Abstract
It is significant to understand the earliest molecular events occurring in the nucleation of the amyloid aggregation cascade for the prevention of amyloid related diseases such as transthyretin amyloid disease. We develop chemical master equation for the aggregation of monomers into oligomers using reaction rate law in chemical kinetics. For this stochastic model, lognormal moment closure method is applied to track the evolution of relevant statistical moments and its high accuracy is confirmed by the results obtained from Gillespie’s stochastic simulation algorithm. Our results show that the formation of oligomers is highly dependent on the number of monomers. Furthermore, the misfolding rate also has an important impact on the process of oligomers formation. The quantitative investigation should be helpful for shedding more light on the mechanism of amyloid fibril nucleation.
Highlights
It is significant to understand the earliest molecular events occurring in the nucleation of the amyloid aggregation cascade for the prevention of amyloid related diseases such as transthyretin amyloid disease
In order to quantitatively explore the process of early amyloidal aggregation, we have developed a stochastic mathematical model about oligomers aggregation from monomers using rate law in chemical kinetics
We have adopted a typical moment method based on lognormal closure to capture the statistical moments, and massive calculations show very good agreement between the semi-analytic method and the Gillespie’s stochastic simulation algorithm (SSA) for the stochastic model
Summary
It is significant to understand the earliest molecular events occurring in the nucleation of the amyloid aggregation cascade for the prevention of amyloid related diseases such as transthyretin amyloid disease. To capture the stochastic effects in early amyloid aggregation, we build a mathematical model of chemical master equation, which is well accepted as probabilistic description in well-mixed and dilute In “Chemical master equation model” we describe the stochastic method of modeling the aggregation of monomers into oligomers and present moment closure method for computing the time evolution of stochastic models.
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