Formal ISR State Variables in the PEM/Energy ODE Model
The existing energy-exhaustion ODE model for PEM lacks variables representing the Integrated Stress Response state. The following extensions are proposed to enable formal modelling of the PEM biphasic ISR cycle hypothesis (PEM as Biphasic ISR Cycle: Adaptive Initiation and Maladaptive Persistence).
With ISR state variables \(I(t)\) and GADD34 dephosphorylation rate \(k_\text{dephos}\), the PEM ODE system admits bifurcation analysis. Key parameters: \(k_\text{dephos}\) (dephosphorylation rate, reduced in ME/CFS) and \(S_0\) (baseline stress influx, increased in ME/CFS).
Predicted bifurcation structure: In the \((k_\text{dephos}, S_0)\) parameter plane, a fold bifurcation exists separating:
- Monostable healthy attractor: \(I_\text{ss} \approx 0\), \(E_\text{max} \approx E_\text{baseline}\)
- Bistable ME/CFS region: stable high-\(I\) and low-\(I\) attractors; hysteresis in PEM recovery
- Monostable ME/CFS attractor: \(I_\text{ss} >> 0\), chronically reduced \(E_\text{max}\)
Therapeutic prediction: Interventions that increase \(k_\text{dephos}\) (GADD34 support) or decrease \(S_0\) (reduce chronic stress influx) collapse the high-\(I\) attractor and enable transition to the low-\(I\) regime. The bifurcation diagram predicts why ME/CFS is difficult to reverse by single interventions: only moving across the fold bifurcation boundary produces lasting recovery.
Certainty: 0.35 — bistability has been proposed in chronic disease ODE models; specific ISR parameters require empirical constraint. Qualitatively motivated by clinical observation of hysteresis in ME/CFS severity trajectories.