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The classical nucleation theory finds the rate of nucleation proportional tothe monomer concentration raised to the power, which is the `critical nucleaussize', ${n_c}$. The implicit assumption, that amyloids nucleate in the sameway, has been recently challenged by an alternative two-step mechanism, whenthe soluble monomers first form a metastable aggregate (micelle), and thenundergo conversion into the conformation rich in ${\beta}$-strands that areable to form a stable growing nucleus for the protofilament. Here we puttogether the elements of extensive knowledge about aggregation and nucleationkinetics, using a specific case of A${\beta_{1\mathrm{-}42}}$ amyloidogenicpeptide for illustration, to find theoretical expressions for the effectiverate of amyloid nucleation. We find that at low monomer concentration insolution, and also at low interaction energy between two peptide conformationsin the micelle, the nucleation occurs via the classical route. At highermonomer concentration, and a range of other interaction parameters betweenpeptides, the two-step `aggregation-conversion' mechanism of nucleation takesover. In this regime, the effective rate of the process can be interpreted as apower of monomer concentration in a certain range of parameters, however, theexponent is determined by a complicated interplay of interaction parameters andis not related to the minimum size of the growing nucleus (which we find to be${\sim}$ 7-8 for A${\beta_{1-42}}$).

Mechanisms and Rates of Nucleation of Amyloid Fibrils