A mechanistic model to predict effects of cathepsin B and cystatin C on β-amyloid aggregation and degradation.

β-Amyloid (Aβ) aggregation is thought to initiate a cascade of neurodegenerative events in Alzheimer's disease (AD). Much effort is underway to develop strategies to reduce Aβ concentration or inhibit aggregation. Cathepsin B (CatB) proteolytically degrades Aβ into non-aggregating fragments but is potently inhibited by cystatin C (CysC). It has been suggested that decreasing CysC would facilitate Aβ clearance by relieving CatB inhibition. However, CysC binds Aβ and inhibits Aβ aggregation, suggesting that an intervention that increases CysC would prevent Aβ aggregation. Both approaches have been tested in animal models, yielding contradictory results, possibly because of the opposing influences of CysC on Aβ degradation versus aggregation. Here, we sought to develop a model that quantitatively predicts the effects of CysC and CatB on Aβ aggregation. Aβ aggregation kinetics in the absence of CatB or CysC was measured. The rate constant for Aβ degradation by CatB and the equilibrium constant for binding of CysC to Aβ were determined. We derived a mathematical model that combines material balances and kinetic rate equations. The model accurately predicted Aβ aggregation kinetics at various CatB and CysC concentrations. We derived approximate expressions for the half-times of degradation and aggregation and show that their ratio can be used to estimate, at any given Aβ, CatB, or CysC concentration, whether Aβ aggregation or degradation will result. Our results may be useful for designing experiments and interpreting results from investigations of manipulation of CysC concentration as an AD therapy.