  Using exhaustive Monte Carlo simulations we study the kinetics and mechanism
of fibril formation using lattice models as a function of temperature and the
number of chains. While these models are, at best, caricatures of peptides, we
show that a number of generic features thought to govern fibril assembly are
present in 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. 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 aggregation-prone
conformation occurs within the oligomers during the second stage. As time
progresses, a dominant cluster emerges that contains a majority of the chains.
In the final stage, the aggregation-prone conformation 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 super-saturated solutions.
