Redox model and capacity calibration

PDF page 13 7.3 Cell-age population statistics (chronic G6PD thresholds) The chronic 14-day primaquine threshold reflects red-cell-age population statistics, which a single-cell model cannot recover (§3.4). A population extension tracking cell-age sub-populations is a separate paper. 7.4 NRF2 simplifications and the efflux-pump caveat V collapses ~100 NRF2 targets into one capacity term. Real KEAP1-mutant chemoresistance also involves multidrug efflux pumps (MRP1/ABCC1) and glutathione-S-transferases that NAC does not modulate. If the predicted selectivity holds but partly for these reasons, the redox channel is doing only part of the work — which is why the 8-oxo-dG biomarker matters: a larger NAC-induced suppression in the NRF2-active stratum would show the redox channel is genuinely active. Separately, NAC is nephroprotective and reduces chemotherapy toxicity, so a systemic benefit could partially mask a tumour-level harm; the stratum- selectivity contrast and the 8-oxo-dG interaction test are included to separate these. 7.5 Lung-parameter robustness (what survives a 2× shift) Calibration rigour decays from erythrocyte (Mode 1) to lung-epithelium (Mode 2) parameters. The table states which conclusions survive a 2× parameter shift. Table 7. Robustness of conclusions to parameter perturbation. Conclusion Survives ±50% / 2× shift? Comment Qualitative regime ordering (Table 2) Yes Robust across all single-parameter perturbations tested. Direction of NAC effect (harm) Yes Sign of ∂Φ/∂G_max is fixed. Subgroup selectivity Mostly Holds unless the absolute Φ axis is mis-placed by ~2×. Exact HR magnitude No Depends on Φ_surv placement and Sayin translation; reported as a range (Table 6). 7.6 What this model does not claim It does not explain all antioxidant trial outcomes — only the GSH-coupled subset. It does not capture full tumour redox ecology (efflux pumps, GST conjugation, immunology, epigenetics). It does not provide a validated HR magnitude — only a conditional, falsifiable estimate across a range. It does not treat plasma 8-oxo-dG as proof of tumour-cell flux — only as a partial projection. It does not derive hormesis, nor red- cell-age population statistics. 8. Discussion The contribution is partial unification through one mathematical object whose parameter regimes generate qualitatively distinct antioxidant outcomes — drug-induced hemolysis, smoker-lung adaptation, ATBC reversibility, KEAP1-mutant chemoresistance, predicted NAC harm — each mapping to a (regime, failure- mode) pair. The G6PD case calibrates Mode 1: biochemically anchored, calibration-validated, with a near- parameter-free threshold β_c ≈ V/V_total. The NSCLC case probes Mode 2: geometrically articulated but empirically scaffolded through an external Φ → DDR mapping not yet calibrated in the relevant cell type. We resist calling these “two faces of one polyhedron”: Mode 1 is a state-space attractor with biochemical anchoring, Mode 2 a flux-output region anchored to literature extrapolation. The asymmetry is the PDF page 14 framework’s central honest feature, and the proposed trial plus the in-cell calibration (§7.1) are what would close it. Read as a redox-biology paper first and a mathematical one second: finite pools, saturable regeneration, thresholds, flux redistribution, and hysteresis are physical constraints that a list of molecules cannot express, and they are what make the harm population-specific. The clinical value of the framework will be decided by the §5 prediction; its theoretical value by whether the dual-failure-mode geometry is the right structural account of GSH-coupled antioxidant harm.

Two failure modes of glutathione homeostasis: a calibrated dynamical model recovers G6PD severe-deficiency contraindications and generates a falsifiable NSCLC trial prediction Daniel John Murray Independent Researcher, Melbourne, Australia Keywords: glutathione; G6PD deficiency; KEAP1/NRF2; non-small cell lung cancer; N-acetylcysteine; contribution has two halves of deliberately unequal evidential status, kept visible throughout. Calibrated result: populated with published erythrocyte kinetics and no fitting to clinical data, the model recovers the established G6PD severe-deficiency contraindications. Falsifiable prediction: the model generates — but does not confirm — a prospective, pre-specified, multi-level falsifiable prediction for adjunctive N- acetylcysteine (NAC) in NRF2-active NSCLC. Highlights • A three-variable dynamical model of GSH homeostasis has two distinct failure modes: oxidative collapse (a tipping point to a depleted-GSH state) and reductive fade (graded loss of damage-surveillance • A slow NRF2-controlled loop produces three regimes — healthy, G6PD-pinned, KEAP1-pinned — each failing primarily in one mode, mapping cleanly to known clinical phenomena. • The model generates a prospective, pre-specified falsifiable prediction for adjunctive NAC in NRF2- active NSCLC: direction (harm) and subgroup selectivity are framework-derived; the hazard-ratio magnitude is explicitly conditional and reported across a sensitivity range, not as a single value. • A within-trial partial flux-proxy biomarker (plasma 8-oxo-dG) and explicit falsification thresholds are stated in advance, making the prediction testable within months. Abstract Background. Antioxidant supplementation helps some patients, harms specific subgroups (G6PD deficiency, hereditary hemochromatosis, KEAP1-mutant lung cancer), and does little in most. Some of this heterogeneity reflects conserved biology; some reflects noise (weak subgroup analyses, imperfect biomarkers, post-hoc interpretation). No mechanistic framework has yet produced quantitative, falsifiable forward predictions for the GSH-coupled subset.

G6PD severe-deficiency single-exposure contraindications; the ordering of threshold-crossing by severity class is robust to ±50% variation in any single parameter. Results — falsifiable prediction. For adjunctive NAC in KEAP1-mutant or NRF2-IHC-high NSCLC on platinum chemotherapy, the model generates a prospective, pre-specified prediction stratified by evidential strength. Direction (harm) and subgroup selectivity (concentrated in the NRF2-active stratum) are framework-derived; the magnitude (progression hazard ratio, central estimate 1.55) is explicitly conditional and reported across a sensitivity range. A within-trial partial flux-proxy biomarker (plasma 8-oxo-dG) and explicit falsification thresholds are committed in advance. The design is a biomarker-stratified randomized trial whose scale sits between conventional Phase II and Phase III. Conclusions. One mathematical object, three regimes, two failure modes. The G6PD result is independently calibrated; the NSCLC result is a falsifiable extrapolation. This split between calibrated result and forward prediction is the central scientific commitment. 1. Introduction 1.1 The clinical paradox Major antioxidant prevention trials have produced apparent paradoxes. Vitamin E supplementation increased prostate cancer risk in men with low baseline selenium [1–2]. β-carotene increased lung cancer in smokers treatment interactions. The scientific task is therefore not to unify every divergent finding, but to distinguish conserved biological structure from noise — and, where structure exists, to express it in a model that makes quantitative, falsifiable predictions. This paper attempts that only for the subset of phenomena coupled to GSH dynamics; it does not claim to explain all antioxidant outcomes. 1.2 Why a list of molecules is not enough Redox biology is frequently narrated as a contest between “bad free radicals” and “good antioxidants.” That framing cannot capture the clinical data, and there is a growing call to move beyond it toward operational,

with two failure modes and three regimes, presented visually and in plain language before any equation; Mode 1 calibration (§3) — the static-capacity case calibrated to erythrocyte biochemistry, recovering G6PD contraindications without fitting; Mode 2 prediction (§5) — the dynamic-capacity case applied to NRF2-active NSCLC to generate a falsifiable forward prediction; Trial falsification (§5.4) — explicit pre-specified thresholds and a within-trial biomarker. Retrospective trial data (§4) appear only as organizing context, not validation; stress-tests (§6) and an honest account of what the model does not derive (§7–8) close the paper. 1.5 Scope of the claim This model applies to GSH-coupled redox systems in which finite regeneration, oxidative drain, and

2.5 Failure mode 2: reductive fade (graded surveillance loss) A cell with very high V and low β produces little flux Φ: its GSH is high, its damage low, its consumption slow. But the DNA-damage response (p53 pulses, ATM activation, γH2AX foci) is driven by the rate of oxidative DNA damage, which scales with Φ. Single-cell imaging shows p53 activation is linearly correlated with the number of DNA breaks without a sharp threshold [14], and γH2AX/pATM/53BP1 foci scale linearly with H₂O₂ over a measured band [15]. Below that band the response curve has a long shallow toe: as Φ drops, fewer p53 pulses fire and damaged cells are cleared more slowly. Reductive fade is therefore graded, not a cliff. It is not a fixed-point attractor and has no bifurcation; it is a region of suppressed flux where the cost arises from an external biological mapping (Φ → surveillance

completeness), not from the redox dynamics themselves. We summarise the regime with an operational band Φ_surv, but treat this as a calibration target with real uncertainty, and in §5 we report the trial prediction across a range of Φ_surv rather than at a single cut. 2.6 Three regimes from the slow loop Table 2. The three regimes and their natural failure modes. Regime Slow loop (V) Primary failure mode Clinical phenomenon Healthy V free in [V_min, V_max] Neither (normal exposure) Supplementation benign supplementation harm These are not three models but three regions of one continuous parameter space (V_min, V_max, β). Hybrid phenotypes are points in between, and the framework predicts their behaviour by interpolation. 2.7 The claims hierarchy — read this to weight every result Because the two halves of the paper differ in evidential status, we place the claims hierarchy up front and add a column stating what would falsify each tier. Mode 1 results sit in the upper, rigorous tiers; Mode 2 results sit in the lower, empirically-scaffolded tiers. Table 3. Claims hierarchy. Each result is tagged by evidential tier and by what would refute it. Tier Mode 1 (oxidative collapse) Mode 2 (reductive fade) What would falsify this tier Geometry- derived β_c ≈ V/V_total; bistability above β_c; boundary-

contraindications are recovered; the chronic thresholds are explicitly out of scope. Existing human data (Visacri et al. 2019: NAC 600 mg/d with cisplatin in non-NRF2-enriched head/neck cancer, efficacy not impaired) are consistent with the framework, which predicts no detectable harm below the dose threshold and outside the NRF2-active subgroup (§5). 4. Retrospective organizing context, not validation This section is organizing context, not validation. The framework was developed with knowledge of these trials; the comparisons are not statistically independent (multiple strata per trial); and the literature is publication-biased toward interesting baseline-by-treatment interactions. Any p-value computed across these comparisons would reflect curation, not prediction. The empirical weight of the paper rests on the G6PD calibration (§3) and the forward test (§5). Organised by predicted (regime, failure-mode) pair, the directional pattern across the major trials (SELECT, NPC, ATBC, CARET, PHS I, SU.VI.MAX, Linxian, the Women’s Health Study, EUROSCAN; full citations and the tiered-label table in the Supplement) is consistent: deficient-stratum benefit, replete-stratum harm, chronic-ROS-load harm, post-cessation reversion, and saturation-regime null. The ATBC post-cessation attenuation is consistent with the model’s slow-loop relaxation; the proposed separation into a fast (NRF2-relaxation) and slower (cell-turnover) timescale is the model-distinctive, falsifiable element, though only the fast single-cell component is simulated here (§6). A previously reported quantitative fit to the ATBC attenuation curve is deferred to a planned population-level analysis and is not relied upon here.

5. Prospective forward prediction: NAC + platinum in NRF2-active NSCLC (falsifiable prediction) A substantial minority of NSCLC tumours, especially adenocarcinomas, carry KEAP1 loss-of-function or NFE2L2 (NRF2) gain-of-function mutations, producing constitutive NRF2 activity and elevated antioxidant capacity [21–22], with documented platinum resistance [10, 23]. In the model these are KEAP1-pinned cells: V locked high, G high, e and Φ low — operating in reductive-fade territory. Adding NAC (which raises G_max tumour cells escape apoptosis. This is consistent with Sayin et al. 2014 [11] and Romero et al. 2017 [24]. We model NAC as raising G_max by 40% (an explicit assumption at the upper edge of the pharmacodynamic range; a conservative +25% shifts the predicted Φ modestly while preserving the ordering, §7.5). 5.1 The prediction has three layers of decreasing certainty Three layers — this split is the central scientific commitment. Layer 1 — Direction (strongest): NAC produces harm (progression HR > 1) in NRF2-active NSCLC on platinum. Framework-derived: Φ is monotone-decreasing in G_max and NAC raises G_max, so adding antioxidant capacity to a cell already in reductive territory drives Φ down. Layer 2 — Subgroup selectivity (strong): harm is concentrated in the Because reductive fade is graded (§2.5), the magnitude is reported as a function of where the surveillance band sits, anchored to the simulated Φ values produced by the dynamic-V model (Table 5). These values are the parameter-faithful output of the deposited reproduction code (no tuning); the prediction depends on the ordering of and ratios between scenarios, which are invariant to the absolute Φ scale, not on the absolute values themselves. Table 5. Surveillance flux Φ during cisplatin pulses, by scenario (dynamic-V model; parameter-faithful values from the deposited code). Φ is averaged over the on-pulse interval. KEAP1-pinned + cisplatin 0.487 0.917 KEAP1-pinned + cisplatin + NAC 0.369 (−24%) 0.680 The ordering is the mechanism behind the selectivity prediction: KEAP1-pinned cells start at lower Φ, so the same fractional NAC suppression drops them deepest into the surveillance-curve toe, while healthy cells remain in the dose-proportional part of the response curve.

Table 6. Predicted progression hazard ratio (NRF2-active arm) as the surveillance band Φ_surv is varied across the operationally defensible window, re-anchored to the parameter-faithful Φ of Table 5. Selectivity = HR(NRF2-active)/HR(control). The central calibration sits between the KEAP1+NAC and KEAP1 values. Φ_surv (µM·min⁻¹) Position vs simulated Φ Predicted HR (NRF2-active) Selectivity (A/B) ≤ 0.38 at/below KEAP1+NAC (0.369) ≈ 1.05–1.15 collapses (≈ 1.0) 0.40 just above KEAP1+NAC ≈ 1.30–1.45 modest (≈ 1.2–1.3) 0.43 (central) between KEAP1+NAC and KEAP1 healthy+NAC ≈ 1.7–2.0 erodes (→ 1.0–1.2) The central prediction (HR ≈ 1.55) is one point on a curve, not a cliff. Direction and selectivity are robust across the defensible Φ_surv window, while magnitude varies smoothly with it; the band’s placement is what the in-cell calibration of §7.1 would fix. At Φ_surv ≤ 0.38 the prediction is loss of harm (HR ≈ 1.0), not reversal to benefit — the model does not predict NAC protection in any regime. 5.3 A partial flux-proxy biomarker (not a decisive readout) We embed plasma 8-oxo-2 -deoxyguanosine (8-oxo-dG) as a partial flux-proxy biomarker. It cannot prove ′ tumour-cell Φ: plasma 8-oxo-dG is systemic, reflecting whole-body oxidative damage, and is one projection of a spatially and temporally complex system. Causality can be inferred only in the overlap between what NAC changes and what the assay can detect. What it can do is test whether NAC shifts the oxidative-damage projection in the predicted direction and whether that shift is larger in the NRF2-active stratum. We therefore frame it as a mechanistic consistency test, not a decisive readout; tumour-specific Φ would require imaging or tissue measurement. 5.4 Trial design and pre-specified falsification thresholds Population: advanced NSCLC, first-line platinum doublet, KEAP1/NFE2L2 status by NGS and NRF2 IHC. Strata: (A) NRF2-active; (B) NRF2-low control. Randomization within each stratum: NAC 1200 mg/d vs placebo. Primary endpoint: 12-month progression-free survival. Biomarker: plasma 8-oxo-dG at four timepoints. Feasibility. Detecting the central HR ≈ 1.55 in the NRF2-active stratum at 80% power (two-sided α = 0.05, adjunctive-trial sense while noting this honestly. Pre-specified, committed in print before any such trial is run: • Direction (primary): NAC vs placebo within stratum A, predicted HR 1.20–2.00 (central 1.55). Falsified if HR ≤ 1.10 with upper 95% CI < 1.30. • Selectivity (secondary): stratum A HR / stratum B HR predicted ≥ 1.30. Falsified if ratio ≤ 1.05. • Biomarker (exploratory): a NAC-vs-placebo 8-oxo-dG difference more negative in stratum A than B (interaction p < 0.05) would support the redox mechanism; failure to observe it would not falsify the core prediction, since plasma 8-oxo-dG is a partial, systemic proxy (§5.3).

A Data Safety Monitoring Board with a pre-specified harm stopping rule (HR > 1.7) and informed consent disclosing the predicted harm are essential; the preclinical equipoise (Sayin 2014; Romero 2017; widespread off-label NAC use) already exists, so the trial refines an existing question rather than raising a new ethical bar. 6. Computational stress-tests of the dynamic-V model The dynamic-V system was stress-tested to separate structurally-derived results from posited ones. The complete reproduction code is openly available as a single self-contained file at Zenodo • Reversibility (fast component derived; population stage requires extension). The model simulates the fast component (single-cell V relaxation, hours). The slower component (weeks–months, from cell turnover) is a prediction, not a simulation; the model-distinctive falsifiable claim is the existence of two separable timescales. • Hormesis (not derived). Preconditioning produced only ~4% change in peak damage: the healthy attractor is too robust for basin-crossing tolerance in this calibration. The paper does not claim hormesis and does not rely on it. purchase. 7.1 Φ_surv is partially calibrated — and the decisive next experiment The Φ → surveillance mapping is external biology (p53/ATM kinetics), not redox dynamics. We anchor Φ_surv to Loewer 2013 [14] and Sakai 2016 [15], but our peak Φ values sit below Sakai’s measured band, so we are extrapolating down the response-curve toe. The decisive next step — doing for Mode 2 what Reed (2008) did for Mode 1 — is an in-cell calibration: matched KEAP1-mutant and wild-type NSCLC lines, ± cisplatin × graded NAC, with real-time GSH/GSSG (Grx1-roGFP2) to read Φ, live-cell p53/γH2AX/caspase-3 for the DDR, and parallel GSH and GR assays to anchor G_max and V in the same cells. This converts Φ_surv from a literature-extrapolated band into a measured, cell-type-specific target. 7.2 Hormesis is outside scope (and not relied upon) This three-variable GSH model does not produce hormesis (§6). Classical hormesis likely lives in broader

V collapses ~100 NRF2 targets into one capacity term. Real KEAP1-mutant chemoresistance also involves multidrug efflux pumps (MRP1/ABCC1) and glutathione-S-transferases that NAC does not modulate. If the predicted selectivity holds but partly for these reasons, the redox channel is doing only part of the work — which is why the 8-oxo-dG biomarker matters: a larger NAC-induced suppression in the NRF2-active stratum would show the redox channel is genuinely active. Separately, NAC is nephroprotective and reduces chemotherapy toxicity, so a systemic benefit could partially mask a tumour-level harm; the stratum- selectivity contrast and the 8-oxo-dG interaction test are included to separate these. It does not explain all antioxidant trial outcomes — only the GSH-coupled subset. It does not capture full tumour redox ecology (efflux pumps, GST conjugation, immunology, epigenetics). It does not provide a validated HR magnitude — only a conditional, falsifiable estimate across a range. It does not treat plasma 8-oxo-dG as proof of tumour-cell flux — only as a partial projection. It does not derive hormesis, nor red- cell-age population statistics. 8. Discussion The contribution is partial unification through one mathematical object whose parameter regimes generate qualitatively distinct antioxidant outcomes — drug-induced hemolysis, smoker-lung adaptation, ATBC reversibility, KEAP1-mutant chemoresistance, predicted NAC harm — each mapping to a (regime, failure- mode) pair. The G6PD case calibrates Mode 1: biochemically anchored, calibration-validated, with a near- parameter-free threshold β_c ≈ V/V_total. The NSCLC case probes Mode 2: geometrically articulated but empirically scaffolded through an external Φ → DDR mapping not yet calibrated in the relevant cell type. We resist calling these “two faces of one polyhedron”: Mode 1 is a state-space attractor with biochemical

thresholds, flux redistribution, and hysteresis are physical constraints that a list of molecules cannot express, and they are what make the harm population-specific. The clinical value of the framework will be decided by the §5 prediction; its theoretical value by whether the dual-failure-mode geometry is the right structural account of GSH-coupled antioxidant harm. Statements and declarations Ethics approval. Not applicable; aggregate previously-published data only. Competing interests. The author declares no competing interests. https://doi.org/10.5281/zenodo.20600332, time-stamped at the date of submission. Run with numpy and scipy, it reproduces, from the stated parameters with no tuning, the Mode 1 threshold-crossing pattern (Table 4) and the Mode 2 surveillance-flux values (Table 5). The §5 prediction (HR band, falsification thresholds, three-tier reading, 8-oxo-dG test) is stated in full here so that it is on record as prospective. Use of generative AI. AI tools (Claude by Anthropic; DeepSeek) assisted with literature search, drafting/editing, mathematical checking, and computational support. All theoretical content, calibration choices, the dual-failure-mode framing, and the forward prediction originated with the author, who has reviewed all content and takes full responsibility. Author contribution. D.J.M. is the sole author. References 1. Klein EA, Thompson IM Jr, Tangen CM, et al. Vitamin E and the risk of prostate cancer (SELECT). JAMA.