A network-level transport model of tau progression in the Alzheimer's brain.

Veronica Tora, Justin Torok, Michiel Bertsch, Ashish Raj
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Abstract

One of the hallmarks of Alzheimer's disease (AD) is the accumulation and spread of toxic aggregates of tau protein. The progression of AD tau pathology is thought to be highly stereotyped, which is in part due to the fact that tau can spread between regions via the white matter tracts that connect them. Mathematically, this phenomenon has been described using models of "network diffusion," where the rate of spread of tau between brain regions is proportional to its concentration gradient and the amount of white matter between them. Although these models can robustly predict the progression of pathology in a wide variety of neurodegenerative diseases, including AD, an underexplored aspect of tau spreading is that it is governed not simply by diffusion but also active transport along axonal microtubules. Spread can therefore take on a directional bias, resulting in distinct patterns of deposition, but current models struggle to capture this phenomenon. Recently, we have developed a mathematical model of the axonal transport of toxic tau proteins that takes into account the effects tau exerts on the molecular motors. Here we describe and implement a macroscopic version of this model, which we call the Network Transport Model (NTM). A key feature of this model is that, while it predicts tau dynamics at a regional level, it is parameterized in terms of only microscopic processes such as aggregation and transport rates; that is, differences in brain-wide tau progression can be explained by its microscopic properties. We provide numerical evidence that, as with the two-neuron model that the NTM extends, there are distinct and rich dynamics with respect to the overall rate of spread and the staging of pathology when we simulated the NTM on the hippocampal subnetwork. The theoretical insights provided by the NTM have broad implications for understanding AD pathophysiology more generally.

阿尔茨海默病大脑中tau蛋白进展的网络水平转运模型。
阿尔茨海默病(AD)的特征之一是tau蛋白毒性聚集体的积累和扩散。AD tau病理的进展被认为是高度定型的,部分原因是tau可以通过连接它们的白质束在区域之间传播。数学上,这种现象用“网络扩散”模型来描述,其中tau蛋白在大脑区域之间的扩散速度与它的浓度梯度和它们之间的白质数量成正比。尽管这些模型可以可靠地预测包括阿尔茨海默病在内的多种神经退行性疾病的病理进展,但tau扩散的一个未被充分探索的方面是,它不仅受扩散控制,还受轴突微管主动运输的控制。因此,扩散可能会有方向性偏差,导致不同的沉积模式,但目前的模型很难捕捉到这一现象。最近,我们开发了一个考虑到tau蛋白对分子马达的影响的有毒tau蛋白轴突运输的数学模型。在这里,我们描述并实现了这个模型的宏观版本,我们称之为网络传输模型(NTM)。该模型的一个关键特征是,虽然它在区域水平上预测tau动力学,但它仅根据微观过程(如聚集和运输速率)进行参数化;也就是说,大脑范围内tau蛋白进展的差异可以用其微观特性来解释。我们提供的数值证据表明,与NTM扩展的双神经元模型一样,当我们在海马亚网络上模拟NTM时,在总体扩散率和病理分期方面存在独特而丰富的动态。NTM提供的理论见解对更广泛地理解阿尔茨海默病的病理生理具有广泛的意义。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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