Simulations of nucleation and elongation of amyloid fibrils

Abstract

We present a coarse-grained model for the growth kinetics of amyloid fibrils from solutions of peptides and address the fundamental mechanism of nucleation and elongation by using a lattice Monte Carlo procedure. We reproduce the three main characteristics of nucleation of amyloid fibrils: ͑1͒ existence of lag time, ͑2͒ occurrence of a critical concentration, and ͑3͒ seeding. We find the nucleation of amyloid fibrils to require a quasi-two-dimensional configuration, where a second layer of ␤ sheet must be formed adjunct to a first layer, which in turn leads to a highly cooperative nucleation barrier. The elongation stage is found to involve the Ostwald ripening ͑evaporation-condensation͒ mechanism, whereby bigger fibrils grow at the expense of smaller ones. This new mechanism reconciles the debate as to whether protofibrils are precursors or monomer reservoirs. We have systematically investigated the roles of time, peptide concentration, temperature, and seed size. In general, we find that there are two kinds of lag time arising from two different mechanisms. For higher temperatures or low enough concentrations close to the disassembly boundary, the fibrillization follows the nucleation mechanism. However, for low temperatures, where the nucleation time is sufficiently short, there still exists an apparent lag time due to slow Ostwald ripening mechanism. Consequently, the lag time is nonmonotonic with temperature, with the shortest lag time occurring at intermediate temperatures, which in turn depend on the peptide concentration. While the nucleation dominated regime can be controlled by seeding, the Ostwald ripening regime is insensitive to seeding. Simulation results from our coarse-grained model on the fibril size, lag time, elongation rate, and solubility are consistent with available experimental observations on many specific amyloid systems.

Nucleation of amyloid fibrils

“…4a) can preserve its equilibrium shape solely by growing in both thickness and length. However, as discussed also by Zhang and Muthukumar, 31 thickening is what actually impedes its growth because of the weak binding of the peptides to the surface of the nucleus outer -sheets, i.e. to the nucleus  h -faces.…”

“…In both real and computer experiments L can be determined by plotting solubility-vs-temperature data in lnC e -vs-(1/T) coordinates. 31,54,55 If L is T-independent, the resulting line is straight, and the L value is obtainable from the slope of this line. Experiments on peptide solubility 54 …”

“…[21][22][23]31,54 Our considerations thus pertain to nanosized amyloid fibrils (protofilaments) built up of successively layered -sheets with fixed width and thickness. represented by that of right rectangular prism with cross-sectional area a 0 (m 2 ) and lateral areas a (m 2 ) and a h (m 2 ) of its two different side surfaces (Fig.…”

“…18,30,44,[51][52][53][54] and computer simulations (e.g., Refs. 31,55) give evidence for the existence of equilibrium peptide concentration and for the dissolution of amyloid fibrils in sufficiently dilute solutions. Knowing the equilibrium concentration of monomeric peptide allows determination of the supersaturation for fibril nucleation, and the fibril dissolution demonstrates that fibril formation is not an irreversible process.…”

Thermodynamics of amyloid formation and the role of intersheet interactions

“…8 By using coarse-grained models, at various levels of resolution, it has been possible to study the formation and stability of larger assemblies 9-35 and also get insight into the thermodynamic forces at play in amyloid formation. [36][37][38][39] However, to map out the thermodynamics of amyloid formation as a function of control parameters such as temperature and concentration is computationally demanding even in simple models.…”