The Flywheel Paradox: Iron-Sulfur Cluster Self-Reference, Thermodynamic Inevitability of Aging, and Optimal Therapeutic Windows for Iron Chelation

A mathematical model of iron homeostasis based on two coupled differential equations describing functional iron concentration (F) and iron management capacity (M). The model's core mechanism is a self-referential loop: iron-containing Fe-S clusters in the mitochondrial electron transport chain produce ATP, which sustains the iron management machinery, which maintains Fe-S cluster integrity. Linear stability analysis reveals a critical gain threshold (G = 1): below it, the system is in a damped mode (health); above it, in flywheel mode (accelerating overload). Three predictions: (1) critical slowing down as G approaches 1, providing a theoretical basis for preclinical iron biomarker variability; (2) a U-shaped therapeutic window for iron chelation, bounded by Fe-S cluster assembly constraints and the flywheel reversal threshold; (3) Fe-S cluster assembly integrity determines cellular sensitivity to combined iron chelation and ferroptosis induction. Calibration with Friedreich's ataxia deferiprone trials yields a therapeutic window of R2* ~ 13-16 s⁻¹ in the dentate nucleus.