Module 5: Reactive Oxygen Species & Oxidative Stress

Mitochondria are the body’s dominant source of reactive oxygen species (ROS): superoxide, hydrogen peroxide, and hydroxyl radicals, produced as inevitable byproducts of incomplete electron transfer to oxygen. At low levels, these species serve as signalling molecules (mitohormesis); at high levels, they damage lipids, proteins, and DNA and drive pathology. Harman’s (1956) free-radical theory of aging, Chouchani’s (2014) succinate/RET mechanism of ischemia-reperfusion injury, and the development of mitochondria-targeted antioxidants (MitoQ) together form a narrative that links molecular chemistry to clinical medicine.

1. Reactive Oxygen Species: Definitions and Chemistry

The term reactive oxygen species collects several oxygen-derived molecules with unpaired electrons or high oxidative potential. The physiologically most important species are:

Superoxide anion (O₂^•-): single-electron reduction product of O₂. Short-lived (~10 µs at physiological pH). Reactive with Fe-S clusters, aconitase, and NO.
Hydrogen peroxide (H₂O₂): dismutation product of 2 O₂^•-. Non-radical, relatively stable, membrane-permeable. Diffuses several microns before reacting. A signalling molecule at nM levels.
Hydroxyl radical (•OH): the most reactive ROS. Generated by Fenton chemistry of H₂O₂ with Fe²⁺ or Cu⁺. Reacts at diffusion-limited rates (k ~10¹⁰ M^-1s^-1) with essentially any biomolecule.
Singlet oxygen (¹O₂): photosensitizer-derived; less common in mitochondria.
Peroxynitrite (ONOO^-): from O₂^•- + NO, diffusion-limited; highly reactive with tyrosines.

The sequential reduction of O₂ to water is a 4-electron process:

\[ \text{O}_2 \xrightarrow{+e^-} \text{O}_2^{\bullet-} \xrightarrow{+e^-,\ 2\text{H}^+} \text{H}_2\text{O}_2 \xrightarrow{+e^-,\ \text{H}^+} \text{H}_2\text{O} + \,^\bullet\!\text{OH} \xrightarrow{+e^-,\ \text{H}^+} 2\,\text{H}_2\text{O} \]

Cytochrome c oxidase avoids releasing intermediates by holding them in the binuclear heme a₃-Cu_B site. Single-electron leaks at C1 and C3 produce the superoxide that seeds the cascade.

Estimates of ROS leak vary widely (0.1% to 2% of electron flow under physiological conditions) and depend on tissue, PMF, and substrate. At \(\Delta p\)= 200 mV, the leak is small; under hyperpolarized conditions (state 4, high PMF), it rises sharply.

2. Sources of Mitochondrial ROS

Murphy (2009, Biochem. J.) provided the definitive modern catalog. The major sources are:

Complex I flavin (FMN): major source during forward electron transport. Electrons leak from reduced FMN to O₂. Releases O₂^•- exclusively into the matrix.
Complex I Q-binding site (RET): during reverse electron transport (high QH₂, high PMF), electrons flow backward from Q to FMN and escape to O₂ at huge rates. The dominant source during ischemia-reperfusion (Chouchani 2014).
Complex III Q_o site: the semiquinone intermediate in the Q-cycle leaks electrons to O₂. Releases superoxide on both sides of the IMM (matrix and IMS).
Monoamine oxidase (MAO): on the outer membrane, oxidizes biogenic amines and generates H₂O₂directly. Elevated in aging brain.
Electron-transferring flavoprotein:Q oxidoreductase (ETF-QOR): fatty acid β-oxidation feed into Q pool; minor but measurable source.
Glycerol-3-phosphate dehydrogenase, pyruvate/2-oxoglutarate dehydrogenase complexes: small contributions.

The topology matters profoundly. C1 releases only to the matrix; C3-Q_oreleases to both sides. Matrix ROS are damped by the high SOD2 and GSH pool; IMS ROS escape to the cytosol through VDAC in the outer membrane and participate in inter-organelle signalling.

RET: the ischemia-reperfusion bomb

Reverse electron transport through C1 is the single most explosive ROS source known. It requires: (1) a highly reduced Q pool (high [QH₂]/[Q]), and (2) a high PMF (\(\Delta p > 180\) mV). Both conditions arise abruptly at reperfusion after ischemia, when succinate accumulated during anoxia is rapidly oxidized by C2, flooding the Q pool with electrons that can no longer flow forward fast enough.

3. Antioxidant Defenses: SOD, Catalase, GPX, Peroxiredoxins

Cells maintain a layered antioxidant defense. The first layer is dismutation of superoxide by superoxide dismutases (SOD):

SOD1 (Cu/Zn-SOD): cytosol and intermembrane space. Mutations cause familial amyotrophic lateral sclerosis (ALS; Rosen et al. 1993, Nature).
SOD2 (Mn-SOD): matrix. The dominant mitochondrial scavenger. SOD2 knockout mice die in the neonatal period (Li et al. 1995).
SOD3 (extracellular Cu/Zn-SOD): plasma and extracellular matrix.

\[ 2\,\text{O}_2^{\bullet-} + 2\,\text{H}^+ \xrightarrow{\text{SOD}} \text{H}_2\text{O}_2 + \text{O}_2 \quad (k = 1.6 \times 10^9\ \text{M}^{-1}\text{s}^{-1}) \]

The reaction is nearly diffusion-limited. With [SOD2] ~10 µM in matrix, [O₂^•-] is held at sub-nanomolar steady state.

The second layer removes H₂O₂:

Catalase: peroxisomal; 2 H₂O₂ → 2 H₂O + O₂. Extraordinarily fast (k ~10⁷ s^-1); minor mitochondrial expression (heart).
Glutathione peroxidase (GPX1, GPX4): matrix and IMS. Uses GSH as reductant: H₂O₂ + 2 GSH → 2 H₂O + GSSG. GPX4 specifically removes lipid peroxides.
Peroxiredoxins (Prx3, Prx5): mitochondrial isoforms. Use a redox-cycling catalytic cysteine; regenerated by thioredoxin-2 (Trx2) and thioredoxin reductase (TrxR2).
Glutathione (GSH) pool: ~5 mM in matrix, buffers H₂O₂ and protein thiols. GSH is synthesized in cytosol and imported into the matrix via a dedicated transporter.
Thioredoxin-2 (Trx2): matrix; maintains protein disulfides in reduced state; regenerated by TrxR2 (NADPH-dependent).

Hydroxyl radical is not scavenged enzymatically—it is too reactive. The only defense is to prevent its formation by removing H₂O₂ before the Fenton reaction can occur, and by sequestering redox-active iron in ferritin.

\[ \text{Fenton:}\quad \text{Fe}^{2+} + \text{H}_2\text{O}_2 \;\to\; \text{Fe}^{3+} + \,^\bullet\!\text{OH} + \text{OH}^- \]

Iron dysregulation (hemochromatosis, neurodegeneration with brain iron accumulation) drives hydroxyl-radical-mediated damage. Parkinson’s substantia nigra has elevated iron.

4. Biomarkers of Oxidative Damage

ROS cause characteristic chemical modifications to biomolecules that serve as clinical biomarkers of oxidative stress:

Major oxidative damage markers:

8-oxoguanine (8-oxoG): DNA base oxidation; mispairs with A to give G→T transversions. Measured by HPLC-MS and immunostaining. Age-increasing in substantia nigra (Alam 1997).
8-hydroxy-deoxyguanosine (8-OHdG): urinary excretion marker; detected by ELISA.
Malondialdehyde (MDA): lipid peroxidation end product; reacts with thiobarbituric acid to form TBARS. Non-specific but widely used.
4-hydroxynonenal (HNE): specific lipid peroxidation aldehyde; immunodetected.
F₂-isoprostanes: prostaglandin-like compounds from arachidonic acid peroxidation; gold-standard lipid peroxidation marker.
Protein carbonyls: oxidation of Lys, Arg, Pro side chains; detected by DNPH derivatization.
3-Nitrotyrosine: peroxynitrite footprint on protein tyrosines.

Accumulation of these markers with age is well documented. In postmitotic tissues (brain, heart, muscle), 8-oxoG in mtDNA rises linearly from 20 to 80 years of age in postmortem studies. Interpretation, however, is contested: are these markers drivers of aging or just correlates?

5. Harman 1956: Free-Radical Theory of Aging

Denham Harman (1956, J. Gerontol.) proposed that aging is caused by cumulative damage from free radicals generated during normal oxygen metabolism. The theory was extended in 1972 to the mitochondrial free-radical theory of aging: mitochondria are the primary source of ROS, and mtDNA in particular is a vulnerable target (no histones, limited repair, close to the electron transport chain).

Evidence supporting the theory:

8-oxoG in mtDNA increases with age in multiple mammalian tissues (Mecocci 1993; Hamilton 2001).
Trifunovic et al. (2004, Nature) “mutator mouse” with proofreading-deficient POLG accumulates mtDNA mutations and develops progeroid phenotype.
Caloric restriction extends lifespan in many species and is associated with reduced ROS production.
Long-lived species (naked mole rats, bats) have lower ROS production per unit metabolic rate than mice.

Evidence against (or complicating) the theory:

Transgenic mice overexpressing catalase in mitochondria (mCAT) show modest lifespan extension, but whole-body antioxidant supplementation does not.
Naked mole rats have high oxidative damage markers yet live 30 years—damage is not lethal in itself.
Antioxidant supplementation trials in humans (vitamin E, beta-carotene) have consistently failed to reduce mortality and sometimes increased it.
Low-dose ROS are now understood to be signalling molecules required for normal physiology (mitohormesis).

The consensus is that the free-radical theory of aging is partially correct but needs updating: oxidative damage accumulates and contributes to dysfunction, but ROS also serve as adaptive signals, and blanket antioxidation is not the solution.

6. Ristow 2009: Mitohormesis and the Case for ROS Signalling

Ristow & Zarse (2009, Exp. Gerontol.) coined the term mitohormesis to describe the phenomenon that low doses of mitochondrial ROS are beneficial. The logic: transient ROS activate adaptive responses (Nrf2 pathway, antioxidant gene expression, mitochondrial biogenesis, autophagy) that produce net health benefits.

Key mechanisms of ROS signalling:

Nrf2 / Keap1 axis: H₂O₂ oxidizes critical cysteines on Keap1, releasing Nrf2 which translocates to the nucleus and drives transcription of antioxidant genes (SOD2, GCLC, HMOX1, NQO1).
HIF-1α stabilization: Complex III ROS inhibit prolyl hydroxylases, stabilizing HIF and driving the hypoxic response.
Reversible protein thiol oxidation: catalytic cysteines on PTP1B, PTEN, GAPDH, and many kinases/phosphatases are redox-regulated. Transient disulfide formation toggles activity.
MAPK and NF-κB activation: ROS stimulate inflammatory signalling pathways, linking mitochondria to innate immunity.

Practical implications:

Exercise transiently raises mitochondrial ROS; this drives adaptive increases in antioxidant capacity and mitochondrial biogenesis.
Antioxidant supplementation (vitamins C and E) during exercise training blunts the adaptive response (Ristow et al. 2009, PNAS).
Caloric restriction and glucose restriction in C. elegans both extend lifespan via transient ROS signalling (Schulz et al. 2007).
Metformin’s beneficial effects on aging may be partly mediated by mild mitochondrial stress and mitohormesis.

7. Chouchani 2014: Succinate Drives Reperfusion Injury

Ischemia-reperfusion (IR) injury is a major clinical problem in stroke, myocardial infarction, and organ transplantation. Restoring blood flow—which is lifesaving—paradoxically causes a burst of oxidative damage that can kill the tissue it was meant to save.

Chouchani et al. (2014, Nature 515, 431–435) identified the mechanism across heart, brain, liver, and kidney:

During ischemia: succinate accumulates in the tissue. Metabolomic LC-MS showed succinate rising 5–10× within minutes of ischemic onset, while fumarate and malate fall. Fumarate reductase activity of SDH runs in reverse.
At reperfusion: succinate is rapidly oxidized by Complex II, over-reducing the Q pool. Because Complex I is still partially inhibited in the deactive (D) state, and Complexes III/IV are starved of the rapid electron throughput they need, the high PMF + reduced QH₂ drives reverse electron transport at Complex I.
RET produces a massive superoxide burst at the C1 flavin site, which triggers mPTP opening, DNA damage, and cell death.
Therapeutic implication: preemptive inhibition of succinate accumulation or oxidation (by malonate or dimethyl malonate, cell-permeable prodrug) reduces infarct size in mouse models by >50%.

\[ \text{ischemia} \Rightarrow [\text{succinate}] \uparrow\uparrow \;\to\; \text{reperfusion} \Rightarrow \text{QH}_2\uparrow\uparrow,\ \Delta p \uparrow\uparrow \;\to\; \text{RET at C1} \;\to\; \text{O}_2^{\bullet-}\ \text{burst} \]

Valls-Lacalle et al. (2016, Cardiovasc. Res.) translated this to in vivo cardiac IR: intracoronary malonate at reperfusion reduced infarct size in pigs. Clinical trials of dimethyl malonate and other SDH modulators are ongoing.

8. Mitochondria-Targeted Antioxidants

Murphy (2008, Biochim. Biophys. Acta) pioneered MitoQ: a ubiquinone derivative conjugated to the lipophilic cation triphenylphosphonium (TPP⁺). The TPP⁺ group is attracted to the negatively charged matrix by the mitochondrial membrane potential and concentrates MitoQ ~1000-fold inside mitochondria relative to the cytosol.

TPP-cation accumulation (Nernst equation):

\(\frac{[\text{MitoQ}]_\text{matrix}}{[\text{MitoQ}]_\text{cyto}} = 10^{\Delta\psi/61.5}\) At \(\Delta\psi = 140\) mV, this gives ~180-fold accumulation; compound mitochondrial+plasma membrane potentials produce ~1000-fold total enrichment.

Other targeted compounds:

MitoTEMPO: TPP-conjugated nitroxide, SOD mimetic.
SkQ1: Skulachev’s TPP-plastoquinone; reported lifespan extension in mice.
SS-31 (elamipretide): cardiolipin-binding tetrapeptide; enhances cristae stability; in trials for Barth syndrome.
Coenzyme Q₁₀ supplementation: no accumulation, but modest benefits in statin-induced myopathy.
N-acetylcysteine (NAC): GSH precursor; broad antioxidant.
Resveratrol: activates SIRT1 and PGC-1α, indirectly improves mitochondrial function.

Clinical trials of MitoQ in Parkinson’s disease (Snow 2010), age-related vascular dysfunction (Rossman 2018), and fatty liver (Gane 2010) have shown modest but real benefits. Robust outcomes in large trials remain elusive, underscoring the difficulty of antioxidant therapy given mitohormetic complexity.

9. Wallace 2010: Mitochondria and the Biology of Aging

Douglas Wallace (2010, Mitochondrion) synthesized three decades of research into a unified mitochondrial paradigm for aging and age-associated diseases:

Mitochondrial bioenergetic capacity declines with age in postmitotic tissues—the so-called “mitochondrial theory of aging.”
mtDNA mutations (both point mutations and the common 4977 bp deletion) accumulate over lifetime, crossing thresholds that compromise OxPhos capacity in clonally-expanded patches.
ROS production rises as OxPhos becomes inefficient, further damaging the system in a positive feedback loop.
Calcium signalling via the mitochondrial permeability transition pore (mPTP) becomes dysregulated, promoting cell death.
Tissue-specific thresholds for mitochondrial dysfunction explain the tissue-specific clinical signature of aging (sarcopenia, cognitive decline, cardiomyopathy).

The paradigm has been expanded and complicated by subsequent work: mitochondrial dysfunction interacts with proteostasis (autophagy, UPR^mt), epigenetic clocks, inflammaging, and cellular senescence. Modern “hallmarks of aging” frameworks (Lopez-Otin 2013) include mitochondrial dysfunction as one of nine (now extended to twelve) pillars, alongside genomic instability, telomere attrition, and others.

10. Clinical ROS in Disease

Mitochondrial ROS have been implicated in a broad spectrum of disease:

Parkinson’s disease: Complex I deficiency in substantia nigra (Schapira 1990); rotenone causes parkinsonian phenotype in rats (Betarbet 2000).
Alzheimer’s disease: elevated brain 8-oxoG; Aβ damages mitochondria; cytochrome c oxidase activity reduced.
Amyotrophic lateral sclerosis (ALS): SOD1 mutations cause familial ALS; toxic gain of function.
Myocardial infarction and stroke: IR injury via RET/succinate axis (Chouchani 2014).
Type 2 diabetes: elevated mitochondrial ROS contributes to insulin resistance; metformin acts partly via Complex I modulation.
Cancer: cancer cells have altered redox balance; some are addicted to mitochondrial ROS signalling (Sabharwal & Schumacker 2014).
Atherosclerosis: oxidized LDL and vascular mitochondrial dysfunction; MitoQ improves endothelial function (Rossman 2018).

Clinical interventions have been disappointing overall—large trials of vitamin E, beta-carotene, and vitamin C have not reduced mortality, and some have increased it (ATBC trial, HOPE-TOO). This underscores the subtlety of ROS biology: systemic antioxidation disrupts signalling as well as damage, producing mixed outcomes. Tissue- and mitochondria-targeted approaches remain the most promising strategies for therapeutic intervention.

11. ROS Sources and Scavengers: A Map

Simulation 1: ROS Steady-State Analysis across Scenarios

We model steady-state concentrations of superoxide, hydrogen peroxide, and hydroxyl radical in the matrix under varying conditions: baseline, antimycin-induced C3 ROS, SOD2 knockout, GPX1 knockout, iron overload, and ischemia-reperfusion. The second panel scans SOD2 expression against [O₂^•-] steady state, showing the dramatic sensitivity of superoxide buildup to SOD2. The third panel maps [H₂O₂] as a 2D grid over SOD and GPX levels. The fourth panel illustrates Harman’s free-radical theory of aging with cumulative lifetime damage.

Python

script.py155 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Mitochondrial ROS steady-state analysis
# ---------------------------------------
# Model sources, scavengers, and steady-state [O2.-], [H2O2], [.OH] in matrix.
#
# Sources (per Murphy 2009 Biochem J):
#   - Complex I flavin site (FMN): major source during forward electron transport
#   - Complex I Q-binding site: during reverse electron transport (RET)
#   - Complex III Q_o site: second major source, into both IMS and matrix
#   - MAO (monoamine oxidase) on OMM
#   - ETF-QOR (fatty acid oxidation)
#
# ROS chemistry:
#   O2 + e-  ->  O2.-                   (superoxide)
#   2 O2.- + 2 H+ -> H2O2 + O2          (SOD dismutation)
#   Fe2+ + H2O2 -> Fe3+ + OH- + .OH     (Fenton, hydroxyl radical)
#   H2O2 + 2 GSH -> 2 H2O + GSSG        (GPX1)
#   2 H2O2 -> 2 H2O + O2                (catalase)
#
# Scavengers:
#   SOD2 (Mn-SOD) in matrix: k ~ 1.6e9 M-1 s-1 (Fridovich)
#   SOD1 (Cu/Zn-SOD) in IMS+cytosol
#   Catalase in peroxisomes + small mito amounts
#   GPX1 glutathione peroxidase: k ~ 5e7 M-1 s-1
#   Peroxiredoxin (Prx3, Prx5 in mito)
#   Glutathione (GSH) pool ~ 5 mM in matrix

rng = np.random.default_rng(31)

# Rate constants (approximate, from Fridovich, Halliwell, Gutteridge)
k_SOD = 1.6e9     # M-1 s-1
k_GPX = 5e7       # M-1 s-1
k_Fenton = 1.0e-3 # s-1 (per [H2O2], assumes steady Fe2+)
k_OH = 1e10       # M-1 s-1 for any target

# Steady-state concentrations in mM
def ros_steady_state(v_O2m_source, SOD=1e-5, GPX=5e-6, GSH=5e-3, Fe=1e-7):
    # O2.- + SOD fast: [O2.-]_ss = v_source / (k_SOD * SOD * [O2.-]_ss) -> solve
    # Use linear approx: [O2.-]_ss ~ v_source / (2 * k_SOD * SOD) for dismutation
    O2m_ss = v_source_to_O2m(v_O2m_source, SOD)
    # H2O2 production from SOD = v_O2m / 2
    v_H2O2 = v_O2m_source / 2.0
    # H2O2 + GPX  + Fenton remove it
    k_removal = k_GPX * GPX * GSH + k_Fenton * Fe
    H2O2_ss = v_H2O2 / k_removal if k_removal > 0 else np.inf
    # .OH from Fenton
    v_OH = k_Fenton * Fe * H2O2_ss
    OH_ss = v_OH / k_OH * 1e-12  # .OH is almost immediately consumed; tiny ss
    return O2m_ss, H2O2_ss, OH_ss

def v_source_to_O2m(v, SOD):
    # [O2.-] at steady state: v = 2 k_SOD [SOD] [O2.-]
    return v / max(2 * k_SOD * SOD, 1e-30)

# Baseline: modest basal ROS
v0 = 1e-9  # M/s basal O2.- production rate
scenarios = [
    ('baseline',           dict(v=v0,      SOD=1e-5, GPX=5e-6, Fe=1e-7)),
    ('antimycin (5x ROS)', dict(v=5*v0,    SOD=1e-5, GPX=5e-6, Fe=1e-7)),
    ('SOD2 KO',            dict(v=v0,      SOD=1e-7, GPX=5e-6, Fe=1e-7)),
    ('GPX1 KO',            dict(v=v0,      SOD=1e-5, GPX=5e-8, Fe=1e-7)),
    ('Fe overload',        dict(v=v0,      SOD=1e-5, GPX=5e-6, Fe=1e-5)),
    ('ischemia-reperfusion (20x)', dict(v=20*v0, SOD=1e-5, GPX=5e-6, Fe=1e-6)),
]

print("Scenario-dependent ROS steady-state concentrations:")
print(f"{'scenario':38s}  {'[O2.-] (nM)':>12s} {'[H2O2] (uM)':>12s} {'[.OH] (fM)':>12s}")
for name, p in scenarios:
    O2m, H2O2, OH = ros_steady_state(p['v'], SOD=p['SOD'], GPX=p['GPX'], Fe=p['Fe'])
    print(f"{name:38s}  {O2m*1e9:12.3f} {H2O2*1e6:12.3f} {OH*1e15:12.3f}")

# Scan SOD2 activity -> O2.- buildup
SODs = np.logspace(-7, -4, 40)
O2ms_vs_SOD = np.array([v_source_to_O2m(v0, s) for s in SODs])

# Scan antioxidant combinations: SOD + GPX grid
grid_SOD = np.logspace(-7, -4, 20)
grid_GPX = np.logspace(-8, -4, 20)
H2O2_grid = np.zeros((len(grid_GPX), len(grid_SOD)))
for i, gpx in enumerate(grid_GPX):
    for j, sod in enumerate(grid_SOD):
        _, h, _ = ros_steady_state(v0, SOD=sod, GPX=gpx, Fe=1e-7)
        H2O2_grid[i, j] = h

# Oxidative damage accumulation over time (8-oxoG proxy)
t_years = np.linspace(0, 100, 100)
k_damage = 0.01  # per year scaled
damage = 1 - np.exp(-k_damage * t_years)  # saturating
damage_integrated = np.trapezoid(damage, t_years)
print(f"\nIntegrated lifetime damage (0-100y, rel units): {damage_integrated:.2f}")

# ---------- Plot ----------
fig, axes = plt.subplots(2, 2, figsize=(13.5, 10))
fig.patch.set_facecolor('#0a0a1a')
for ax in axes.ravel():
    ax.set_facecolor('#0a0a1a')
    ax.tick_params(colors='#cbd5e1')
    for s in ax.spines.values(): s.set_color('#334155')
    ax.grid(True, color='#334155', alpha=0.35)

ax1, ax2, ax3, ax4 = axes.ravel()

# Panel 1: bar chart of [O2.-] across scenarios
names = [s[0] for s in scenarios]
O2ms = [ros_steady_state(p['v'], SOD=p['SOD'], GPX=p['GPX'], Fe=p['Fe'])[0]*1e9
        for _, p in scenarios]
colors = ['#22c55e', '#fbbf24', '#fb923c', '#f472b6', '#a78bfa', '#ef4444']
ax1.barh(names, O2ms, color=colors, edgecolor='#1e293b')
ax1.set_xscale('log')
ax1.set_xlabel('[O2.-] steady state (nM)', color='#cbd5e1')
ax1.set_title('Matrix superoxide across scenarios',
              color='#fed7aa', fontweight='bold')
ax1.tick_params(axis='y', labelsize=9)

# Panel 2: SOD titration
ax2.loglog(SODs*1e3, O2ms_vs_SOD*1e9, '-o', color='#fb923c',
           linewidth=2.4, markersize=6)
ax2.axhline(1.0, linestyle='--', color='#22d3ee', alpha=0.7, label='1 nM (physiological)')
ax2.axvline(1e-2, linestyle=':', color='#fbbf24', alpha=0.7, label='typical SOD2 (10 uM)')
ax2.set_xlabel('[SOD2] (mM)', color='#cbd5e1')
ax2.set_ylabel('steady-state [O2.-] (nM)', color='#cbd5e1')
ax2.set_title('SOD2 concentration vs. superoxide steady state',
              color='#fed7aa', fontweight='bold')
ax2.legend(facecolor='#0f172a', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=10)

# Panel 3: heatmap of H2O2 vs SOD x GPX
im = ax3.pcolormesh(np.log10(grid_SOD*1e3), np.log10(grid_GPX*1e3),
                     np.log10(H2O2_grid*1e6), cmap='plasma', shading='auto')
ax3.set_xlabel('log10 [SOD2] (mM)', color='#cbd5e1')
ax3.set_ylabel('log10 [GPX1] (mM)', color='#cbd5e1')
ax3.set_title('Matrix [H2O2] as function of antioxidant levels',
              color='#fed7aa', fontweight='bold')
cbar = plt.colorbar(im, ax=ax3)
cbar.set_label('log10 [H2O2] (uM)', color='#cbd5e1')
cbar.ax.yaxis.set_tick_params(color='#cbd5e1')
plt.setp(cbar.ax.yaxis.get_ticklabels(), color='#cbd5e1')

# Panel 4: lifetime oxidative damage accumulation (mitohormesis band)
ax4.plot(t_years, damage, color='#fb923c', linewidth=2.5, label='cumulative 8-oxoG damage')
ax4.fill_between(t_years, damage-0.1, damage+0.1, color='#fb923c', alpha=0.2)
# Harman free-radical theory: damage drives aging
ax4.axvspan(70, 100, color='#ef4444', alpha=0.15, label='senescence phase')
ax4.set_xlabel('age (years)', color='#cbd5e1')
ax4.set_ylabel('cumulative damage (a.u.)', color='#cbd5e1')
ax4.set_title('Harman 1956: lifetime oxidative damage accumulation',
              color='#fed7aa', fontweight='bold')
ax4.legend(facecolor='#0f172a', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=10)

plt.tight_layout()
plt.savefig('output.png', dpi=120, bbox_inches='tight', facecolor='#0a0a1a')

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Simulation 2: Chouchani 2014 Ischemia-Reperfusion ROS Burst

ODE simulation of the Chouchani 2014 succinate-RET-ROS mechanism. We model three phases: baseline (0–5 min), ischemia with O₂ removed (5–15 min) during which succinate accumulates, and reperfusion (15–30 min) during which the over-reduced Q pool and high PMF drive reverse electron transport at Complex I, producing a massive superoxide burst at the flavin site. Preemptive malonate treatment (second curve) blocks succinate oxidation at C2, preventing QH₂ accumulation and dramatically reducing the ROS burst at reperfusion—a result validated clinically by Valls-Lacalle et al. (2016).

Python

script.py158 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
from scipy.integrate import odeint

# Chouchani 2014 Nature: ischemia-reperfusion succinate accumulation + RET ROS burst
# ---------------------------------------------------------------------------------
# Under ischemia, the respiratory chain halts: no O2, no electron acceptor for
# Complex IV. The Q pool becomes fully reduced. Succinate cannot be oxidized
# (fumarate reductase runs backward in some tissues, accumulating succinate).
# When reperfusion restores O2, succinate is rapidly oxidized by Complex II,
# the Q pool is highly reduced, and the PMF builds fast. Under these
# conditions, electrons flow BACKWARD through Complex I (reverse electron
# transport, RET), producing a massive burst of superoxide at the flavin.
#
# Chouchani et al. (2014 Nature 515:431) demonstrated that this mechanism
# drives ischemia-reperfusion injury in heart and brain, and that preemptive
# inhibition by malonate (a C2 inhibitor) prevents the succinate buildup and
# reduces infarct size.
#
# We simulate:
#   Phase 1 (baseline):   t = 0..5 min
#   Phase 2 (ischemia):   t = 5..15 min, O2 = 0
#   Phase 3 (reperfusion):t = 15..30 min, O2 restored
# Species: [O2], [succinate], [fumarate], QH2, PMF, [ROS] (cumulative).

def ir_model(y, t, O2_func, malonate=0.0):
    succ, fum, QH2, PMF, ROS = y
    O2 = O2_func(t)

# SDH forward reaction succ -> fum + QH2 (through C2)
    v_SDH = 5.0 * succ * (1 - QH2) * (1 - malonate)

# C3 + C4 forward flow: requires O2
    v_C3C4 = 8.0 * QH2 * O2 / (O2 + 0.01)

# Complex I normal flow: needs NADH (we hold constant), forward only if PMF < 210
    pmf_brake = 1.0 / (1.0 + np.exp((PMF - 210) / 15.0))
    v_C1 = 4.0 * (1 - QH2) * pmf_brake * O2/(O2+0.01)  # forward

# Reverse electron transport (RET) through C1: forward if QH2 high AND PMF high
    ret_factor = (QH2 - 0.5) * max(0, (PMF - 180)/30.0)
    v_RET = 6.0 * max(0, ret_factor) * O2/(O2+0.01)

# Dynamics
    dsucc = -v_SDH + (0.3 if O2 < 0.01 else 0.0)   # succinate accumulates during ischemia
    dfum  =  v_SDH
    dQH2  =  v_SDH + v_C1 - v_C3C4 - v_RET
    # PMF
    dPMF  = 1.5*(2*v_C3C4 + 4*v_C1 - 3*PMF)  # proton pumping vs leak+ATPase
    # ROS: generated by RET at C1 flavin + C3 Qo
    dROS  = 0.5 * v_RET + 0.05 * QH2
    return [dsucc, dfum, dQH2, dPMF, dROS]

def O2_profile(t):
    # minutes; baseline 1, ischemia 0..5-15, reperfusion 15-30
    if t < 5:   return 1.0
    if t < 15:  return 0.001
    return 1.0

t = np.linspace(0, 30, 2000)

# Control scenario
y0 = [0.2, 0.2, 0.3, 180, 0]   # initial succ, fum, QH2, PMF, ROS
sol_control = odeint(ir_model, y0, t, args=(O2_profile, 0.0))
sol_malonate = odeint(ir_model, y0, t, args=(O2_profile, 0.8))  # preemptive malonate

# Print key outputs
print("Chouchani 2014 ischemia-reperfusion simulation:")
print(f"  Peak succinate (control): {sol_control[:,0].max():.3f}")
print(f"  Peak succinate (malonate): {sol_malonate[:,0].max():.3f}")
print(f"  Peak PMF (control):       {sol_control[:,3].max():.1f} mV")
print(f"  Peak PMF (malonate):      {sol_malonate[:,3].max():.1f} mV")
print(f"  Cumulative ROS (control):  {sol_control[-1,4]:.2f}")
print(f"  Cumulative ROS (malonate): {sol_malonate[-1,4]:.2f}")

# Integrated ROS exposure (area under curve)
ros_integ_ctrl = np.trapezoid(sol_control[:, 4], t)
ros_integ_mal  = np.trapezoid(sol_malonate[:, 4], t)
print(f"\nIntegrated ROS exposure (AUC):")
print(f"  control:  {ros_integ_ctrl:.2f}  (a.u. x min)")
print(f"  malonate: {ros_integ_mal:.2f}  (a.u. x min)")
print(f"  reduction: {100*(1 - ros_integ_mal/ros_integ_ctrl):.1f} %")

# Dose-response on malonate
mal_doses = np.linspace(0, 1, 11)
ros_final = []
succ_peak = []
for md in mal_doses:
    sol = odeint(ir_model, y0, t, args=(O2_profile, md))
    ros_final.append(sol[-1, 4])
    succ_peak.append(sol[:,0].max())
ros_final = np.array(ros_final)
succ_peak = np.array(succ_peak)

ax1, ax2, ax3, ax4 = axes.ravel()

# Panel 1: succinate time course
ax1.plot(t, sol_control[:, 0], color='#fb923c', linewidth=2.4, label='control')
ax1.plot(t, sol_malonate[:, 0], color='#22c55e', linewidth=2.4, label='+ malonate')
ax1.axvspan(5, 15, color='#ef4444', alpha=0.15, label='ischemia')
ax1.axvline(15, linestyle='--', color='#22d3ee', alpha=0.7, label='reperfusion')
ax1.set_xlabel('time (min)', color='#cbd5e1')
ax1.set_ylabel('[succinate] (a.u.)', color='#cbd5e1')
ax1.set_title('Chouchani 2014: succinate accumulation during ischemia',
              color='#fed7aa', fontweight='bold')
ax1.legend(facecolor='#0f172a', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=10)

# Panel 2: QH2 pool - peaks in ischemia, drives RET at reperfusion
ax2.plot(t, sol_control[:, 2], color='#fb923c', linewidth=2.4, label='control')
ax2.plot(t, sol_malonate[:, 2], color='#22c55e', linewidth=2.4, label='+ malonate')
ax2.axvspan(5, 15, color='#ef4444', alpha=0.15)
ax2.axvline(15, linestyle='--', color='#22d3ee', alpha=0.7)
ax2.set_xlabel('time (min)', color='#cbd5e1')
ax2.set_ylabel('QH2 fraction', color='#cbd5e1')
ax2.set_title('Ubiquinone redox state through ischemia-reperfusion',
              color='#fed7aa', fontweight='bold')
ax2.legend(facecolor='#0f172a', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=10)

# Panel 3: ROS burst at reperfusion
ax3.plot(t, sol_control[:, 4], color='#ef4444', linewidth=2.6, label='control ROS')
ax3.plot(t, sol_malonate[:, 4], color='#22c55e', linewidth=2.6, label='+ malonate ROS')
ax3.axvspan(5, 15, color='#ef4444', alpha=0.15, label='ischemia')
ax3.axvline(15, linestyle='--', color='#22d3ee', alpha=0.7)
ax3.fill_between(t, 0, sol_control[:, 4], color='#ef4444', alpha=0.2)
ax3.set_xlabel('time (min)', color='#cbd5e1')
ax3.set_ylabel('cumulative ROS (a.u.)', color='#cbd5e1')
ax3.set_title('Reverse-electron-transport ROS burst at reperfusion',
              color='#fed7aa', fontweight='bold')
ax3.legend(facecolor='#0f172a', edgecolor='#334155', labelcolor='#cbd5e1', fontsize=10)

# Panel 4: malonate dose-response
ax4.plot(mal_doses, ros_final, '-o', color='#ef4444', linewidth=2.5,
         markersize=8, label='final ROS')
ax4.set_xlabel('malonate inhibition fraction', color='#cbd5e1')
ax4.set_ylabel('final cumulative ROS (a.u.)', color='#ef4444')
ax4.tick_params(axis='y', labelcolor='#ef4444')
ax4b = ax4.twinx()
ax4b.plot(mal_doses, succ_peak, '-s', color='#fb923c', linewidth=2.2,
          markersize=8, label='peak succinate')
ax4b.set_ylabel('peak [succinate] (a.u.)', color='#fb923c')
ax4b.tick_params(axis='y', labelcolor='#fb923c')
ax4.set_title('Preemptive malonate reduces ROS (Valls-Lacalle 2016)',
              color='#fed7aa', fontweight='bold')

plt.tight_layout()
plt.savefig('output.png', dpi=120, bbox_inches='tight', facecolor='#0a0a1a')

Click Run to execute the Python code

Code will be executed with Python 3 on the server

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