Time evolution of amyloid fibril length distribution described by a population balance model

Abstract

The formation of toxic protein aggregates is thought to be the key event in several neurodegenerative human diseases. In the last years, the combination of experimental characterization and kinetics models based on mass action laws or molecular dynamics gained important insights into the mechanistic description of the aggregation process. In this work, we investigate the fibrillation of β-lactoglobulin, a common model protein for amyloid aggregation studies with relevant applications in the food industry. In addition to the determination of the fibrillation kinetics by Thioflavin-T, we measure the time evolution of the fibril length distribution during the aggregation process, in both stagnant and shaking conditions. A population balance equation model is used to simulate the experimental data. The model describes successfully the kinetics and the complete fibril length distribution in both conditions. We show that the description of the length distribution is fundamental in discriminating the correct mechanistic picture of the aggregation process. In particular, secondary nucleation due to length-dependent breakage is found to occur in both conditions, with larger extent under shaking conditions. However, it is found that, at least for the system under investigation, fragmentation by breakage alone cannot justify the absence of the lag phase when shaking is applied. This is also related to the effect of shaking on the primary nucleation rate and on the morphology of nuclei and fibrils formed in the early stages of aggregation. This effect is possibly to be attributed to the presence of hydrophobic air interfaces created through shaking.