The Levinthal Problem in Amyloid Aggregation: Sampling of a Flat Reaction Space

The formation of amyloid fibrils has been associated with many neurodegenerative disorders, yet the mechanism of aggregation remains elusive, partly because aggregation time scales are too long to probe with atomistic simulations. A microscopic theory of fibril elongation was recently developed that could recapitulate experimental results with respect to the effects of temperature, denaturants, and protein concentration on fibril growth kinetics (Schmit, J. D. J. Chem. Phys. 2013, 138 (18), 185102). The theory identifies the conformational search over H-bonding states as the slowest step in the aggregation process and suggests that this search can be efficiently modeled as a random walk on a rugged one-dimensional energy landscape. This insight motivated the multiscale computational algorithm for simulating fibril growth presented in this paper. Briefly, a large number of short atomistic simulations are performed to compute the system diffusion tensor in the reaction coordinate space predicted by the analytic theory. Ensemble aggregation pathways and growth kinetics are then computed from Markov state model (MSM) trajectories. The algorithm is deployed here to understand the fibril growth mechanism and kinetics of A,316_22 and three of its mutants. The order of growth rates of the wild-type and two single mutation peptides (CHA19 and CHA20) predicted by the MSM trajectories is consistent with experimental results. The simulation also correctly predicts that the double mutation (CHA19/CHA20) would reduce the fibril growth rate, even though the degree of rate reduction with respect to either single mutation is overestimated. This artifact may be attributed to the simplistic implicit solvent model. These trends in the growth rate are not apparent from inspection of the rate constants of individual bonds or the lifetimes of the mis-registered states that are the primary kinetic traps but only emerge in the ensemble of trajectories generated by the MSM.