Stochastic master equation for early protein aggregation in the transthyretin amyloid disease

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.

Evidence for a semisolid phase state of aerosols and droplets relevant to the airborne and surface survival of pathogens

“…This suggests some variability in the size and number of the organic-dense, rigid regions. This likely reflects the stochastic nature of many phase transitions and suggests a nucleation-initiated process ( 40 , 41 ). However, in all cases, LB existed as an amorphous semisolid.…”

Stochastic Modeling and Simulation of Filament Aggregation in Alzheimer’s Disease

“…There are thousands of studies conducted using these hypotheses [5][6][7][8]. The first hypothesis is the amyloid hypothesis [5][6][7][9][10][11][12][13][14][15], which is a neuron-centric model, and the second is the Warbug hypothesis, which is the neuron-astrocytic model [8,[15][16][17]. The neuron-centric model suggests that a mutation in the nuclear genome induces the overproduction of (Aβ) and tau, which become toxic to neurons [8,16,17].…”

“…All of this self-assembly of the proteins, be it functional or dysfunctional, involves the assembly of elementary units to the ends of the growing structure [9,13,14]. Hence, on that note, we are interested in studying the early aggregation of monomers forming the structure, like oligomers and filaments.…”

“…Hence, on that note, we are interested in studying the early aggregation of monomers forming the structure, like oligomers and filaments. These filaments are the most toxic structure [13] and need attention for both understanding the disease and deriving the potential cure. Studies suggest that the aggregation of a primary structure, such as monomers, into the intermediate species, such as oligomers and unbreakable filaments, are correlated with cellular toxicity [13], and such is the case of most amyloid-based diseases, including AD.…”

“…These filaments are the most toxic structure [13] and need attention for both understanding the disease and deriving the potential cure. Studies suggest that the aggregation of a primary structure, such as monomers, into the intermediate species, such as oligomers and unbreakable filaments, are correlated with cellular toxicity [13], and such is the case of most amyloid-based diseases, including AD. In AD, the aggregation of soluble APP, into non-soluble amyloid fibrils is the major cause of cognitive loss, including NFT [5,[9][10][11][12].…”