Dynamical modeling of TNF-α, IL-6, and IL-10 interactions in stroke-induced inflammation

In acute stroke, dysregulated cytokine interactions drive secondary injury, yet bidirectional feedback mechanisms between pro-inflammatory mediators (TNF-α, IL-6) and the anti-inflammatory mediator IL-10 remain poorly quantified. We developed a systems biology model using nonlinear ordinary differential equations (ODEs) to resolve these dynamics, incorporating Nuclear Factor kappa-light-chain-enhancer of activated B cells (NF-κB)-mediated cross-activation, delayed IL-10 induction via a Hill function, and empirical parameterization from stroke data. Mathematical analysis revealed bistable inflammatory states via bifurcation theory, mechanistically explaining divergent inflammatory trajectory. Steady-state and stability analyses identified a critical IL-10 suppression threshold ( γ T 1 0 ≈ 0 . 0 6 hr ⁻ ¹·nM ⁻ ¹) governing transitions between pro-inflammatory dominance and resolution phases. The model replicated experimentally observed cytokine dynamics, including TNF-α/IL-6 peaks (6–24 hours) and delayed IL-10 elevation (48 hours). Global sensitivity analysis highlighted IL-10 production ( k 1 0 T ) and TNF-α suppression ( γ T 1 0 ) as key control parameters. Simulations predicted that IL-10 augmentation accelerates resolution, while TNF-α inhibition attenuates IL-10 induction, potentially compromising long-term recovery. By integrating dynamical systems theory with translational immunology, this model provides a mechanistic basis for optimizing immunomodulatory therapies in stroke and related inflammatory pathologies.