Confounding the Paradigm: Peculiarities of Amyloid Fibril Nucleation

Abstract

Fibrils of amyloid proteins are currently of great interest because of their involvement in various amyloid-related diseases and nanotechnological products. In a recent kinetic Monte Carlo simulation study (Cabriolu, R.; Kashchiev, D.; Auer, S. J. Chem. Phys.2012, 137, 204903), we found that our simulation data for the rate of amyloid fibril nucleation occurring by direct polymerization of monomeric protein could not be described adequately by nucleation theory. It turned out that the process occurred in a peculiar way, thus confounding the nucleation paradigm and demanding a new theoretical treatment. In the present study, we reconsider the theoretical approach to nucleation of amyloid fibrils and derive new expressions for the stationary rate of the process. As these expressions provide a remarkably good description of the simulation data, by using them we propose a theoretical dependence of the amyloid-β(40) fibril nucleation rate on the concentration of monomeric protein in the solution. This dependence reveals the existence of a threshold concentration below which the fibril nucleation in small enough solution volumes is practically arrested, and above which the process occurs vigorously, because then each monomeric protein in the solution acts as fibril nucleus. The presented expressions for the threshold concentration and for the dependence of the fibril nucleation rate on the concentration of monomeric protein can be a valuable guide in designing new therapeutic and/or technological strategies for prevention or stimulation of amyloid fibril formation.

Communication: Non-monotonic supersaturation dependence of the nucleus size of crystals with anisotropically interacting molecules

“…This peculiar behaviour is a departure from the classical behaviour predicted by CNT. The transition values correspond with those predicted by Kashchiev et al 20,22 for jumps in the solubility of amyloid fibril, where each supersaturation region is defined by the number of rows a cluster requires in order to grow irreversibly. A general formula for the transition supersaturations can be derived; 20 S i = 2ψ y /i where i is the number of rows in a cluster, a row being defined as growth in the strong bonding direction, x.…”

“…A similar nucleation mechanism has recently been observed in oligomer formation experiments of amyloid fibrils. 32 Based on the correspondence between our results and the theoretical model, 22 additional simulations were performed to investigate the causes of the non-monotonic decay in n* vs s. The shape of the cluster was recorded and analysed at each size n for different combinations of s and ξ and again averages and distributions were evaluated using 1000 completed trajectories. Figure 3(a) shows the average number of rows in a cluster, i , against the cluster size n. While the anisotropy is varied from ξ = 1 to 8, the supersaturation is held fixed at s = 1.7, a point where there is significant variation in n* with changes in ξ .…”

“…[19][20][21][22][23][24] The propensity for a macroscopic crystal to nucleate can be characterised by the nucleus size, n* (also known as the critical nucleus size), the size a growing cluster must surpass to be more likely to grow than dissolve. According to classical nucleation theory (CNT) 25 in a single component system, there exists a well defined n* at the cluster size which requires maximal work for its formation.…”

“…Recent computational and theoretical research has shown that introducing anisotropy into the interactions between molecules creates ambiguity, changing the well defined nucleus size to a distribution of nucleus sizes. 21,22 The resultant change to the nucleation mechanism has been shown to affect the solubility of clusters, 20 crystal nucleation rate, 26 and nucleation pathway. 3 Here, we directly measure the distribution of nucleus sizes, characterise the dependence on the interaction anisotropy and supersaturation, and relate this to the nucleus shape to explain the peculiar behaviour of n*.…”

“…For ξ = 1 and 3 the average number of rows grows unbounded but at higher anisotropy (ξ = 5 and 8) the rate of row increase has dramatically slowed and has stopped at i = 2 when ξ = 8, indicating that the clusters are elongated and in agreement with the model. 22 To quantify the shape of the clusters during the nucleation process, the shape factor λ = n/i 2 , is introduced. Greater λ values correspond to elongated cluster shapes.…”