Statistical Mechanics and Kinetics of Amyloid Fibrillation

Abstract

Amyloid fibrillation is a protein self-assembly phenomenon that is intimately related to wellknown human neurodegenerative diseases. During the past few decades, striking advances have been achieved in our understanding of the physical origin of this phenomenon and they constitute the contents of this review. Starting from a minimal model of amyloid fibrils, we explore systematically the equilibrium and kinetic aspects of amyloid fibrillation in both dilute and semi-dilute limits. We then incorporate further molecular mechanisms into the analyses. We also discuss the mathematical foundation of kinetic modeling based on chemical mass-action equations, the quantitative linkage with experimental measurements, as well as the procedure to perform global fitting.

Differential Modulation of the Aggregation of N‐Terminal Truncated Aβ using Cucurbiturils

“…To gain a better understanding about the mechanisms of supramolecular inhibition, we referred to the chemical kinetics analysis . Generally speaking, nuclei were formed by monomers through primary nucleation, a rate‐limiting step in fibrillation.…”

“…Generally speaking, nuclei were formed by monomers through primary nucleation, a rate‐limiting step in fibrillation. Short protofibrils further grew into long mature fibrils through elongation, which exhibits either a linear (nonsaturated) or sub‐linear (saturated) dependence on the monomer concentration . In addition, surface catalysed secondary nucleation also played a role by providing an alternative way for generating new seeds in replace of primary nucleation and thus dramatically accelerating the aggregation process …”

“…Through carefully analysing the data from ThT kinetics measurement (Figure S8, Supporting Information), we found that the fibrillation of Aβ 1‐40 and Aβ 4‐40 both followed the NE*S mechanism, which included the primary nucleation, saturated elongation and surface catalysed secondary nucleation (Figure ). Here, concentration saturation played a role in Aβ 1‐40 growth but was not apparent in Aβ 4‐40 growth (see Figure S8).…”

“…As a further validation, we explored other possible inhibition mechanisms besides fibril‐end binding to see whether they can explain the data. Here, three additional mechanisms, inhibition of elongation, primary nucleation and secondary nucleation, were considered, respectively . In the first two cases, it was assumed that CB[7]/CB[8] could bind with Aβ monomers, which in turn decreased the effective monomer concentration and thus slowed down the fibril elongation/primary nucleation processes.…”

“…Combining the NE*S mechanism for Aβ fibrillation and fibril‐end inhibition mechanism for CB[7] and CB[8], the amounts of Aβ fibrils evolved according to the following ODEs [Eq. ]: …”