Quasihomogeneous nucleation of amyloid beta yields numerical bounds for the critical radius, the surface tension, and the free energy barrier for nucleus formation

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Abstract
Amyloid aggregates are believed to grow through a nucleation mediated pathway, but important aggregation parameters, such as the nucleation radius, the surface tension of the aggregate, and the free energy barrier toward aggregation, have remained difficult to measure. Homogeneous nucleation theory, if applicable, can directly relate these parameters to measurable quantities. We employ fluorescence correlation spectroscopy to measure the particle size distribution in an aggregating solution of Alzheimer’s amyloid beta molecule ( A β 1 – 40 ) and analyze the data from a homogeneous nucleation theory perspective. We observe a reproducible saturation concentration and a critical dependence of various aspects of the aggregation process on this saturation concentration, which supports the applicability of the nucleation theory to A β aggregation. The measured size distributions show a valley between two peaks ranging from 5 to 50 nm , which defines a boundary for the value of the nucleation radius. By carefully controlling the conditions to inhibit heterogeneous nucleation, we can hold off nucleation in a 25 times supersaturated solution for at least up to 3 h at room temperature. This quasi-homogeneous kinetics implies that at room temperature, the surface energy of the A β ∕ water interface is ⩾ 4.8 mJ ∕ m 2 , the free energy barrier to nucleation (at 25 times supersaturation) is ⩾ 1.93 × 10 − 19 J , and the number of monomers in the nucleus is ⩾ 29 .