Quantifying nanoscopic alterations associated with mitochondrial dysfunction using three-dimensional single-molecule localization microscopy

Mitochondrial morphology provides unique insights into their integrity and function. Among fluorescence microscopy techniques, 3D super-resolution microscopy uniquely enables the analysis of mitochondrial morphological features individually. However, there is a lack of tools to extract morphological parameters from super-resolution images of mitochondria. We report a quantitative method to extract mitochondrial morphological metrics, including volume, aspect ratio, and local protein density, from 3D single-molecule localization microscopy images, with single-mitochondrion sensitivity. We validated our approach using simulated ground-truth SMLM images of mitochondria. We further tested our morphological analysis on mitochondria that have been altered functionally and morphologically in controlled manners. This work sets the stage to quantitatively analyze mitochondrial morphological alterations associated with disease progression on an individual basis.


Introduction
Fluorescence microscopy is widely used in cell and molecular biology to label and image cellular organelles and proteins of interest selectively.Several fluorescence imaging studies have linked cellular function with spatial information about their organelles [1][2][3].Mitochondria are of particular interest as mitochondrial dysfunction has been linked to numerous pathologies, including mitochondrial diseases [4], cancer [5,6], diabetes [7,8], diabetic complications [9,10], Alzheimer's disease [11,12], and Parkinson's disease [13,14].It has been long postulated that a significant correlation exists between mitochondrial structure and functions [15,16].
Morphological imaging of mitochondria using fluorescence microscopy has led to essential observations about mitochondrial function [17][18][19].Among all mitochondria's morphological alterations, fusion and fission are the most metabolically relevant events [16].In mitochondrial fusion, two discrete mitochondria merge.In mitochondrial fission, the inner and outer mitochondrial membranes of a single, continuous mitochondrion are pinched off, forming two separate mitochondria.Mitochondrial fusion promotes the exchange of complementary genetic products, minimizing stress-related mitochondrial damage.Mitochondrial fission ensures the distribution of mitochondria throughout the cell, is an essential step in cell apoptosis, and promotes mitophagy to degrade damaged or ineffective mitochondria.While mitochondrial morphology is highly heterogeneous in most healthy cell types, in many cell lines, there is a broad correlation between the extent of mitochondrial elongation from fusion and mitochondrial metabolic capacity [20][21][22].Therefore, under specific conditions, a comprehensive characterization of mitochondrial morphology can provide insight into cellular metabolic function and health with statistical significance.
Several groups have developed tools, such as MitoSegNet [23], Mitohacker [24], and mitometer [25], to assess mitochondria imaged by wide-field or confocal microscopy with diffraction-limited spatial resolution rather than super-resolution imaging.As a result, these tools generated anomalous results when applied to pointillist single-molecule localization microscopy (SMLM) images.They also cannot perform analyses only feasible at the super-resolution scale, such as identifying the interface between individual mitochondria or precisely measuring individual mitochondrial shape and volume.
SMLM [26,27] is a fluorescence microscopy technique that achieves super-resolution at a spatial precision of ∼15 nm using samples labeled with stochastically blinking fluorophores.
In each frame of an SMLM dataset, only a sparse subset of fluorophores emits light, and each fluorescence emission yields a point spread function (PSF) on an array detector, usually approximated by a two-dimensional (2D) Gaussian function.The peak of this Gaussian function is treated as the true location of the fluorescence emitter.Maximum likelihood estimation is often used to localize each emitter by identifying the Gaussian peak with high precision [28].The final SMLM image is a histogram consisting of all localizations of fluorophores.Through novel optical designs to manipulate the PSFs, researchers also achieved 3D SMLM [29][30][31].As SMLM images are histograms of discontinuous localizations of discrete fluorescence emissions, SMLM provides unique information about local protein distribution and density [32].This can be particularly interesting when evaluating mitochondrial outer membrane cohesion, closely associated with mitochondrial health [33,34].
Previous studies have used SMLM and other super-resolution microscopy techniques to draw quantitative conclusions about mitochondria.For example, Appelhans et al. [35,36] tracked mitochondrial proteins over time and showed that diffusion characteristics were associated with specific proteins and membrane compartments.They also showed a correlation between diffusion trajectory and morphology.While this is useful for characterizing specific parameters, it does not provide a direct metric of mitochondrial structure or morphology.Furthermore, it requires the user to input time-lapse videos of live mitochondria rather than still images.Dlaskova et al. [37] showed that Ripley's K-function clustering could characterize nucleoids of mitochondrial DNA and cristae widths in 3D images of mitochondria.
As super-resolution imaging is increasingly incorporated into studies extracting functional and pathological information from intracellular structures [38][39][40], methodologies are needed to quantitatively correlate pathological alterations with morphological parameters at the nanoscopic scale.In this study, we show that 3D SMLM can detect changes in individual mitochondrial volume and 3D morphology and alterations in mitochondrial membrane protein density.We simulated 3D SMLM images of mitochondria with various morphologies and protein densities to validate these abilities.We also show that 3D SMLM can detect drug-induced changes in mitochondrial morphology associated with membrane potential drop induced by ATP synthase inhibition and alterations in protein density associated with the early stages of apoptosis [41].

Axial calibration
We performed axial calibration using red fluorescent nanospheres (F8807, Thermo Fisher).We scanned the nanospheres across a 2-µm axial range with an interval of 20 nm.Then, we used maximum likelihood estimation [28] to fit an anisotropic 2D Gaussian function to the image of the nanosphere in each frame.Finally, we plotted a calibration curve of the Gaussian sigma as a function of the nanosphere's axial position relative to the objective lens (Fig. S1B.)

Sample preparation
We grew HeLa cells in cell culture flasks (T-75 Thermo Fisher) to 80% confluency in a DMEM medium.Then, we detached them using trypsin-EDTA and plated a 1:10 dilution in DMEM on an 8-well chamber (Lab-Tek 1.0 borosilicate glass, Thermo Fisher), which we let grow overnight.We fixed the cells with 10% PFA for 10 minutes at room temperature, permeabilized the cell membranes with 0.5% Triton-X-100 for 10 minutes, and blocked the cells with 2.5% goat serum for 30 minutes.Next, we prepared a 1:100 dilution of rabbit anti-TOM20 antibody (HPA011562, Millipore Sigma) [42] in 2.5% goat serum and incubated the cells on a rocker overnight at 4°C.We rinsed the cells three times with a washing buffer (0.2% BSA, 0.1% Triton X-100 in PBS) for 5 minutes at room temperature.We then added a 1:200 dilution of AF-647-conjugated goat anti-rabbit antibody (A-21245, Invitrogen) in blocking buffer to each well and incubated the cells for 45 minutes at room temperature.Finally, we rinsed the cells twice with washing buffer and twice with PBS for 5 minutes at room temperature.

Image acquisition and image processing
We added a buffer made from 50 mM Tris, 10 mM NaCl, 0.5 mg/mL glucose oxidase (Sigma, G2133), 2000 U/mL catalase (Sigma, C30), 10% (w/v) D-glucose, and 100 mM cysteamine to the samples to induce fluorescent blinking.During data acquisition, we replaced the buffer every two hours.Our excitation wavelength was 647 nm with an excitation power of 45 W/mm2.We captured 10,000 frames with 20-ms exposure time.For each field of view (FOV), we acquired two sets of frames: one with the objective focused at -250 nm and one with the objective focused at +250 nm.This ensured that the axial depth of field was sufficiently large to capture all the mitochondria in each cell.
We used the ImageJ plug-in Thunderstorm [43] to localize the astigmatic PSFs based on the maximum likelihood function to fit a 2D ellipsoid Gaussian to each PSF [29].We performed cross-correlation-based drift correction on each image.When the cell size was larger than the FOV, we captured multiple FOVs with overlapping areas and stitched the images.To stitch two images, we first computed the 2D cross-correlation of the images, which were normalized by the total number of overlapping pixels at each coordinate.Next, we found the coordinates of the maximum of this 2D map from which we subtracted the size of the first image.We then translated the second image by the resulting value.
We performed manual mitochondrial segmentation on FIJI/ImageJ using the black pencil tool with a width of 2 pixels.To test operator-operator variability, 3 lab members each performed segmentation on the same two images (Fig. S2 A&B) independently.We then thresholded the images to remove the background and compared the results for each combination of two people.To compare the two segmentation results, we calculated the centroid of each identified mitochondrion and compared it to the mitochondrion with the closest centroid.We calculated the DICE score for each mitochondrion (Fig. S2C), showing good agreement (medians > 0.92, means > 0.83).We used the manually segmented mitochondria as training data to develop a neural network for automatic mitochondrial segmentation.We performed subsequent morphology analyses described in the results section using home-built Matlab codes, available on github (https://github.com/FOIL-NU/Mitochondria).Our codes are dependent on the Matlab Image Processing and Optimization toolboxes.We performed Voronoi tessellation using ClusterSiu, as reported by Adronov et al. [44].We trained and implemented the automated segmentation neural network in a Python environment.This and the dependent MatLab scripts and functions are also available on the github.

Mitochondrial membrane potential (MMP) measurement
We plated 15,000 HeLa cells per well in a 96-well plate (3894, Costar) and incubated them overnight at 37°C.Then, we washed the wells with PBS, added 10 µM JC-1 (tetraethylbenzimidazolylcarbocyanine iodide), an MMP reporter dye that targets mitochondria [45] (Abcam, mitochondrial membrane potential assay kit), to the control and treated groups, and incubated them for 10 minutes at 37°C.Next, we washed the wells three times with PBS and added 100 µM FCCP (carbonyl cyanide 4-(trifluoromethoxy) phenylhydrazone) to the depolarization control, 10-µM staurosporine (STS) to the STS treated group, and 2.5-µM oligomycin and 1-µM antimycin (OA) [23,46] to the OA treated group in dilution buffer (ab113850, Abcam) with 10% fetal bovine serum and incubated at 37°C.After the designated treatment times (3 hours OA to induce mitochondrial depolarization and fragmentation [23], 2 hours STS to induce a pre-apoptotic state [47], and 4 hours FCCP for the depolarization control as suggested by the Abcam kit protocol), we transferred the plate to a plate reader (Cytation 5, BioTek) at 37°C.We set the plate reader to document fluorescence with an excitation wavelength of 475 ± 10 nm and emission wavelengths of 590 ± 10 nm and 530 ± 10 nm.Finally, we took the ratio between fluorescence intensities in the 590-nm channel to fluorescence intensities in the 530-nm channel, referred to as the relative fluorescent units (RFU), as a measure of MMP.

Three-dimensional confocal imaging
We performed 3D confocal microscopy using a Leica SP5 microscope.We excited the samples at 633 nm and captured fluorescence emissions from 650 nm to 710 nm.We used a pixel size of 116 µm and performed 3-line averaging and then 2-frame averaging.We acquired a depth range of 4 µm with an interval of 125 nm.

Statistical analysis
We performed statistical analysis using GraphPad Prism 9. We used the unpaired t-test to determine the significance of differences between cell treatment groups.

Results
Figure 1 illustrates mitochondrial fragmentation and biochemical validation of JC-1 for measurement of MMP, and validation of our imaging techniques in the untreated conditions.Figures 1(A) & 1(B) illustrate how mitochondrial fission results in a more fragmented mitochondrial morphology.Figure 1(C) shows that MMPs in untreated HeLa cells are higher than in cells treated with FCCP, the depolarization control [45] 1H shows an X-Z cross-section of a mitochondrion captured using confocal microscopy, indicating that the hollow structure of the mitochondrial outer-membrane cannot be clearly resolved axially by confocal imaging.In the SMLM XZ cross-section (Fig. 1I), we observed that mitochondria interior regions had lower intensity than the boundaries due to their natural hollow structures, which are not evident in the confocal microscopy images (Fig. 1H).SMLM's high spatial resolution is particularly important in quantifying geometrical parameters in densely packed mitochondrial networks in cells.Fig. 1J is a confocal microscopy image of several densely packed mitochondria, where it is challenging to segment individual mitochondria due to poorly resolved mitochondrial boundaries.In contrast, SMLM resolved the boundaries between individual mitochondria (Fig. 1K,) enabling geometrical analysis of individual mitochondria.To further demonstrate the improved axial resolution in 3D SMLM, we show the depth profiles of what we presume to be two mitochondria stacked on top of each other (based on the axial depth of the high signal) in confocal microscopy (Fig. 1L) and SMLM (Fig. 1M) from the locations respectively highlighted in Fig. 1J and Fig. 1K.The depth profile from the confocal microscopy image suggests that it is nearly impossible to segment densely packed mitochondria due to diffraction-limited axial resolution.In contrast, the depth profile from the SMLM image shows three distinct peaks spaced ~750 nm and 600 nm apart, corresponding to the mitochondrial membranes and matching published reports [48].In Fig. sharper boundaries.Accurate 3D imaging of mitochondria is essential to quantify mitochondrial volume.Fig. S3(A) shows the 3D renderings of the healthy mitochondria from the same volume as Fig. 1(F).Figure 1 (H) shows an X-Z cross-section of a mitochondrion captured using confocal microscopy, indicating that the hollow structure of the mitochondrial outer-membrane cannot be clearly resolved axially by confocal imaging.In the SMLM XZ cross-section (Fig. 1(I)), we observed that mitochondria interior regions had lower intensity than the boundaries due to their natural hollow structures, which are not evident in the confocal microscopy images (Fig. 1 (H)).
SMLM's high spatial resolution is particularly important in quantifying geometrical parameters in densely packed mitochondrial networks in cells.Figure 1(J) is a confocal microscopy image of several densely packed mitochondria, where it is challenging to segment individual mitochondria due to poorly resolved mitochondrial boundaries.In contrast, SMLM resolved the boundaries between individual mitochondria (Fig. 1 (K),) enabling geometrical analysis of individual mitochondria.To further demonstrate the improved axial resolution in 3D SMLM, we show the depth profiles of what we presume to be two mitochondria stacked on top of each other (based on the axial depth of the high signal) in confocal microscopy (Fig. 1 (L)) and SMLM (Fig. 1 (M)) from the locations respectively highlighted in Fig. 1(J) and Fig. 1 (K).The depth profile from the confocal microscopy image suggests that it is nearly impossible to segment densely packed mitochondria due to diffraction-limited axial resolution.In contrast, the depth profile from the SMLM image shows three distinct peaks spaced ∼750 nm and 600 nm apart, corresponding to the mitochondrial membranes and matching published reports [48].In Fig. S4, we compared more depth profiles of randomly selected individual mitochondria imaged by confocal microscopy and SMLM.Previous 3D electron microscopy studies of adherent HeLa cells showed that mitochondrial axial thickness typically ranges from 600 nm to 900 nm [48], which agrees with our SMLM measurements (Fig. S4A.)The confocal microscopy measurement of mitochondrial axial thickness was over 1300 nm (Fig. S4B).
We quantified the mitochondrial morphology and outer membrane protein distribution to characterize alterations in 3D SMLM images of HeLa cell mitochondria.We loaded the mitochondrial localization data into 3D 8-bit image files with a 25 nm pixel size.We applied a corrective factor to the z-localizations for the refractive index mismatch, as described by Huang et al. [29].We also corrected for a magnification difference in the x-direction induced by the cylindrical lens.We then isolated the mitochondrial signal from the background signal by applying an intensity threshold to each frame.The threshold was determined by where MV pos is the mean value of the positive pixels in the image and 0.1875 is an empirically determined factor.We formed 3D objects out of the thresholded image, filled the objects, filtered out objects in each frame of less than 0.15 µm 2 in area, then counted the total number of positive pixels to compute the total mitochondrial volume.Figures 2(A)&2(B) are the results after the background removal via thresholding and the manual segmentation of overlapping mitochondria, respectively.In this case, segmentation was performed on the 2D projection because the cells were adherent, and the mitochondrial network was primarily projected in the lateral direction.As a result, nearly every case of mitochondrial overlap was visible in the 2D projection.However, all subsequent image analysis was done using the 3D image stacks.Each mitochondrion is outlined in red in Fig. 2(B), based on which we calculated each mitochondrion volume.
S4, we compared more depth profiles of randomly selected individual mitochondria imaged by confocal microscopy and SMLM.Previous 3D electron microscopy studies of adherent HeLa cells showed that mitochondrial axial thickness typically ranges from 600 nm to 900 nm [48], which agrees with our SMLM measurements (Fig. S4A.)The confocal microscopy measurement of mitochondrial axial thickness was over 1300 nm (Fig. S4B).
We quantified the mitochondrial morphology and outer membrane protein distribution to characterize alterations in 3D SMLM images of HeLa cell mitochondria.We loaded the mitochondrial localization data into 3D 8-bit image files with a 25 nm pixel size.We applied a corrective factor to the z-localizations for the refractive index mismatch, as described by Huang et al. [29].We also corrected for a magnification difference in the x-direction induced by the cylindrical lens.We then isolated the mitochondrial signal from the background signal by applying an intensity threshold to each frame.The threshold was determined by  = 0.1875 *   , (1) where   is the mean value of the positive pixels in the image and 0.1875 is an empirically determined factor.We formed 3D objects out of the thresholded image, filled the objects, filtered out objects in each frame of less than 0.15 μm 2 in area, then counted the total number of positive pixels to compute the total mitochondrial volume.Figs.2A&2B are the results after the background removal via thresholding and the manual segmentation of overlapping mitochondria, respectively.In this case, segmentation was performed on the 2D projection because the cells were adherent, and the mitochondrial network was primarily projected in the lateral direction.As a result, nearly every case of mitochondrial overlap was visible in the 2D projection.However, all subsequent image analysis was done using the 3D image stacks.Each mitochondrion is outlined in red in Fig. 2B, based on which we calculated each mitochondrion volume.
To increase the analysis throughput, we developed a machine-learning-based automatic segmentation of mitochondria, using our manually segmented mitochondria as the training data.We cascaded the instance segmentation architecture YOLOv8 developed by Ultralytics [49]  To increase the analysis throughput, we developed a machine-learning-based automatic segmentation of mitochondria, using our manually segmented mitochondria as the training data.We cascaded the instance segmentation architecture YOLOv8 developed by Ultralytics [49] with the segment anything model (SAM) developed by Meta AI [50].In our workflow, our trained YOLOv8 network generates bounding boxes around each identified mitochondrion to be used as the inputs to the SAM.SAM then generates a mask for each identified mitochondrion and outputs a stack of mitochondria instance masks.We processed the stack to remove overlapping masks by subtracting each smaller mask from the overlapping larger mask and generated two image files containing the mitochondria mask and the original 3D SMLM image with added borders around each mitochondrion.Figs.S5A&S5B show the automatic mask generation results on a mitochondrial network with elongated morphology, while Figs.S5C&S5D show the results on a mitochondrial network with fragmented morphology.Figs.S5E-S5F show automated segmentation results super-imposed on a magnified region of the images.The results show reasonably high agreement between automatic and manual segmentation results (Fig. S5 G), with a mean DICE score of over 0.76 and a median of >0.85 (Fig. S5 H).For further improved segmentation accuracy, the users are recommended to manually correct any overlapping mitochondria that were not picked up by the automatic segmentation.
Figures 2(C)&2(D) depict the skeletonization process of mitochondria, wherein each 3D mitochondrion is collapsed to a single, one-dimensional line that traces the contour of its main axis.The resulting skeletons are shown in orange in Fig. 2(C) and follow the mitochondrial contours in all three dimensions, as shown in Fig. 2(D).We used graph theory [51] to eliminate the branches of each mitochondrial skeleton (Fig. S6A).We designated each skeletal branchpoint and endpoint as a node connected to the other nodes by links (Fig. S6B), then identified the single longest 3D path connecting two nodes (Figs.S6C-S6F).We then treated this path as the central axis of the mitochondria and its length as the mitochondrial length.
We measured the mean radius of the intersection between the plane perpendicular to the central mitochondrial axis at each point along the axis (Fig. S7A) and the mitochondrial outer membrane (Fig. S7B).We took the mean value of these measured radii as half the mitochondrial width (Fig. S7C), then took the ratio of mitochondrial length to mitochondrial width to calculate the mitochondrial aspect ratio.We compared the quality of measuring the mitochondrial length and aspect ratio on 3D images and 2D projection images.We found that measurements from 2D projection images introduced significant variability in mitochondrial length (Figs.S8A-S8B), with a 25% lower average length and a standard deviation between 26% and 28% (Figs.S8C-S8D) compared with measurements from 3D images.
We tested reported mitochondrial morphology analysis tools using our 3D SMLM images (Fig. S9A).These reported tools were designed for wide-field and confocal microscopy images and performed well in these contexts.MiNa [52], an ImageJ plugin that uses skeletonization, showed excessive branches when applied to SMLM images (Fig. S9B) compared to our skeletonization code (Fig. S9C).This is attributable to the rough outer surface and uneven intensity distribution of SMLM images, requiring branch pruning via graph theory.Mitometer [25], a thresholding-based method, also resulted in anomalous images (Fig. S9D) compared to our method (Fig. S9E).Such abnormality is likely due to the uneven intensity profile in SMLM, which causes holes and disconnections in thresholded objects.Therefore, an image analysis tool designed explicitly for SMLM is still needed.
To analyze the protein localization density, we used 3D Voronoi tessellation [44], allowing us to measure the density of TOM20 localizations.Voronoi tessellation takes advantage of the pointillist nature of SMLM, wherein the dataset is a point cloud, or 3D histogram, with each pixel representing a labeled protein.This allows us to quantify the distribution of individual proteins with nanoscale resolution directly and identify protein distribution changes over small distances.Figure 2(E) shows a tessellated whole HeLa cell color-coded by localization density, in which smaller polygon volumes are purple and larger volumes are orange.Figure 2(F) shows a tessellated whole HeLa cell with lower TOM20 density, in this case likely induced by a pre-apoptotic state, which results in the disassociation of lipid membranes such as the mitochondrial outer membrane.
To avoid the influence of factors such as antibody binding efficiency and blinking dynamics, we took the ratio of mitochondrial signal density to cytoplasmic signal density, which is associated with unbound TOM20 proteins [53] and nonspecific staining.Since both metrics increase with higher labeling density or binding efficiency, the ratio between them would remain constant.A lower ratio indicates dissociation of the mitochondrial membrane.We plotted a histogram of the log density, which contained two peaks, one associated with the mitochondria-bound TOM20 and one associated with unbound TOM20.We used least squares fit to obtain two Gaussian distributions to each histogram, then subtracted the value of the low-density peak from the value of the high-density peak to get the ratio.Figure 2 (G) shows the histogram of the log density of the image in Fig. 2(E) and the same histogram approximated by two fitted Gaussian functions.The blue line represents the estimated background density, the orange line represents the estimated true signal density, the black line is the sum of the blue and orange lines, and the red line is the original histogram contour.These two fitted Gaussian functions are relatively distinct from each other, indicating a notable difference in densities between bound and unbound TOM20.In contrast, the two Gaussian functions in Fig. 2 (H), which shows the histogram of the log density in Fig. 2(F), are more overlapped, indicating a reduced difference between the bound and unbound TOM20.
To validate our extraction of morphological parameters and protein density from mitochondria images, we tested our analyses on simulated ground-truth mitochondrial images.The simulation aimed to act as an additional verification method for our process.By creating simulated images of mitochondria, we can analyze a dataset in which the true values of parameters are known.We simulated ground-truth 3D mitochondria structures using a worm-like chain model [54] with a lateral persistence length of 0.6 µm and axial persistence length of 4.8 µm (Fig. S10).These parameters were extracted from our experimental mitochondrial images.
To generate elongated (Fig. 3(A)), moderately elongated (Fig. 3(B)), and fragmented (Fig. 3(C)) mitochondria, we set the mitochondrial lengths to 4 µm, 1.5 µm, and 0.65 µm, respectively.To transform the worm-like chains from curved lines into objects with specified volumes, we convolved each defined point along the chain with an ellipsoid of radius where i is the position along the mitochondria; Rad i is the mitochondrial radius at position i on the mitochondria; and rndn is a random number generated from a Gaussian distribution with a mean of 0 and a standard deviation of 1.
The initial radius of each ellipsoid was 0.325 µm in the lateral and axial directions.The lateral and axial radii at each point were determined independently.These parameters and relationships were generated empirically and iteratively by measuring parameters from our experimental SMLM images of mitochondria.
We generated 20-50 mitochondria per simulated image, depending on the extent of elongation.As shown in Fig. 3(D), a 32-nm thick slice of an experimental 3D SMLM image, when the outer membrane of two mitochondria meet each other, they form an interface and do not overlap.To reflect this, if the chain of one mitochondrion overlapped with a previously established mitochondrion, we ceased its generation.This is shown in Fig. 3(E), which shows that the simulated mitochondria do not overlap.The interfaces are important in recognizing boundaries during segmentation.
After generating the ground-truth mitochondria, we simulated fluorescence emission and the imaging process using parameters from literature and experimental observation.We split the ground-truth volumes into 16 × 16 × 16 nm pixels.If a pixel contained the outer mitochondrial To validate our localization density analysis, we simulated datasets with compact membrane proteins and datasets with dissociated membrane proteins and measured their TOM20 densities using the method shown in Fig. 2. We found that simulated dissociated membranes had significantly lower signal density than the simulated compact membrane, as shown in Fig. 3k.membrane in a designated TOM20 cluster region, we gave it a 13% chance of containing at least one labeled TOM20 protein.If the pixel was located within the mitochondria, we gave it a 0.66% chance of containing at least one labeled protein.If the pixel was in the cytoplasm, we gave it a 0.125% chance of containing at least one labeled protein.These percentages were extrapolated from labeling densities reported by Wurm et al. [40] and from the observed ratios of label density in the cytoplasm and within the mitochondria in our SMLM images.This rule resulted in each simulated image containing roughly 150,000 labeled TOM20 proteins.Using a uniform distribution, we randomly translated these fluorophores within 17.5 nm of the ground truth location to reflect the size of the primary and secondary antibody probes [40,55].Based on observed localization numbers in our images with similar size and mitochondrial density, we randomly generated 380,000 localizations from these 150,000 labeled proteins using an exponential distribution for the number of blinks per localization [56].We then applied lateral and axial uncertainties to each localization based on the observed parameters from maximum likelihood estimation (MLE) fitting in our experimental data.As a result, we could simulate 3D SMLM images (Fig. 3(F)) from our ground truth data.
To validate our localization density analysis, we simulated datasets with compact membrane proteins and datasets with dissociated membrane proteins and measured their TOM20 densities using the method shown in Fig. 2. We found that simulated dissociated membranes had significantly lower signal density than the simulated compact membrane, as shown in Fig. 3 (k).
Figure 4 shows the testing of our geometrical analysis of mitochondrial fragmentation in HeLa cells treated with OA.OA treatment inhibits ATP synthase activity and leads to mitochondrial fragmentation and loss of MMP [46].Fig. S13A shows our validation of MMP loss in OA-treated HeLa cells compared to untreated cells using JC-1 labeling.Figure 4(A) shows the 2D projection SMLM image of an OA-treated HeLa cell with a magnified view of the highlighted area, showing a fragmented morphology.Confocal microscopy also shows a fragmented morphology (Figs.4(B)).Fig. S3B shows a 3D visualization of one SMLM-imaged OA-treated cell.While confocal microscopy roughly showed the morphological features of the mitochondria, the individual mitochondrial hollow outer-membrane structures were unresolvable due to diffractionlimited axial resolution.We compared the cross sections of SMLM and confocal microscopy imaged OA-treated mitochondria in Figs.4(C)&4(D), which are extracted from the locations highlighted in Figs.4(A)&4(B), respectively.These cross-sectional views further validated that confocal microscopy cannot resolve 3D mitochondrial morphology.We quantified mitochondrial morphology in 14 OA-treated and 18 untreated cells.For each cell, we computed the average Figure 4 shows the testing of our geometrical analysis of mitochondrial fragmentation in HeLa cells treated with OA.OA treatment inhibits ATP synthase activity and leads to mitochondrial fragmentation and loss of MMP [46].Fig. S13A shows our validation of MMP loss in OA-treated HeLa cells compared to untreated cells using JC-1 labeling.Fig. 4A shows the 2D projection SMLM image of an OA-treated HeLa cell with a magnified view of the highlighted area, showing a fragmented morphology.Confocal microscopy also shows a fragmented morphology (Figs.4B).Fig. S3B shows a 3D visualization of one SMLM-imaged OA-treated cell.While confocal microscopy roughly showed the morphological features of the mitochondria, the individual mitochondrial hollow outer-membrane structures were unresolvable due to diffraction-limited axial resolution.We compared the cross sections of SMLM and confocal microscopy imaged OA-treated mitochondria in Figs.4C&4D, which are extracted from the locations highlighted in Figs.4A&4B, respectively.These cross-sectional views further validated that confocal microscopy cannot resolve 3D mitochondrial morphology.We quantified mitochondrial morphology in 14 OA-treated and 18 untreated cells.For each cell, we computed the average mitochondrion volume and aspect ratio.The mitochondrial aspect ratio (Fig. 4E) and the total mitochondrial volume (Fig. 4F) quantified from 3D SMLM became significantly lower in OA-treated cells.We compared the performance of our super-resolution mitochondrial analysis pipeline with confocal microscopy using the previously published Matlab package Mitometer [25].We selected Mitometer because it also measures the aspect ratio of individual mitochondria and can be used on 3D datasets (Figs.S11A-S11F).We used the same sample sizes (n=14 and n=18 for OA and untreated cells, respectively) in this test.Mitometer detected the same trend in the aspect ratio as our pipeline, with untreated cells showing significantly elongated mitochondria compared with oligomycin-treated cells (Fig. S11G).However, the statistical significance was less (P=0.0024 for confocal vs P<0.0001 for super-resolution), suggesting a higher sensitivity for the super-resolution analysis pipeline.In addition, the Mitometer failed to show a statistically significant difference between untreated and OA-treated cells in mitochondrial volumes from confocal microscopy images, suggesting a larger sample size is necessary.Figure 5 shows the testing of our quantification of mitochondrial outer membrane decompaction in normal and pre-apoptotic HeLa cells (induced by 2 hours of incubation with STS).Fig. 5A shows a whole STS-treated cell imaged by SMLM with a magnified view of the area highlighted.Both images showed a more blurred mitochondrial outer membrane compared to untreated cells (Fig. 1K), indicating possible dissociation of the TOM20 proteins from the mitochondrial membrane.FRC analysis showed a comparable resolution between SMLM imaging of treated and untreated cells, which confirms that the boundary-blurring is not caused by a reduction in spatial resolution.In contrast, confocal microscopy images (Fig. 5C) of STStreated HeLa cell mitochondria did not exhibit significant changes in the compactness of the outer membrane.The 2D projections appeared similar to the confocal images of untreated cells (Figs. 1D&1E).This is likely due to the low resolution of the confocal images, which made them insensitive to changes in local protein density.Also, while the super-resolution crosssections of the STS-treated mitochondria still resolved the hollow structure (Fig. 5C), the confocal cross-sections did not (Fig. 5D).Applying Voronoi tessellation, we found that the proteins were significantly denser in the untreated cells than in the STS-treated cells (Fig. 5E), suggesting membrane dissociation in the early stages of apoptosis.Our SMLM observation agrees with literature reports [33,41].Cells treated with STS also experienced higher MMP mitochondrion volume and aspect ratio.The mitochondrial aspect ratio (Fig. 4(E)) and the total mitochondrial volume (Fig. 4(F)) quantified from 3D SMLM became significantly lower in OA-treated cells.
We compared the performance of our super-resolution mitochondrial analysis pipeline with confocal microscopy using the previously published Matlab package Mitometer [25].We selected Mitometer because it also measures the aspect ratio of individual mitochondria and can be used on 3D datasets (Figs.S11A-S11F).We used the same sample sizes (n = 14 and n = 18 for OA and untreated cells, respectively) in this test.Mitometer detected the same trend in the aspect ratio as our pipeline, with untreated cells showing significantly elongated mitochondria compared with oligomycin-treated cells (Fig. S11 G).However, the statistical significance was less (P = 0.0024 for confocal vs P < 0.0001 for super-resolution), suggesting a higher sensitivity for the super-resolution analysis pipeline.In addition, the Mitometer failed to show a statistically significant difference between untreated and OA-treated cells in mitochondrial volumes from confocal microscopy images, suggesting a larger sample size is necessary.
Figure 5 shows the testing of our quantification of mitochondrial outer membrane decompaction in normal and pre-apoptotic HeLa cells (induced by 2 hours of incubation with STS). Figure 5(A) shows a whole STS-treated cell imaged by SMLM with a magnified view of the area highlighted.Both images showed a more blurred mitochondrial outer membrane compared to untreated cells (Fig. 1 (K)), indicating possible dissociation of the TOM20 proteins from the mitochondrial membrane.FRC analysis showed a comparable resolution between SMLM imaging of treated and untreated cells, which confirms that the boundary-blurring is not caused by a reduction in spatial resolution.In contrast, confocal microscopy images (Fig. 5(C)) of STS-treated HeLa cell mitochondria did not exhibit significant changes in the compactness of the outer membrane.The 2D projections appeared similar to the confocal images of untreated cells (Figs. 1(D)&1(E)).This is likely due to the low resolution of the confocal images, which made them insensitive to changes in local protein density.Also, while the super-resolution cross-sections of the STS-treated mitochondria still resolved the hollow structure (Fig. 5(C)), the confocal cross-sections did not (Fig. 5(D)).Applying Voronoi tessellation, we found that the proteins were significantly denser in the untreated cells than in the STS-treated cells (Fig. 5(E)), suggesting membrane dissociation in the early stages of apoptosis.Our SMLM observation agrees with literature reports [33,41].Cells treated with STS also experienced higher MMP than untreated cells, as indicated by JC-1 fluorescence in the 590 nm range (Fig. S13B), agreeing with prior studies [57].

Discussion and conclusions
In this work, we developed methodologies to analyze the geometrical parameters of individual mitochondria, including volume and aspect ratio, for 3D SMLM.To this end, we trained a neural network to automatically segment the mitochondria, requiring minimal user adjustment.We also developed a stochastic simulation-based method to generate ground truth SMLM images of healthy and pathological mitochondria for the first time.Using simulated images, we validated the ability to detect alterations in individual mitochondrial morphology and outer mitochondrial membrane protein distribution.We further tested our method and correlated detected changes with chemically induced perturbations in mitochondrial function.We found that mitochondria aspect ratio and volume decreased with OA treatment and that STS-treated cells had a lower mitochondrial outer membrane density than the untreated cells.
We validated that our method can identify conditions such as mitochondrial elongation, pointing to greater metabolic demands and mitochondrial damage from sources such as oxidative stress.We also validated that our method can identify mitochondrial fragmentation, potentially correlated with a decreased metabolic demand or ability, or cells in a quiescent or apoptotic state [16,20].Finally, we confirmed that our method can evaluate the density of mitochondrial outer membrane protein density, another metric of impending apoptosis and outer-membrane damage [41].In the future, we can apply our method to evaluate the role and extent of mitochondrial dysfunctions in various metabolic diseases, such as diabetic retinopathy associated with retinal hypoxia and retinal angiogenesis [58].
Our method is unique among existing mitochondrial morphology analysis tools because it exploits the fine features only resolvable by SMLM.Namely, it can quantify mitochondria individually and the distribution of proteins on the mitochondrial membrane.Disclosures.The authors declare no conflict of interest.
Figure1illustrates mitochondrial fragmentation and biochemical validation of JC-1 for measurement of MMP, and validation of our imaging techniques in the untreated conditions.Figures1(A) & 1(B) illustrate how mitochondrial fission results in a more fragmented mitochondrial morphology.Figure1(C) shows that MMPs in untreated HeLa cells are higher than in cells treated with FCCP, the depolarization control[45], Fig.1(D) is the 2D projection confocal image of an untreated HeLa cell (the colormap indicates axial position), and Fig. 1(E) is the magnified view of the highlighted region in Fig. 1(D), showing the blurred boundaries of individual mitochondria.Figures 1(F) & 1 (G) show the 2D projection of the 3D SMLM images of an untreated HeLa cell (Fig. 1 (G) is the magnified view of the highlighted region in Fig. 1(F)) with labeled TOM20, where the long and healthy mitochondria are better visualized than Figs.1(D) & 1(E) with

Fig. 1 .
Fig. 1.Illustration of (A) an elongated mitochondrion and (B) fragmented mitochondria.The intermembrane space is colored turquoise, and the cristae are colored green; (C) Normalized RFU of JC-1-labeling of untreated and FCCP-treated HeLa cells; (D) Projection view of TOM20-labeled mitochondria imaged by confocal microscopy with a color bar to indicate z-position.Scale bar: 5 μm; (E) Magnified view of the area highlighted in panel D. Scale bar: 2.5 μm; (F) Projection view of TOM20-labeled mitochondria imaged by SMLM.Scale bar: 5 μm; (G) Magnified view of the area highlighted in panel F. Scale bar: 2.5 μm; (H) Mitochondrial cross-section from the position highlighted in panel E. Scale bar: 250 nm; (I) Mitochondrial cross-section from the position highlighted in panel G. Scale bar: 250 nm; (J) Projection view of densely packed mitochondria imaged by confocal microscopy.Scale bars: 2 μm; (K) Projection view of densely packed mitochondria imaged by SMLM.Scale bars: 2 μm; (L) Depth profile from the position highlighted in panel J. (M) Depth profile from the position highlighted in panel K.

Fig. 1 .
Fig. 1.Illustration of (A) an elongated mitochondrion and (B) fragmented mitochondria.The intermembrane space is colored turquoise, and the cristae are colored green; (C) Normalized RFU of JC-1-labeling of untreated and FCCP-treated HeLa cells; (D) Projection view of TOM20-labeled mitochondria imaged by confocal microscopy with a color bar to indicate z-position.Scale bar: 5 µm; (E) Magnified view of the area highlighted in panel D. Scale bar: 2.5 µm; (F) Projection view of TOM20-labeled mitochondria imaged by SMLM.Scale bar: 5 µm; (G) Magnified view of the area highlighted in panel F. Scale bar: 2.5 µm; (H) Mitochondrial cross-section from the position highlighted in panel E. Scale bar: 250 nm; (I) Mitochondrial cross-section from the position highlighted in panel G. Scale bar: 250 nm; (J) Projection view of densely packed mitochondria imaged by confocal microscopy.Scale bars: 2 µm; (K) Projection view of densely packed mitochondria imaged by SMLM.Scale bars: 2 µm; (L) Depth profile from the position highlighted in panel J. (M) Depth profile from the position highlighted in panel K.

Fig. 2 .
Fig. 2. (A) Projection view of TOM20-labeled mitochondria imaged by 3D SMLM.Scale bar: 3 μm; (B) Segmentation results with highlighted boundaries; (C) Skeletonization results overlayed onto the binarized individual mitochondria pesudo-colored in green; (D) Volumetric visualization of panel C; (E) Tessellation map of an untreated HeLa cell.Scale bar: 10 μm; (F) Tessellation map of a low-density (STS-treated) mitochondrial membrane structure.Scale bar: 10 μm; (G) Histogram and two fitted Gaussian functions of localization density from the cell shown in panel E; (H) Histogram and two fitted Gaussian functions of localization density from the cell shown in panel F.

Fig. 2 .
Fig. 2. (A) Projection view of TOM20-labeled mitochondria imaged by 3D SMLM.Scale bar: 3 µm; (B) Segmentation results with highlighted boundaries; (C) Skeletonization results overlayed onto the binarized individual mitochondria pesudo-colored in green; (D) Volumetric visualization of panel C; (E) Tessellation map of an untreated HeLa cell.Scale bar: 10 µm; (F) Tessellation map of a low-density (STS-treated) mitochondrial membrane structure.Scale bar: 10 µm; (G) Histogram and two fitted Gaussian functions of localization density from the cell shown in panel E; (H) Histogram and two fitted Gaussian functions of localization density from the cell shown in panel F.

Fig. 3 .
Fig. 3. Simulated 3D SMLM images of (A) elongated (4.0 μm length), (B) moderately elongated (1.5 μm length), and (C) fragmented (0.65 μm length) mitochondria.Scale bar: 3 μm; (D) A 32-nm thick section of an experimental SMLM image of mitochondria in a healthy HeLa cell; (E) A 32-nm thick slice of a simulated ground truth mitochondrial shape.A 32-nm thick section of a simulated 3D SMLM mitochondrial image based on the generated shapes shown in panel E with (F) normal, (G) compact, and (H) disassociated outer membrane proteins.Scale bars: 500 nm; (I) Measured aspect ratio values from simulated mitochondria with varying lengths (N=20); (J) Measured mitochondrial volume values from simulated mitochondria with varying lengths (N=20); (K) Measured log-density values from simulated mitochondria with varying membrane dissociation levels (N=20).

Fig. 3 .
Fig. 3. Simulated 3D SMLM images of (A) elongated (4.0 µm length), (B) moderately elongated (1.5 µm length), and (C) fragmented (0.65 µm length) mitochondria.Scale bar: 3 µm; (D) A 32-nm thick section of an experimental SMLM image of mitochondria in a healthy HeLa cell; (E) A 32-nm thick slice of a simulated ground truth mitochondrial shape.A 32-nm thick section of a simulated 3D SMLM mitochondrial image based on the generated shapes shown in panel E with (F) normal, (G) compact, and (H) disassociated outer membrane proteins.Scale bars: 500 nm; (I) Measured aspect ratio values from simulated mitochondria with varying lengths (N = 20); (J) Measured mitochondrial volume values from simulated mitochondria with varying lengths (N = 20); (K) Measured log-density values from simulated mitochondria with varying membrane dissociation levels (N = 20).

Fig. 5 .
Fig. 5. (A) Projection view of TOM20-labeled mitochondria in an STS-treated HeLa cell imaged by SMLM (scale bar: 5 μm) with a magnified area highlighted (scale bar: 2.5 μm); (B) Projection view of TOM20labeled mitochondria in an STS-treated HeLa cell imaged by confocal microscopy (Scale bar: 5 μm) with a magnified area highlighted (scale bar: 2.5 μm); (C) Mitochondrial cross-section from the position highlighted in panel B. Scale bar: 300 nm; (D) Mitochondrial cross-section from the position highlighted in panel B. Scale bar: 300 nm; (E) Comparison of membrane protein disassociation between untreated (N=15) and STS-treated groups (N=10).

Fig. 5 .
Fig. 5. (A) Projection view of TOM20-labeled mitochondria in an STS-treated HeLa cell imaged by SMLM (scale bar: 5 µm) with a magnified area highlighted (scale bar: 2.5 µm); (B) Projection view of TOM20-labeled mitochondria in an STS-treated HeLa cell imaged by confocal microscopy (Scale bar: 5 µm) with a magnified area highlighted (scale bar: 2.5 µm); (C) Mitochondrial cross-section from the position highlighted in panel B. Scale bar: 300 nm; (D) Mitochondrial cross-section from the position highlighted in panel B. Scale bar: 300 nm; (E) Comparison of membrane protein disassociation between untreated (N = 15) and STS-treated groups (N = 10).