Department of Mathematics and Statistics and Neuroscience Institute, Georgia State University, Atlanta, GA 30303, USA.
Zarbio, Chapel Hill, NC 27516, USA.
Curr Alzheimer Res. 2023;20(6):440-452. doi: 10.2174/1567205020666230821141745.
A major gap in amyloid-centric theories of Alzheimer's disease (AD) is that even though amyloid fibrils per se are not toxic in vitro, the diagnosis of AD clearly correlates with the density of beta-amyloid (Aβ) deposits. Based on our proposed amyloid degradation toxicity hypothesis, we developed a mathematical model explaining this discrepancy. It suggests that cytotoxicity depends on the cellular uptake of soluble Aβ rather than on the presence of amyloid aggregates. The dynamics of soluble beta-amyloid in the cerebrospinal fluid (CSF) and the density of Aβ deposits is described using a system of differential equations. In the model, cytotoxic damage is proportional to the cellular uptake of Aβ, while the probability of an AD diagnosis is defined by the Aβ cytotoxicity accumulated over the duration of the disease. After uptake, Aβ is concentrated intralysosomally, promoting the formation of fibrillation seeds inside cells. These seeds cannot be digested and are either accumulated intracellularly or exocytosed. Aβ starts aggregating on the extracellular seeds and, therefore, decreases in concentration in the interstitial fluid. The dependence of both Aβ toxicity and aggregation on the same process-cellular uptake of Aβ-explains the correlation between AD diagnosis and the density of amyloid aggregates in the brain.
We tested the model using clinical data obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI), which included records of beta-amyloid concentration in the cerebrospinal fluid (CSF-Aβ42) and the density of beta-amyloid deposits measured using positron emission tomography (PET). The model predicts the probability of AD diagnosis as a function of CSF-Aβ42 and PET and fits the experimental data at the 95% confidence level.
Our study shows that existing clinical data allows for the inference of kinetic parameters describing beta-amyloid turnover and disease progression. Each combination of CSF-Aβ42 and PET values can be used to calculate the individual's cellular uptake rate, the effective disease duration, and the accumulated toxicity. We show that natural limitations on these parameters explain the characteristic distribution of the clinical dataset for these two biomarkers in the population.
The resulting mathematical model interprets the positive correlation between the density of Aβ deposits and the probability of an AD diagnosis without assuming any cytotoxicity of the aggregated beta-amyloid. To the best of our knowledge, this model is the first to mechanistically explain the negative correlation between the concentration of Aβ42 in the CSF and the probability of an AD diagnosis. Finally, based on the amyloid degradation toxicity hypothesis and the insights provided by mathematical modeling, we propose new pathophysiology-relevant biomarkers to diagnose and predict AD.
淀粉样蛋白假说认为阿尔茨海默病（AD）是由β-淀粉样蛋白（Aβ）的异常聚集引起的，但该假说无法解释为什么 Aβ 纤维本身在体外没有毒性，而 AD 的诊断却与 Aβ 沉积的密度密切相关。基于我们提出的淀粉样蛋白降解毒性假说，我们开发了一个数学模型来解释这一差异。该模型表明，细胞毒性取决于可溶性 Aβ 的细胞摄取，而不是淀粉样蛋白聚集物的存在。脑脊液（CSF）中可溶性β-淀粉样蛋白的动态和 Aβ 沉积的密度通过微分方程组来描述。在该模型中，细胞毒性损伤与 Aβ 的细胞摄取成正比，而 AD 诊断的概率则由疾病持续期间累积的 Aβ 细胞毒性来定义。摄取后，Aβ 在溶酶体内浓缩，促进细胞内纤维形成种子。这些种子不能被消化，要么在细胞内积累，要么被外排。Aβ 开始在细胞外种子上聚集，因此在细胞外间隙中的浓度降低。Aβ 毒性和聚集都依赖于同一过程——Aβ 的细胞摄取，这解释了 AD 诊断与脑内淀粉样蛋白聚集密度之间的相关性。
我们使用来自阿尔茨海默病神经影像学倡议（ADNI）的临床数据来测试该模型，这些数据包括脑脊液中β-淀粉样蛋白浓度（CSF-Aβ42）和使用正电子发射断层扫描（PET）测量的β-淀粉样蛋白沉积密度。该模型预测 AD 诊断的概率作为 CSF-Aβ42 和 PET 的函数，并在 95%置信水平下拟合实验数据。
我们的研究表明，现有的临床数据允许推断描述β-淀粉样蛋白周转和疾病进展的动力学参数。可以使用 CSF-Aβ42 和 PET 值的每种组合来计算个体的细胞摄取率、有效疾病持续时间和累积毒性。我们表明，这些参数的自然限制解释了人群中这两个生物标志物的临床数据集的特征分布。
该数学模型解释了 Aβ 沉积密度与 AD 诊断概率之间的正相关关系，而无需假设聚集的β-淀粉样蛋白具有任何细胞毒性。据我们所知，该模型是第一个从机制上解释 CSF 中 Aβ42 浓度与 AD 诊断概率之间负相关的模型。最后，基于淀粉样蛋白降解毒性假说和数学建模提供的见解，我们提出了新的与病理生理学相关的生物标志物来诊断和预测 AD。
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