Eugène Sarah, Xue Wei-Feng, Robert Philippe, Doumic Marie
INRIA de Paris, 2 Rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France.
School of Biosciences, University of Kent, Canterbury, Kent CT2 7NJ, United Kingdom.
J Chem Phys. 2016 May 7;144(17):175101. doi: 10.1063/1.4947472.
Self-assembly of proteins into amyloid aggregates is an important biological phenomenon associated with human diseases such as Alzheimer's disease. Amyloid fibrils also have potential applications in nano-engineering of biomaterials. The kinetics of amyloid assembly show an exponential growth phase preceded by a lag phase, variable in duration as seen in bulk experiments and experiments that mimic the small volumes of cells. Here, to investigate the origins and the properties of the observed variability in the lag phase of amyloid assembly currently not accounted for by deterministic nucleation dependent mechanisms, we formulate a new stochastic minimal model that is capable of describing the characteristics of amyloid growth curves despite its simplicity. We then solve the stochastic differential equations of our model and give mathematical proof of a central limit theorem for the sample growth trajectories of the nucleated aggregation process. These results give an asymptotic description for our simple model, from which closed form analytical results capable of describing and predicting the variability of nucleated amyloid assembly were derived. We also demonstrate the application of our results to inform experiments in a conceptually friendly and clear fashion. Our model offers a new perspective and paves the way for a new and efficient approach on extracting vital information regarding the key initial events of amyloid formation.
蛋白质自组装成淀粉样聚集体是一种与阿尔茨海默病等人类疾病相关的重要生物学现象。淀粉样纤维在生物材料的纳米工程中也有潜在应用。淀粉样组装动力学显示在一个滞后期之前有一个指数增长阶段，其持续时间在大量实验和模拟小细胞体积的实验中各不相同。在这里，为了研究目前确定性成核依赖机制无法解释的淀粉样组装滞后期中观察到的变异性的起源和性质，我们构建了一个新的随机最小模型，尽管其简单，但能够描述淀粉样生长曲线的特征。然后我们求解模型的随机微分方程，并给出成核聚集过程样本生长轨迹的中心极限定理的数学证明。这些结果为我们的简单模型提供了一个渐近描述，从中得出了能够描述和预测成核淀粉样组装变异性的封闭形式分析结果。我们还展示了如何以概念上友好且清晰的方式将我们的结果应用于为实验提供信息。我们的模型提供了一个新的视角，并为一种新的高效方法铺平了道路，该方法用于提取有关淀粉样形成关键初始事件的重要信息。
