Modeling fibril fragmentation in real-time.

During the application of the mass-action-equation models to the study of amyloid fiber formation, time-consuming numerical calculations constitute a major bottleneck. To conquer this difficulty, here an alternative efficient method is introduced for the fragmentation-only model. It includes two basic steps: (1) simulate close-formed time-evolutionary equations for the number concentration P(t) derived from the moment-closure method; (2) reconstruct the detailed fiber length distribution based on the knowledge of moments obtained in the first step. Compared to direct calculation, our method speeds up the performance by at least 10,000 times (from days to seconds). The accuracy is also satisfactory if suitable functions for the approximate fibril length distribution are taken. Further application to the sonication studies on PI264-b-PFS48 micelles performed by Guerin et al. confirms our method is very promising for the real-time analysis of the experiments on fibril fragmentation.