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Fibrillar aggregates can grow by monomer addition and then break into fragments that could spread into neighboring cells. The rate constants for fibril elongation and fragmentation have been measured but it is not known how large an aggregate needs to be before fibril formation is thermodynamically favorable. This critical size is an important parameter controlling at what stage in an aggregation reaction fibrils can form and replicate. We determined this value to be approximately 70 monomers using super\u2010resolution and atomic force microscopy imaging of individual \u03b1\u2010synuclein aggregates formed in solution over long time periods. 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