Moment dynamics of oligomer formation in protein amyloid aggregation with secondary nucleation

The abnormal aggregation of proteins into amyloid fibrils, usually implemented by a series of biochemical reactions, is associated with various neurodegenerative disorders. Considering the intrinsic stochasticity in the involving biochemical reactions, a general chemical master equation model for describing the process from oligomer production to fibril formation is established, and then the lower-order statistical moments of different molecule species are captured by the derivative matching closed system, and the long-time accuracy is verified using the Gillespie algorithm. It is revealed that the aggregation of monomers into oligomers is highly dependent on the initial number of misfolded monomers; the formation of oligomers can be effectively inhibited by reducing the misfolding rate, the primary nucleation rate, elongation rate, and secondary nucleation rate; as the conversion rate decreases, the number of oligomers increases over a long time scale. In particular, sensitivity analysis shows that the quantities of oligomers are more sensitive to monomer production and protein misfolding; the secondary nucleation is more important than the primary nucleation in oligomer formation. These findings are helpful for understanding and predicting the dynamic mechanism of amyloid aggregation from the viewpoint of quantitative analysis.