Observation of two-step aggregation kinetics of amyloid-βproteins from fractal analysis

Self-aggregation in proteins has long been studied and modeled due to its ubiquity and importance in many biological contexts. Several models propose a two step aggregation mechanism, consisting of linear growth of fibrils and secondary growth involving branch formation. Single molecule imaging techniques such as total internal reflection fluorescence (TIRF) microscopy can provide direct evidence of such mechanisms, however, analyzing such large data-sets is challenging. In this paper, we analyze for the first time, images of growing amyloid fibrils obtained from TIRF microscopy using the techniques of fractal geometry, which provides a natural framework to disentangle the two types of growth mechanisms at play. We find that after an initial linear growth phase, identified by a plateau in the average fractal dimension with time, the occurrence of branching events leads to a further increase in the fractal dimension, with a final saturation value≈2. This provides direct evidence of the two-step nature of the aggregation kinetics of amyloid-βproteins, with an initial linear elongation phase followed by branching at later times.