Semi-automated 3D fluorescence speckle analyzer (3D-Speckler) for microscope calibration and nanoscale measurement

Fluorescence microscopy has become an essential tool in biological research due to its capacity to identify multiple biological components with high specificity using a diverse array of fluorophores (Hickey et al., 2021; Lichtman and Conchello, 2005). This advantage has led to attempts to resolve the subcellular locations, structures, and functions of specific biomolecules and biomolecular complexes, which range in length scales from nanometers to microns. Since light diffraction limits the resolution of light microscopes to hundreds of nanometers, much work has been done to develop techniques that can surpass this obstacle to effectively achieve “super-resolution” imaging. Among these developed techniques include confocal, STED, SIM, STORM, and TIRF, many of which require image reconstruction, image registration, and position estimation to overcome diffraction limits (Davidovits and Egger, 1971; Fish, 2009; Hell and Wichmann, 1994; Neil et al., 1997; Rust et al., 2006). These requirements, coupled with the increasing desire for quantitatively accurate measurements, have given rise to the need to determine the sizes, intensities, and locations of fluorescent particles precisely and efficiently to accurately gain insight into biological structures.

It is critical to characterize and routinely calibrate imaging systems for the maintenance of integrity and reproducibility. Unfortunately, the importance of this is often less appreciated due to the lack of optimal workflow. Imaging system characterization and calibrations include determinations of resolution limit, optical alignment, illumination flatness, and aberrations using multispectral fluorescence beads of known sizes (Montero Llopis et al., 2021). Resolution determination involves determining the lateral (XY) and axial (Z) sizes of beads, which is typically performed via a Full-Width-Half-Maximum (FWHM) calculation from a least-squares fitted Gaussian over an axis-oriented 2D intensity profile at the best focal plane of an object (Betzig et al., 2006; Pertsinidis et al., 2010). The point spread function (PSF) limits the resolution of ideal fluorescence microscopes to ∼250 nm laterally and ∼600 nm axially (Liu et al., 2018). Beads smaller than PSF size (i.e., ≤100 nm) are used for determining resolution limits (Cole et al., 2011), whereas beads larger than the PSF size (i.e., ≥300 nm) are used to determine whether imaging systems can measure expected sizes (Ding et al., 2020; Schweitzer et al., 2004). Unfortunately, FWHM measurements are often performed manually, limiting widespread microscope calibration and exploration of fluorescent object sizes.

Quantitative fluorescence microscopy is widely used to determine cellular protein localization, amount, and stoichiometry through ratiometric comparison (Suzuki et al., 2015; Verdaasdonk et al., 2014; Waters, 2009). For proper insight into the underlying biology, accurate intensity measurements must be made, which depend on minimizing various sources of optical errors, such as non-uniform illumination and background (BG) signal. Accurate intensity measurements require proper BG correction, which is commonly performed by subtracting the image by the average intensity in a user defined region of interest (ROI) within the image void of true signal. This method uses a single value, which does not correct for the variance from BG noise (Waters, 2009). A more accurate form of BG correction involves correcting by the local BG; however, this often involves manual intervention (Hoffman et al., 2001; Lawrimore et al., 2011; Suzuki et al., 2015; Verdaasdonk et al., 2014).

Fluorescence microscopes possess multiple aberrations, however in multi-wavelength fluorescent particle localization, a major source of aberration is chromatic aberration (CA; Manders, 2003). Although CAs can vary between imaging systems, they often exhibit errors in the range of ±100 s of nanometers, making CA correction critical for co-localization study (Egner and Hell, 2006). Proper CA correction requires localization determinations and matching of numerous multiply labeled targets, which can be time-consuming and inefficient. Fluorophore localization is typically determined using Gaussian-based models or analytical functions that attempt to capture the PSF shape (Babcock and Zhuang, 2017; Mortensen et al., 2010; Samuylov et al., 2019). Gaussian-based models are comparatively computationally inexpensive (Babcock and Zhuang, 2017; Stallinga and Rieger, 2010), and thus are commonly used for biological application in 2D (Churchman et al., 2005; Roscioli et al., 2020) and 3D (Roscioli et al., 2020; Wan et al., 2009), often without accounting for axis rotations.

Many measurement tools have been developed for fluorescent puncta quantification, resulting in a substantial range of options for researchers. Suboptimal user experience, compatibility issues, and lack of comprehensive quantification options limit many developed tools from widespread use in biological research, prompting many researchers to develop their own in-house analysis programs or use dated methods of analysis. Here, we introduce 3D-Speckler, a user-friendly, MATLAB-based software that enables high throughput quantification of fluorescent particle location, size, 2D/3D spatial orientation, intensity, and more in 2D/3D fluorescence microscopy images with high accuracy and precision in a semi-automated manner. We validate 3D-Speckler measurement and calibration capabilities using multispectral fluorescent beads, as well as demonstrate its capabilities for quantitative analysis in biological image datasets.

Detailed, user-oriented descriptions of the software and algorithms are available in the Materials and methods. 3D-Speckler was optimized for fluorescent puncta detection and analysis with nanometer-scale accuracy. The processing pipeline is outlined in eight simple steps (Fig. 1, A and B): (1) User selects a 2D/3D image file with up to four channels. (2) User selects the analysis package and options, which include local BG correction, particle filters, and CA correction. (3) User thresholds image for particle detection through single/multi thresholding options. (4) 2D/3D Gaussian fits with rotations are performed on detected particles. (5) User reviews particle selection. (6) Points can be matched/aligned across channels. (7) Distance matrices and CAs are calculated amongst channels for CA and colocalization analysis. (8) Export all quantification results into an excel file for further downstream analysis (Fig. S1 A).

3D-Speckler detects particles and determines their respective bounding boxes (BBs) through threshold-based image binarization (Fig. 2 A). Traditionally, particle detection is performed using single threshold binarization. This method works in images where the particle population have relatively homogenous intensities with high signal-to-noise ratios (SNRs), such as with isolated microspheres of a fixed size (Fig. 2 A, top). On the other hand, accurate particle detection is limited in images with a heterogeneous population (Fig. 2 A, middle). Single thresholding results in BB overestimations for brighter particles, BB underestimations for dimmer particles, and the inability to distinguish two close particles as separate particles (Fig. 2 A, middle, and Fig. 2 B, a and b). To improve detection accuracy, 3D-Speckler introduces a multi-thresholding option. The user chooses a threshold by which to commit the image to and 3D-Speckler will detect the particles at that threshold, remove those particles from the image based on their BBs, and display the new image to the user for additional thresholding. This process can be repeated, and all detected particles from all multi-thresholding rounds will be compiled and displayed at the end of thresholding (Fig. 2 A, bottom, and Fig. 2 B, c–e).

After particle detection, overlap and size filters can be applied to further improve detection and measurement accuracy. The overlap filter allows exclusion of particles that have overlapping BBs (Fig. 2 C). The size filter allows exclusion or inclusion of particles within a specified size range for datasets with heterogenous populations of different-sized objects (Fig. 2 D). 3D-Speckler also has a built-in particle matching/alignment algorithm for matching particles between channels for CA determination and/or colocalization analyses (Fig. 2 E). 3D-Speckler also allows the user to set the ROI for analysis, allowing omission of undesired regions from analysis without necessitating pre-cropping (Fig. 2 F).

Since computation speed for detection and downstream analysis is important for throughput and usability, we tested the speed of 3D-Speckler using images with different numbers of 100-nm beads. 3D-Speckler could detect ∼1,800 beads within 3 s (Fig. S1 B). Subsequent 2D and 3D Gaussian fits to these particles were performed within 17 s and 7.5 min, respectively, using a general laboratory computer, demonstrating 3D-Speckler detection, fitting robustness, and throughput. After fitting, 3D-Speckler will label outliers based on Gaussian fitting errors to aid in dataset evaluation (Fig. S1 C).

Size determination of a fluorescent point source is commonly used to determine the effective resolution of an imaging system. This is typically performed through an FWHM calculation from a Gaussian profile fitted over its intensity profile (Schweitzer et al., 2004). Intensity profiles are commonly generated from line scans drawn across a punctum of interest through the estimated centroid and restricted to pixel grids, reducing measurement consistency and accuracy. To minimize potential errors from improperly oriented line scans, 3D-Speckler fits either a 2D or 3D Gaussian with rotation to each particle to determine the particle center and orientation in space before drawing a line scan across the particle at the fitted angle and through the true particle center (Fig. 3 A, see Materials and methods). 3D-Speckler provides three different FWHM measurements: true FWHM (tFWHM), interpolated FWHM (iFWHM), and Gaussian FWHM (gFWHM). The tFWHM is obtained by mapping the intensity values of the pixels within half the lateral resolution of the image to the line scan. Since tFWHM can be sensitive to profile shape and existing pixel values, the iFWHM is determined using a C¹ natural neighbors interpolation of the intensity values at the location of the line scan sampled at the interval of the lateral resolution in XY and axial resolution in Z dimensions. The gFWHM is determined through the Gaussian FWHM relation from the σ values obtained from the fits for each dimension.

To explore the performance of each of these FWHM measurement options in different scenarios above and below the diffraction limit, we first performed a simulation of both a 100- and 500-nm diameter sphere with nano-scale emitters (Fig S1 D) following various distributions. The probability distribution functions and cumulative distribution functions are shown in Fig. 3 B. Artificial 3D image stacks were generated using 200-nm z-steps, where the image at each z-step was created from the combined sum of each PSF contribution from each emitter (Fig. S1 D). We found that fluorophore distribution has relatively little effect on the resulting image and the three different FWHM measurements in simulated 100-nm beads, likely due to the size being below the diffraction limit (Fig. 3, B and C). The gFWHM measurement is more stable for sub-diffraction limit objects (ranging ∼2 nm) compared to iFWHM or tFWHM (ranging ∼7 nm) across a wide range of fluorophore distributions in lateral size, on the other hand, tFWHM/iFWHM showed more stable measurements in axial size. The 500-nm bead scenarios are more complicated. Fluorophore distribution has a significant effect on both the resulting image and on all FWHM measurements, with distributions where the fluorophores are more centrally concentrated (Gaussian 50/80) yielding smaller measurements than distributions where the fluorophores are more peripherally concentrated (Sigmoidal 60/30 and surface only; Fig. 3, B and D). Additionally, the fluorophore distribution is also important for the relationship between gFWHM with tFWHM and iFWHM, with centrally concentrated distributions yielding larger gFWHM measurements and peripherally concentrated distributions yielding smaller gFWHM measurements than tFWHM/iFWHM in both lateral and axial sizes (Fig. 3 D). These results indicate that objects larger than PSF require consideration of fluorophore distribution to determine the ideal FWHM size measurement method.

To examine whether the FWHM trends observed in simulated beads hold in real beads, we explored each FWHM measurement option on real beads. Representative line scans for comparison and relationships between tFWHM, gFWHM, and iFWHM measurements of 100- and 500-nm beads are shown in Fig. 3, E and F; Fig. S1 E; and Fig. S2 A. For lateral (X, Y) size measurements of objects smaller than PSF (100- nm beads), both tFWHM and gFWHM work equally well, whereas iFWHM measurements were larger likely due to insufficient datapoints for appropriate interpolation (Fig. 3 E and Fig. S2 A). On the other hand, for our 500-nm beads, gFWHM measurements exhibited significantly smaller values than tFWHM/iFWHM, suggesting a peripherally concentrated fluorophore distribution (Fig. 3 F and Fig. S2, A and B). For axial (Z) size measurements, tFWHM often exhibited smaller values than gFWHM/iFWHM in both 100- and 500-nm beads due to overestimations in peak amplitude (Fig. 3, E and F, and Fig. S1 E). Unlike lateral measurements, iFWHM smoothed the variations in the intensity profiles seen in pixel-mapped axial line scans and yielded values between gFWHM and tFWHM (Fig. 3, E and F). Based on these results, we used tFWHM for lateral measurements and iFWHM for axial measurements moving forward unless otherwise stated.

We demonstrated lateral and axial size measurements of 500- and 100-nm fluorescent beads with various objectives using a spinning disc confocal microscope and a super-resolution microscope (SoRa) taken with 50-nm z-steps (Fig. 4, A and B). As expected, we found both lateral and axial FWHM size measurements became increasingly accurate with higher magnification and numerical aperture (NA) objectives in 500-nm beads (actual size 490 nm; Fig. 4 A). Lateral tFWHM measurements of 100-nm beads exhibited ∼230 nm for the higher NA 100× objective and ∼150 nm for the same objective with SoRa (Fig. 4 B). Additionally, tFWHM of 200-nm beads using the 100× objective exhibited ∼245 nm, indicating the maximum achievable lateral resolution of our confocal system is ∼230–250 nm and objects smaller than this suffer from lateral PSF effects (Fig. 4 C). To compare with expected resolution limits, we obtained theoretical PSF images with parameters matching our imaging conditions and determined lateral sizes using 3D Speckler. This yielded results of ∼398, ∼236, and ∼192 nm for 40× objective (NA 0.75), 60× (NA 1.40), and 100× (NA 1.49), respectively (Fig. S2 C). Our actual measurements of 100- and 200-nm beads were significantly larger than these theoretical values, demonstrating the importance of determining the actual resolution limits of the imaging systems used for experiments.

We also determined the 3D size of 500-nm beads using a wide-field scope, which uses the same microscope body, z-step size, and objective as the confocal scope (Fig. 4 D). Wide-field exhibited nearly identical lateral sizes; however, the confocal scope exhibited significantly improved axial resolution. Additionally, we found deconvolution, a common post-processing method for improving image quality or resolution, significantly improved the measured sizes of 100-nm beads (Fig. 4 B); however, it causes significant underestimation of 500-nm bead sizes (Fig. 4 E), suggesting serious caution must be used when performing deconvolution on images with objects larger than PSF for size quantification. Notably, performing deconvolution on our 500-nm beads reveals an image that visually matches our simulated sigmoidal/surface distributions with the matching FWHM trend of a smaller gFWHM measurement as compared with tFWHM/iFWHM (Fig. 3, B–D, and Fig. 4 E). Altogether, this shows that 3D-Speckler can offer not only imaging system resolution limits but also give insight into the size and fluorophore distribution of a fluorescent object above diffraction limit.

We next asked whether z-step size affected z-resolution. A 200-nm step is commonly used and considered sufficient for high-resolution 3D imaging since it is considered over-sampling based on theoretical PSF. To validate this, we imaged 500-nm beads with different z-steps (50 nm to 1 µm) using a spinning-disc confocal microscope with 60× Air, 60× Oil, and 100× Oil objectives, and measured lateral and axial sizes (Fig. 5 A). As expected, there were no significant differences in lateral size measurements in all conditions, including a 60× air objective with a large refractive index mismatch, between 50 to 300 nm steps, whereas measurements errors (and variances) became greater above 300 nm steps likely due to deviation of the best focal plane from the center of the beads. On the other hand, unexpectedly, a 50-nm step exhibited the smallest axial size measurement, which significantly increased with step size. For further verification, we performed similar experiments using 100-nm beads (Fig. S2 D). Consistent with the 500-nm bead results, there was significant deviation in the lateral and axial size measurements from those attained using 50-nm step size with higher z-step sizes.

Next, we asked how the pixel size and NA of objectives affect axial size measurements. For this, we took 3D images of the same beads using 50-nm z-steps and the same confocal microscope with different objectives and measured lateral and axial sizes (Fig. 5, B and C). In lateral size measurements, there were no significant differences between 100× (NA 1.49) to 60× (NA 0.75 Air) objectives (476–494 nm). Although 60×, 40×, and 20× air objectives have the same NA (0.75), lateral sizes were significantly overestimated and inversely correlated with objective magnification. Furthermore, there was significant overestimation of axial size using the 60× (NA 1.4) objective as compared to 100× (NA 1.4). These results suggest that resolution not only depends on NA but also on pixel sizes. To test this, we simulated 500-nm bead images (NA 1.4) and pixelated based on 20×, 40×, 60×, and 100× objective pixel sizes (Fig. S2 E), allowing us to test the impact of pixel sizes in lateral size measurements. Consistent with actual bead measurements, larger pixel sizes exhibited overestimation in lateral sizes. Collectively, these results indicate that higher NA objectives, smaller pixel sizes, a higher-resolution camera, and smaller z-step sizes yield higher resolution.

We found that the measured axial size of 500-nm beads still showed overestimation from actual size, suggesting there are still significant PSF effects axially, even at 500 nm (Fig. 4 A). Although part of the overestimation of axial size may be caused by spherical aberration, this was minimized in our imaging conditions, suggesting the major cause of overestimation of axial size in 500-nm beads is PSF. To confirm this, we measured lateral and axial sizes with 0.1, 0.2, 0.5, 1, and 4 µm beads, and determined axial PSF effects of a 100× NA 1.4 objective (Fig. 5 D). Whereas both lateral and axial lengths were the same in 4 µm beads, axial lengths were still significantly overestimated in 1 µm beads, indicating there are still significant axial PSF effects in 1 µm beads with a spinning-disc confocal microscope and a high NA 100× objective, and that axial sizes (and volumes) are likely overestimated in objects of this size.

Additionally, we found that multispectral beads, which are widely used for calibration purposes, can significantly decrease in size by age and/or mounting medium (Fig. S2 F). Whereas the FWHM size of 500-nm beads showed the expected size of 490 nm in a freshly mounted sample, the FWHM size can vary between 5 and 30% smaller (∼330–460 nm) with the age of the beads mounted by curing mounting medium or on a commercial calibration slide. This suggests that bead size measurements may be impacted by their age and mounting media, in addition to excitation/emission wavelengths. We recommend that freshly prepared bead samples or newer commercial calibration slides be used and validated first with a high NA and magnification objective.

Quantification of fluorescent particle intensity is commonly used to determine illumination profile flatness and protein amount within an immunolabeled fluorescent puncta (i.e., kinetochores; Hoffman et al., 2001; Johnston et al., 2010; Lawrimore et al., 2011; Suzuki et al., 2015). For this, 3D-Speckler provides both maximum and integrated intensity measurements (Fig. 6 A). 3D-Speckler has the option to apply local BG correction, which is one of the most accurate methods of BG correction and has been used to accurately determine the kinetochore protein copy numbers and stoichiometry required for faithful chromosome segregation (Suzuki et al., 2015; Verdaasdonk et al., 2014). 3D-Speckler performs local BG correction in 2D/3D scenarios using a user-defined n% larger BB with automated BG exception handling (Fig. 6 A). Our local BG correction algorithm could efficiently remove BG signal while avoiding fluorescence overcorrection (Fig. S3, A and B). Although integrated intensity depends on BB size and does not converge without local BG correction, we found it quickly converged to a value with local BG correction given a sufficiently encapsulating BB (Fig. S3 C). We demonstrate the importance of local BG correction using 3D-Speckler with variable noise or signal simulation scenarios with PSFs of different SNRs (Fig. S3 D). In both scenarios, no local BG correction yields erroneous measurements (red), whereas local BG correction yields expected values (blue), particularly under low SNR conditions.

By applying the 3D-Speckler local BG correction to 500-nm beads and measuring integrated intensity, we found a subpopulation of beads with ∼2× the intensity of the rest of the population, indicating bead aggregation (Fig. 6 B). Interestingly, the maximum intensity values of these bead aggregates did not always imply multiple beads, indicating maximum intensity is not ideal for determination of target copy number or density. Additionally, some of these bead aggregates have larger lateral sizes, while some have larger axial sizes with seemingly no correlation (Fig. 6 B). We postulated that this disparity may be due to differences in bead aggregate geometry. To test whether it is possible that two 500-nm beads can appear as a single object due to geometry and PSF, we generated simulated images of two 500-nm spheres using 100× objective conditions (65 nm/pixel with 200-nm z-steps) as described before (Fig. S1 D) at different angles 0–90° and measured the sizes, max intensity, and integrated intensity using 3D-Speckler (Fig. 6, C–E). Although a 500-nm bead is above the lateral resolution limit, two adjacent 500-nm beads became indistinguishable and exhibited as a single object at angles >45° (Fig. 6 D). The relationships between sizes/intensities and angles are shown in Fig. 6 E. Since simulation conditions are perfectly ideal, it is reasonable to assume that actual imaging system/conditions can make some two-bead aggregates at angles <45° exhibit as single objects as well. We then attempted to visualize and categorize the two-bead aggregates we observed in Fig. 6 B. An example image containing single and indistinguishable double 500-nm beads (likely 75–90° orientation) is shown in Fig. 6 F. We found that the images of actual bead aggregates followed closely to the simulated 500-nm bead images and based on simulation results, we were able to classify the geometries of the bead aggregates in Fig. 6 B using the color codes in Fig. 6, D and G. These results demonstrate that 3D-Speckler can offer insight into an object’s geometry.

Light traveling through a microscope’s optical path cannot uniformly illuminate a field of view (FOV), leading to gradual reduction in illumination towards the edges of the FOV (Brown et al., 2015; Khaw et al., 2018). It is critical to determine the flatness of the illumination profile for accurate fluorescence measurement. Using intensity and localization measurements obtained from 3D-Speckler, we were able to determine the illumination profile of our imaging system (Fig. S3, E and F). Our results show that particles at the center of the FOV can be up to 30% brighter than particles at the periphery in our imaging condition using a 60× oil immersion objective. After illumination profile determination, corrections can be made by the user for intensity measurements of puncta based on their radial distances from the center of the FOV for improved accuracy. To aid the user in characterizing field-dependent effects, 3D-Speckler outputs surface plots visualizing the intensities as well as FWHM measurements across an imaging FOV (Fig. S3, G and H).

Correcting for CA is critical for achieving nanometer-scale measurement accuracy in localization determination. Since CAs are not uniform across the FOV, it is necessary to measure many multispectral beads to determine average aberrations and their variances within the FOV for CA correction (Suzuki et al., 2018). Although Gaussian fitting is most used for particle center determination, since nanometer-scale emitters exhibit as PSFs and not Gaussians, we tested the localization accuracy of 3D-Speckler using simulated images of 3D PSFs at various SNRs and using Gaussian fits to PSF profiles (Fig. 7 A). We generated 10 trials of 5 randomly distributed 3D PSFs within a 2,000 × 2,000 × 2,000 nm box and created an artificial image stack with a 50-nm z-step and applied a 65-nm lateral resolution binning (equivalent to a 100× objective with a high-resolution camera) for each run (Fig. 7 B). The original 3D coordinates of 3D PSF locations before pixelation were recorded for post-fitting comparison. Artificial noise was introduced to each image stack, resulting in a SNR of either 10 or 3, to test localization accuracy in noisy images. We found that the 3D-Speckler could determine the location of particles within ∼1 nm accuracy in both 2D and 3D scenarios without noise and ∼2 nm accuracy with higher noise (Fig. 7 C). We also considered potential contributions of binning to localization measurements by applying 15–30 nm bin shifts before pixelation (Fig. 7 A). We found no significant differences in localization accuracy with or without bin shifts, further demonstrating the robustness of Gaussian fitting in localization determination. To characterize the limits of 3D-Speckler localization methods in imaging systems with large aberrations, we imaged the same 500-nm beads mounted in glycerol-based medium using six different objectives with different NA and immersion media, then determined the distance of each bead to a reference bead. Differences in the distances obtained using 100× (NA 1.49) with SoRa are shown in Fig. 7 D. Air objectives (lower NA) exhibited significant errors in both 2D and 3D distances likely due to the refractive index mismatch. Similar to previous size measurements, using the same NA objective with lower magnification (larger pixel sizes) also increases localization error. Overall, significant aberrations brought upon by low magnification and/or refractive index mismatch can result in significant localization error regardless of the accuracy of the localization determination method used.

Next, we measured CAs in our imaging system using 3D-Speckler (Fig. 7, E–G). Even particles within a single FOV can often have CA differences in magnitude and direction between different channels (Fig. 7 F). As expected, the bead centers in the blue (405 excitation) channel are located further away from the other wavelength channels. Additionally, the average CAs in the X and Y dimensions were equal in magnitude, but opposite in direction, and the aberrations in the Z dimension were universally greater in magnitude than the X and Y aberrations (Fig. 7 G).

To further improve accuracy in distance measurements, local CA correction should be performed instead mean CA correction. 3D-Speckler offers two options for local CA corrections: non-rigid geometric affine transform and polynomial surface correction. In the affine transform, 3D-Speckler uses the measured CA in all dimensions to determine a best affine transform between different combinations of color channel pairs (Fig. 8 A). For polynomial surface correction, 3D-Speckler fits a polynomial surface for the spatial dependence of CA in each X, Y, and Z dimension for different combinations of color channel pairs across the FOV (Fig. 8 B). In our imaging system with the polynomial surface, we found that CA in X and Y between channels had strong dependence on XY and not on XZ or YZ. Additionally, CA in Z between channels had a stronger dependence on XY than on XZ or YZ (Fig. S4 A). CA in X and Y fit best to a poly 11 model, whereas CA in Z fit best to a poly 22 model (Fig. 8 B and Fig. S4 A). 3D-Speckler allows the user to choose a CA correction option, create CA calibrations, save CA calibrations for later import, and then correct local CAs in subsequent localization analyses.

We demonstrated the performance of local CA corrections using 100-, 200-, and 500-nm beads using different image sets for obtaining CA calibrations and correction of CAs (Fig. 8, C and D, and Fig. S4, B and C). We found that both affine transform and polynomial surfaces significantly corrected CA and suppressed variances as compared with the common averaging method (Fig. 8 C). We confirmed that this holds true for 100- and 500-nm beads as well (Fig. S4, B and C). To determine the number of beads needed for CA correction central limit convergence, we performed CA correction using affine transform, polynomial surface, and averaging using different numbers of 100- and 200-nm beads and found that ∼200 beads across a FOV of a 100× oil objective is required for proper CA correction (Fig. 8 D and Fig. S4 D). We found that local CA corrections worked significantly better in 200- and 500-nm beads as compared to 100-nm beads likely due to decreased measurement precision from smaller size and lower signal in our imaging condition. We recommend using brighter beads of sizes smaller than PSF for better corrections.

Altogether, this demonstrates that 3D-Speckler can determine the location of fluorescent particles with nanometer-scale accuracy, provide, and characterize the CAs of an imaging system, and allow users to correct for local CAs in their images and quantification with improved precision as compared to previous methods. Additionally, 3D-Speckler can output affine transform CA-corrected 2D/3D image stacks of every color channel using an imported affine transform calibration for downstream visualization purposes (Fig. 8 E).

There exist many biological entities that present as fluorescent foci, such as kinetochores, centrosomes, labeled genomic loci, monomeric/multimeric compositions, and more. We asked whether 3D-Speckler can be utilized for quantifying proteins in a cell. First, we used 3D-Speckler with a proximity ligation assay (PLA) to quantify foci number. PLA assays are widely used to detect in situ protein–protein interactions and should only exhibit as fluorescent foci if the target proteins are within 40 nm apart. Mitotic U2OS cells with either RanGap1-RanBP2 (positive) or RanGap1 only (negative) were imaged and numbers of PLA puncta were quantified. Consistent with previous work, we found significantly more fluorescent puncta in the RanGap1-RanBP2 condition as compared to the RanGap1 only with 273 ± 102 and 32 ± 10 puncta, respectively (Fig. S4 E; Mills et al., 2017).

Kinetochores are protein platforms built on the centromeric chromatin by which microtubules bind in mitosis and are essential for chromosome segregation. It is known that some kinetochores are clustered during interphase (Andronov et al., 2019). We attempted to reveal how kinetochores are clustered in normal human RPE1 cells, which stably maintain 46–47 chromosomes (Fig. 9 A; Passerini et al., 2016; Potapova et al., 2019). 3D-Speckler detected 36 ± 4 kinetochore foci marked by CENP-A in interphase, whereas 92 ± 2 kinetochores were detected in mitosis (Fig. 9 B), which suggests kinetochores are clustered in interphase and declustered in mitosis. We found that some kinetochores in interphase have BG-corrected integrated intensities that were integer multiples of the average intensity of most of the population, further suggesting kinetochore clustering. An example interphase cell had only 33 CENP-A foci, but it had clustered kinetochores with integrated intensity measurements implying two, three, and six kinetochores (Fig. 9, A and C). Taking this into account, we could correct the number of kinetochores in this cell to 47. By using this kinetochore correction method, we measured 47 ± 2 kinetochores across 20 interphase cells (Fig. 9 B). These quantitative analyses also demonstrated that ∼24% of kinetochores in interphase RPE1 cells are clustered and that most clustered kinetochores have 2–3 kinetochores (Fig. 9 D). Occasionally, we found that >5 kinetochores are tightly clustered.

Next, we examined the size of kinetochores in metaphase rat kangaroo PtK2 cells. Previous studies using EM found the average length and width of kinetochore outer plates in PtK2 cells to be ∼400 and ∼70 nm, respectively (McEwen et al., 1993; McEwen et al., 1998; Salmon et al., 2005). We labeled Ndc80/Hec1, an essential component of kinetochore outer plates (DeLuca et al., 2005), and measured the 3D lengths of the Ndc80/Hec1-labeled kinetochore. Consistent with EM data, the average Hec1 length was 406 nm (Fig. 9 E); however, the width measured 341 nm, which was overestimated as compared with EM measurements. We hypothesized that this overestimation is due to PSF effects and kinetochore 3D orientation. To test this, we simulated a Hec1 plate with a uniform distribution of fluorophores and dimensions matching EM measurements (400 × 400 × 70 nm) at various rotation angles about the X and Y axes, generated an artificial 3D image stack at each rotation angle, and determined the length and width FWHM measurements (Fig. 9 F). As expected, the length was less sensitive to rotations about both the X and Y axes. On the other hand, the width significantly increased with the Y axis rotation. Across the range of rotation angles between 0 and 60°, the length varied only ∼30 nm, whereas the width varied ∼150 nm, which includes our measured 341 nm (Fig. 9 F). Although the orientations of objects inside of cells are more complicated due to combinations of rotations about all axes and antibody sizes must be considered, our results suggest that fluorescent object spatial orientation and PSF can significantly affect the measured FWHM sizes.

Kinetochores exhibit elastic properties, stretching up to ∼100 nm in a force-dependent manner (Suzuki et al., 2018; Wan et al., 2009). It is known that this stretching is important for both mitotic checkpoint control and proper kinetochore-microtubule attachment (Dumont et al., 2012; Maresca and Salmon, 2009; Suzuki et al., 2014; Uchida et al., 2009). Using 3D-Speckler, we determined the intra-kinetochore distance between CENP-A and Hec1 in metaphase HeLa cells, then performed local CA correction. The average CA correction measurements were 85 ± 35 and 94 ± 34 nm in 2D and 3D, consistent with previously reported values (Suzuki et al., 2014; Suzuki et al., 2018). Both affine transform and polynomial surface corrections exhibited significantly improved precision as compared to mean CA correction, showing 79 ± 14 and 79 ± 13 nm for 2D affine and 2D polynomial surface correction, respectively, and 3D measurements showing 90 ± 16 and 91 ± 17 nm, respectively (Fig. 9 G). Note that previous studies could only measure ∼20–30 kinetochores per cell via manual selection (Suzuki et al., 2018), whereas 3D-Speckler results came from the semi-automated detection of ∼92 kinetochores per cell, increasing sample size while decreasing analysis time and avoiding selection bias.

We further explored the importance of taking the 3D orientation of an object into account for localization and size determination using 500-nm beads and PtK kinetochores stained by Hec1 (Fig. S4 F). We found 2D methods can result in additional lateral size measurement errors of ∼14 nm and localization errors of 3–6 nm and 5–10 nm in 500-nm beads and kinetochores, respectively, as compared to 3D measurements. Altogether, these results demonstrate that 3D-Speckler can be used to elucidate information about protein architectures, dynamics, or interactions in biological fluorescent images through count, intensity, size, and distance measurements.

Fluorescence microscopy remains an essential tool for direct visualization of target structures and providing insight into underlying biology. As such, methods and tools for quantitative analysis of microscopy images are constantly being developed and improved. Quantitative accuracy largely depends on the quality of the images, imaging system, and analysis tools being used (Waters, 2009). Ideally, an imaging system should be routinely characterized and calibrated for maintenance of integrity and reproducibility. These characterizations often involve the use of analysis tools for fluorescent puncta quantification, many of which are not user-friendly and lack both a cohesive pipeline and proper measurement options. A comparison chart of general and special features, to the best of our knowledge, amongst 3D-Speckler and other software is shown in Table S1. Other software face issues such as requiring pre-cropped images of single puncta, manual determination of particle sizes, manual intensity corrections, not accounting for 2D/3D orientation, and multi-software or multi-platform pipelines, which contribute toward suboptimal workflow. 3D-Speckler resolves these issues and provides an Excel file containing quantified fluorescent particle sizes, intensities, 3D coordinates, and more. These can be used for routine calibration including determination of PSF (resolution limit) in 2D/3D, illumination flatness, and characterization of CAs with nm-scale accuracy.

3D-Speckler allows for the automated quantification of thousands of fluorescent beads for expeditious CA characterization and without additional manual intervention or multiple platform pipelines, as compared with previous tools (Cole et al., 2011; Leiwe et al., 2021; Matsuda et al., 2020). The user has the option to use the output CA values to perform the traditional average CA correction or perform local CA correction, which overcomes the disadvantage of the higher variances in average CA correction methods. We showed that 3D-Speckler can determine object locations with nm-accuracy using an unaberrated Gibson-Lanni PSF model (Fig. 7, B and C). To support this, previous studies showed Gaussian-based localization methods could accurately determine location under general conditions, however, it could result in localization errors of tens of nanometers with larger aberrations (Li et al., 2018; Stallinga and Rieger, 2010). Therefore, further validation is needed for 3D-Speckler localization accuracy in systems with larger aberrations. A potential limitation of 3D-Speckler in distance measurements is the matching object function between channels. 3D-Speckler uses a nearest neighbor method within a user-defined distance to find a pair. This worked well in most of the cases we tested, however it may exhibit matching errors in situations with many clustered, distinguishable particles.

Size measurements of fluorescent particles can offer accurate PSF determination of microscope systems as well as insight into protein architecture and dynamics. They are commonly determined through FWHM following a manually drawn line scan across the pixels of a puncta of interest without considering particle 3D spatial orientation, which often result in size measurement inaccuracies (Fig. S4 F). We showed that use of 2D methods, even when properly considering spatial orientation, result in higher errors in localization and size determination as compared to 3D methods (Fig. S4 F). This suggests that previous measurement methods, which did not properly consider spatial orientation, may result in additional errors in localization and size measurements. Furthermore, the widely used deconvolution method must be used with caution, as it can cause significant underestimation in size measurements, particularly with objects larger than PSF since deconvolution assumes the source of fluorescence signals follows the PSF profile (Fig. 4 E; Sage et al., 2017; Sarder and Nehorai, 2006). In theory, the resolution of an imaging system depends on NA and not magnification, however our results indicate the image pixelation size is also an important factor. Therefore, in objectives with the same NA, the higher magnification objective exhibits higher resolution under same image conditions.

For maintenance of integrity and reproducibility, we recommend performing microscope calibrations monthly using at least 100-, 200-, and 500-nm fluorescence beads. Both 100- and 200-nm beads can be used to determine the resolution limit and CAs of the imaging system, whereas 500-nm beads can be used to determine the accuracy of size measurements and characterization of the axial PSF. The sizes of the beads used in this study were specified by the manufacturer to have been measured using transmission EM on dry, unstained microspheres. Although the physical size determined by EM is the most accurate, EM and light microscope imaging conditions are different and the specified bead sizes may not be maintained in all microscopy imaging conditions. In support of this, we found aged commercial calibration slides or house-made slides using curing mounting medium can cause beads to become significantly smaller (Fig. S2 F). Therefore, it is important to prepare fresh bead samples when curing mounting medium is used or to obtain new commercial calibration slides. We recommend preparing fresh bead samples, mounting in a non-curing medium, imaging with a high NA and high magnification objective, and imaging using a smaller z-step when characterizing an imaging system.

3D-Speckler is a powerful tool for quantitative fluorescence microscopy. It uses the Bio-Formats (OME) software tool, which can open most image file formats (Linkert et al., 2010). It can run on both Windows and Mac operating systems, does not require manual selection or manipulation of fluorescent puncta/images, and provides comprehensive 2D and 3D analysis options and capabilities in a user-friendly and intuitive interface. 3D-Speckler streamlines analyses, improves access to rigorous quantitative methods, and improves throughput by providing the most important quantitative measurements and corrections relevant to microscope calibration and biological study including size, intensity, location, and orientations of fluorescent particles.

The source code and user manual of 3D-Speckler are available on GitHub (https://github.com/suzukilabmcardle/3D-Speckler). The source code, bfmatlab, user manual, and example test images are available at the following link: https://drive.google.com/drive/u/3/folders/1jKqiYFm31cJ0VVhGhLFhRuLI_ZiqmRjF. 3D-Speckler can be installed on both Windows and Mac OS with MATLAB (2019 and above). For users who do not have access to a MATLAB license, we provide a standalone, executable application made through MATLAB compiler. The standalone 3D-Speckler and user manual are available at following website: Windows: https://drive.google.com/drive/u/3/folders/1iV5AbqgJhIkQV2lAoZyrNN0BRRq5_JrX and Mac: https://drive.google.com/drive/u/3/folders/1wrVNDN-6H0QAMgidj0Ql_XTvt44GGkFR. Running standalone 3D-Speckler requires installation of the correct version of MATLAB Runtime, thus we provided an installer for the correct version in the same download folder. 3D-Speckler utilizes the Bio-Formats (OME) software tool for opening and reading over 140 different image file formats (Linkert et al., 2010).

The 3D-Speckler fits a 3D Gaussian model with rotations to the pixel intensity values within a 3D particle BB, to determine the particle center and the particle 3D orientation. After determining the rotation of the particle about the X, Y, and Z axes, the particle is reoriented based on the fitted rotations and line scans are drawn through the particle center in the X, Y, and Z dimensions independent of pixel grids for intensity profile generation. In a 2D scenario, the 3D-Speckler will fit a 2D Gaussian model with rotation to the pixel intensity values within a 2D particle BB that is from either a 2D image or the best focal plane of the particle of interest from a 3D image stack. Similarly, the particle will be reoriented after determination of the particle center and rotation and line scans will be drawn through the particle center in the X and Y dimensions for intensity profile generation.

RPE1, U2OS, and PtK2 cells were grown in DMEM (Gibco) or DMEM-F12 medium (Gibco) supplemented with 10% FBS (Sigma-Aldrich) or 20% (for PtK2), 100 U/ml penicillin, and 100 mg/ml streptomycin (Gibco) at 37°C in a humid atmosphere with 5% CO₂. RPE1, U2OS, and PtK2 cells were kindly gifted from Drs. Mark Burkard (Department of Medicine, University of Wisconsin-Madison, Madison, WI, USA; Lera et al., 2016), Michael Emanuele (Department of Pharmacology, University of North Carolina, Chapel Hill, NC, USA; Mills et al., 2017), and Edward Salmon (Department of Biology, University of North Carolina, Chapel Hill, NC, USA; Wan et al., 2009), respectively.

Calibration slides (F36909; Thermo Fisher Scientific), 100-, and 490-nm tetra-spec beads (T7279 and T7281; Thermo Fisher Scientific) were used for calibrations. Appropriate concentrations of both beads were mixed, then mounted with ProLong Gold, ProLong Diamond, ProLong Glass (Thermo Fisher Scientific), or house-made glycerol-based mounting medium (20 mM Tris, pH 8.0 [Sigma-Aldrich], 0.5% N-propyl gallate [Sigma-Aldrich], 90% Glycerol [Sigma-Aldrich]) on #1.5 high precision coverslips (thickness of 170 ± 5 µm; Marienfeld GmbH & Co). Samples mounted in ProLong were allowed to cure until refraction index stabilized before imaging.

Cells were fixed with 3% PFA (Sigma-Aldrich) in PHEM buffer (120 mM Pipes [Sigma-Aldrich], 50 mM Hepes [Sigma-Aldrich], 20 mM EGTA [Sigma-Aldrich], 4 mM magnesium acetate; pH 7.0 [Sigma-Aldrich]) at 37°C without pre-permeabilization. Cells were then rinsed with 0.5% NP40 and incubated in 2% BSA (Sigma-Aldrich) and Boiled Donkey Serum (017-000-121; Jackson ImmunoResearch). The following primary antibodies were used: rabbit anti-CENP-A (kindly gifted from Dr. Aaron Straight, Department of Biochemistry, Stanford University, Stanford, CA, USA; Wan et al., 2009), mouse anti-Hec1 (9G3, ab3613; Abcam), and mouse anti-tubulin (#3873; DM1A, mAb). Minimum cross-react Donkey anti-rabbit and mouse conjugated with Alexa 488 or Rhodamine Red X were used as secondary antibodies (711-545-152 and 715-295-150; Jackson ImmunoResearch, respectively). Samples were stained using DAPI (Thermo Fisher Scientific) after incubations with secondary antibodies. Stained samples were mounted with Prolong Gold (Thermo Fisher Scientific) and incubated until the refractive index stabilized. PLA assay was performed using the Sigma Duolink in Situ Red Kit (Sigma-Aldrich). Cells were fixed as described above then stained following company protocol with primary antibodies against RanGAP1 and RanBP2 (kindly gifted from Dr. Michael J. Emanuele, Department of Pharmacology, University of North Carolina, Chapel Hill, NC, USA; Mills et al., 2017).

For confocal image acquisition, a high-resolution Nikon Ti-2 inverted microscope equipped with a Yokogawa SoRa-W1 super-resolution spinning-disc confocal installed Uniformizer and a high-resolution Hamamatsu Flash V3 CMOS camera or a Nikon Ti-2 inverted microscope equipped with a Yokogawa W1 spinning-disc confocal and a Hamamatsu Flash V2 CMOS camera was used. For wide-field image acquisition, a Nikon Ti-2 inverted microscope equipped with a Hamamatsu Flash V2 CMOS camera or a Nikon TE2000 inverted microscope equipped with a Hamamatsu Orca ER camera was used. The following objectives were used with the above scopes; 20× (NA 0.75 air), 40× (NA 0.75 air), 60× (NA 0.75 air and NA 1.4 oil), 100× (NA 1.4 oil, NA 1.45 oil, and NA 1.49 oil). 3D stacked images were obtained sequentially with 50-, 100-, or 200-nm z-steps using Nikon Elements software or MetaMorph software (Molecular Device). Deconvolution (Nikon Elements) was used for part of Fig. 4, B and E.

Precision 5820 Tower with Intel Core i7-9800X (3.8 GHz), Windows 10 Pro 64, 64 GB 2666 MHz DDR4, and Radeon Pro WX5100 8 GB was used for speed test of detection and downstream analysis in Fig. S2 C.

In 3D-Speckler, all fitting is performed on either the raw data or background corrected raw data. Partial removal of one particle due to multi-thresholding commitment of a nearby particle will not significantly affect the resulting analysis if the BBs do not significantly overlap. 3D-Speckler fits a 3D Gaussian model with rotations to the pixel intensity values within a 3D particle bounding box to determine the particle center and the particle 3D orientation. After determining the rotation of the particle about the X, Y, and Z axes, the particle is reoriented based on the fitted rotations and line scans are drawn through the particle center in the X, Y, and Z dimensions independent of pixel grids for intensity profile generation. In a 2D scenario, the 3D-Speckler will fit a 2D Gaussian model with rotation to the pixel intensity values within a 2D particle bounding box that is from either a 2D image or the best focal plane of each selected particle of interest from a 3D image stack.

Gaussian fits were performed via nonlinear least-squares as follows:

Polynomial models:

All 1D-Gaussian profile fits over the mapped intensity profiles from line scans in Fig. 3, E and F, and Fig. S1 E are for visualization purposes only. 3D-Speckler determines the gFWHM from the gFWHM relation above.

All PSF simulations were performed using a modified Gibson-Lanni model described in Li et al. (2018). Briefly, the integration term of the Gibson-Lanni model was replaced with a Bessel series approximation. The exponential phase term was replaced with a linear combination of rescaled Bessel functions with complex-valued coefficients for improved computational efficiency. PSFs were generated in 3D as 1,600 × 1,600 × 2,200 images at 1 nm/pixel and 2 nm/z-step with 1.4 NA, 520 nm emission wavelength, 1.5 specimen refractive index, and 1.5 glass refractive index.

For 500-nm beads, a sphere with a 500-nm diameter was simulated with 500,000 fluorophores with the radial distances of the fluorophores following different probability distribution functions. For Gaussian 50 and Gaussian 80, the fluorophore radial distances followed the above Gaussian probability distribution function centered at μ_r = 0 with σ_r = 50 and 80, respectively. For the Sigmoidal distributions, the fluorophore radial distances followed the above Sigmoidal probability distribution function with Sigmoidal 60 having A = 0.75, μ_r = 125, and s = 60 and Sigmoidal 30 having A = 0.5, μ_r = 125, and s = 30.

For 100-nm beads, a sphere with a 100-nm diameter was simulated with 1,800 fluorophores with the radial distances of the fluorophores following different probability distribution functions. For Gaussian 50 and Gaussian 80, the fluorophore radial distances followed the above Gaussian probability distribution function centered at μ_r = 0 with σ_r = 10 and 20, respectively. For the Sigmoidal distributions, the fluorophore radial distances followed the above Sigmoidal probability distribution function with Sigmoidal 12 having A = 0.75, μ_r = 25, and s = 12 and Sigmoidal 8 having A = 0.5, μ_r = 25, and s = 8.

Hec1 was simulated as a 3D rectangle with a width, length, and height of 70, 400, and 400 nm, respectively. The distance between adjacent fluorophores along the length of Hec1 was assumed to be 50 nm and along the width to be 10 nm. PSFs were generated as described above and a 3D image stack was created with 200-nm Z steps centered around the object at the origin (0,0,0). The plate was then rotated around either the X or Y axis at angles between 0 and 60° and the FWHM measurements were quantified using 3D-Speckler.

All statistical tests for significance between two conditions were performed using two-tailed t-tests. All statistical tests for significance amongst multiple conditions were performed using one-way ANOVA. We denote P < 0.05, P < 0.01, and P < 0.001 as *, **, and ***, respectively.

Fig. S1 shows 3D-Speckler features and FWHM size measurements. Fig. S2 shows experimental and theoretical validation of 3D-Speckler size measurements. Fig. S3 shows validation of the 3D-Speckler local background correction algorithm and visualization of field dependency plots. Fig. S4 shows 3D-Speckler local CA correction and biological application.

We would like to thank Drs. Benjamin Gilles, Colleen Lavin, Nathan Claxton, Hiroshi Nishida, Yoshitaka Sekizawa, Anjon Audhya, John Galli, Lance Rodenkirch, the University of Wisconsin Optical Imaging Core, SMPH Shared Services IT, Yokogawa Electrical Corporation, Nikon Japan, and Nikon USA for critical equipment and technical support. We also would like to thank Drs. William Sugden, Arthur Sugden, and Beth Weaver for the critical reading of this manuscript. We thank all reviewers for providing valuable suggestions, particularly reviewer #2 for suggestions exploring the effects of fluorophore distribution on the different FWHM measurements. We also thank Ying Lin for help with part of Fig. 8 B.

Part of this work is supported by National Institutes of Health grant NIGMS R35GM147525, Wisconsin Partnership Program, and start-up funding from University of Wisconsin-Madison School of Medicine and Public Health, University of Wisconsin Carbone Cancer Center, and McArdle Laboratory for Cancer Research (to A. Suzuki).

Author contributions; J. Loi developed the software and simulations with guidance by A. Suzuki. J. Loi, X. Qu, and A. Suzuki performed experiments and data analysis. A.Suzuki designed and supervised the research. J. Loi and A. Suzuki drafted the manuscript. All authors revised and contributed to the manuscript.