Extended Data Fig. 3. Rotation of Individual NPC Clusters.

a, Estimating the rotational phase angle (φ). The angles of individual localizations relative to the double-circle centroid of well-localized NPC clusters (Extended Data Fig. 2d) were estimated and binned (5° bins, θ = 0-45°). Four examples are shown here for a range of localizations/cluster (the number of localizations/cluster, n, is given in each figure panel). Distributions were fit to y = 1/9 + (1/20.6)*cos[8(θ-φ)]. The 1/9 term reflects the 9 bins, and the cosine scaling factor is a reasonable average based on simulations. This amplitude scaling factor is insensitive to the goodness-of-fit due to orthogonality – the phase angle shifts the curve laterally, and identical phase angles are obtained by the fitting routine regardless of the scaling factor. The fixed scaling factor enables rapid convergence of the fit. The phase angles from these fits were used to rotate pore clusters before aligning them based on their centroids. b, Angular distribution of localizations in the initially aligned pore clusters (Fig. 2i). Inset: Fig. 2i, bar: 50 nm. c, Angular distribution of rotationally-corrected localizations (Fig. 2k). Inset: Fig. 2k, bar: 50 nm. Pore clusters were rotated based on the phase angle as determined in (a) before aligning. The distribution was fit to y = y₀ + c₁*sin(8(x-ϕ)), where y₀, c₁ and ϕ are fit parameters. The minima define the angles of the dashed spokes in Fig. 2m. Source numerical data are provided in source data.