1.

Introduction

Superresolution localization microscopy (hereafter referred to as localization microscopy), including (fluorescence) photo-activated localization microscopy^1,2 and (direct) stochastic optical reconstruction microscopy,^3,4 has become a powerful imaging tool to reveal the ultrastructures and understand the mechanisms behind cellular functions. In localization microscopy, a small subset of densely labeled fluorophores is switched “on” to obtain sparsely distributed emitters in a single frame, and the central position of each emitter is determined at nanometer precision by a proper localization algorithm, then these fluorophores are switched “off”; by repeating this process, the spatially densely labeled fluorophores are thus temporally isolated. After accumulating localization events from thousands of imaging frames, a final reconstructed superresolution image can be obtained with up to 10 times better spatial resolution, compared with conventional diffraction-limited fluorescence microscopy.⁵

From the principle of localization microscopy mentioned above, it is straightforward that localization microscopy does not produce a conventional digital image which comprises arrays of camera-recorded pixels with values representing the fluorescence intensity at those locations. Instead, the raw dataset in localization microscopy is a list of coordinates of the localized fluorophores (called localization events). Therefore, localization microscopy requires several data analysis steps to present a final superresolution image. First, because of the relatively long data acquisition time, sample drift must be corrected to guarantee a high spatial resolution.^6,7 Second, since there is inherent background noise (originated from autofluorescence, out-of-focus fluorescence, or nonspecifically labeled fluorescent molecules) inside a superresolution image, these localization events need to be filtered out to provide a clean background.^8,9 Third, due to the pointillist nature of the localization dataset, localization microscopy requires a critical image rendering step to translate the localization dataset into a final reconstructed image.¹⁰

A certain number of techniques for processing a localization dataset have been developed, where methods utilizing structural information usually outperform others. For example, using the inherent structural information within subsets of localization events imaged at different times, several highly accurate methods for sample drift correction have been proposed to overcome the shortcomings of introducing fiducial markers for drift correction.⁶ Moreover, benefiting from structural pattern average, nanometer¹¹ or subnanometer localization precision¹² has been achieved. However, methods for localization event filtering using structural information remain poorly explored.

In localization microscopy, background noise within the localization dataset usually appears as nonpolymeric localizations or nonspecific clusterings.⁹ First, due to autofluorescence, out-of-focus fluorescence or camera noise in data acquisition,¹ nonpolymeric localizations with poor localization precision, and low localization density are usually observed. Second, nonspecific labeling is a common problem in localization microscopy and has been discussed in literature.^13,14 More specifically, although antibodies usually have high specificity, there are still some reactions between antibodies and nonspecific antigens. Moreover, the fixation, blocking, washing in sample preparation procedures, and antibody concentration could all affect the degree of nonspecific labeling.^9,13,14 Nonspecific labeling in localization microscopy usually appears as clusterings.⁹ In current methods for localization event filtering, the localization events associated with poor localization precision or low localization density are discarded,^8,15 where the cutoff value is usually manually determined. This scheme is effective in filtering out backgrounds with nonpolymeric localization. However, they usually fail to filter out backgrounds with nonspecific clusterings, because the clusters usually exhibit normal localization precision and density.

In this paper, we present a new method for localization event filtering in localization microscopy. The method is based on the fact that most biological structures intrinsically exhibit anisotropy characteristic (hereafter called structural anisotropy). We demonstrate that structural anisotropy could naturally act as a metric in differentiating data of interest from background noise, thus providing a cleaner superresolution image.

2.

Methods

3.

Results and Discussion

First, we evaluate the performance of structural anisotropy quantification described above using an ideal simulated dataset. The test dataset comprises of three different types of structures: filament, ring, and randomly distributed cluster [Fig. 1(a)]. The former two types of anisotropic structures are referred to as foreground, while the clusters are referred to as background. We calculated the anisotropy coefficient of the dataset. As a result, the $g$ map of the dataset [Fig. 1(b)] intuitively separates the background from the foreground, even when they are very close to each other [Figs. 1(a) and 1(b)]. The $g$ histogram also differentiates the foreground from the background [Fig. 1(c)]. Additionally, when two filaments are nearly perpendicular to each other, we observe low anisotropy strength in the intersections [Fig. 1(a)].

Fig. 1

The performance of the adaptive structural anisotropy quantification in analyzing simulated ground-truth datesets. (a) A simulated ground-truth dataset containing filament and ring structures, as well as background clusters. (b) The anisotropy coefficient map ($g$ map) of (a). The color map is shown in the lower right. (c) The histogram of $g$ of the simulated ground-truth dataset. Scale bar: 500 nm in (a) and (b).

We further investigate the performance of the proposed method on imperfect simulated datasets with various localization precision ($\sigma$) and localization density ($\rho$). We generated localization datasets with $\sigma$ ranging from 0 to 30 nm and $\rho$ ranging from 5000 to $\mathrm{100,000}\mu {\mathrm{m}}^{-2}$. The simulation covers typical experimental scenarios. As shown in Figs. 2(a)–2(b), although the performance of the structure differentiation slightly degrades with the decreases of $\sigma$ and $\rho$, structural anisotropy effectively separates the background from the foreground under various conditions. For the dataset with a typical $\sigma$ (15 nm) and $\rho$ ($\mathrm{50,000}\mu {\mathrm{m}}^{-2}$), our method exhibits a similar result as the ground-truth dataset [Figs. 2(c) and 2(e)]. In the scenario of low $\rho$ [$5000\mu {\mathrm{m}}^{-2}$, see Figs. 2(d) and 2(f)], our method is still effective for differentiating a background with foreground, even though the absolute anisotropy strength of the foreground is lowered by the poor sampling density. These results indicate that structural anisotropy is an effective metric in describing biological structures in localization microscopy.

Fig. 2

The performance of adaptive structural anisotropy quantification in analyzing simulated datasets with various localization precision ($\sigma$) and localization density ($\rho$). (a) The averaged $g$ value of the filament, ring, and background clusters as a function of $\sigma$ under $\rho =\mathrm{50,000}\mu {\mathrm{m}}^{-2}$. (b) The averaged $g$ value of the same structures in (a) as a function of $\rho$ under $\sigma =15\mathrm{nm}$. The error bar indicates the standard deviation values from five independent simulations. Close-up views of the datasets with $\rho =\mathrm{50,000}\mu {\mathrm{m}}^{-2}$ (c) and $\rho =5000\mu {\mathrm{m}}^{-2}$ (d), respectively. Here, $\sigma$ is 15 nm in both (c) and (d). (e) and (f) show the corresponding g maps of (c) and (d).

Then we use both simulated and experimental datasets to evaluate the performance of using structural anisotropy in localization event filtering. First, we use the imperfect simulated datasets with various $\sigma$ and $\rho$ (the same datasets used in Fig. 2) to quantify the performance of the SALEF method. The quantification is characterized by two parameters: detection rate and false-positive rate. The detection rate is the ratio between the real identified background localization event and the simulated background; while the false-positive rate is the ratio between the localization events that are falsely recognized as background and the total identified background localization events. We show that SALEF provides robust performances under various $\sigma$ and $\rho$ conditions [Figs. 3(a) and 3(b)]. The detection rate is larger than 80% for typical $\sigma$ and $\rho$ conditions. When $\rho$ is lowered to $5000\mu {\mathrm{m}}^{-2}$, the detection rate decreased to $\sim 60\%$. The false-position rate is lower than 10% for typical $\sigma$ and $\rho$ conditions and increases with the decrease of $\sigma$ and $\rho$. Intuitively, for a typical dataset with $\sigma =15\mathrm{nm}$ and $\rho =\mathrm{50,000}\mu {\mathrm{m}}^{-2}$, SALEF provides a cleaner image than the original one [Figs. 3(c) and 3(d). Note that the same regions are shown in Figs. 1(c) and 1(d)]. Because of the average filtering, the localization events in the intersections of two perpendicular filaments, where low anisotropy strength had exhibited, are well preserved. However, the averaging process also has a side effect: a small fraction of the background located close to the foreground could not be filtered out. This side effect slightly reduces the detection rate.

Fig. 3

The performance of SALEF in analyzing simulated datasets. (a) The detection and false-positive rates as a function of $\sigma$ in recognizing background events under $\rho =\mathrm{50,000}\mu {\mathrm{m}}^{-2}$. (b) The detection and false-positive rates as a function of $\rho$ in recognizing background events under $\sigma =15\mathrm{nm}$. (c) A close-up view of a simulated dataset with $\rho =\mathrm{50,000}\mu {\mathrm{m}}^{-2}$ and $\sigma =15\mathrm{nm}$. (d) The resulting image of (c) after applying the SALEF method. The images are generated by histogram binning. Scale bar: 500 nm.

We further investigate the performance of SALEF using real experimental images of microtubule structures. In the microtubule dataset, a total number of 303,221 fluorophores were identified from a field-of-view of $419\mu {\mathrm{m}}^2$. The structure surface was estimated to be $8.87\mu {\mathrm{m}}^2$, thus the localization density was $\sim \mathrm{34,000}\text{molecules}/\mu {\mathrm{m}}^2$. The average localization precision of the datasets was calculated to be 12.7 nm using a theoretical equation¹⁹ which accounts for the excess noise in EMCCD camera.^20,21

A reconstructed superresolution image from the dataset suffers from a nonspecific background which is randomly distributed over the field-of-view {Fig. 4[a(i)]}. By calculating the structural anisotropy coefficient from the image, we found that the structural anisotropy could effectively discriminate the foreground from the background [Figs. 4(a)–4(c)]. Note that there is an abnormal peak in the $g$ value between 0 and 0.05 [see the $g$ histogram in Fig. 4(d)]. Therefore, we filter out the localization events whose $g$ values are smaller than 0.05, and obtain a clean superresolution image [Figs. 4(a)–4(c)]. On the contrary, if we use a popular density-based localization event filtering method, which discards 5% of the localization events with the lowest localization density, the background cannot be effectively filtered out [Figs. 4(a)–4(c)]. Note the localization dataset in Fig. 4[a(i)] is filtered using a localization precision threshold of 50 nm. The image resulting from SALEF [Figs. 4(a)–4(c)] presents a Fourier ring correlation (FRC) resolution²² of 56.1 nm, which is better than that of the original image {57.1 nm in Fig. 4[a(i)]}, but is lower than that from the density-based localization event filtering method (51.9 nm). The reason is that SALEF only filters out the background and preserves the foreground, while the density-based localization event filtering method filters out both low localization density components in the foreground and background. Note that the FRC resolution will become higher when there are fewer low localization density components.

Fig. 4

The performance of SALEF in analyzing experimental dataset. (a) The original localization dataset (i), its anisotropy coefficient map (ii), the reconstructed image after applying SALEF (iii) and the reconstructed image after density-based localization event filtering (vi), respectively. The color map of [a(ii)] is shown in the lower-right. (b) and (c) Close-up views of the boxed regions in each column of (a). (d) The g histogram for the image in [a(ii)]. (e) The FRC resolution curves of the datasets in (a). The estimated FRC resolution is: 57.1 nm [a(i)], 56.1 nm [a(iii)] and 51.9 nm [a(vi)], respectively. All the images are histogram binning images of the corresponding localization dataset. Scale bar: $5\mu \mathrm{m}$ in (a); 500 nm in (b); 250 nm in (c).

4.

Conclusion

We investigated the structural anisotropy characteristics of the datasets in superresolution localization microscopy, and presented a method for localization event filtering. Using both simulated and experimental images, we verified that SALEF, our new localization event filtering method based on structural anisotropy, is able to provide a much cleaner superresolution image than previous localization filtering methods.

However, the method presented in this study is not applicable to isotropic structures, e.g., the cell membrane proteins that are organized in small and radially symmetric clusters, simply because there is no structural anisotropy difference between the background and the foreground. In this case, other image processing techniques, including segmentation²³ and cluster analysis,²⁴ can be used.