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.

WarningLimitation: Cascade Example Assumptions

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.