Metal-Ion-Mediated Amyloid- β Aggregation in Alzheimer's Disease: A Mathematical Model of Chelation and Inhibitory Therapies.

We develop a novel, comprehensive, and rigorously validated mathematical framework to investigate the kinetics of amyloid- β (A β ) aggregation in the presence of biologically relevant metal ions, chelating agents, and inhibitor drugs. Building upon and extending existing aggregation models, our approach integrates metal-assisted aggregation, A β self-assembly, and therapeutic interventions within a unified and mechanistically consistent formulation. The model captures the microscopic reaction pathways governing A β dynamics and explicitly incorporates the catalytic roles of copper, zinc, and iron ions-key contributors to neurotoxic plaque formation in Alzheimer's disease. Distinctively, the framework combines dual therapeutic strategies: (i) metal chelation therapy, which sequesters free metal ions, and (ii) direct inhibition of A β aggregation. Numerical simulations across multiple kinetic regimes reveal how these interventions modulate aggregation pathways, both independently and synergistically. To further validate the model, we perform a quantitative comparison with experimental data by reconstructing aggregate morphology distributions and benchmarking them against reported AFM measurements. The model successfully captures key experimental features, including peak structure and metal-dependent heterogeneity, thereby demonstrating its predictive capability. Overall, this work provides an extended and unified modeling platform that advances the quantitative understanding of metal-mediated amyloid aggregation and offers a predictive tool for evaluating and optimizing therapeutic strategies for Alzheimer's disease.