Kinetic theory of amyloid fibril templating

Abstract

The growth of amyloid fibrils requires a disordered or partially unfolded protein to bind to the fibril and adapt the same conformation and alignment established by the fibril template. Since the H-bonds stabilizing the fibril are interchangeable, it is inevitable that H-bonds form between incorrect pairs of amino acids which are either incorporated into the fibril as defects or must be broken before the correct alignment can be found. This process is modeled by mapping the formation and breakage of H-bonds to a one-dimensional random walk. The resulting microscopic model of fibril growth is governed by two timescales: the diffusion time of the monomeric proteins, and the time required for incorrectly bound proteins to unbind from the fibril. The theory predicts that the Arrhenius behavior observed in experiments is due to off-pathway states rather than an on-pathway transition state. The predicted growth rates are in qualitative agreement with experiments on insulin fibril growth rates as a function of protein concentration, denaturant concentration, and temperature. These results suggest a templating mechanism where steric clashes due to a single mis-aligned molecule prevent the binding of additional molecules.

Fibril Elongation by Aβ17–42: Kinetic Network Analysis of Hybrid-Resolution Molecular Dynamics Simulations

“…58 Indeed, this assumption has been supported by all-atom simulations of fibril elongation by short Aβ segments like Aβ 16–22 , 34 Aβ 35–40 37 and Aβ 37–42 . 36 If the same assumption is also true for Aβ 17–42 , one would expect that fibril structures extend to the middle regions (NMID and CMID) after the initial contact form in region CHC or CTHR.…”

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

“…The growth rate of the fibril is determined by three timescales 28 (Fig. 1B): the diffusion time for a free peptide to form the initial interactions ( τ diff or 1/k diff ), the average residence time required for the non-registered state to evolve to either the fully bound or dissociated states ( τ residence ), and the average time required for a fully bound peptide to dissociate from the fibril end ( τ off ): $$k_{\mathrm{italicgrowth}}=k_{on}-k_{\mathrm{italicoff}}=\frac{P_{\mathrm{italiccommittor}}}{1\frac{1}{k_{\mathit{diff}}}+{\tau }_{\mathit{residence}}}-\frac{1}{{\tau }_{\mathrm{italicoff}}},$$ where P committor is the probability that an incoming peptide becomes incorporated into the fibril in a fully-bound in-register state.…”

Pseudo-one-dimensional nucleation in dilute polymer solutions

“…Following [20], we approximate k diff by the rate of particles striking an absorbing sphere of radius a , k diff = 4 πaC 1 D p , where D p is the monomer diffusion constant. This rate assumes that all collisions result in binding and, therefore, neglects sequence effects that enforce specific alignments between the molecules.…”

“…These clusters will add a molecule with rate k diff and lose a molecule when either terminal strand breaks all x bonds with the neighboring molecules. The rate of such loss events is given by [20] $$k_{\text{loss}}^{-1}=-\frac{1}{2v_{\mathrm{f}}}+\frac{D}{2v_{\mathrm{f}}^2}{e}^{v_{{\mathrm{normalf}}^x}/D}false(1-e^{-v_{\mathrm{f}}/D}false),$$where v f is given by Eq. 8 with f = f αα , the factor of two accounts for the two ends of the fibril, and the substitution x → 2 x should be made for hairpin molecules.…”