Multiscale Models for Fibril Formation: Rare Events Methods, Microkinetic Models, and Population Balances

Growth kinetics of amyloid-like fibrils: An integrated atomistic simulation and continuum theory approach

Amyloid fibrils have long been associated with many neurodegenerative diseases. The conventional picture of the formation and proliferation of fibrils from unfolded proteins comprises primary and secondary nucleation of oligomers followed by elongation and fragmentation thereof. In this work, we first employ extensive all-atom molecular dynamics (MD) simulations of short peptides to investigate the governing processes of fibril growth at the molecular scale. We observe that the peptides in the bulk solution can bind onto and subsequently diffuse along the fibril surface, which leads to fibril elongation via either bulk- or surface-mediated docking mechanisms. Then, to guide the quantitative interpretation of these observations and to provide a more comprehensive picture of the growth kinetics of single fibrils, a continuum model which incorporates the key processes observed in the MD simulations is formulated. The model is employed to investigate how relevant physical parameters affect the kinetics of fibril growth and identify distinct growth regimes. In particular, it is shown that fibrils which strongly bind peptides may undergo a transient exponential growth phase in which the entire fibril surface effectively acts as a sink for peptides. We also demonstrate how the relevant model parameters can be estimated from the MD trajectories. Our results provide compelling evidence that the overall fibril growth rates are determined by both bulk and surface peptide fluxes, thereby contributing to a more fundamental understanding of the growth kinetics of amyloid-like fibrils.

Extracellular interplay of amyloid fibrils and neural cells

Some neurological disorders such e.g. as Alzheimer disease are accompanied by the appearance of amyloid fibrils inside and outside cells. Herein, I present a generic coarse-grained kinetic mean-field model describing at the extracellular level the interplay of fibrils and cells. It includes the formation and degradation of fibrils, activation of healthy cells with respect to the fabrication of fibrils, and death of activated cells. The corresponding analysis indicates that the disease development can occur in two qualitatively different regimes. The first one is controlled primarily by the intrinsic factors resulting in slow increase of fibril production inside cells. The second one implies faster self-promoted growth of the fibril population by analogy with explosion. This prediction reported as a hypothesis is of interest for conceptual understanding of the neurological disorders.

Multiscale Exploration of Concentration-Dependent Amyloid-β(16-21) Amyloid Nucleation

Atomic descriptions of peptide aggregation nucleation remain lacking due to the difficulty of exploring complex configurational spaces on long time scales. To elucidate this process, we develop a multiscale approach combining a metadynamics-based method with cluster statistical mechanics to derive concentration-dependent free energy surfaces of nucleation at near-atomic resolution. A kinetic transition network of nucleation is then constructed and employed to systematically explore nucleation pathways and kinetics through stochastic simulations. This approach is applied to describe Aβ_16-21 amyloid nucleation, revealing a two-step mechanism involving disordered aggregates at millimolar concentration, and an unexpected mechanism at submillimolar concentrations that exhibits kinetics reminiscent of classical nucleation but atypical pathways involving growing clusters with structured cores wrapped by disordered surface. When this atypical mechanism is operative, critical nucleus size can be reflected by the nucleation reaction order. Collectively, our approach paves the way for a more quantitative and detailed understanding of peptide aggregation nucleation.