe-2S] ISC becomes oxidized by downstream redox centers, the flavin radical passes the second electron to this ISC and becomes fully oxidized (FAD). Similarly, consecutive one-electron transfers from the ISCs to the Q reductase site reduce Q to QH₂. As a part of this process, a stable semiquinone (SQ) is formed (4, 6, 7). The overall catalytic reaction is as follows.

In mammalian mitochondria, 11 sites including SDH are known to produce reactive oxygen species (ROS) (8, 9). In this paper, ROS refers to superoxide (${\text{O}}_2^{\overline{·}}$) or hydrogen peroxide (H₂O₂) and will be explicitly defined where needed for clarity. ROS were historically considered toxic and inevitable byproducts of aerobic respiration (10). However, it now appreciated that in the physiological setting, ROS act as important and beneficial signaling molecules (11–13). That said, toxic levels of ROS do contribute to a milieu of pathological processes (14–19). Complex III is commonly argued as the dominate source of ROS under resting condition, whereas complex I is attributed as the primary source of ROS under many pathological conditions, including ischemia/reperfusion (I/R) injury. However, the role of complex II is less certain (20).

The most common implication of SDH in disease is its role in creating the environment favorable for excessive ROS production in I/R injury. Specifically, SDH reverses during ischemia due to excess fumarate produced by purine nucleotide breakdown (15). Succinate accumulation occurs because complex I continues forward electron transport, regenerating QH₂ needed to sustain the reverse reaction of complex II (21). In this setting, succinate replaces oxygen as the final electron acceptor. Succinate accumulates in the surrounding tissue until either fumarate is exhausted or reperfusion begins. During reperfusion, SDH metabolizes the available succinate to produce QH₂, leading to hyperreduction of the Q pool and hyperpolarization of the inner mitochondrial membrane (21). The combination of a highly reduced Q pool and a hyperpolarized membrane potential drives complex I to enter the so-called reverse electron transport (RET) state. In the RET state, complex I produces ROS at extremely high rates (21, 22). Note that it is more accurate to describe complex I during RET as entering a near-equilibrium state (14, 21, 23). In this state, the redox centers on complex I are maintained in a highly reduced state, which can lead to the generation of significant amounts of free radicals. As late reperfusion transitions to normoxia, fluxes through the ETS and TCA cycle return to normal and ROS levels subside (15, 16). Therefore, in the current paradigm, the primary role of SDH in I/R injury–induced oxidative stress is to create environmental factors that favor ROS production.

Recent studies have shown that SDH may significantly contribute to total mitochondrial ROS production in a variety of physiological and pathological settings (13, 17, 24–28). For instance, when complexes I and III are inhibited and the succinate concentration is low (∼100 μm), SDH produces ROS at high rates relative to complexes I and III (24, 29). In addition, skeletal muscle mitochondria respiring on succinate have been shown to produce high rates of ROS (30). Moreover, ROS from SDH have been recently shown to play key roles in promoting the pro-inflammatory phenotype in macrophages (27) and differentiation of helper T cells (28). Mutations that alter ROS production by SDH have also been implicated in some cancers (31–33). These new lines of evidence inevitably raise the question that SDH plays a more deterministic role in health and disease than previously thought. They also suggest that the enzyme is an overlooked target in developing therapies that target mitochondrial oxidative stress.

The renewed interest in SDH as a therapeutic target in mitigating mitochondrial oxidative stress necessitates a precise mechanistic understanding of how ROS is produced by the enzyme. Unfortunately, experimental studies on the origin of ROS production by SDH are inconclusive. In one study, the flavin site of SDH was reported to produce comparable amounts of ROS as the quinone-binding site of complex I in mitochondria respiring on fatty acid substrates (34). In a different study, Quinlan et al. (8, 24) demonstrated that, in mitochondria isolated from rat skeletal muscle respiring on succinate, the flavin site of SDH produces the most ROS at low levels of succinate or when QH₂ oxidation is inhibited. In a corroborating study using bovine submitochondrial particles (SMPs), Siebels and Dröse (35) showed that SDH generates ROS from the flavin site when its Q site is inhibited by atpenin. However, Paraganama et al. (36) have argued that the Q site can produce comparable amount of ROS as the flavin site. Evidence of an additional ROS production site, the ISC near the Q site, was recently put forth in a study by Grivennikova et al. (37). Whereas these studies all agree that the flavin site can generate a significant amount of ROS, they differ on the contribution by the Q site. Each study measured ROS production using the Amplex UltraRed assay in combination with site-specific inhibitors. (8, 13, 24, 34–36, 38); however, this approach does not uniquely identify the mechanisms or precise conditions for ROS production by SDH. As such, the mechanisms of ROS production by SDH are an ongoing topic of debate.

Nevertheless, a unified mechanism may underlie the results from these different studies. To explore this possibility, computational modeling is an essential tool. With computational modeling, it is possible to parse the intricate interactions among the various components of a complex biological system, such as an enzyme. It also enables further insight into how these components work together and respond to environmental factors. Motivated to elucidate the precise mechanisms of ROS production by SDH under physiological (11) and pathological conditions (15), we herein developed a comprehensive computational model of SDH kinetics and ROS production. Adopting a similar approach to our previous studies (14, 21, 23), the model framework is based on fundamental laws of thermodynamics and involves a rigorous model calibration process. Specifically, the model parameters are adjusted until the model outputs, such as succinate oxidation rates or total ROS production, are consistent with the experimental data. This iterative process results in a model that is not only thermodynamically consistent but also capable of reproducing the experimental data.

Our analysis of the model presented herein reveals that although the FAD site does produce ROS, the primary source is the [3Fe-4S] ISC under normal physiological conditions. However, the FAD site is the dominant site and produces significant levels of H₂O₂ when the Q reductase site of SDH is inhibited by atpenin or the respiratory chain downstream of SDH is blocked. Moreover, the model shows that the inhibitory effects of atpenin are not simply attributable to competitive binding at the Q site but also include allosteric effects that modulate the enzyme catalytic turnover. Last, the model can be integrated into large-scale models of metabolism and used to explore the role of SDH in bioenergetics and free radical homeostasis at the organelle, cell, and tissue levels.

Results

Details on model construction are given under “Materials and methods” and briefly summarized here. A brief overview of the model development, fitting, and corroboration procedure is given in Fig. S1. The model is constructed based on structural, thermodynamic, and kinetic data relevant to the enzyme (Fig. 1A). Each partial reaction used for model construction is shown in Fig. 1B. Succinate oxidation presents a major route of entry for electrons in the SDH complex. Electrons entering the FAD site, however, can be blocked by other non-SDH dicarboxylate substrates that are present in the mitochondrial matrix, including malonate, malate, and oxaloacetate. In addition, oxaloacetate causes the enzyme to enter an inactive state (39). Quinol oxidation at the Q_p site is another way by which SDH is reduced. This manner of reduction can be inhibited by atpenins, potent competitive inhibitors of quinone binding at the Q_p site. Of the atpenins, atpenin A5 is the most specific and is referred to in this study as atpenin for simplicity. Other inhibitors acting upstream or downstream of SDH can also influence the enzyme's oxidation state. Some of the most common inhibitors used in experimental settings include myxothiazol, stigmatellin, and rotenone. Myxothiazol and stigmatellin inhibit electron flow downstream, whereas rotenone inhibits electron flow upstream of the enzyme complex.

Figure 1.

Overview of the SDH model. A, the ribbon diagram shows the four subunits along with the major redox centers of SDH. The SDHA subunit constitutes a covalently bound FAD in the dicarboxylate binding site, where succinate is oxidized to fumarate to generate the fully reduced flavin. The SDHB subunit contains three iron-sulfur clusters ([2Fe-2S], [4Fe-4S], and [3Fe-4S]) that shuttle electrons one at a time to produce QH₂ at the proximal Q site (Q_p) and the heme group at the interface between the SDHC and SDHD subunits. A distal quinone-binding site has been proposed (Q_d). B, the redox state transition diagram depicts the possible redox states (E_i) of the enzyme in which i is the redox state that corresponds to the total number of electrons residing on the enzyme. The transition rates among these redox states are denoted k_ij (for details, see the supporting material). Relevant redox reactions that underlie redox state transitions are either one- or two-electron–mediated. C, at each enzyme oxidation state, the percentage of each redox center that is in a reduced state is determined. A fully oxidized Q pool and pH 7 were used to calculate the percentages. The SDH ribbon diagram was generated from the crystal structure by Sun et al. (3) using PyMOL. *, in addition to competing with succinate at the dicarboxylate binding site, oxaloacetate also causes the enzyme to resume an inactive conformation.

Under normal conditions, succinate oxidation is coupled to quinone reduction and mediated by one- or two-electron reactions (Fig. 1B). As these reactions occur, the enzyme transitions among different oxidation states (E_i) at specific rates (k_ij) determined by substrate/product concentrations and environmental conditions. Once electrons enter the complex, they rapidly equilibrate to the lowest-energy state determined by the redox center midpoint potentials (Fig. 1C). However, when redox centers on SDH capable of interacting with oxygen become reduced, ROS are formed as side reactions. To gain insight into how these reactions govern SDH kinetics and ROS production, a mathematical model encompassing all the relevant components of the enzyme was constructed, calibrated, and corroborated.

The data used in model fitting and validation are summarized in Table 1 (35, 37, 40–42). A dot plot of data collected in-house is presented in Fig. S2. In selecting experimental data to calibrate the model, several key factors were considered. First, the data come from only mammalian sources. This criterion allows for a more consistent data set to construct a model that can be integrated into large-scale metabolic network simulations relevant to mammals. Second, a wide range of experimental conditions are necessary to eliminate biases inherent to experimental conditions so that the model can account for different experimental results. As such, we chose data sets derived from purified enzyme, submitochondrial particles, and permeabilized mitochondria. Third, the experimental protocols must contain sufficient information for model simulations in order to minimize the number of adjustable parameters otherwise needed to simulate different environmental conditions. For example, we did not choose data obtained from intact mitochondria to avoid confounding issues such as the activity of ROS-scavenging pathways and metabolite transport. Fourth, the data must comprehensively address the distinct kinetic and ROS production behaviors of SDH. Considering all these criteria, data on bothsuccinate oxidation and ROS production rates are included. Altogether, the studies listed in Table 1 yield a comprehensive and detailed data set capable of supporting the parameterization of a biophysically detailed SDH kinetic model.

Table 1.

Experimental data used for model fitting

Species and enzyme origin	Electron acceptor	Kinetic data	ROS data	pH	Temperature	Scaling factors	Reference
					°C
Pig heart enzyme	PMS	Yes	No	7.8	25	1.0	Zeijlemaker et al. (40)
Bovine heart enzyme	TMPD	Yes	No	6.5–9	22	0.82	Vinogradov et al. (41)
Bovine heart SMP	DQ, Q10a	Yes	No	7.4	32	4.0	Jones and Hirst (42)
Bovine heart SMP	Q10, PMS	Yes	Yes	7.5	30	0.56	Grivennikova et al. (37)
Bovine heart SMP	Q10	Yes	Yes	7.2–8	37	3.7	Siebels and Dröse (35)
Guinea pig heart isolated mitochondria	DQ, Q10	Yes	Yes	7.2	37	3.0	This study

^aQ₁₀, ubiquinone.

The fixed model parameters consist of many thermodynamic parameters obtained from the literature. They include midpoint potentials and pK_a values and are given in Table S2. The adjustable model parameters consist of forward rate constants of product formation and ROS production rates; the dissociation constants for substrates, products, and inhibitors; and other factors necessary to properly simulate the environmental conditions (Table 2).

Table 2.

Model adjustable parameters

Parameter	Definition	Value	Sensitivity	Rank
$k_{f_0}^{\text{SUC}}$	Rate constant for succinate oxidation	52.9 s−1	0.532	6
$k_{f_0}^{{\text{QH}}_2}$	Rate constant for QH2 production	2.48 × 107 s−1	0.162	13
$K_{\text{SUC}}$	Succinate dissociation constant	355 μm	0.336	9
$K_{\text{FUM}}$	Fumarate dissociation constant	1.0 mm	0.105	14
$K_{\text{Q}}$	Quinone dissociation constant	0.29 nm	0.039	19
$K_{{\text{QH}}_2}$	Quinol dissociation constant	0.19 nm	0.079	17
$k_f^{\text{P}}$	Rate constant for phenazine reduction	7.47 × 109 m−1 s−1	0.470	7
$k_f^{\text{TMPD}}$	Rate constant for TMPD reduction	8.29 × 109 m−1 s−1	0.560	4
$K_{\text{H}}$	H+ dissociation constant at Qp site	170 nm	0.098	15
$K_{\text{MALO}}$	Malonate dissociation constant	14.8 μm	0.559	5
$K_{\text{MAL}}$	Malate dissociation constant	294 μm	0.724	2
$K_{\text{OAA}}$	Oxaloacetate dissociation constant	0.822 μm	0.620	3
$K_{\text{Ap}}$	Atpenin dissociation constant at Qp site	1.67 × 10−4 pm	0.377	8
$K_{\text{Ad}}$	Atpenin dissociation constant at Qd site	68.3 nm	0.066	18
${\text{β}}_{\text{atpenin}}$	Atpenin-inhibitory factor	14.6	0.170	12
$E_m^{\text{Q}/\text{Q}\overline{{}^{•}}}$	Q/${\text{Q}}^{\overline{·}}$ midpoint potential	284 mV	1.72	1
$k_{f_0}^{{\text{FADH}}^{•}}$	Rate constant for ${\text{O}}_2^{\overline{·}}$ production by FADH•	8.15 × 105 m−1 s−1	0.281	11
$k_{f_0}^{3\text{Fe}-4\text{S}}$	Rate constant for ${\text{O}}_2^{\overline{·}}$ production by [3Fe-4S]	6.68 × 109 m−1 s−1	0.300	10
$k_{f_0}^{{\text{FADH}}_2}$	Rate constant for H2O2 production by FADH2	2.61 × 103 m−1 s−1	0.075	17

All the adjustable parameters are in a physiologically suitable range, and nearly all are identifiable. Identifiable parameters are highly sensitive and independent of other parameters. A small change in the value of a sensitive parameter causes a large change in a model output. The opposite is true for an insensitive parameter. The normalized sensitivity coefficients in Table 2 give information about the contribution of each parameter to the model output. The normalized sensitivity coefficients are computed using Equation S98. Correlation coefficients are presented in Fig. S3 as a heat map. The correlation coefficients provide information on the degree the model parameters are linearly dependent with each other in a local region of parameter space. The residual analysis given in Fig. S4 shows that the residuals follow a normal distribution, which indicates that there are no systematic biases in the model simulations.

Whereas the model consists of 19 adjustable parameters to simulate the data, they are the minimum number required to simulate all the data in a thermodynamically consistent manner. Each parameter governs the model's biochemical and biophysical behavior under a large range of experimental conditions. That said, some parameter correlation is unavoidable due to the limited amount of data available for each simulated reaction. For example, the rate constant for QH₂ production, the quinone/semiquinone midpoint potential, and the atpenin dissociation constant at the proximal binding site are the only parameters strongly correlated with each other (>0.8). To decorrelate these parameters, additional measurements of quinone-binding affinities and their modulation by Q-site inhibitors are required. The top five most sensitive parameters are associated with the semiquinone reduction potential, dicarboxylate inhibition constants (malonate, malate, and oxaloacetate), and TMPD reduction rate constant. Not surprisingly, some parameters associated with the quinone-binding site are among the least sensitive. We designed and ran additional experiments to perturb the Q pool described below to improve the identifiability of these parameters, but they only led to a marginal increase in identifiability. This is because quantitative measurements of the quinone and quinol concentrations using kinetic assays are required to significantly improve their identifiability. A novel MS-based method to collect end point measurements of the Q pool was recently developed (43), but it is extremely resource-intensive and cannot capture dynamic changes. Unfortunately, there does not exist a simple and straightforward approach to accurately measure the dynamic changes of these metabolites.

Model simulations of succinate oxidation rates under different conditions are faithful to experimental data

Model simulations and experimental data of succinate oxidation kinetics using PMS and TMPD as electron acceptors are shown in Fig. 2 (37, 40, 41). Overall, the model is able to simulate experimental data very well. For simplicity, the reduction of PMS and TMPD is assumed to obey second-order kinetics (i.e. there is no stable ES complex formed). For details concerning the reduction kinetics, see Equations S75–S88. As seen in Fig. 2, the succinate oxidation rates when either PMS or TPMD is the electron acceptor are similar for a given concentration. Thus, the fitted second-order rate constants given in Table 2 are similar in magnitude. The model is also able to reproduce pH-dependent succinate oxidation rates. Specifically, at pH >8, the reaction becomes independent of pH and precipitously drops in a manner dependent on both pH and electron acceptor concentration. When the acceptor concentration is high, the rate does not drop until the pH falls below 7.5; however, when the acceptor concentration is low, the rate begins to drop near pH 8. This is because higher concentrations of electron acceptors compensate for lower concentrations of the enzyme in the right protonation state. This pH effect is ascribed to an active-site sulfhydryl group with a pK_a around 7 near the flavoprotein that is believed to be required for succinate oxidation (44, 45). In the model, these results are obtained using an explicit pH dependence for succinate oxidation at the flavin site as shown in Equation S13.

Figure 2.

Succinate oxidation rates at varied concentrations of different electron acceptors. Model simulations (lines) are compared with experimental data (open circles) from Refs. 37 and 40. A and B, the effect of varying succinate and PMS concentrations on succinate oxidation rates. The PMS concentrations are 67 µm (blue), 100 µm (red), 167 µm (yellow), 300 µm (purple), and 2000 µm (green) in A and 50 µm (blue), 200 µm (red), and 2000 µm (yellow) in B. For B, the malonate concentration was 50 μm. C, model simulations of the effect of varying succinate and TMPD concentrations compared with the data from Ref. 41. The TMPD concentrations are 50 µm (blue), 66 µm (red), 100 µm (yellow), and 333 µm (purple). Malonate was present at 100 μm. D, model simulations of the effect of varying pH and TMPD concentrations on succinate oxidation rates compared with the data from Ref. 41. The concentrations of TMPD are 50 µm (blue), 66 µm (red), 100 µm (yellow), 200 µm (purple), and 1000 µm (green). The succinate concentration was fixed at 100 μm.

In a series of titration experiments, the effects of substrates and inhibitors at the FAD and Q sites on succinate oxidation are shown in Fig. 3. Data from Jones and Hirst (42) are shown in Fig. 3 (A–C) (top row), and data from Siebels and Dröse (35) are shown in Fig. 3 (D–F) (bottom row). Both data sets are obtained using bovine heart SMP but differ in the enzyme and substrate concentrations. The data from Jones and Hirst (42) were obtained using 0.30 µg/ml complex II, 5 mm succinate, and 100 μm decylubiquinone. In Siebels and Dröse (35), SMPs were present at 0.12 mg/ml with 100 μm succinate (35). Atpenin A5 titration leads to a significant drop in succinate oxidation rates in both data sets. However, the atpenin-titration results are quantitatively different. This is likely due to the different enzyme concentrations and experimental conditions used. For example, at an atpenin concentration of 25 nm, succinate oxidation is 93% inhibited in the Jones and Hirst (42) data set (Fig. 3B), but at 30 nm, it is only inhibited by 65% in the Siebels and Dröse (35) data set (Fig. 3D). To fit these disparities, the model fitting results in a compromise where it underestimates the atpenin-dependent inhibition for the Jones and Hirst (42) data set and overestimates it for the Siebels and Dröse (35) data set. Without any additional information, these experimental discrepancies cannot be reconciled. The atpenin inhibition data were modeled by assuming that atpenin binds to the Q_p site and prevents Q or QH₂ binding. In addition to the Q_p site, atpenin at high concentrations has been shown to occupy the Q_d site, also known as the noncanonical Q site (5, 46). Atpenin binding to the Q_d site has been speculated to affect succinate oxidation. This mechanism was found necessary to include in the model to obtain the best fits to the data.

Figure 3.

Succinate oxidation kinetics in the presence of SDH inhibitors using bovine heart SMP. Model simulations (lines) are compared with experimental data (open circles). Experimental data are from Jones and Hirst (42) (A–C) and Siebels and Dröse (35) (D–F). Data from Jones and Hirst (42) were obtained using 30 µg/ml solubilized membranes, 5 mm succinate, and 100 μm decylubiquinone. A, succinate oxidation rate saturates near 5 mm succinate with an apparent K_m of 2 mm. B and C, relative succinate oxidation rates are significantly inhibited with increasing concentrations of atpenin (0–100 nm) and malonate (0–5 mm). E and F, data from Siebels and Dröse (35) were obtained using 0.12 mg/ml SMP and 100 μm succinate. Relative succinate oxidation rates are significantly inhibited with increasing concentrations of atpenin (0–250 nm), malate (0–10 mm), and oxaloacetate (0–30 μm).

Titrating the succinate competitive inhibitors malonate, malate, and oxaloacetate also decreases succinate oxidation rates (Fig. 3, C–F). The concentration required to inhibit succinate oxidase is different for each inhibitor. Oxaloacetate is the most potent SDH inhibitor, followed by malonate and malate. These results coincide with the fitted dissociation constants shown in Table 1. In the presence of these dicarboxylates, fewer FAD sites are available for succinate binding, and thus enzyme turnover is decreased.

Model simulations are consistent with experimental ROS production rates

ROS production by SDH displays a biphasic succinate dependence, as shown in Fig. 4. At low concentrations, ROS production is stimulated; however, ROS production is suppressed at higher concentrations. The model was calibrated using data sets from two independent studies. In the experiments by Grivennikova et al. (37), peak ROS production occurs at around 50 μm succinate (Fig. 4A). In Siebels and Dröse (35), the peak is shifted to ∼150 μm (Fig. 4B). The primary difference between these two studies is the presence of myxothiazol in Grivennikova et al. (37) and atpenin in Siebels and Dröse (35). Whereas atpenin competitively inhibits QH₂ binding at the Q_p site of SDH, myxothiazol competitively inhibits QH₂ binding to complex III at the heme b_L site. The model simulates ROS production rates reported in both studies using the same model framework by exploring the distinct effects of myxothiazol and atpenin. The model predicts that the FAD site is the primary site of ROS under the conditions used in both studies. However, the major ROS species is different between studies. In the Grivennikova et al. (37) simulation, H₂O₂ originated from the fully reduced flavin, FADH₂, is the primary ROS species (Fig. 4). When myxothiazol is present, the Q pool is nearly fully reduced and capable of reducing SDH via QH₂ oxidation at the Q_p site. The result is that a higher proportion of the enzyme is reduced and capable of producing ROS. In contrast, in the Siebels and Dröse (35) simulation, ${\text{O}}_2^{\overline{·}}$ derived from the flavin radical is the primary ROS species, followed by H₂O₂ from the fully reduced flavin (Fig. 4D). Model simulations reveal that this is primarily because the FAD site is not as reduced as compared with when atpenin is absent. The predominant form of the flavin under this condition is the flavin radical, which only produces ${\text{O}}_2^{\overline{·}}$. The shift of the peak succinate concentration for maximal ROS production is also explained by the different effects by these inhibitors on the enzyme oxidation state. When atpenin is present, the only reductant for SDH is succinate. Therefore, it takes a higher concentration of succinate to reduce enough of the enzyme to reach peak ROS production rates, which shifts the succinate titration curve to the right in Siebels and Dröse (35). In addition, as stated above, succinate also blocks ROS production from the FAD site, so the ability of succinate to drive ROS production is limited.

Figure 4.

Maximum ROS produced by SDH occurs at submillimolar concentrations of succinate. Model simulations (lines) are compared with experimental data (open circles) from bovine heart SMP. A, experimental $J_{{\text{H}}_2}{}_{{\text{O}}_2}$ values were obtained in the presence of 10 µm rotenone, 1.6 μm myxothiazol, 2 units/ml HRP, and 6 units/ml bovine SOD (37). B, experimental $J_{{\text{H}}_2}{}_{{\text{O}}_2}$ values were obtained in the presence of 50 nm atpenin (35). C, model simulations of site-specific ROS production rates for the conditions shown in A. C, model simulations of site-specific ROS production rates for the conditions shown in B. In both C and D, rates are given with respect to the same electron equivalents as in A and B.

The difference in total and site-specific ROS production rates in the presence of stigmatellin or atpenin as the succinate concentration is increased is shown in Fig. 5. Stigmatellin competitively inhibits QH₂ binding to complex III near the Rieske ISP site. Similar to when myxothiazol is present, the Q pool is fully reduced with stigmatellin, and quinol oxidation at the Q_p site serves as an additional source of electrons for free radical production. So turnover at both electron input and output (reverse) of the enzyme complex results in the highest ROS production rates. In the presence of either inhibitor, the FAD is the major source of ROS, and ${\text{O}}_2^{\overline{·}}$ from the FAD site at low succinate concentrations is highest among ROS species. As the succinate concentration increases, H₂O₂ production from the FAD site exceeds the ${\text{O}}_2^{\overline{·}}$ rate from this site. But as the succinate concentration further increases, the ROS production rate from the FAD site decreases due to succinate binding to the FAD, making it unavailable to interact with oxygen. However, when atpenin is present, electron transfer from the ISC to quinone or oxygen is blocked (46, 47). Therefore, ${\text{O}}_2^{\overline{·}}$ production from the FAD remains the dominate source of ROS, and the ISC produces no ROS when atpenin is present (Fig. 5C). In addition, the enzyme is more oxidized compared with when stigmatellin is present, so the amount of enzyme with a fully reduced flavin is lower. Thus, the rate of H₂O₂ production is lower.

Figure 5.

Succinate-dependent ROS production of SMPs in the presence of stigmatellin or atpenin. A, model simulations (lines) are compared with experimental data (open circles) from Siebels and Dröse (35). B, site-specific ROS production rates when 1 μm stigmatellin is present. C, site-specific ROS production rates when 250 nm atpenin is present. Site-specific rates are given with respect to the same electron equivalents as in A.

The effects of titrating atpenin and non-SDH dicarboxylate substrates on ROS production rates are presented in Fig. 6. Increasing atpenin concentrations lead to an increase in the ROS production rate, which reaches a maximum at 250 nm. In the presence of 250 nm atpenin, increasing malate or oxaloacetate concentration causes the ROS production rate to significantly decrease. Malate concentrations in the millimolar range lead to a significant drop in ROS production rates (Fig. 6B). Oxaloacetate is much more potent and completely inhibits ROS production after 20 μm (Fig. 6C). These data further corroborate that the availability of the FAD site for oxygen binding is necessary for ROS formation by complex II. As more FAD sites are occupied by non-SDH dicarboxylate substrates, less ROS is produced despite the optimal atpenin concentration. These results are supported by prior work demonstrating that ROS are produced from the FAD site when the dicarboxylate site is unoccupied and the enzyme is reduced (13, 34). As these TCA cycle dicarboxylates regulate SDH turnover, it is fortunate that they also do not lead to excess ROS production like the Q site inhibitor atpenin. This would necessarily lead to oxidative stress when these dicarboxylates accumulate under conditions such as I/R injury. However, if electron exit is blocked at the FAD site while the enzyme is maintained in a highly reduced state from a reduced Q pool, ROS from the [3Fe-4S] ISC can produce significant amounts of ROS, as shown by Quinlan et al. (24).

Figure 6.

Effects of titrating atpenin and non-SDH dicarboxylate substrates on ROS production by complex II. Model simulations (lines) are compared with experimental data (open circles) for each panel (35). Experimental data were obtained from bovine heart SMP. A, rate of H₂O₂ production is increased at increasing concentrations of atpenin (0–250 nm), a potent and specific inhibitor of quinone reductase activity. B and C, in the presence of 250 nm atpenin, ROS production rates are decreased as the concentrations of malate and oxaloacetate are increased. Malate and oxaloacetate compete with succinate at the FAD-binding site.

Titrating fumarate in the presence of varying succinate concentrations results in a drop in ${\text{O}}_2^{\overline{·}}$ and total ROS production rates, as shown in Fig. 7. When atpenin was absent from the experiments, it was assumed that the quinone/quinol redox couple was in equilibrium with the fumarate/succinate couple. Therefore, the equilibrium relationship between the free energies associated with the fumarate/succinate and quinone/quinol couples was used to calculate the quinone and quinol concentrations. When aptenin was present, the Q pool redox state predictor functions (Equation S1) were used to calculate the quinone and quinol concentrations. At a given fumarate/succinate ratio, the ROS production rate is higher in the presence of complex III inhibitors alone compared with when atpenin is included. Without atpenin present, significant turnover at the Q_p site of complex II, in addition to turnover at the FAD site, leads to a more reduced FAD fraction and hence more ROS production. Whereas atpenin stimulates ROS production from the FAD site, the rate is one-third to one-half of that with stigmatellin alone. This difference highlights the importance of the Q_p site as a source of electrons via quinol oxidation for the ROS production at the FAD site. Whereas the [3Fe-4S] ISC and FAD sites can all produce ROS, both experimental data and model simulations suggest that most of ROS comes from the reduced flavin under these conditions. In addition, the model simulations show that H₂O₂ production rates are significantly suppressed in the presence of fumarate. These findings further corroborate that a reduced flavin unobstructed by metabolites and other molecules is required to produce significant amounts of ROS.

Figure 7.

Effects of varying fumarate/succinate ratios on atpenin and complex III inhibitor induced ROS production. Model simulations (lines) are compared with experimental data (open circles). A, data were obtained from Grivennikova et al. (37). Bovine heart SMPs (0.1 mg/ml) were prepared in the presence of 1.6 μm myxothiazol and 10 μm rotenone. Atpenin was added to the final concentration of 1 μm. B and C, data are from Siebels and Dröse (35). Bovine heart SMPs (0.12 mg/ml) were prepared without myxothiazol or rotenone. B, stigmatellin was added to the final concentration of 1 μm. C, atpenin was added to the final concentration of 50 nm. In all conditions, increasing the fumarate concentration led to a decrease in ROS production rates. D–F, site-specific ROS production rates corresponding to their respective panels above. Site-specific rates are given with respect to the same electron equivalents as in the above panels.

The model simulations show distinct pH-dependent ROS profiles for stigmatellin and atpenin as shown in Fig. 8. ROS production from the FAD site was best fit when the FAD radical or fully reduced FAD cofactor was deprotonated as shown in Equations S15 and S17. In the presence of stigmatellin, both ROS species increase as pH is increased (Fig. 8, A and C). This is due to the pH-dependent partial reactions occurring at FAD and Q_p sites of the complex. As pH becomes more alkaline, both succinate and quinol oxidation become more favorable from a mass action perspective. As a result, the enzyme oxidation status becomes more reduced, and the fraction of reduced FAD is significantly elevated. In contrast, this rise in ROS production as the conditions become more alkaline is not observed when atpenin is present (Fig. 8, B and D). With atpenin, quinol oxidation at the Q_p site is inhibited. FAD reduction arises only from succinate oxidation, which does not reduce the FAD as much as when quinol oxidation was also allowed to contribute. Therefore, ROS production is overall lower under this condition despite the thermodynamic favorability of ROS production from the FAD site in alkaline conditions.

Figure 8.

The effects of pH on ROS production rates in the presence of inhibitors. A, the stigmatellin concentration was 1 μm. In B, the atpenin concentration was 250 nm. Model simulations (lines) are compared with experimental data (open circles) from Siebels and Dröse (35). Experimental data show ${\text{O}}_2^{\overline{·}}$ in blue and total ROS (H₂O₂ + ${\text{O}}_2^{\overline{·}}$) in orange using bovine heart SMP. Malonate of 1.5 mm was added in both experiments. As discussed by Grivennkova et al. (37), we assumed the presence of a small but significant amount of contaminating superoxide dismutase in these experiments. Based on model analysis, this amounts to an approximate 65% underestimation of the superoxide production rate in the Siebels and Dröse (35) experiments. This factor was explicitly included when simulating these data. C and D, site-specific ROS production rates corresponding to their respective panels above. Site-specific rates are given with respect to the same electron equivalents as in above panels.

Model testing and corroboration

The experimental data used above to constrain the SDH model lacked sufficient perturbations to the endogenous Q pool to adequately identify some of the Q site–related parameters. Therefore, we designed some experiments using uninhibited guinea pig cardiac SDH and the quinone analog decylubiquinone (DQ), as shown in Fig. 9. Decylubiquinone was used to manipulate the endogenous Q pool redox levels. In these experiments, we first quantified ROS production by SDH at different succinate concentrations as done in prior studies (Fig. 9A). Our results show that ROS production from cardiac guinea pig SDH possesses the same succinate dependence as SDH from other rodents. We then chose two succinate concentrations, 200 μm and 5 mm, to use in the DQ titration experiments to perturb the endogenous Q pool (Fig. 9B). At the lower succinate concentration, adding DQ resulted in a dramatic drop in ROS production by SDH. This is due to a decrease in both the succinate and QH₂ concentrations and an increase in fumarate and Q concentrations catalyzed by SDH. The result was predicted by the model. The decreased ROS in the DQ titration experiment at 200 μm succinate led to the prediction of a similar trend at 5 mm succinate. In contrast, the addition of DQ when the succinate concentration is higher (5 mm) leads to a surprising increase in ROS production. In the absence of SDH, the addition of DQ leads to zero ROS as expected. Therefore, the increase in ROS when SDH is present is due to SDH-catalyzed production of DQH₂ and the near-instantaneous reaction of DQH₂ with oxygen in the buffer. This rapid reaction was confirmed by adding DQH₂ to the assay buffer in the absence of SDH. When this was done, all Amplex UltraRed was immediately converted to resorufin, as indicated by the rapid color change of the ROS reporter. Thus, the increase in ROS at high succinate concentrations when DQ is titrated is enzyme-mediated. This rapid reduction of DQ by succinate is facilitated by SDH. This result underscores the importance in considering the impact of environmental changes when interpreting ROS data with DQ present.

Figure 9.

Decylubiquinone can directly reduce oxygen and amplify resorufin fluorescence. A, succinate-dependent SDH ROS production kinetics from freeze-thawed guinea pig cardiac mitochondria show the same trend as rat SDH. In these experiments, the guinea pig cardiac mitochondria were inhibited with 4 μm rotenone and 2 μm myxothiazol. For more details, see “Materials and methods.” B, net hydrogen peroxide emission rates in DQ titration experiments reveal that DQ decreases ROS at low succinate concentrations (200 μm) and increases ROS at high succinate concentrations (5 mm). The model quantitatively predicted this drop in ROS; however, an additional parameter, $k_{{\text{O}}_2{\text{,DQH}}_2}$, was required to fit the increase in ROS at high succinate concentrations. The value of this parameter in these simulations was 0.0022 m⁻¹ s⁻¹. C, model analysis reveals that for the low-succinate condition, DQH₂-derived ROS is negligible, but it becomes significant when the concentration of succinate is high. Shown are the experimental means (open circles) and S.D. (error bars) from at least three biological replicates. Model simulations are represented by the solid lines. The ODE system used to simulate the concentration dynamics is given in Equations S97–S105 in the supporting material.

These experiments were then modeled using the SDH model presented above and a small ODE model given in the supporting material (see Equations S97–S103). Results from this simulation are shown in Fig. 9C. The ODE model was necessary to simulate the dynamics of DQ, O₂ and ROS species. The model was able to reproduce both the succinate titration and DQ titration data at the 200 μm succinate concentration without any additional parameters other than a scaling factor to account for differences in SDH activity across species. However, a new parameter, $k_{{\text{O}}_2{\text{,DQH}}_2}$ was required to simulate the DQ titration experiments at the 5 mm succinate concentration. This parameter is a lumped rate constant that incorporates the rapid SDH-mediated reaction between succinate and DQ to form DQH₂ and the subsequent diffusion-limited reaction between DQH₂ and O₂. The model simulations of this process reveal that the impact of DQH₂-mediated ROS production is negligible at the lower succinate concentration. However, at the higher succinate level, the majority of ROS detected by the reporter assay is from DQH₂. For example, at 5 mm succinate concentration, DQH₂-derived ROS when DQ is 200 μm accounts for over half of the total experimentally measured ROS. Therefore, our model analysis reveals the importance of accounting for DQ-mediated side reactions when a quinone analog is employed.

The model was also corroborated using the experimental data from Grivennikova et al. (48). In this study, ROS production rates from SMPs were measured with a variety of substrates, inhibitors, and oxygen concentrations. From these data, the SDH-specific data were selected and used to test model validity. As shown in Fig. 10, the model reproduces the experimental data with high fidelity without tuning the adjustable parameter set. It reproduces the linear relationship between ROS production and oxygen concentration in Fig. 10A. In addition, the model matches the kinetic rate of succinate oxidase under the conditions described by Grivennikova et al. (48). The quinol concentration and SDH oxidation state fractions are shown as predictions during the conditions in Fig. 10, B and C, respectively. Furthermore, the contribution of SDH to the total ROS detected during this experiment is shown in Fig. 10D. Comparing this value to the total value Grivennikova et al. (48) measured during this experiment reveals that SDH contributes ∼1% to the total ROS produced by SMPs during their experimental protocol.

Figure 10.

Model corroboration of ROS production and SDH kinetics. The data are from Grivennikova et al. (48). The enzyme concentration for these simulations was 2 nm in A and 22 nm in B–D. The ODE system used to simulate oxygen concentration dynamics is given in Equations S97–S105 in the supporting material.

Together, model analysis demonstrates that ROS production by SDH occurs in both the “forward” and “reverse” modes. It does not matter where the electrons come from: either succinate in the forward mode or QH₂ in the reverse mode. To quantify the amounts of ROS produced by the major redox centers when SDH works in the reverse direction, a simulation was performed in which the Q pool redox status determines the enzyme oxidation state distribution (Fig. 11). The model predicts that, despite acting on SDH at different sites, atpenin (1 μm) and malonate (0.5 mm) lead to nearly identical ROS production rates by the enzyme (Fig. 11A). This result is corroborated by a prior study from the Brand group (24). However, site-specific ROS production rates are distinct. When the Q_p site is inhibited, ${\text{O}}_2^{\overline{·}}$ derived from the flavin radical is the primary source of ROS (Fig. 11B). Superoxide derived from the [3Fe-4S] ISC and H₂O₂ originated from the fully reduced flavin are negligible. When the flavin site is inhibited, most of the total ROS originates from the [3Fe-4S] ISC (Fig. 11C). The predictions are consistent with the inhibitory mechanisms associated with atpenin and malonate. Because malonate occupies the flavin, it prevents electrons from leaving the enzyme by which the [3Fe-4S] ISC becomes reduced and primed to participate in a one-electron redox reaction with oxygen. Therefore, the model suggests that both the flavin and [3Fe-4S] ISC can be a significant source of ROS and that environmental factors dictate which one is the primary ROS contributor.

Figure 11.

Model prediction of site-specific ROS production when the enzyme oxidation state is determined by the Q pool redox state. A, inhibiting SDH at either the flavin or Q_p site results in an ∼90% reduction in total ROS production. B, the primary enzyme-produced ROS is superoxide originating from the flavin radical when SDH is inhibited at the Q_p site. C, in the presence of 0.5 mm malonate, most of the enzyme ROS is from the [3Fe-4S] ISC, with a significant fraction originating from the FAD site when the Q pool is highly reduced. Under both conditions, hydrogen peroxide originating from the fully reduced flavin is negligible.

To test the model's ability to simulate ROS production from intact mitochondria, it was integrated into a recent model of oxidative phosphorylation (49). The integrated model was then used to simulate succinate-dependent leak-state and ADP-stimulated respiration and ROS emission reported in an earlier study (22). These results are given in Table 3 and demonstrate that the model simulations quantitatively match the experimental measurements. The consistency between the model simulations and experimental results upon integration highlights the importance of constructing biophysically accurate and thermodynamically consistent enzyme models when attempting to simulate metabolic phenomena at a systems level.

Table 3.

Integrated model simulation results

Respiration and ROS production	Experiment	Model
Leak-state $J_{{\text{O}}_2}$ (nmol mg−1 min−1)	106 ± 7	113
Leak-state $J_{{\text{H}}_2}{}_{{\text{O}}_2}$ (pmol mg−1 min−1)	234 ± 10	225
Oxphos-state $J_{{\text{O}}_2}$ (nmol mg−1 min−1)	363 ± 31	341
Oxphos-state $J_{{\text{H}}_2}{}_{{\text{O}}_2}$ (pmol mg−1 min-1)	87 ± 10	79

Model predicts the [3Fe-4S] ISC is the primary source of ROS

Last, the model was used to predict succinate oxidation and ROS production rates as a function of the succinate/fumarate and quinol/quinone ratios in the absence of inhibitors, as shown in Fig. 12. The succinate oxidation rate is maximum when the succinate/fumarate ratio is high and the quinol/quinone ratio is low. The turnover in the forward direction predicted by the model is in the range previously determined by other groups (39, 50, 51). The model also predicts that enzyme's turnover in the reverse direction is approximately equal to the forward direction. This has a profound effect on the enzyme behavior during pathological conditions, such as ischemia, whereby this enzyme is speculated to be responsible for the significant accumulation of succinate (15, 16). In contrast to the inhibitor-based experiments described above, the model predicts that ROS production from the [3Fe-4S] ISC is the primary source of free radicals when no inhibitors are present (Fig. 12E). This is not surprising, considering that, under inhibitor-free conditions, the enzyme is mostly in the E₀, E₁, and E₂ oxidation states (Fig. 12F). In these states, electrons on the complex have a higher probability residing on the ISCs instead of the FAD. Therefore, ROS production from the FAD contributes to a lesser extent to the total ROS production in an uninhibited, fully functional mitochondrion. Under these conditions, H₂O₂ production by SDH is negligible and occurs only when the oxidation state E₄ is elevated. Under conditions that favor the oxidation state E₄, the probability of a fully reduced FAD is high (Fig. 1C). These include when fumarate is absent or present in the low micromolar range, and inhibitors at or downstream of the Q_p site are present.

Figure 12.

Model simulations of succinate and ROS turnover of SDH as a function of succinate/fumarate and QH₂/Q ratios. A, steady-state turnover rates of succinate oxidation. B, steady-state production of total ROS. C, steady-state ROS production from the FAD site. D, steady-state ROS production from the [3Fe-4S] ISC site. E, log₂ -fold change of steady-state ROS production rates from the [3Fe-4S] ISC site relative to the FAD site. F, steady-state enzyme oxidation states for these conditions. The simulations were conducted at 37 °C with a total Q pool of 20 mm, with succinate + fumarate = 20 mm, [O₂] = 20 μm, and at pH 7. The ${\text{O}}_2^{\overline{·}}$ and H₂O₂ concentrations were set to zero.

Discussion

In SDH, the two major sites for ROS production are proposed to be the covalently bound FAD and the Q site (13, 24, 29, 34, 52). The [3Fe-4S] ISC site has recently been suggested to produce ROS (37). However, which site is the dominant source, what ROS species is formed, and what conditions are conducive for ROS production at each site have not been quantitatively addressed. Using Saccharomyces cerevisiae as an experimental model, several groups determined that the Q site is a strong contender for most ROS production (38, 53). Additional studies on Escherichia coli support the Q site origin hypothesis (52, 54). However, studies using Ascaris suum argued that both the FAD and the Q sites can produce ROS (36). In contrast, other studies reported that only the FAD site produces ROS (13, 52). In mammalian SDH, studies have shown that ROS is produced when the enzyme is supplied with succinate only after the Q site is inhibited (24, 34). But no study demonstrably showed whether ${\text{O}}_2^{\overline{·}}$ (37) or H₂O₂ (35) is the dominant ROS species formed. In contrast, it has been argued that SDH from E. coli mainly produces ${\text{O}}_2^{\overline{·}}$ from the FAD site (52). This and other studies concluded that quinol fumarate oxidoreductases generate ${\text{O}}_2^{\overline{·}}$ from the fully reduced FAD (4, 52). However, the mechanism underlying the ROS production was not elucidated. To answer these questions, we developed, analyzed, and corroborated a computational model of SDH that quantitatively describes the necessary conditions for ROS production, the contribution of each site responsible for ROS production, and the factors that control how much ROS is produced by SDH.

The kinetics of succinate oxidation by reconstituted SDH has been thoroughly investigated (39–41). Despite the different experimental conditions across studies, succinate oxidation depends on succinate concentrations, the concentrations of electron acceptors, pH, the presence of non-SDH dicarboxylate substrates, and quinone reductase inhibitors (Figs. 2 and 3). The model simulates these data sets as faithfully as possible and uses a single framework to reproduce both succinate oxidation kinetics and ROS production rates. Based on model analysis, key differences reported across different studies are due to experimental conditions. More importantly, the model supports the notion that the noncanonical Q binding (Q_d) site modulates succination oxidation. Specifically, including this site and its effects on succinate oxidation was necessary to simultaneously fit the data from Jones and Hirst (42) and Siebels and Dröse (35) (Fig. 3). The model result is supported by crystal structures that show occupancy of the Q_d site at high atpenin concentrations (5, 46).

The model is capable of simulating ROS production rates under a variety of experimental conditions. In two succinate titration experiments, Grivennikova et al. (37) and Siebels and Dröse (35) reported different succinate concentrations that correspond to peak ROS production rates, depending on the inhibitors present (Figs. 4 and 5). To fit these data sets, the Q pool redox poise is simulated using equations that account for either complex III or SDH inhibitors. Model analysis reveals that a key determinant of SDH-derived ROS is the Q pool redox poise, which is set by a specific inhibitor. In the presence of atpenin, QH₂ oxidation by complex III results in an oxidized Q pool. As a result, ROS production from SDH is decreased. When complex III inhibitors are present, electron turnover downstream of SDH is inhibited, which leads to a more reduced Q pool. This results in QH₂ oxidation at the Q_p site of SDH and increases the number of reduced redox centers on the complex. Thus, ROS production rates are higher in the presence of stigmatellin and myxothiazol than atpenin (Fig. 7). The distinct pH dependence of ROS production also reflects the unique effects of SDH and complex III inhibitors on the Q pool redox poise (Fig. 8). Quinol oxidation, which liberates a proton, is favorable as pH increases. However, this reaction is minimized when atpenin occupies the Q_p site. Thus, total ROS production reaches a plateau at alkaline pH in the presence of atpenin but continues to increase in the presence of complex III inhibitors (Fig. 8).

Prior studies have argued that the FAD site is able to produce both ${\text{O}}_2^{\overline{·}}$ and H₂O₂ (13, 24, 29, 34, 52). However, which is the dominant species and under which conditions is still an open question. In the study by Siebels and Dröse (35), it was determined that H₂O₂ was the primary ROS species produced from the FAD site. We suspect that their preparation contained low, yet significant, amounts of superoxide dismutase contamination as described by Grivennikova et al. (37). In support of this, the simulations shown in Fig. 8 reveal that, under both stigmatellin- and atpenin-induced ROS production, SDH mainly produces ROS as ${\text{O}}_2^{\overline{·}}$ from the FAD site. The results from these simulations are supported by several studies that used rat skeletal muscle mitochondria to show that most ROS originating from the FAD site is ${\text{O}}_2^{\overline{·}}$ (8, 24). In addition, a different study found that the vast majority of total ROS produced by E. coli SDH is also ${\text{O}}_2^{\overline{·}}$ (52). These findings and the model simulation results strongly point to ${\text{O}}_2^{\overline{·}}$ as the major free radical species originating from the FAD site.

In addition to the FAD site, the Q_p site is another candidate for major ROS production by SDH. Recently, the ISCs have been also suggested to produce significant amounts of ROS. Model analysis reveals that ROS originate mostly from the FAD site or the [3Fe-4S] ISC. We initially included ROS production from the bound semiquinone but found its inclusion superfluous when fitting the data. The production of ROS at the FAD site and [3Fe-4S] ISC requires that they are in a reduced state and unoccupied. These prerequisites explain the decreased ROS production rates in the presence of malonate, malate, and oxaloacetate (Figs. 6 and 7). The non-SDH dicarboxylate substrates can bind to the FAD site, preventing succinate from reducing the enzyme and oxygen accessing the reduced flavin. Likewise, binding of molecules such as atpenin to the Q_p site can also physically block the ISC from reacting with oxygen. However, because the ISC does not interact with the non-SDH dicarboxylate substrates, ISC-derived ROS is sensitive to only atpenin or other Q_p site inhibitors.

To address the uncertainty associated with the kinetics of quinone binding and oxidation/reduction at the Q sites, we designed an experiment using isolated mitochondria from guinea pig cardiomyocytes and DQ to perturb the endogenous Q pool (Fig. 9). Our experimental data show that succinate oxidation kinetics in guinea pig exhibits a similar trend observed in other mammals. In addition, ROS production profile is uniquely dependent on succinate concentration. At 200 μm succinate, ROS production decreases as DQ level rises. At 5 mm succinate, the opposite is true. Our model analysis demonstrates that this is due to DQH₂-derived ROS at high succinate concentrations. The model analysis highlights the importance of careful consideration of the SDH-mediated DQH₂ production and its subsequent reaction with oxygen in the buffer. Failure to account for this side reaction leads to overestimation of SDH-derived ROS.

Following model calibration, we validated the model using the SDH-specific data set from Grivennikova et al. (48). The validation step is necessary to ensure that key aspects of the model are tested against experimental data not used during parameter fitting. That said, as additional data become available, model improvements should be made. The model as presented herein is able to reproduce the oxygen dependence of ROS production without tuning the adjustable parameters. The validation process further shows that, under the prevailing conditions, ROS production obeys second-order kinetics. In these conditions, oxygen availability and the Q pool redox poise are the key determinants of ROS production (Fig. 10). When either of these factors becomes limited, ROS production drops. In this context, the Q pool redox poise is important for ROS formation because it dictates the enzyme oxidation state. Therefore, any environmental factors that affect the Q pool redox poise—such as the use of Q_p site complex III inhibitors—will affect the enzyme oxidation state and ROS production. Our simulation in Fig. 11 again highlights this notion.

Finally, we used the model to deconstruct the kinetics underlying ROS production in uninhibited, fully functional mitochondria (Fig. 12). As discussed, ROS production depends on electrons supplied by succinate (forward mode) or QH₂ (reverse mode). In the absence of inhibitors, most of the enzyme population is in the E₀, E₁, and E₂ oxidation states. In these states, electrons are most likely to occupy the [3Fe-4S] ISC and give rise to ${\text{O}}_2^{\overline{·}}$. The FAD site is also a significant source of ${\text{O}}_2^{\overline{·}}$ but contributes less to total ROS than the [3Fe-4S] ISC in the absence of inhibitors. Thus, by using experimental data from studies that employ inhibitors, our modeling approach results in a model that allows us to understand ROS production in the absence of inhibitors.

The SDH model is the ideal choice to include in metabolic simulations when scaling up the cell or tissue level, because the model simulates both the primary biochemical reaction and the side reactions that produce ROS using an algebraic expression. Large-scale metabolic models can be used to understand both normal and pathological metabolic scenarios involving mitochondrial succinate metabolism as in I/R injury (15, 16), mitochondrial ROS production as in skeletal muscle bioenergetics (55), and immune responses (27, 56, 57). However, simulating these types of models is computationally expensive. Nearly all large-scale models of metabolism are systems of nonlinear ordinary (one independent variable (e.g. time)) or partial (multiple independent variables (e.g. time and space)) differential equations. As a result, any enzymatic or transport process that is also modeled as a system of differential equations adds to the complexity and computational cost. Thus, a model that can simulate multiple reactions using algebraic expressions significantly reduces the simulation cost and is very advantageous to use in the large-scale models of metabolism. There are several models similar to our SDH model that simulate the kinetics of the main reaction along with side reactions, such as ROS production (58–62), but these models are systems of differential equations themselves. Integrating them into large-scale models of metabolism dramatically increases the computational cost. Therefore, our approach provides a unique way to model these primary reactions along with their associated side reactions in large-scale models without significantly adding to the computational complexity and associated cost.

In summary, our study resolves the critical issue pertaining to the identity, origin, and conducive conditions of ROS production by SDH. The model suggests that the primary species formed is ${\text{O}}_2^{\overline{·}}$. During physiological conditions, the [3Fe-4S] ISC is the primary source; however, the FAD can become a major source during pathological conditions. Hydrogen peroxide is produced in appreciable quantities only when SDH is inhibited and fumarate is absent. In the physiological setting, the fumarate concentration will never be zero; therefore, H₂O₂ production by SDH is an experimental phenomenon. In developing our model, we included succinate oxidation and linked it to ROS production, as succinate is an important source of electron for SDH. The model presented herein is the only comprehensive SDH model that can simulate both the enzyme kinetics and ROS production rates for a wide range of conditions. As a result, this model is ideal for integrating into large-scale models of mitochondrial metabolism to study ROS production from the ETS during physiological and pathophysiological conditions.

Materials and methods

Model construction

The modeling approach for this study is based on our prior work (14, 23). In brief, structural, thermodynamic, and kinetic data are used to constrain the model, and enzyme-state transitions are governed by the law of mass action. The model includes the redox biochemistry reactions that occur at the FAD, ISCs, and Q sites. The FAD site contains the binding site for succinate and other dicarboxylates. Whereas ubiquinone and its analogues can hypothetically bind to both the proximal and distal Q sites, quinone reduction has been shown to occur at the proximal Q site, the Q_p site. The function of the distal Q site, the Q_d site, is still unknown (4, 63). Reactions at these sites are assumed to be independent of each other (i.e. there are no long-distance conformational changes required for enzyme catalysis between the Q_p and the FAD sites). However, the Q_d site is assumed to exert some control over turnover at the FAD and proximal Q sites when atpenin or other molecules are bound to this site.

The enzyme kinetic model consists of five oxidation states, which constitute the oxidation state of the entire enzyme. For example, all redox centers are oxidized in the E₀ state, at least one redox center is one-electron–reduced in the E₁ state, and so on and so forth. A minimum of five oxidation states were necessary to fit the experimental data. Including more did not improve fits to the data. Transitions between oxidation states are governed by the Gibbs' free energies of the redox reactions involved. Two-electron reactions involve the succinate/fumarate (SUC/FUM), Q/QH₂, and O₂/H₂O₂ couples. One-electron reactions involve the O₂/${\text{O}}_2^{\overline{·}}$ couple. Binding of substrates, products, and inhibitors at the FAD and Q sites is assumed to be faster than state transition rates. Forward state transition rate constants are estimated from experimental data, whereas the reverse rate constants are calculated from the forward rates and equilibrium constants for the respective reaction. The equilibrium constants are computed from the midpoint potentials taken from the literature (Table S1) and adjusted to account for the effects of pH and temperature. The rates corresponding to these reactions are shown in Equations S78–S91. The transitions between each oxidation state are fully reversible and governed by the law of mass action.

Within each oxidation state, the enzyme complex can exist in various substates characterized by the combination of redox centers reduced or oxidized. Because electrons on the complex reorganize on very fast time scales (less than microseconds) relative to turnover, we compute these substates using the Boltzmann distribution, as shown in Equation 1.

In Equation 1, $S_r^k$ is the fraction of redox centers r existing in the oxidation state k that is reduced, and $\Delta G_r^k$ is the free energy change for each redox center r calculated from the linear superposition of the midpoint potentials. The redox centers r can consist of a single redox center or any combination of redox centers in the complex. To calculate the free energy change for the combination of redox centers, the individual free energies for the redox center reactions are summed (i.e. they are independent from each other). The number of combinations of reduced redox centers for each state is given by the binomial coefficient, where n is the number of redox centers and k is the number of electrons on the complex. For details on calculating substates, see Equations S45–S77.

As mentioned above, substrates and products are assumed to bind/unbind much faster than transitions among oxidation states of the enzyme. It is assumed that binding events are independent of substates and that binding events at the Q and FAD sites are independent of each other. When the enzyme is in the appropriate enzyme-substrate complex configuration, the appropriate redox reaction proceeds. Binding polynomials (BPs) are used to give the fraction of the enzyme in a certain enzyme-substrate configuration. The BP for the Q_p site (P_Qp) partitions this binding site into the unbound and the Q-, QH₂-, and atpenin-bound fractions. The expressions 1/P_Qp, [Q]/K_Q/P_Qp, [QH₂]/K_Q/P_Qp, and [atpenin]/K_A/P_Qp indicate the fractions of the total Q sites unbound or bound to ubiquinone, ubiquinol, or atpenin, respectively. In a similar manner, the Q_d site can be partitioned into free and bound states as well. The BP for the FAD site (P_FAD) partitions this binding site into the unbound, succinate-, fumarate-, malate-, malonate-, and oxaloacetate-bound fractions. Similarly, the expressions 1/P_FAD, [succinate]/K_SUC/P_FAD, [fumarate]/K_FUM/P_FAD, [malate]/K_MAL/P_FAD, [malonate]/K_MALO/P_FAD, and [oxaloacetate]/K_OAA/P_FAD give the fractions of the total FAD sites bound to succinate, fumarate, malate, malonate, and oxaloacetate, respectively. The BPs for the FAD and Q sites are given below.

Steady-state turnover of succinate oxidation and ROS production rates are calculated using the solution of the linear equations governing the oxidation state transitions as shown in Equation S92. The first five rows correspond to the permissible oxidation state transitions. The last row is used to set the steady-state solution to fractions of one (i.e. ∑_iE_i = 1; see the supporting material for further details). The Moore–Penrose pseudo-inverse is then used to calculate the unique solution to the linear system of equations (64). The edges connecting to the oxidation states shown in Fig. 1 represent the partial reactions that govern how state i is connected to state j. These reaction rates, k_ij, represent molecular processes, such as the reduction of FAD to FADH₂ by succinate, oxidation of FADH^• or FADH₂ by oxygen, and Q reduction at the Q site. The equations for the partial reactions are given in the supporting material (Equations S78–S91). Before the enzyme can transition between oxidation states, it must be in the appropriate enzyme-substrate complex configuration. For example, succinate oxidation can only occur when the FAD-binding site is available for succinate to bind and the FAD is fully oxidized. Binding polynomials (Equations 2–4) are used to calculate the fraction of succinate bound to the complex, and the Boltzmann distribution (Equation 1) is used to calculate the fraction of the protein complex with a fully oxidized FAD within a given oxidation state. The net steady-state rate of succinate oxidation is then computed by summing over the oxidation state transition rates as shown in Equation 5. Next, the net steady-state ${\text{O}}_2^{\overline{·}}$ production rate is computed by summing the net ${\text{O}}_2^{\overline{·}}$ production when the FADH^• or [3Fe-4S] reacts with oxygen, as shown in Equation 6. The steady-state H₂O₂ production rate is computed when the fully reduced flavin reacts with oxygen, as given in Equation 7. Last, the steady-state QH₂ production rate is given by Equation 8. Because mass and energy conservation are strictly obeyed, phenazine and TMPD reduction rates are also computed using Equation 8. For simplicity, we assume that reduction of these exogenous electron acceptors occurs in rapid, sequential one-electron steps and lump them together as a two-electron reduction reaction.

Experimental data

The model was calibrated using a variety of literature data listed in Table 1. These data include succinate oxidation, Q reduction, and ${\text{O}}_2^{\overline{·}}$ and H₂O₂ production rates under different experimental conditions. The data set contains information about the kinetics and ROS production by SDH necessary to identify model parameters. Most of the kinetic data on succinate oxidation are from bovine heart mitochondria (41, 42), and some are from pig heart mitochondria (40). The ROS data set is from bovine heart mitochondria and includes both ${\text{O}}_2^{\overline{·}}$ and H₂O₂ production rates (35, 37). We did not use data from Quinlan et al. (24), as the reported data include an unknown contribution of the ROS-scavenging system. Both succinate oxidation and ROS data sets are obtained under a variety of experimental conditions, including variations in enzyme concentrations, temperatures, pH, substrate concentrations, and inhibitor concentrations. Experimental conditions are explicitly stated to simulate the experiments as faithfully as possible. However, the use of scaling factors is still necessary to account for experimental differences among the data sets, such as species-dependent differences in enzyme kinetics. Even so, the values are in the acceptable range of 0.5 to 5, showing that only minor adjustments were needed to fit the data. Also, in some experiments, endogenous quinone was used as the electron acceptor without any information on the redox state of the Q pool (35, 37, 42). To simulate these data, we relied on monotonic functions of succinate and inhibitors to predict the Q pool redox state. These equations are given in the supporting material (Equations S1–S3).

Experimental details

Animal care and handling conformed to the National Institutes of Health's Guild for the Care and Use of Laboratory Animals and was approved by Michigan State University's Institutional Animal Care and Use Committee. Mitochondria from Hartley guinea pig ventricular myocytes were isolated based on a protocol described previously (22, 49, 65), which will be briefly summarized here. Animals (4–6 weeks, 350–450 g) were decapitated after being anesthetized with 5% isoflurane and tested to be unresponsive to noxious stimuli. The heart was then immediately perfused with ice-cold cardioplegic solution until no blood was seen in the coronary arteries and cardiac veins. The cardioplegic solution consisted of 25 mm KCl, 100 mm NaCl, 10 mm dextrose, 25 mm MOPS, and 1 mm EGTA at pH 7.15. The heart was then excised and washed with ice-cold isolation buffer (IB). IB consisted of 200 mm mannitol, 50 mm sucrose, 5 mm K₂HPO₄, and 0.1% (w/v) BSA at pH 7.15. Connective tissues, thymus, and the great vessels were removed, and the ventricles were minced in ice-cold IB until small pieces of about 1 mm³ remained. The homogenate was then transferred to a 50-ml canonical tube containing 0.5 units/ml protease (Bacillus licheniformis) in 25 ml of IB. Tissue homogenization was done using an Omni handheld homogenizer at 18,000 rpm for 20 s. Mitochondria were obtained using gradient centrifugation in IB at 4 °C. Mitochondrial protein was quantified using the BCA assay and an Olis DM-245 spectrofluorometer with a dual-beam absorbance module. The mitochondria were then subjected to three freeze-thaw cycles at −80 °C and stored at −80 °C until use. The net H₂O₂ production rate was monitored using the Amplex UltraRed assay on the Olis DM-245 spectrofluorometer with dual-beam absorbance module. Amplex UltraRed (AmpUR) (excitation 560 nm, emission 590 nm) was dissolved to a stock concentration of 10 mm and stored according to the manufacturer's instructions. Type II horseradish peroxidase (HRP) and superoxide dismutase (SOD) were individually dissolved to the stock concentrations of 500 units/ml and stored at the appropriate temperatures. Myxothiazol and rotenone stock concentrations were 2 and 1 mm, respectively. The buffer (pH 7.2) contained 120 mm KCl, 5 mm HEPES, 1 mm EGTA, and 0.3% (w/v) BSA. Hydrogen peroxide calibration curves were made using a working solution of 200 μm H₂O₂ prepared fresh on the day of every experiment.

Fluorescence was monitored after mitochondria and inhibitors had been added to the buffer. After 2 min, succinate was added to the desired final concentrations. In the succinate titration experiments, the final concentrations were 50, 100, 200, 300, 500, 1000, 3000, and 5000 μm succinate. The rate of ROS production was measured after SDH was fully activated, and the rate became linear as shown previously (37). In the DQ titration experiments, succinate concentrations were either 200 μm or 5 mm. After 10 min, DQ was added to the final concentrations of 12.5, 25, 50, 75, 100, 150, and 200 μm. The final concentrations were 10 μm Amplex UltraRed, 1 unit/ml HRP, 10 units/ml SOD, 4 μm rotenone, 2 μm myxothiazol, and 0.1 mg/ml mitochondria. Following DQ additions, signal was monitored for at least 10 min. At least three replicates were performed at each condition, and all experiments were performed at 37 °C.

Model simulations

The model was numerically simulated using MATLAB (R2019a). The parameter optimization was performed on a Dell desktop PC (64-bit operating system and x64-based processor Intel^® core™ i7-7700 CPU @3.60 GHz and 16 GB RAM) using the Parallel Computing Toolbox. A parallelized simulated annealing algorithm was first used to globally search for feasible parameters, which were then refined using a local, gradient-based optimization algorithm. The analytic solutions for the state-steady oxidation states were obtained with the MATLAB symbolic toolbox. When the S.D. value for data was not given, an S.D. of 10% of the maximum value in a given data set was used during parameter estimation.

Data availability

All data, model equations, and model codes are provided in the article or supporting material.