Kuznetsov I A, Kuznetsov A V
Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA.
Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA.
Proc Math Phys Eng Sci. 2018 Feb;474(2210):20170777. doi: 10.1098/rspa.2017.0777. Epub 2018 Feb 7.
We develop a mathematical model that enables us to investigate possible mechanisms by which two primary markers of Alzheimer's disease (AD), extracellular amyloid plaques and intracellular tangles, may be related. Our model investigates the possibility that the decay of anterograde axonal transport of amyloid precursor protein (APP), caused by toxic tau aggregates, leads to decreased APP transport towards the synapse and APP accumulation in the soma. The developed model thus couples three processes: (i) slow axonal transport of tau, (ii) tau misfolding and agglomeration, which we simulated by using the Finke-Watzky model and (iii) fast axonal transport of APP. Because the timescale for tau agglomeration is much larger than that for tau transport, we suggest using the quasi-steady-state approximation for formulating and solving the governing equations for these three processes. Our results suggest that misfolded tau most likely accumulates in the beginning of the axon. The analysis of APP transport suggests that APP will also likely accumulate in the beginning of the axon, causing an increased APP concentration in this region, which could be interpreted as a 'traffic jam'. The APP flux towards the synapse is significantly reduced by tau misfolding, but not due to the APP traffic jam, which can be viewed as a symptom, but rather due to the reduced affinity of kinesin-1 motors to APP-transporting vesicles.
我们开发了一个数学模型，通过该模型能够研究阿尔茨海默病（AD）的两个主要标志物——细胞外淀粉样斑块和细胞内缠结——可能的关联机制。我们的模型研究了由有毒的tau聚集体导致的淀粉样前体蛋白（APP）顺行轴突运输衰退，进而致使APP向突触运输减少以及在胞体中积累的可能性。因此，所开发的模型耦合了三个过程：（i）tau的慢速轴突运输，（ii）tau错误折叠和聚集（我们使用Finke-Watzky模型进行模拟），以及（iii）APP的快速轴突运输。由于tau聚集的时间尺度远大于tau运输的时间尺度，我们建议使用准稳态近似来制定和求解这三个过程的控制方程。我们的结果表明，错误折叠的tau最有可能在轴突起始端积累。对APP运输的分析表明，APP也可能在轴突起始端积累，导致该区域APP浓度升高，这可以解释为一种“交通堵塞”。tau错误折叠会显著降低APP向突触的通量，但这并非由于APP交通堵塞（可将其视为一种症状），而是由于驱动蛋白-1马达对运输APP的囊泡的亲和力降低。
