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The project was supported by grants from the National Institutes of Health (NIH GM116204 and GM122552 to W.Y.).

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Correspondence to Weidong Yang.

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Integrated supplementary information

Supplementary Figure 1 Optimal bin-size determination with chi-square error and P-value analysis.

(A) Data sets were simulated in three dimensions. Color bar indicates z position of the simulated points. This representative data set contains 1,000 single molecule locations. (B) Each data sets was simulated first with an ideal 23-nm radius (RI). (C) Subsequently, a localization error (σLE) of 10 nm was added to each point. Using a 10-nm bin size for demonstration, the 2D histogram of the simulated data set with a 23-nm radius and 10-nm localization precision was determined. (D) The 3D density histogram was then obtained via the 2D to 3D transformation algorithm and the peaks were fit with Gaussian distributions. (E) The 10-nm bin-size area matrix was calculated and multiplied by the 3D density distribution in (D) to reconstruct the 2D distribution (any negative values in the density distribution were set to zero) as shown in F. (F) The values of the reconstructed 2D distribution were then compared bin-by-bin to the original 2D distribution (as shown in C) using the Chi-square analysis equation where ‘o’ refers to the observed histogram values in (F), ‘e’ refers to the expected histogram values in (C), ‘i’ refers to the bin, and ‘n’ refers to the total number of bins with histogram values in them. (G) For any given set of simulated data, the bin size is varied from 1 nm to 20 nm in this example. The Chi-square test statistic and p-value were then plotted across the potential bin size values. A p-value ≤ 0.01 indicates that the 2D histograms in (C) and (F) are different from each other, suggesting the lack of enough data to allow sufficient sampling from each bin. On the other hand, a p-value > 0.05 suggests that the 2D histograms are statistically similar and likely have enough data points to accurately measure the value in each bin. Chi-square analysis was performed 1,000 times for each set of simulation parameters. (H) A 3D density histogram displaying large errors (negative density values) due to a bin size selection that was too small. Such errors occur when the single molecule density is not uniform throughout a given radial bin. This non-uniformity is due to under-sampling. (I) A 3D density histogram displaying no errors and a clear Gaussian distribution due to a properly selected bin size.

Supplementary Figure 2 The effects of varying bin size while using Ruba et al.’s categorization routine.

In response to Tu et al’s analysis of the effect of bin size, we repeated their simulations (100 simulated single molecule localization and 8 nm simulated localization precision) with bin sizes ranging from 4-20 nm in the context of our categorization routine. The bar chart represents the categorization success for each bin width, the rainbow-colored scatter plot illustrates a sample simulated data set of 100 points, and the legend displays a general schematic of each type of distribution with the colors corresponding to the bar chart. The central route was always accurately categorized > 99.8%, the peripheral route saw modest increases in categorization success and plateaued at ~75% before dropping off as the bin size increased, while the bimodal and uniform had strong linear increases in categorization success with increasing bin size to reach their optimal bin size before dropping off.

Supplementary Figure 3 Simulation and route-categorization algorithm from Figure 1T compared across all solution space.

(A) Simulation results for a peripheral distribution with parameters of 100-1000 simulated single molecule localizations, 10 nm localization precision, 23 nm peripheral radius, 0 nm central radius, and 10-20 nm bin sizes obtained from optimization algorithm. Instead of comparing each simulated dataset trial to the peripheral, central, bimodal, and uniform ground truth distribution with the same peripheral radius, central radius, and simulated localization precision parameters, every ground truth distribution in the entire solution space as defined by Tu et al was simulated and compared via SAR to each simulated dataset trial during the categorization routine. Total solution space was designated as 1) categorization as either a peripheral, central, bimodal, or uniform distribution, 2) mean peak fittings will not exceed 50 nm, and 3) standard deviation of the peak fittings (a measure of the peak width) will not exceed 25 nm. The colorbar to the right of each graph represents the number of dataset trials that fell at a particular location on the simulated localization precision vs. distribution type axis. With the parameters stated above, no dataset trials fell outside the peripheral categorization. B) Simulation results from (A) showing the standard deviation of both the peak mean and peak width converging on the original simulation parameters (23 nm peripheral radius and 10 nm simulated localization precision), within a few nm with only a few hundred localizations.

Supplementary Figure 4 Experimentally obtaining a reliable 3D distribution of Imp β1 in the NPC.

(A) Schematic of the nuclear pore complex with a model trajectory for Alexa Fluor 647-labeled Importin β1. Scale bar = 50 nm. (B) Experimental data for Imp β1 obtained from 20 NPCs of 20 cells. 2D single-molecule data is shown for the entire NPC region (from -120 to 120 nm in the x dimension and from -80 to 80 nm in the y dimension – 3,188 single molecule locations in total) as well as for an enlarged view of the central pore region (-20 to 20 nm for the x dimension and -80 to 80 nm for the y dimension as shown in boxed area – 450 single molecule locations in total). (C) Precision distribution of the data points shown in (B) with a cutoff limit of 10 nm. The weighted mean results in an effective precision of 8.6 nm. A table is shown demonstrating how many points were obtained for each precision. (D) Plot of the reproducibility percentage obtained from simulated data using a 23-nm radius and the experimentally determined mixed localization precisions. The dashed line indicates the minimum amount of data points needed for a 90% acceptability rate. As shown, ~100 points are needed for 8.6-nm effective precision data to reconstruct a reliable and consistent distribution in the R dimension. With 450 points, a reproducibility rate of 100% is obtained. (E) Random samplings from the pool of 450 data points for Imp β1. Samplings were conducted using random samples of 100 and 200 points. Gaussian peak positions are shown to demonstrate reliable and consistent results between samplings. As shown in the demonstrations, peak fittings show little deviation in the final results generated from 100 to 450 points.

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Fig. 1: Route-categorization simulation.
Supplementary Figure 1: Optimal bin-size determination with chi-square error and P-value analysis.
Supplementary Figure 2: The effects of varying bin size while using Ruba et al.’s categorization routine.
Supplementary Figure 3: Simulation and route-categorization algorithm from Figure 1T compared across all solution space.
Supplementary Figure 4: Experimentally obtaining a reliable 3D distribution of Imp β1 in the NPC.