Consolidated Cascade Example
The preceding worked examples illustrate each subsystem in isolation. In ME/CFS, however, the subsystems interact: impairment at one level propagates through the others. This section traces the cascade for a single patient to show how modest individual deficits compound into severe energy failure.
Patient profile. A moderate ME/CFS patient with 35% Complex I impairment (\(\alpha_{\text{CI}} = 0.65\)) and 30% \(\text{NAD}^\text{+}\) depletion (\(\gamma = 0.7\)).
Step 1: Electron transport chain — the cliff effect. The ATP synthase driving force depends on how far the mitochondrial membrane potential \(\Delta \Psi\) exceeds its minimum operating threshold (\(\Delta \Psi_{\text{threshold}} \approx 110\) mV). From atp synthase:
\[ \text{Driving force} = \frac{\Delta \Psi - \Delta \Psi_{\text{threshold}}}{\Delta \Psi} \]
In health, \(\Delta \Psi \approx 160\) mV: driving force \(= (160 - 110)/160 = 31%\) of theoretical maximum. With \(\alpha_{\text{CI}} = 0.65\), reduced proton pumping lowers \(\Delta \Psi\) to \(\approx 135\) mV: driving force \(= (135 - 110)/135 = 19%\) of maximum. This is a 39% reduction in ATP synthase output from 35% Complex I damage—disproportionate because the nonlinear threshold term amplifies impairment as \(\Delta \Psi\) approaches \(\Delta \Psi_{\text{threshold}}\).
Step 2: Krebs cycle — \(\text{NAD}^\text{+}\) bottleneck. The Krebs cycle flux depends on \(\text{NAD}^\text{+}\) availability through krebs flux:
\[ J_{\text{Krebs}} \propto \frac{[\text{NAD}^+]}{[\text{NAD}^+] + [\text{NADH}]} \]
In health, this ratio \(\approx 0.85\). With \(\gamma = 0.7\) (30% \(\text{NAD}^\text{+}\) depletion), the ratio drops to \(\approx 0.60\). Reduction: \((0.85 - 0.60)/0.85 = 29%\). The Krebs cycle feeds electrons to the ETC via NADH, so this 29% reduction in Krebs output further reduces the already-impaired ETC flux. The two deficits compound multiplicatively: effective ATP production is approximately $ 0.61 = 0.43$ of healthy—a 57% total reduction from two individually moderate impairments.
Step 3: Reactive oxygen species — amplified damage. ROS production scales with unused ETC capacity (ros production):
\[ J_{\text{ROS}} \propto 1 - \frac{J_{\text{CI}}}{J_{\text{CI,max}}} \]
In health, Complex I runs at ~95% capacity: ROS factor \(= 1 - 0.95 = 0.05\). At \(\alpha_{\text{CI}} = 0.65\): ROS factor \(= 1 - 0.65 = 0.35\). Ratio: $ 0.35/0.05 =$ 7-fold increase in ROS production. This elevated ROS damages ETC complexes further, creating a positive feedback loop that the antioxidant system must counterbalance. If antioxidant capacity is not proportionally upregulated, oxidative damage accumulates, progressively reducing \(\alpha_{\text{CI}}\) and deepening the deficit.
Combined picture. Two individually moderate deficits (35% Complex I impairment, 30% \(\text{NAD}^\text{+}\) depletion) produce: 57% reduced ATP production (multiplicative), 7-fold elevated ROS (self-reinforcing damage), and an energy envelope so narrow that ordinary activities trigger PEM. This cascade explains why ME/CFS severity is often disproportionate to any single measurable abnormality—it is the interaction between subsystems that generates the clinical phenotype.
This example treats the three effects as independent multiplicative factors. In the full coupled ODE system (Integrated Multi-System Models), the interactions are more complex: ROS-mediated damage reduces \(\alpha_{\text{CI}}\) over time, \(\text{NAD}^\text{+}\) depletion affects both Krebs and ETC flux, and the membrane potential depends on all proton-pumping complexes, not just Complex I. The multiplicative approximation is a pedagogical simplification; the true cascade dynamics require numerical simulation of the coupled system.