Mathematical Modeling of AA Amyloidosis: Coupling SAA-HDL Binding Dynamics with Path-Dependent Renal Aging

AA amyloidosis is a severe complication of chronic inflammatory diseases characterized by fibrillar protein deposition in the kidneys, leading to progressive organ failure. This study presents a mathematical model coupling SAA-HDL binding dynamics with renal amyloid aggregation kinetics to elucidate disease pathogenesis. Under normal conditions, Serum Amyloid A (SAA) circulates bound to high-density lipoprotein (HDL), which acts as a molecular chaperone preventing misfolding. However, during chronic inflammation, SAA production exceeds HDL binding capacity, resulting in free SAA that undergoes renal filtration. The model calculates free SAA concentration from reversible binding equilibrium and incorporates renal filtration, mesangial accumulation, and conversion to amyloid fibrils through primary nucleation and autocatalytic growth mechanisms. A central contribution of this work is quantifying accumulated nephrotoxicity arising from AA oligomers, which inflict cumulative cytotoxic damage to mesangial and tubular cells over time. Because oligomers are continuously generated during ongoing aggregation, their toxic burden integrates across the entire duration of the disease. Combined nephrotoxicity, encompassing both oligomer-mediated cellular injury and fibril-driven mechanical disruption of renal architecture, therefore reflects not merely the current disease state but the full inflammatory trajectory of the patient. This cumulative damage defines renal biological age, a measure of functional deterioration whose portion attributable to accumulated nephrotoxicity is irreversible. Renal biological age is also path-dependent: two patients with identical present-day SAA levels may carry different renal damage burdens depending on the duration, timing, and severity of their prior inflammatory episodes. Sensitivity analysis reveals that HDL concentration and SAA cleavage rate are critical determinants of amyloid burden.