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

Why does chronic inflammation cause AA amyloidosis in only some patients, even when serum amyloid A (SAA) remains elevated in many? This study proposes that disease progression is governed by two linked nonlinear processes: saturation of the finite SAA-binding capacity of high-density lipoprotein (HDL), followed by autocatalytic aggregation of amyloid A (AA) in the kidney. A hypothesis-generating mathematical model is developed that couples reversible SAA-HDL binding to renal filtration of free SAA, lysosomal cleavage to AA fragments, Finke-Watzky aggregation, oligomer deposition, and fibril turnover. As total SAA rises beyond the effective HDL binding capacity, the model predicts a disproportionate increase in free, filterable SAA available for renal amyloid formation. A dimensionless reduction reveals two kinetic regimes separated by a threshold at which autocatalytic oligomer production balances oligomer loss. Below this threshold, aggregation is nucleation-limited; above it, the system becomes supply-limited and is controlled mainly by upstream SAA delivery. In the zero-primary-nucleation limit, the two steady-state branches exchange stability at this threshold, giving a transcritical bifurcation that finite primary nucleation smooths into a continuous transition. The baseline parameter set lies in the supply-limited regime, explaining why total SAA concentration and effective HDL binding-site capacity have the largest local sensitivities, with SAA-HDL affinity and lysosomal cleavage next in rank, whereas the aggregation rate constants have small local effects but can still determine which regime applies. The model further predicts that the temporal pattern of inflammation matters: intermittent SAA flares can produce several-fold more renal damage than sustained inflammation with the same mean SAA, and earlier SAA suppression leaves a lower renal biological-age index, a calibrated measure of cumulative damage, than later suppression. Published SAA-outcome data are consistent with the predicted SAA dependence. By linking HDL buffering to renal SAA delivery, nonlinear aggregation, and cumulative injury, the model provides a quantitative framework for identifying amyloidogenic transitions and testing how SAA control can alter renal disease progression.