Mathematical Stability Analysis of the Full SREBP-2 Pathway Model: Insights into Cholesterol Homeostasis

We present a mathematical analysis of the sterol regulatory element-binding protein 2 (SREBP-2) pathway, a key regulator of intracellular cholesterol homeostasis. Using a compartment model formulated as a nonlinear system of ordinary differential equations, we investigate stability via M-matrix theory and norm-based criteria. We show that the Frobenius norm ∥B∥F≥1 cannot ensure stability, whereas the infinity norm condition ∥B∥∞<1 provides a practical guarantee that the spectral radius ρ(B)<1. The spectral norm ∥B∥2 yields sharper intermediate bounds. Numerical simulations confirm these results, highlighting parameter regions of stability and showing that the dissociation rate k−1 has the strongest influence on system behavior. These findings demonstrate the robustness of the ℓ∞ criterion, clarify the role of dissociation kinetics in cholesterol regulation, and provide a rigorous framework for assessing homeostatic control in the SREBP-2 pathway.