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In this work, we develop and use a method that analyzes single-molecule fluorescence burst data of freely diffusing molecules in solution based on molecular diffusion theory and maximum likelihood method. We demonstrate that the photon count rate, diffusion time, population, and F\u00f6rster resonance energy transfer (FRET) efficiency can be accurately determined from simulated data and the experimental data of a known oligomerization system, the tetramerization domain of p53. We used this method to characterize the oligomers of the 42-residue amyloid-\u03b2 (A\u03b242) peptide. Combining peptide incubation in a plate reader and single-molecule free-diffusion experiments allows for the detection of stable oligomers appearing at various stages of aggregation. We find that the average size of these oligomers is 70-mer and their overall population is very low, less than 1\u2005nM, in the early and middle stages of aggregation of 1\u2005\u00b5M A\u03b242 peptide. Based on their average size and long diffusion time, we predict the oligomers have a highly elongated rod-like shape.<\/jats:p>","DOI":"10.1093\/pnasnexus\/pgad253","type":"journal-article","created":{"date-parts":[[2023,8,1]],"date-time":"2023-08-01T11:16:23Z","timestamp":1690888583000},"source":"Crossref","is-referenced-by-count":15,"title":["Single-molecule FRET and molecular diffusion analysis characterize stable oligomers of amyloid-\u03b2 42 of extremely low population"],"prefix":"10.1093","volume":"2","author":[{"given":"Fanjie","family":"Meng","sequence":"first","affiliation":[{"name":"Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health , Bethesda, MD 20892-0520 , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2105-1590","authenticated-orcid":false,"given":"Jae-Yeol","family":"Kim","sequence":"additional","affiliation":[{"name":"Laboratory of Chemical 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