Figure 1.
Fluorophore blinking affects superresolution image quality.
(A) Simplified kinetic scheme of a photoactivatable fluorophore such as mEos2. The fluorophore is irreversibly photoactivated with rate constant k1, can transiently access a nonfluorescent state with rate constant k2, return to the fluorescent state with rate constant k3, and irreversibly photobleach with rate constant k4. (B) Superresolution image of an E. coli cell expressing FtsZ-mEos2 generated with conventional clustering thresholds: spots within 167 nm (1 camera pixel) and 50 ms (1 frame) of each other were grouped together and plotted once. The cytoplasmic cluster (left inset) consists of spots detected very closely in time, suggesting that they came from the same fluorophore, whereas a dense section inside the Z-ring (right inset) contains spots detected throughout the experiment. Scale bar, 500 nm. Inset grid size, 30 nm.
Figure 2.
Effects of threshold selection on Z-ring width measurement.
(A) Representative Z-ring width measurement of a simulated image where each molecule is only represented once. The intensity along the short axis of the cell is projected onto one dimension (red circles), and then fit to a Gaussian distribution (gray line). The FWHM (97 nm, blue dotted line) is calculated as 2.35*σ, where σ is the fitted Gaussian standard deviation. (B) and (C) Z-ring width values (indicated by the heat map) calculated from images generated by applying different threshold pairs for an experimental dataset (B) and a simulated dataset (C). The simulated dataset was generated using the following parameters: Ntotal = 2000 (50% in the Z-ring), σ = 15 nm, <nblink> = 2, <τoff> = 1 frame, <τon> = 1 frame, <τ0act> = 5 frames (1 frame = 50 ms). The Z-ring width calculated from the reference image (A), where each molecule is represented only once, is 97 nm, which is similar to the measurements made from images constructed using low values of tThresh or dThresh.
Figure 3.
Effects of threshold selection on mean and relative molecule density.
(A) and (B) Total number of molecules, N, in images generated by applying different threshold pairs to an experimental dataset (A) and a simulated dataset (B). (C) Fractional difference |(N-Nref)/Nref| between each reconstructed simulated image and the number of molecules in the reference simulated image (Nref = 1248). Images with small fractional differences (dark areas) are generated from threshold pairs found along two intersecting valleys. (D) and (E) Fraction of molecules located at the midplane (fmidcell) in images generated by applying different threshold pairs for an experimental dataset (D) and a simulated dataset (E). In the reference image, fmidcell = 0.53, which is most similar to the values calculated from images generated using low values of both dThresh and tThresh. Datasets analyzed are the same as those shown in Figure 2.
Figure 4.
Effects of threshold selection on molecule density distribution in the Z-ring.
(A) Histogram (gray bars) of molecules per pixel (15 nm ×15 nm) inside the Z-ring of a simulated image that was not processed with a clustering algorithm. (B) Histogram (gray bars) of molecules per pixel of the corresponding reference image, where each molecule is represented only once. Poisson distributions simulated with the sample means, 3.9 (A) and 1.2 (B) molecules per pixel, are shown in red. The ratio of mean values reflects the localization of each molecule approximately three times due to the simulated photoblinking kinetics (<nblink> = 2, <τoff> = 1 frame, <τon> = 1 frame). Poisson goodness-of-fit tests resulted in pGOF = 0 for distribution in (A), suggesting that blinking results in deviations from a Poisson density distribution (pGOF = 0.74 for the reference distribution in (B)). Insets show the cropped Z-ring regions used to generate the histograms. (C) p-values from the KS-test when the molecule density distribution of the Z-ring generated by the reference image (B) is compared with distributions in images generated with different threshold pairs. Distributions that resulted in pKS >0.05 are not significantly different from the distribution in the reference image. Dataset analyzed is the same simulated dataset shown in Figure 2–3.
Figure 5.
Accuracy of images generated with different threshold pairs.
(A) Region of threshold space (white squares) that resulted in <10% difference from the reference measurements of Z-ring width, N, and fmidcell, and that yielded Z-ring density distributions not significantly different from the reference distribution (pKS >0.05). (B) Jaccard index values at each threshold pair. Higher Jaccard index values indicate more accurate single-molecule clustering. (C) The peak of the Jaccard index plot (B, white squares) is within the region where all four quantitative measurements are within 10% of the reference measurements (A). Dataset analyzed is the same simulated dataset shown in Figure 2–4.
Figure 6.
Quantitative measurements of a simulated cluster dataset.
(A) Representative cluster diameter measurement for a reference image with no repeat localizations. Each cluster is identified by eye, and then fit to a two-dimensional, symmetrical Gaussian distribution (blue mesh). The cluster diameter is measured as the FWHM, calculated as 2.35*σ, where σ is the fitted Gaussian standard deviation. The average FWHM of these four clusters is 74±1 nm. (B) Cluster diameter values (average of four clusters) calculated from images generated by applying different threshold pairs to the same simulated dataset. The measured diameters decrease with increasing threshold values, similarly to the Z-ring width measurement. (C) The fraction of molecules located in clusters (fcluster) is most similar to that measured in the reference image (0.47) for low values of both dThresh and tThresh. (D) As with the Z-ring simulation, fractional difference between each reconstructed image and the number of molecules in the reference image (Nref = 1212) is lowest along two intersecting valleys. (E) The Jaccard index peak position for the cluster simulation is similar to that in the Z-ring simulation where identical kinetic parameters were used (Figure 5B). This simulated dataset was generated using the following parameters: Ntotal = 2000 (50% in clusters), <molecules/cluster> = 200, FWHMcluster = 50 nm, σ = 15 nm, <nblink> = 2, <τoff> = 1 frame, <τon> = 1 frame, <τ0act> = 5 frames (1 frame = 50 ms).
Figure 7.
Relationship between Jaccard index, measurement error, and activation rate across different simulated datasets.
(A) Minimum combined measurement error, εall, for each dataset plotted against and the corresponding Jaccard index value. εall was defined as the worst fractional measurement error of the three bulk measurements: N, fmidcell, and ring width when compared to the reference image. Images with low measurement error do not always correlate with high clustering accuracy (Jaccard index), and thus cannot ensure reliable lists of molecule counts and positions. (B) Maximum Jaccard index plotted against the ratio of the average time between localizations in the 255 nm ×255 nm maximum density region, Δtmax, and the average time between repeat localizations of the same molecules, Δtrepeat, calculated for each simulated dataset. Simulations with higher ratios of Δtmax/Δtrepeat result in higher Jaccard index values. (C) Comparison of maximum Jaccard index with Jaccard index identified at the intersection of the |(N-Nref)/Nref| plot for each simulated dataset. The two values agree well when the maximum Jaccard index is greater than 0.8. Simulation parameters can be found in Table S1 and S2. In all plots, Z-ring simulations are shown in blue and cluster simulations are shown in red.
Figure 8.
In vitro characterization of mEos2.
(A) A typical in vitro image of purified mEos2 molecules sparsely distributed on a cover glass, acquired using the same PALM imaging condition as the in vivo cell sample. All localized positions are indicated by small, filled circles that are colored by detection time. Localizations belonging to the same molecule are enclosed in a larger, open circle, which is colored by the mean detection time of all the enclosed localizations. The inset shows details of a single cluster, which contains four localizations (filled circles with black outlines). (B) Histogram of localizations per molecule from 515 molecules fitted with an exponential distribution (red line), which yielded a mean of 0.9±0.1 localizations per molecule. The value of α (2.4±2.8) represents the mean of observed molecules that lasted at least one frame, and is consequently larger than the fitted mean.
Figure 9.
Determination and application of optimal threshold pair to an experimental image.
(A) |(N-Nref)/Nref| plot of the experimental dataset used in Figure 1–3. The plot was generated using the Nref number (547) calculated from the measured α value from combined in vitro and in vivo characterizations of mEos2 (Figure 8 and Figures S4). The optimal threshold pair was identified at 0.4 s and 60 nm (blue circle). (B) and (C) Images constructed using the optimal threshold pair (B) and without any clustering algorithm (C). Clusters that are reduced by the optimized clustering algorithm are indicated by white arrows. Clusters that remain bright in the optimal image, which may represent oligomeric states of FtsZ-mEos2, are indicated by green arrows. Scale bars, 500 nm.
Table1. Quantitative measurements made from the optimized experimental image.