Anisotropic diffusion and traveling waves of toxic proteins in neurodegenerative diseases

• Published in: Physics letters. A 2020-12, Vol.384 (36), p.126935, Article 126935
• Main Authors: Kevrekidis, P.G., Thompson, Travis B., Goriely, Alain
• Format: Article
• Language: English
• Subjects: Alzheimer disease; Amyloid-β; Brain; Chemical kinetics; FKPP models; Reaction-diffusion equations; Traveling waves; τ-Proteins
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2020.126935

•A 2D Model for healthy and toxic proteins in Alzheimer's disease is devised.•The model is intended to capture (healthy and toxic) τ proteins and amyloid β (4 species).•The anisotropic nature of the diffusion of toxic waves is illustrated.•Two scenarios of “tauopathies” are illustrated based on the system's fixed points.•A Fisher-KPP reduction of the model is shown to adequately capture the dynamics. Neurodegenerative diseases are closely associated with the amplification and invasion of toxic proteins. In particular Alzheimer's disease is characterized by the systematic progression of amyloid-β and τ-proteins in the brain. These two protein families are coupled and it is believed that their joint presence greatly enhances the resulting damage. Here, we examine a class of coupled chemical kinetics models of healthy and toxic proteins in two spatial dimensions. The anisotropic diffusion expected to take place within the brain along axonal pathways is factored in the models and produces a filamentary, predominantly one-dimensional transmission. Nevertheless, the potential of the anisotropic models towards generating interactions taking advantage of the two-dimensional landscape is showcased. Finally, a reduction of the models into a simpler family of generalized Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) type systems is examined. It is seen that the latter captures well the qualitative propagation features, although it may somewhat underestimate the concentrations of the toxic proteins.