Innate Immunity Dynamics
1 NK Cell Activity Model
Natural killer (NK) cells are a critical component of innate immunity, and reduced NK cell cytotoxic function is one of the most replicated immunological findings in ME/CFS (Hardcastle et al. 2016). The NK cell model tracks three populations: resting NK cells (\(N_r\)), activated NK cells (\(N_a\)), and exhausted NK cells (\(N_e\)):
\[ \begin{aligned} \frac{d N_r}{d t} &= s_N - d_r N_r - k_{\text{act}}(\mathbf{C}) N_r + k_{\text{recov}} N_e \\ \frac{d N_a}{d t} &= k_{\text{act}}(\mathbf{C}) N_r - k_{\text{exh}} N_a - d_a N_a \\ \frac{d N_e}{d t} &= k_{\text{exh}} N_a - k_{\text{recov}} N_e - d_e N_e \end{aligned} \tag{1}\]
where \(s_N\) is the bone marrow production rate, \(d_r\), \(d_a\), \(d_e\) are death rates for each population, \(k_{\text{act}}(\mathbf{C})\) is the cytokine-dependent activation rate, \(k_{\text{exh}}\) is the exhaustion rate, and \(k_{\text{recov}}\) is the recovery rate from exhaustion. The activation rate depends on the cytokine milieu \(\mathbf{C}\):
\[ k_{\text{act}}(\mathbf{C}) = k_{\text{act,0}} \cdot \frac{[\text{IL-12}] + [\text{IL-15}]}{K_a + [\text{IL-12}] + [\text{IL-15}]} \cdot \frac{K_i^{\text{IL-10}}}{K_i^{\text{IL-10}} + [\text{IL-10}]} \tag{2}\]
where IL-12 and IL-15 are activating cytokines, IL-10 is an inhibitory cytokine, and \(K_a\), \(K_i^{\text{IL-10}}\) are the respective half-saturation constants. In ME/CFS, the model represents reduced cytotoxicity through two mechanisms: (1) increased \(k_{\text{exh}}\) (accelerated exhaustion due to chronic stimulation) and (2) reduced \(k_{\text{recov}}\) (impaired recovery, possibly linked to energy deficits modeled in Energy Metabolism Models). This produces a steady state with elevated \(N_e\\/N_a\) ratio—more exhausted than active NK cells—consistent with the functional impairment observed clinically.
2 Cytokine Network Model
Cytokines mediate communication between immune cells and between the immune system and other organ systems. The cytokine network model tracks the concentrations of key pro-inflammatory (IL-1\(\beta\), IL-6, TNF-\(\alpha\), IFN-\(\gamma\)) and anti-inflammatory (IL-10, TGF-\(\beta\)) cytokines. Each cytokine \(C_i\) follows:
\[ \frac{d C_i}{d t} = \sum_{j} \sigma_{i j}(\mathbf{C}, \mathbf{N}) - \delta_i C_i \tag{3}\]
where \(\sigma_{i j}\) represents production of cytokine \(i\) by cell type \(j\) (dependent on the full cytokine vector \(\mathbf{C}\) and immune cell populations \(\mathbf{N}\)), and \(\delta_i\) is the degradation rate. The production terms encode the network topology—which cytokines stimulate or inhibit the production of which other cytokines.
Hornig et al. identified distinct cytokine signatures in ME/CFS that vary with disease duration: patients with illness duration \(\leq 3\) years showed elevated pro-inflammatory cytokines, while those with longer illness showed a mixed or suppressed profile (Hornig et al. 2015). Montoya et al. confirmed that cytokine levels correlate with symptom severity, with IL-6 and TNF-\(\alpha\) among the strongest correlates (Montoya et al. 2017). The model captures this transition through a bifurcation in the cytokine network: early disease corresponds to a high-inflammation attractor, while chronic disease transitions to a “remodeled” state where feedback inhibition (via IL-10, cortisol) partially suppresses acute inflammation but fails to restore normal homeostasis.
The IL-6 dynamics illustrate the feedback structure:
\[ \frac{d [\text{IL-6}]}{d t} = \sigma_{\text{IL-6}}^{\text{mono}} \cdot f_{\text{act}}(\mathbf{C}) \cdot M_a + \sigma_{\text{IL-6}}^{\text{Th17}} \cdot T_{17} - \delta_{\text{IL-6}} [\text{IL-6}] \tag{4}\]
where \(M_a\) is the activated monocyte/macrophage population, \(T_{17}\) is the Th17 cell population, and \(f_{\text{act}}(\mathbf{C})\) is an activation function incorporating stimulation by TNF-\(\alpha\) and IL-1\(\beta\) and inhibition by IL-10. IL-6 in turn promotes Th17 differentiation (creating a positive feedback loop) and stimulates acute-phase protein production by hepatocytes.
3 Chronic Immune Activation
Sustained immune activation imposes a substantial metabolic cost. Activated immune cells can increase glucose consumption 10–20-fold, shifting from oxidative phosphorylation to aerobic glycolysis (the immunological Warburg effect). The model couples immune activation to energy metabolism (Energy Metabolism Models) through an immune energy demand term:
\[ J_{\text{immune}} = e_r N_r + e_a N_a + e_M M_a + e_T (T_a + T_{17}) \tag{5}\]
where \(e_r \leq e_a\) (activated cells consume far more energy than resting cells). This term enters the ATP demand in atp balance, creating a direct link between immune activation and energy deficit. In ME/CFS, chronic immune activation increases \(J_{\text{immune}}\), reducing the energy available for other functions and narrowing the energy envelope (Post-Exertional Malaise Modeling).