2026/06/27 by Sun Lee, Wenrui Hao · 1 voice
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #q-bio.QM #nlin.PS
Alzheimer's disease (AD) is characterized by the accumulation of Amyloid-β (Aβ) plaques and hyperphosphorylated Tau proteins. However, many individuals exhibit substantial Aβ and Tau pathology without developing dementia, suggesting that disease progression may depend not only on pathological burden but also on the spatial organization of these proteins. Motivated by this observation, we adapt Gray-Scott reaction-diffusion model to investigate pattern formation arising from the interactions between Aβ and Tau. % To systematically identify stable spatial configurations, we employ a Companion-Based Multi-Level Finite Element Method (CBMFEM) on both two-dimensional domains and anatomically realistic cortical surface meshes. Numerical simulations reveal a rich landscape of multiple steady-state solutions, which are subsequently classified into representative pattern phenotypes using principal component analysis and clustering techniques. The results demonstrate that the coupled Aβ--Tau system admits numerous stable spatial patterns rather than a single pathological endpoint. % These findings provide a potential mathematical framework for understanding the heterogeneity of Alzheimer's disease and the existence of cognitively resilient individuals despite significant pathological burden. More broadly, the proposed framework suggests a pattern-based therapeutic paradigm in which disease dynamics are guided toward favorable stable states rather than solely targeting the elimination of pathological proteins.