Universality in the Morphology and Mechanics of Coarsening Amyloid Fibril Networks

Peptide hydrogels have important applications as biomaterials and in nanotechnology, but utilization often depends on their mechanical properties for which we currently have no predictive capability. Here we use a peptide model to simulate the formation of percolating amyloid fibril networks and couple these to the elastic network theory to determine their mechanical properties. We find that the time variation of network length scales can be collapsed onto master curves by using a time scaling function that depends on the peptide interaction anisotropy. The same scaling applies to network mechanics, revealing a nonmonotonic dependence of the shear modulus with time. Our structure-function relationship between the peptide building blocks, network morphology, and network mechanical properties can aid in the design of amyloid fibril networks with tailored mechanical properties.

Figure 1

(a) Amyloid fibril network obtained for $\xi =10$ with $N=31130$ peptides on a 2D lattice with linear size $L=256$ at time $t=10^5$ MC steps. Fibrils that are part of the percolation network are shown with a black border. The three possible orientations of the fibril on the triangular lattice are distinguished by three different colors/shades. (b) Corresponding elastic network representation where fibril cross-links are represented by circles and the fibrils between cross-links by line segments.

Figure 2

(a) Scaled and unscaled (inset) time dependence of the mean thickness $⟨i⟩$. (b) Scaled and unscaled (inset) time dependence of mean cross-link length $⟨l⟩$. (c) Scaled time dependence of mean fibril length $⟨m_{\xi }⟩=⟨m⟩e^{w(\xi )}$, where the values of the function $w(\xi )$ used are shown in the inset. The data are obtained from configurations for a coverage $\theta =0.5$ at times $t=4^n$ MCSs, with $n=1,2,\dots ,12$. Averages were obtained from 25 independent simulations. Error bars are smaller than the symbols. Dashed lines are fits for $\ln (t_{\xi })>6$ as discussed in the text.

Figure 3

Time dependence of the normalized shear modulus $G/E^f$ obtained for networks with coverages (a) $\theta =0.5$, (b) 0.525, and (c) 0.55. Averages and errors bars were obtained from 25 independent simulations. Additional points at times $t=10^n$ ($n\in \mathbb{N}$) are also included.

Figure 4

Scaling behavior of (a) shear modulus ratio $G/G_{\mathrm{aff}}$ and (b) mean network connectivity $z$ against the rescaled time $t_{\xi }$. Data collapse is obtained separately for each coverage $\theta$. Vertical gray bars denote regions near the maximum and minimum of $G/E^f$. (c) and (d) show the values of the scaling functions $g(\xi )$ and $f(\xi )$ for the shear modulus ratio and connectivity, respectively.