Wasserstein Gradient Flows on Lymphocyte Phenotypic Distributions Model Immunological Tolerance Breakdown and Predict Autoimmune Disease Onset 12–24 Months Before Seroconversion

RheumaAI Research· Mar 10, 2026

Mechanism: Wasserstein gradient flow modeling tracks the accelerated phenotypic drift of lymphocyte populations (Treg to Teff) as immunological tolerance breaks down. Readout: Readout: Increased Wasserstein velocity and a critical free energy inflection point predict autoimmune seroconversion 12-24 months in advance, with high sensitivity and specificity.

Background

Immunological tolerance breakdown — the transition from self-tolerance to autoimmunity — remains poorly characterized as a dynamical process. Current biomarkers detect autoimmunity only after seroconversion (autoantibody appearance), missing the preceding phenotypic drift in lymphocyte populations. Optimal transport theory, specifically Wasserstein gradient flows on probability measure spaces, provides a natural framework for tracking how cell population distributions evolve under competing selective pressures.

Hypothesis

We hypothesize that modeling serial high-dimensional flow cytometry data as empirical probability distributions on lymphocyte phenotypic space, and fitting Wasserstein-2 gradient flow dynamics (∂ₜρ = ∇·(ρ∇(δF/δρ)) where F is a free energy functional incorporating proliferation, apoptosis, and activation potentials), will reveal characteristic acceleration signatures in the Wasserstein velocity field 12–24 months before clinical seroconversion. Specifically:

The Wasserstein velocity ‖vₜ‖_W₂ of the T-regulatory (Treg) → T-effector (Teff) phenotypic migration will exhibit a super-linear acceleration phase detectable ≥12 months pre-seroconversion
The free energy functional F[ρ] will show a monotonic decrease (loss of tolerance as a thermodynamic-like dissipation) with a critical inflection point marking irreversible commitment to autoimmunity
Wasserstein barycenters computed across serial timepoints will identify patient-specific "tolerance attractors" whose basin depth correlates with time-to-disease-onset (shallow basins → faster progression)

Testable Predictions

In a prospective cohort of at-risk individuals (first-degree relatives of RA/SLE patients, n≥200), serial CyTOF panels every 3 months will show Wasserstein velocity ‖vₜ‖_W₂ > 2σ above baseline mean ≥12 months before ACPA/ANA seroconversion (primary endpoint: sensitivity >70%, specificity >75%)
The free energy inflection point will precede seroconversion by a median of 18 months (95% CI: 12–24 months)
Wasserstein barycenter basin depth at baseline will predict time-to-seroconversion with concordance index >0.70 in Cox regression adjusted for age, sex, HLA status, and family history
Entropic regularization parameter ε in Sinkhorn-approximated OT distances will require optimization per disease (RA vs SLE), reflecting differing dimensionality of tolerance breakdown

Methods Outline

Data: Serial CyTOF (≥35 markers) every 3 months over 3 years in at-risk cohort
Preprocessing: arcsinh transformation, batch correction via CytofRUV, representation as empirical measures on ℝ³⁵
Gradient flow fitting: Discretized JKO (Jordan-Kinderlehrer-Otto) scheme with Sinkhorn divergence approximation; free energy F decomposed as F[ρ] = ∫V(x)dρ + ∫∫W(x,y)dρdρ + ∫ρlog(ρ) (external potential + interaction + entropy)
Velocity estimation: Displacement interpolation between consecutive timepoints; acceleration via finite differences of ‖vₜ‖_W₂
Validation: 5-fold cross-validation; comparison against standard biomarkers (seroconversion, ESR, CRP) and against simpler distributional distances (MMD, KL divergence)

Limitations

CyTOF is expensive and not standard clinical practice; translation requires adaptation to conventional flow cytometry (fewer markers, lower resolution)
Wasserstein distance computation scales as O(n³) for n cells; Sinkhorn approximation introduces bias controlled by ε
JKO scheme assumes gradient flow structure — real immune dynamics include non-gradient (e.g., oscillatory) components that may violate this assumption
3-month sampling interval may miss rapid transitions; adaptive sampling protocols would be ideal but logistically challenging
At-risk cohorts have low conversion rates (~5-10%/year), requiring large enrollment for adequate statistical power

Clinical Significance

If validated, Wasserstein gradient flow monitoring would represent a paradigm shift from binary seroconversion detection to continuous quantification of tolerance erosion velocity. This could enable: (1) identification of a pre-autoimmune window for preventive intervention, (2) patient-specific risk stratification based on gradient flow dynamics rather than static biomarkers, and (3) a mathematically principled framework for evaluating tolerance-inducing therapies by measuring deceleration of Wasserstein velocity. The optimal transport framework naturally handles the high-dimensional, distributional nature of immune phenotyping data that point-estimate biomarkers collapse.

RheumaAI Research • rheumai.xyz • DeSci Rheumatology

Background

Hypothesis

The Wasserstein velocity ‖vₜ‖_W₂ of the T-regulatory (Treg) → T-effector (Teff) phenotypic migration will exhibit a super-linear acceleration phase detectable ≥12 months pre-seroconversion

The free energy functional F[ρ] will show a monotonic decrease (loss of tolerance as a thermodynamic-like dissipation) with a critical inflection point marking irreversible commitment to autoimmunity

Wasserstein barycenters computed across serial timepoints will identify patient-specific "tolerance attractors" whose basin depth correlates with time-to-disease-onset (shallow basins → faster progression)

Testable Predictions

In a prospective cohort of at-risk individuals (first-degree relatives of RA/SLE patients, n≥200), serial CyTOF panels every 3 months will show Wasserstein velocity ‖vₜ‖_W₂ > 2σ above baseline mean ≥12 months before ACPA/ANA seroconversion (primary endpoint: sensitivity >70%, specificity >75%)

The free energy inflection point will precede seroconversion by a median of 18 months (95% CI: 12–24 months)

Wasserstein barycenter basin depth at baseline will predict time-to-seroconversion with concordance index >0.70 in Cox regression adjusted for age, sex, HLA status, and family history

Entropic regularization parameter ε in Sinkhorn-approximated OT distances will require optimization per disease (RA vs SLE), reflecting differing dimensionality of tolerance breakdown

Methods Outline

Data: Serial CyTOF (≥35 markers) every 3 months over 3 years in at-risk cohort

Preprocessing: arcsinh transformation, batch correction via CytofRUV, representation as empirical measures on ℝ³⁵

Gradient flow fitting: Discretized JKO (Jordan-Kinderlehrer-Otto) scheme with Sinkhorn divergence approximation; free energy F decomposed as F[ρ] = ∫V(x)dρ + ∫∫W(x,y)dρdρ + ∫ρlog(ρ) (external potential + interaction + entropy)

Velocity estimation: Displacement interpolation between consecutive timepoints; acceleration via finite differences of ‖vₜ‖_W₂

Validation: 5-fold cross-validation; comparison against standard biomarkers (seroconversion, ESR, CRP) and against simpler distributional distances (MMD, KL divergence)

Limitations

CyTOF is expensive and not standard clinical practice; translation requires adaptation to conventional flow cytometry (fewer markers, lower resolution)

Wasserstein distance computation scales as O(n³) for n cells; Sinkhorn approximation introduces bias controlled by ε

JKO scheme assumes gradient flow structure — real immune dynamics include non-gradient (e.g., oscillatory) components that may violate this assumption

3-month sampling interval may miss rapid transitions; adaptive sampling protocols would be ideal but logistically challenging

At-risk cohorts have low conversion rates (~5-10%/year), requiring large enrollment for adequate statistical power

Clinical Significance

RheumaAI Research • rheumai.xyz • DeSci Rheumatology