Department of Physics, Drexel University, Philadelphia, Pennsylvania 19104, USA.
J Phys Chem B. 2013 May 30;117(21):6574-83. doi: 10.1021/jp401586p. Epub 2013 May 20.
We propose a kinetic model for the self-aggregation by amyloid proteins. By extending several well-known models for protein aggregation, the time evolution of aggregate concentrations containing r proteins, denoted c(r)(t), can be written in terms of generalized Smoluchowski kinetics. With this approach, we take into account all possible aggregation and fragmentation reactions involving clusters of any size. Correspondingly, an aggregate of size x + y could be formed by or break up into two smaller constituent aggregates of sizes x and y. The rates of each aggregation or fragmentation reaction, called kernels, are specified in terms of the aggregate size, and we solve c(r)(t) for large cluster sizes using numerical techniques. We show that by using Smoluchowski kinetics many pathways to fibrillation are possible and quantities, such as the aggregate length distribution at an arbitrary time, can be calculated. We show that the predicted results of the model are in agreement with the experimental observations.
我们提出了一个用于淀粉样蛋白自聚集的动力学模型。通过扩展几个著名的蛋白质聚集模型，包含 r 蛋白的聚集体浓度 c(r)(t) 的时间演化可以用广义的 Smoluchowski 动力学来表示。通过这种方法，我们考虑了所有可能的涉及任何大小的聚集体的聚集和碎裂反应。相应地，大小为 x + y 的聚集体可以由或分解成两个大小为 x 和 y 的较小的组成聚集体。每个聚合或碎裂反应的速率，称为核，是根据聚集体的大小来指定的，我们使用数值技术来求解大的聚集体的 c(r)(t)。我们表明，通过使用 Smoluchowski 动力学，纤维化的许多途径是可能的，并且可以计算出任意时间的聚集体长度分布等数量。我们表明，模型的预测结果与实验观察结果一致。
