Thermodynamic properties of amyloid fibrils in equilibrium

Abstract

In this manuscript we use a two-dimensional coarse-grained model to study how amyloid fibrils grow towards an equilibrium state where they coexist with proteins dissolved in a solution. Free-energies to dissociate proteins from fibrils are estimated from the residual concentration of dissolved proteins. Consistent with experiments, the concentration of proteins in solution affects the growth rate of fibrils but not their equilibrium state. Also, studies of the temperature dependence of the equilibrium state can be used to estimate thermodynamic quantities, e.g., heat capacity and entropy.

FIG. 1

(a) Structure of a fibril made from residues 16–21 of the amyloid-β protein (PDB ID: 3OW9). Backbone and side chains of proteins are depicted using cartoon-like and bead representations, respectively. (b) Schematic representation of a protein in the model. Side chain and backbone beads are highlighted as well as Hbond arms. The representation of a dimer depicts the vectors (blue arrow) used in Eq. 3 to account for Hbonds. The representation of an amyloid fibril shows two β-sheets made of three peptides each stack on top of each other. The fibril axis is also shown. (c) Phase diagram showing monomeric (MR), oligomeric (OR) and fibrillar states as well as representative snapshots of the system at these states computed at the same density 0.1 and temperatures (d) 0.25, (e) 0.15, and (f) 0.1.

FIG. 2

Time dependence of the fraction of monomers f_o in the system. Only a fraction of the whole trajectory is shown. Dashed and full lines correspond to systems in the monomeric (i.e., ρ = 0.02) and oligomeric (ρ = 0.1) states, respectively. The thermal energy of the system is 0.15 and each point in the figure is an average over 10 MC cycles. Lines correspond to exponential fits of the data.

FIG. 3

(a) Dependence of the equilibrium density of monomers ${\rho }_o^{\ast }$ on the density of proteins ρ in the system at the reduced temperature 0.15. Vertical dashed lines separate monomeric (MR), oligomeric (OR), and Fibril regions. The full line corresponds to the fit of ${\rho }_o^{\ast }$ to Eq. 3 for data points in the monomeric region. The horizontal dashed line shows that the equilibrium density of monomers in the fibril state is independent of ρ. Error bars were estimated using block average in which simulations were divided in 20 blocks. (b) Time dependence of ρ_o compute at ρ = 0.17 (dashed line) and ρ = 0.25 (full line). Only a fraction of the whole trajectory is shown. The horizontal dashed line shows the equilibrium density of monomers.

FIG. 4

Dependence of the free-energy ΔF to dissociate a protein from a fibril on temperature. The best fit of the data point to Eq. 6 is shown.

FIG. 5

Dependence of ΔF on temperature for the honeycomb peptide lattice model of fibril formation [41]. Lines correspond to best fit of the data point to Eq. 6.