Probing the mechanisms of fibril formation using lattice models

Using exhaustive Monte Carlo simulations we study the kinetics and mechanism of fibril formation using lattice models as a function of temperature $\left(T\right)$ and the number of chains $\left(M\right)$ . While these models are, at best, caricatures of peptides, we show that a number of generic features thought to govern fibril assembly are captured by the toy model. The monomer, which contains eight beads made from three letters (hydrophobic, polar, and charged), adopts a compact conformation in the native state. In both the single-layered protofilament (seen for $M⩽10$ ) and the two-layer fibril $(M>10)$ structures, the monomers are arranged in an antiparallel fashion with the “strandlike” conformation that is perpendicular to the fibril axis. Partial unfolding of the folded monomer that populates an aggregation prone conformation $\left({\mathbf{N}}^{*}\right)$ is required for ordered assembly. The contacts in the ${\mathbf{N}}^{*}$ conformation, which is one of the four structures in the first “excited” state of the monomer, are also present in the native conformation. The time scale for fibril formation is a minimum in the $T$ -range when the conformation ${\mathbf{N}}^{*}$ is substantially populated. The kinetics of fibril assembly occurs in three distinct stages. In each stage there is a cascade of events that transforms the monomers and oligomers to ordered structures. In the first “burst” stage, highly mobile oligomers of varying sizes form. The conversion to the ${\mathbf{N}}^{*}$ conformation occurs within the oligomers during the second stage in which a vast number of interchain contacts are established. As time progresses, a dominant cluster emerges that contains a majority of the chains. In the final stage, the aggregation of ${\mathbf{N}}^{*}$ particles serve as a template onto which smaller oligomers or monomers can dock and undergo conversion to fibril structures. The overall time for growth in the latter stages is well described by the Lifshitz–Slyazov growth kinetics for crystallization from supersaturated solutions. The detailed analysis shows that elements of the three popular models, namely, nucleation and growth, templated assembly, and nucleated conformational conversion are present at various stages of fibril assembly.