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. 2022 Mar 18;12:4682. doi: 10.1038/s41598-022-08245-6

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Analysis methods for single-filament data of protein self-assembly. (A) Kinetic model of the simulated nucleation and conversion process. For nucleation, k⁺_nuc and k⁻_nuc are changed to k⁺_poly and k⁻_poly as soon as the nucleus size is reached (here three monomers). For a conversion mechanism, only the assembly step associated with conversion (i.e., for example a restructuring of the assembled oligomer) shows k⁺_conv and k⁻_conv. Earlier and later steps follow k⁺_poly and k⁻_poly. For the conversion step, three main possibilities could lead to the slower kinetics as indicated by the black box: (1) the pre-existing oligomer needs to rearrange prior to the next binding event, (2) the restructuring occurs upon binding or (3), the restructuring occurs after binding of the next monomer. All possibilities result in a slower kinetic step and are treated the same in the simulations. (B) Example trace of a simulated growth process undergoing a nucleation mechanism with a nucleus size of four monomers (black) with Gaussian noise (grey). The distribution of time spent at a certain oligomer size (blue histogram) contains information about the nucleation mechanism when it is applied to many single oligomer traces (C). (C) Visitation analysis on a nucleation (blue) or a conversion mechanism (yellow). The visitation analysis identifies the nucleation mechanism as well as the nucleus size for nucleation or conversion. (D, E) Average rates analysis. (D) Average traces of a nucleation (blue) or conversion (yellow) mechanism. From the average trace of many individual filaments growing from the same starting point, average rates can be calculated from the average time it takes to reach the next oligomer size. (E) Average rates plotted versus the monomer number (oligomer size). Different nucleation mechanisms show individual signatures. The nucleation and conversion kinetics were simulated to show slower association rates than the polymerization kinetics.