Department of Applied Mathematics and Computer Science, Universidad del Rosario, Bogotá, 111711, Colombia.
Institut Jacques Monod, CNRS UMR 7592, Université Paris Diderot, Université de Paris, 750205, Paris, France.
J Math Biol. 2021 Mar 25;82(5):39. doi: 10.1007/s00285-021-01593-3.
The misconformation and aggregation of the protein Amyloid-Beta (A[Formula: see text]) is a key event in the propagation of Alzheimer's Disease (AD). Different types of assemblies are identified, with long fibrils and plaques deposing during the late stages of AD. In the earlier stages, the disease spread is driven by the formation and the spatial propagation of small amorphous assemblies called oligomers. We propose a model dedicated to studying those early stages, in the vicinity of a few neurons and after a polymer seed has been formed. We build a reaction-diffusion model, with a Becker-Döring-like system that includes fragmentation and size-dependent diffusion. We hereby establish the theoretical framework necessary for the proper use of this model, by proving the existence of solutions using a fixed point method.
蛋白质淀粉样-β（A[Formula: see text]）的错误折叠和聚集是阿尔茨海默病（AD）传播的关键事件。已经鉴定出不同类型的聚集体，在 AD 的晚期会有长纤维和斑块沉积。在早期阶段，疾病的传播是由形成和空间传播称为寡聚物的小无定形聚集体驱动的。我们提出了一个专门用于研究几个神经元附近以及形成聚合物种子后的早期阶段的模型。我们构建了一个反应-扩散模型，其中包含了片段化和尺寸相关扩散的 Becker-Döring 样系统。我们通过使用不动点方法证明解的存在，从而为正确使用该模型建立了必要的理论框架。
