Abstract 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.

中文翻译：

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神经退行性疾病中有毒蛋白质的各向异性扩散和行波

摘要 神经退行性疾病与毒性蛋白的扩增和侵袭密切相关。特别是阿尔茨海默病的特征在于大脑中淀粉样蛋白-β 和 τ-蛋白的系统性进展。这两个蛋白质家族是耦合的，据信它们的联合存在大大增强了由此产生的损害。在这里，我们在两个空间维度检查了一类健康和有毒蛋白质的耦合化学动力学模型。预期沿轴突通路在大脑内发生的各向异性扩散在模型中被考虑在内，并产生丝状的、主要是一维的传输。尽管如此，各向异性模型利用二维景观产生相互作用的潜力得到了展示。最后，检查将模型简化为更简单的广义 Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) 类型系统系列。可以看出，后者很好地捕捉了定性传播特征，尽管它可能有点低估了有毒蛋白质的浓度。