Neuroplasticity Attractor Dynamics

The preceding sections model ME/CFS as a multi-system disease with coupled energy–immune–neuroendocrine dynamics. This section extends the framework to incorporate neuroplasticity, central sensitization, and thyroid hormone interactions—formalizing the “pathological attractor state” concept from the clinical brainstorm (Speculation The Attractor Landscape Model: ME/CFS as a Pathological Stable State).

Limitation: Conceptual Scaffold, Not Quantitative Model

The ODE system presented below is a conceptual scaffold: it formalizes the hypothesized causal structure (which variables affect which, and in what direction) but contains no empirically constrained parameters. No ME/CFS-specific measurement exists for any rate constant in the model.

Model Parameter Status. To distinguish what is measured from what is assumed or illustrative:

Model parameter status: measured / physiologically bounded / assumed / illustrative. Parameters listed as “assumed” or “illustrative” are modelling choices whose values determine qualitative model behaviour; the formal results (bistability, combination cliffs, separatrix structure) depend on these choices and should not be interpreted as empirically derived predictions.
Parameter	Status
Hill exponent $n$ (energy-immune coupling)	Assumed ($n = 2$); $n = 1$ cannot be excluded a priori for all immune cell types
Loop gains $G_1, G_2, G_3, G_4$	Illustrative ($ 1.5$ each); not measured for any ME/CFS loop
Threat signal weights $w_\text{cyto}, w_\text{ROS}, w_\text{LPS}, w_V$	Illustrative ($ 0.35, 0.25, 0.20, 0.20$); not independently measured
Kindling parameters $\alpha, \beta$	Illustrative; values freely adjustable
Complex I inhibition fraction $\alpha_\text{CI}$	Measurable in principle (seahorse assay); no ME/CFS-specific population values
ATP degradation rate $e_a$	Physiologically bounded; not calibrated to ME/CFS
Pro-inflammatory cytokine clearance rate	Physiologically bounded; not calibrated to ME/CFS

The mathematical formalism serves three purposes: (1) forcing explicit specification of causal links rather than verbal hand-waving; (2) deriving qualitative predictions (e.g., multiplicative combination effects) that follow logically from the assumed structure; and (3) identifying what measurements would be needed to constrain the model. It does NOT provide quantitative predictions, and the fixed-point analysis describes what the model implies IF its structure is correct—not what will happen in patients. The verbal summary of the model’s content is: “kindling, T3 depletion, microglial activation, and epigenetic locking may reinforce each other; treating multiple ones simultaneously may work better than treating one at a time.” The ODE formalism adds one genuinely novel prediction beyond this verbal statement: that combination effects should be multiplicative (detectable as interaction terms in factorial trials), not merely additive. Readers should evaluate whether the mathematical apparatus is justified by this single additional prediction.

1 Multi-Loop Feedback Model

The core observation motivating this model is that ME/CFS appears to be maintained by multiple self-reinforcing feedback loops operating simultaneously. None of the proposed loops has been demonstrated as a complete closed loop in ME/CFS patients—each is assembled from cross-disease evidence (see individual hypothesis limitations in Chapters Neurological and Neurocognitive Dysfunction and Endocrine and Metabolic Dysfunction). The model therefore explores the consequences of assuming these loops exist, not their existence per se. The neuroplasticity-relevant loops are:

\[ \begin{aligned} \text{Loop 1 (Kindling):} \quad &\text{PEM} \rightarrow \text{microglial priming} \rightarrow \text{lower threshold} \rightarrow \text{more PEM} \\ \text{Loop 2 (T3 depletion):} \quad &\text{inflammation} \rightarrow \downarrow \text{DIO2} \rightarrow \downarrow \text{T3} \rightarrow \downarrow \text{BDNF} \rightarrow \text{M1 microglia} \rightarrow \text{inflammation} \\ \text{Loop 3 (Epigenetic lock):} \quad &\text{chronic inflammation} \rightarrow \text{HDAC-mediated silencing} \rightarrow \downarrow \text{plasticity genes} \\ \text{Loop 4 (Energy failure):} \quad &\downarrow \text{T3} \rightarrow \downarrow \text{mitochondrial OXPHOS} \rightarrow \downarrow \text{ATP} \rightarrow \text{impaired immune regulation} \end{aligned} \]

We formalize these as a coupled ODE system. Let $K$ represent the kindling state (cumulative microglial priming), $T$ the effective brain T3 level, $M$ the microglial activation level, and $E$ the epigenetic consolidation depth:

\[ \begin{aligned} \frac{d K}{d t} &= \alpha \cdot P(t) - \beta \cdot K \cdot u_\text{AK}(t) - \gamma \cdot K \\ \frac{d T}{d t} &= \delta \cdot (T_0 - T) - \epsilon \cdot M \cdot T + \zeta \cdot u_\text{T3}(t) \\ \frac{d M}{d t} &= \eta \cdot K + \theta \cdot (1 - T / T_0) - \mu \cdot M \cdot u_\text{AI}(t) - \nu \cdot M \\ \frac{d E}{d t} &= \kappa \cdot M \cdot (1 - E) - \lambda_0 \cdot E - \lambda_1 \cdot E \cdot u_\text{HDAC}(t) \end{aligned} \tag{1}\]

where:

$P(t)$ is the PEM event rate (crashes per unit time)
$u_\text{AK}(t)$ is the anti-kindling intervention strength (e.g., levetiracetam)
$u_\text{T3}(t)$ is the exogenous T3 supplementation rate
$u_\text{AI}(t)$ is the anti-inflammatory intervention strength (e.g., LDN, levetiracetam)
$u_\text{HDAC}(t)$ is the HDAC inhibitor intervention strength (e.g., valproate)
$T_0$ is the healthy baseline brain T3 level
Greek letters ($\alpha, \beta, \gamma, \delta, \epsilon, \zeta, \eta, \theta, \mu, \nu, \kappa, \lambda_0, \lambda_1$) are rate constants; all are positive. Parameter estimation requires longitudinal multi-biomarker data not currently available for ME/CFS (see Limitation box at end of section)

2 Fixed-Point Analysis

Setting all derivatives to zero and all interventions to zero ($u = 0$), the system has two classes of fixed points:

Healthy fixed point: $(K^*, T^*, M^*, E^*) = (0, T_0, 0, 0)$ — no kindling, normal T3, quiescent microglia, no epigenetic locking. Stability requires $P(t) = 0$ (no PEM events).

Disease fixed point: A non-trivial equilibrium exists where kindling, T3 depletion, microglial activation, and epigenetic consolidation are all elevated and mutually sustaining. At this fixed point:

\[ K^* = \frac{\alpha P^*}{\gamma} , \quad M^* = \frac{\eta K^* + \theta(1 - T^* / T_0)}{\nu} , \quad T^* = \frac{\delta T_0}{\delta + \epsilon M^*} , \quad E^* = \frac{\kappa M^*}{\kappa M^* + \lambda_0} \]

The disease fixed point is stable when the loop gains reinforce each other: microglial activation ($M$) suppresses T3, which increases microglial activation further (loop 2); kindling ($K$) increases $M$, which increases $E$, which prevents resolution of $M$ (loops 1+3). The Jacobian eigenvalues at the disease fixed point determine stability and timescale separation.

3 The “Combination Cliff” Prediction

The most consequential prediction of this model concerns the effect of multi-target interventions. Define the effective loop gain $G$ as the product of individual loop gains:

\[ G = G_1 \cdot G_2 \cdot G_3 \cdot G_4 \]

where each $G_i$ depends on the corresponding intervention: $G_1(u_\text{AK})$, $G_2(u_\text{T3})$, $G_3(u_\text{HDAC})$, $G_4(u_\text{AI})$. The disease attractor is stable when $G > 1$ and unstable when $G < 1$.

Each intervention reduces its corresponding loop gain: $G_i(u_i) = G_i(0) \cdot (1 - u_i / u_{i,max})$ (linear dose-response for simplicity). The total intervention effect is multiplicative, not additive:

\[ G(\mathbf{u}) = product_{i=1}^4 G_i(0) \cdot (1 - u_i / u_{i,max}) \]

This multiplicative structure predicts a combination cliff: if the disease attractor requires $G > 1$ for stability, then addressing each loop partially can push $G$ below 1 even though no single loop is fully broken. Suppose each untreated loop has gain $G_i(0) = 1.5$ (50% amplification per cycle). Four untreated loops give $G = 1.5^4 = 5.06$ (strongly stable attractor). Reducing each loop gain by 40% ($G_i \rightarrow 0.6 \cdot G_i(0) = 0.9$):

\[ G = 0.9^4 = 0.66 < 1 \quad \text{(attractor collapses)} \]

while addressing only one loop ($G_1 \rightarrow 0.9$, others unchanged):

\[ G = 0.9 \cdot 1.5^3 = 3.04 \quad \text{(attractor persists)} \]

Speculation: Multiplicative Combination Effect in ME/CFS Treatment

Certainty: 0.35. The multi-loop attractor model predicts that combination treatments targeting $\geq$ 3 independent feedback loops should produce dramatically larger effect sizes than any single intervention—not through pharmacological synergy but through attractor destabilization. Specifically: (a) a factorial trial design (e.g., 2$\\times$ 2$\\times$ 2 for lithium $\\times$ T3 $\\times$ levetiracetam) should show a significant three-way interaction term, where the triple combination effect exceeds the sum of individual and pairwise effects; (b) there exists a critical number of loops ($N_\text{crit}$) below which interventions produce negligible benefit and above which they produce disproportionate improvement.

Post-hoc fitting caveat: The observation that single-agent ME/CFS trials have historically shown modest effects is consistent with the attractor model but cannot be cited as evidence FOR the model, since the model was constructed partly to explain this observation. Alternative explanations for single-agent trial failures—disease heterogeneity, underpowered trials, wrong drug targets, wrong patient selection—are equally or more parsimonious and are not excluded by the model.

Falsification: If a well-powered factorial combination trial targeting three mechanistically independent loops shows purely additive effects (no significant interaction terms), the multiplicative attractor model would be falsified in favor of a simpler additive damage model. If the trial shows no benefit from any arm, the underlying loop hypotheses (not just the integration framework) are weakened.

4 PEM Threshold Recovery Model

The PEM kindling hypothesis (Section Kindling Analogy: Neurological Extrapolation Without ME/CFS Data, Chapter Neurological and Neurocognitive Dysfunction) proposed that each crash lowers the subsequent PEM threshold: $T(n) = T(0) / \alpha^n$. With anti-kindling therapy, a recovery term appears:

\[ T(n+1) = \frac{T(n)}{\alpha} + \beta \cdot (T_max - T(n)) \tag{2}\]

where $\beta$ is the anti-kindling recovery rate (e.g., from levetiracetam or lithium). At steady state ($T(n+1) = T(n) = T_\text{ss}$), rearranging gives:

\[ T_\text{ss} = \frac{\beta \cdot T_max}{1 - 1 / \alpha + \beta} \]

Clinical interpretation:

For any $\alpha > 1$ and $\beta > 0$, $T_\text{ss} > 0$ — anti-kindling therapy always prevents complete collapse.
The steady-state threshold increases with $\beta$ (stronger anti-kindling) and decreases with $\alpha$ (more severe kindling per crash).
If $\beta = 0$ (no treatment): $T_\text{ss} = 0$ — inevitable collapse to zero threshold (severe disease).
The clinically meaningful question is whether $T_\text{ss}$ exceeds a functional threshold $T_\text{func}$ below which activities of daily living become impossible.

For the illustrative values from the original hypothesis ($\alpha = 1.5$), anti-kindling alone ($\beta = 0.3$) gives:

\[ T_\text{ss} = \frac{0.3 \cdot T_max}{1 - 0.667 + 0.3} = \frac{0.3 \cdot T_max}{0.633} \approx 0.47 \cdot T_max \]

With strict pacing reducing $\alpha$ from 1.5 to 1.2 (fewer and milder crashes), the combined effect yields:

\[ T_\text{ss} = \frac{0.3 \cdot T_max}{1 - 0.833 + 0.3} = \frac{0.3 \cdot T_max}{0.467} \approx 0.64 \cdot T_max \]

This predicts stabilization at approximately 64% of maximum threshold—a substantial functional improvement that depends critically on both pacing (reducing $\alpha$) and pharmacological anti-kindling (increasing $\beta$). Pacing alone ($\beta = 0$) gives $T_\text{ss} = 0$; anti-kindling alone ($\alpha = 1.5$, $\beta = 0.3$) gives $T_\text{ss} \approx 0.47 \cdot T_max$. The combination achieves more than either alone because pacing reduces the denominator while anti-kindling increases the numerator.

5 T3-Neuroplasticity Phase Space

The T3-neuroplasticity interaction can be visualized as a 2D phase plane with coordinates ($T$, $\Pi$), where $T$ is the effective brain T3 concentration and $\Pi$ is the neuroplasticity capacity (0 = fully locked, 1 = fully plastic):

\[ \begin{aligned} \frac{d T}{d t} &= \sigma \cdot (T_0 - T) - \rho \cdot (1 - \Pi) \cdot T + u_\text{T3} \\ \frac{d \Pi}{d t} &= \phi \cdot T / T_0 \cdot (1 - \Pi) - \omega_0 \cdot \Pi - \omega_1 \cdot (1 - T / T_0) \cdot \Pi + u_\text{Li} \end{aligned} \tag{3}\]

where:

$\sigma$: natural T3 homeostasis rate
$\rho$: inflammation-mediated T3 suppression (stronger when plasticity is low, i.e., neuroinflammation is high)
$\phi$: T3-driven plasticity enhancement (via BDNF, LTP)
$\omega_0$: baseline plasticity decay rate (natural turnover of plastic synaptic connections)
$\omega_1$: additional plasticity loss from T3 deficiency (epigenetic locking, reduced BDNF)
$u_\text{T3}$: exogenous T3 supplementation
$u_\text{Li}$: lithium-driven plasticity enhancement (GSK-3$\beta$ inhibition, BDNF, autophagy)

At the healthy equilibrium ($u = 0$), $\Pi_0$ and $T^*$ are determined simultaneously from the coupled nullclines. Setting $d \Pi / d t = 0$ at $T = T_0$ gives $\Pi_0 = \phi / (\phi + \omega_0)$, but substituting into $d T / d t = 0$ yields a residual $-\rho (1 - \Pi_0) T_0 \neq 0$ since $\Pi_0 < 1$. The true healthy fixed point therefore has $T^* < T_0$, shifted slightly below the nominal setpoint by the baseline plasticity-mediated suppression term. When $\rho$ is small relative to $\sigma$ (strong T3 homeostasis), $T^* \approx T_0$ and $\Pi_0 \approx \phi / (\phi + \omega_0)$ remains a good approximation. The disease equilibrium is at a substantially lower $(T^{\text{disease}}, \Pi^{\text{disease}})$ where low T3 and low plasticity mutually reinforce each other. A separatrix divides the two basins.

Treatment vectors in phase space:

T3 supplementation: pushes the state rightward (toward normal $T$)
Lithium: pushes the state upward (toward normal $\Pi$)
The separatrix determines the minimum combination of T3 and lithium needed to escape the disease attractor

The model predicts that: (1) T3 alone is insufficient if plasticity is too locked (the system slides back along the $T$-nullcline); (2) lithium alone is insufficient if T3 is too low to support BDNF-mediated plasticity; (3) the combination crosses the separatrix that neither alone can cross—the quintessential multi-loop effect formalized in Section Conceptual Scaffold, Not Quantitative Model.

Limitation: Neuroplasticity Attractor Model: Parameter Uncertainty

All parameters in the neuroplasticity attractor model (neuroplasticity attractor, pem threshold recovery, t3 plasticity) are illustrative. No ME/CFS-specific measurements of kindling rates, DIO2 suppression kinetics, microglial priming dynamics, or epigenetic consolidation timescales exist. The model’s value lies in its qualitative predictions (multiplicative combination effects, threshold behaviors, separatrix crossing) rather than quantitative forecasts. Parameterization requires longitudinal multi-biomarker studies tracking kindling state (PEM threshold), T3 levels, inflammatory markers, and cognitive function simultaneously with sufficient temporal resolution to fit ODE dynamics.