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

Abstract

The formation of amyloid fibrils has been associated with many neurodegenerative disorders, yet the mechanism of aggregation remains elusive, partly because aggregation timescales 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. Chem. Phys. 2013). 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 multi-scale 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 Aβ16-22 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 over estimated. 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.

The dark side of amyloid aggregation: Exploring the productive and non-productive pathways with multi-scale modeling

“…For residues in both extended and coil structures, larger FCL leads to longer H-bond formation times. The overall H-bond formation timescales from explicit solvent simulations are similar to those from implicit solvent simulations(27). The H-bond breakage times, in contrast, are ~ 5 times slower in explicit solvent.…”

“…1) is based on the discretization of the elongation process into a series of states based on the microscopic theory of fibril elongation. (27,32) The elongation process starts from an unstructured monomer in the bulk solvent, which "docks" to a pre-formed fibril core and "locks" as a new structured layer. (12,13,16) Thus, the process can be divided into three stages.…”

“…The slow elongation rate of amyloid fibrils is due to a relatively flat energy landscape which is pitted with numerous local minima. (27) Since the long aggregation time arises from transitions between substates, the problem of simulating the elongation process can be solved by efficiently sampling the transitions between different substates with proper reaction coordinates. Multi-scale methods and enhanced sampling have been applied to the simulation of amyloid aggregation.…”

“…We have recently developed a theoretical and computational framework that can systematically explore productive and unproductive pathways of protein fibril growth. (27,32) In this framework, the hydrogen bonding (H-bond) number and alignment (referred to as the 'registry' here) between an incoming peptide and the existing fibril core are used as the primary reaction coordinates of the aggregation process. The slow process of exploring different registries is then converted to a series of H-bond formation and breakage events.…”

“…We have previously deployed this multi-scale computational algorithm to predict the binding and aggregation process of small amyloid-forming peptides in implicit solvent (27). That work established the feasibility of using the analytic theory as a framework to access long timescales and more extensive sampling of trajectories.…”