Toward drift-free high-throughput nanoscopy through adaptive intersection maximization (2024)

Hongqiang Ma, Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing,^1,2,* Maomao Chen, Software,¹ Phuong Nguyen, Resources,^1,2 and Yang Liu, Conceptualization, Data curation, Funding acquisition, Project administration, Resources, Supervision, Validation, Writing - original draft, Writing - review & editing^1,3,*

General principle of AIM

In SMLM, one super-resolution image is composed of a set of localization coordinates for fluorescent emitters acquired during a long period of image acquisition, spanning tens of thousands of frames to accumulate a sufficient number of localizations. In such a dataset, it is common for multiple localizations to originate from the same emitters, recorded across various temporal instances. Ideally, in a drift-free system, the coordinates of these localizations originating from the same emitters can be repeatedly detected in multiple image frames acquired at different time points and should be “intersected” within a threshold distance determined by localization precision, as illustrated in Fig. 1. The spatial drift reduces the number of these intersected localizations obtained at different time points, thus resulting in a lower number of intersected localizations.

AIM introduces a drift correction approach by maximizing the intersection of localization pairs across temporally distinct datasets (Fig. 1A), enabling accurate estimation of spatial drift. Conventional methods partition the entire dataset into many (n) temporally segmented blocks (Fig. 1B), using the partial subset as the reference for registration across blocks via image correlation (8) or entropy minimization (10). While effective, these methods are limited by their dependence on the partial data (1/n of the entire dataset), which can compromise their robustness and precision, especially for high-frequency drift where the number of localizations at each temporal segment is low. AIM addresses these limitations via a two-stage adaptive processing strategy. The initial stage generates a preliminary drift estimated by maximizing the intersection of localizations across temporal segments (Fig. 1A). Following this, the entire dataset, now preliminarily corrected for drift, is used as a new reference for a second, more refined stage of drift estimation (Fig. 1B). This process retains the full information content of the entire dataset and enhances the precision and robustness.

Moreover, distinct from complex image-based correlation or other optimization methods, AIM, centered around the counting of intersected localization points, stands out for its computational efficiency and robustness. Figure S1 further illustrates that the precision of drift tracking is enhanced with the increase in the image size and the number of intersected localizations, attributing to the greater information content leveraged.

Numerical simulations

We first benchmarked the performance of AIM using simulated datasets that mimic a typical dataset captured by high-throughput localization microscopy, which contains 26 million localizations from 20,000 images with an image size of 2048 × 2048 pixels and a pixel size of 100 nm. In comparison with the ground truth, the most commonly used drift correction algorithm, RCC (8), and the recently reported state-of-the-art algorithm, DME (10), we demonstrated the impact of correcting high-frequency drift (>0.5 Hz) on image resolution. As shown in Fig. 2, our result showed that AIM can precisely track both high-frequency and slow-varying drift (Fig. 2, F to H) with a subsecond tracking interval (0.2 s or 20 frames), which results in a sub-angstrom residual drift error (~0.09 nm). In contrast, for the same dataset, RCC can only use low tracking frequency (every 2000 frames) to track the slow-varying drift, which is mainly limited by the large memory consumption of RCC. As the RCC algorithm estimates the drift by calculating the correlation efficiency map of the temporally segmented super-resolution images, it requires a large amount of random-access memory (RAM) (up to ~40 GB with 10 segments or every 2000 frames used in this study) to cache a series of the temporally segmented super-resolution images with a high-performance computation platform. On the other hand, DME can use a higher tracking frequency (every few frames) to achieve a high tracking precision (10) for high-frequency drift. However, because of insufficiently accurate initial estimates from RCC, DME sometimes fails to converge to global minima. Both compromised tracking frequency in RCC and limited robustness in DME result in a larger drift correction error (35 and 22 nm, respectively), making them difficult to identify the ultrafine structures spaced at 10 nm apart. In addition, DME and RCC require a large memory size and long computational time (Fig. 2I) to handle the large localization set generated from the high-throughput localization microscopy. In contrast, AIM is a localization coordinate-driven algorithm, and it only uses small RAM (<4 GB) to store the localization coordinates and is rather computationally efficient for big SMLM datasets without the need for high-end computational resources.

We also evaluated the drift tracking precision and computation speed of AIM in various scenarios (e.g., tracking frequency, emitter density, spatial resolution, and magnitude of drift), as shown in fig. S2. We found that for a high tracking frequency (5 Hz), higher emitter density and spatial resolution help to improve the tracking precision of AIM. However, their influence becomes minimal for lower tracking frequencies. We also note that the tracking precision starts to deteriorate at a very high tracking frequency (10 Hz), due to the reduced number of emitters for each drift subset used in the first-stage drift estimation. On the other hand, the tracking precision is largely affected by a lower tracking frequency when the magnitude of drift is large. At a high tracking frequency (e.g., 2 Hz), the tracking precision remains subnanometer scale regardless of the magnitude of system drift. This result suggests that a high tracking frequency is critical for maintaining a robust performance of drift correction. Last, as the tracking frequency increases, the computation time increases with higher emitter density and tracking frequency. The scenarios within the lines in fig. S2 are those that can achieve computation speed faster than the data acquisition speed at subnanometer precision. It should be noted that for a high tracking frequency of 2 Hz or more, the precision of 0.1 nm can be achieved for moderate emitter density and spatial resolution in SMLM.

Experimental high-throughput DNA-PAINT imaging of DNA origami

We next validated the performance of AIM in super-resolution imaging of DNA origami. As shown in Fig. 3, AIM-based drift correction provides an optimized resolution of 16 nm, which is improved by 28 and 41 nm compared to those corrected by DME and RCC, consistent with our simulation results. The tracking interval for RCC and DME is set to be 2000 frames and 2 frames, respectively, limited by the memory of our workstation and from the recommended settings (8, 10). The three-line patterns of DNA origami spaced at 40 nm apart are clearly visible in the image corrected by AIM but not in those corrected by DME or RCC. It is of note that the computation speed for AIM is also the fastest (140 s), especially compared to the computationally intensive DME (~7 hours).

Experimental high-throughput STORM imaging of cell and tissue section

We further illustrated the improved image resolution of AIM-based drift correction on biological cells on image resolution of biological cells. Figure 4 shows the reconstructed stochastic optical reconstruction microscopy (STORM) images of CCCTC-binding factor (CTCF) structure in MCF10A cells. AIM-based drift correction improves the Fourier-ring correlation (FRC) resolution of reconstructed STORM images by 8 and 19 nm, compared to DME and RCC approaches, respectively. Given the lack of ground truth in the biological samples, as shown in Fig. 4 (E to H), the STORM image reconstructed from the first half of localizations in the temporal dimension (green) is compared with a second STORM image reconstructed from the second half of localization points (red). Given the same labeled targets, in a drift-free system, these two STORM images should show the highest colocalization rate. As shown in Fig. 4 (F to H), the two STORM images with AIM-based drift correction show the best colocalization with an average colocalization rate of 52%, significantly better than that of DME (35%) and RCC (26%). AIM also achieves the smallest colocalization error (1 nm) compared to those without drift correction (46 nm) and with DME (12 nm) and RCC (21 nm). The colocalization error here is defined as the relative distance between the two clusters. The global colocalization ratio is defined as the number of co-occurrences of localizations from two channels within a distance less than the localization precision, divided by the total number of localizations. This result further demonstrated the improved resolution for AIM together with its computational efficiency (150 s), over other drift correction methods (DME, 9 hours) and RCC (350 s).

Figure 5 shows the super-resolution image of heterochromatin from a colon tissue section after AIM-based drift correction. AIM-based drift correction improves the image resolution defined by FRC by 24 nm (from 45 to 21 nm), compared to RCC. The recovered system drift trajectory by AIM clearly shows the presence of both high-frequency and low-frequency drift, while RCC shows only the recovered low-frequency drift trajectory.

AIM can also be applied in three-dimensional (3D) high-throughput SMLM images. As shown in Fig. 6, by correcting both high-frequency and low-frequency drift, AIM improves the image resolution by 8 nm from 35 to 27 nm. Note that DME cannot handle large datasets with more than 30 million localizations (data used for Figs. 5 and ​and6)6) on our computer due to its high computational complexity. AIM uses a standard consumer-level computer and does not require a high-end computation platform (e.g., graphics processing unit (GPU) and high memory requirement) to achieve this performance. Therefore, AIM meets the big-data demand for a high-throughput high-content SMLM system with a large imaging field of view (FOV) that generates hundreds of millions of molecules in a single SMLM data (16–18).

Algorithm of AIM

For SMLM, the spatial drift can be considered as a 3D translational motion (8, 10). A super-resolution image consists of a set of localized fluorescent emitter coordinates C = {p(x₁, y₁, z₁, t₁), …p(x_m, y_m, z_m, t_m)} acquired at different time throughout the entire imaging process, where x, y, and z are each emitter’s spatial coordinates, t is the emitter’s temporal position, and m is the total number of localizations for the entire dataset. In a drift-free system, those localized emitters originating from the same sets of emitters should “intersect” within a threshold distance D determined by localization precision (σ) (Fig. 1). Drift reduces the number of intersected emitters. By maximizing the number of intersected emitters between the temporally separated segments, their relative shift can be estimated. However, because each temporal segment only contains a small portion of all localized points (m/n), the estimated drift often lacks sufficient accuracy. AIM uses a two-stage processing. The initial stage estimates a preliminary drift to compensate the entire dataset, which is used as a new reference for a second, more refined stage of drift estimation. During this second phase, the now drift-corrected reference set, which retains the complete dataset information, facilitates the identification of the maximal number of intersected localizations. This process allows for enhanced precision and robustness in the drift estimation. The detailed procedures are described below.

1) We first partition all localized emitters (C) into n temporally segmented subsets (C₀, C₁… C_n−1) where each temporal subset contains a specified number of image frames with approximately 1/n of all localized emitters, acquired within a certain temporal interval T (e.g., 20 image frames at an exposure time of 10 ms within a time interval T = 0.01 ×20 = 0.2 s). The first (initial) temporal subset coordinate (C₀) is referred to as the reference subset (C_r), and the subsequent subsets (C₁, C₂… C_n−1) are denoted as the drift subsets.

2) Next, we describe how to identify the relative drift between the reference subset (i.e., C_r = C₀) and a drift subset C_d (e.g., C_d = C₁ for the first drift subset), by calculating the peak shift position on an intersected shift-map [I(d)]. When the distance of the localized coordinate pairs (d) from the reference subset and the shifted subset is less than a threshold D (e.g., 20 nm), this pair is considered as intersected. The intersected shift-map is created by calculating the number of the intersected coordinate pairs between the reference subset (C_r) and a shifted subset (C_s), denoted as I(d) = n(C_r ⋂ C_s). To create a shifted subset (C_s), the coordinates of the drift subset C_d are shifted with a step size of D in a local region with a radius of R, where R should be larger than the maximum drift between two adjacent subsets (e.g., 60 nm). Then, the peak position with shift vector Si→=dix,diy,diz is calculated on the intersection shift-map via the computationally simple and fast Fourier harmonic analysis (20) to determine the drift.

3) For the next subset (C_i+1) (e.g., C₂), the previously determined drift Si→ is corrected to obtain an adaptively drift-corrected subset (Cd=Ci+1−Si→), which is used as an updated C_d to find the shift vector Si+1→ for the next temporal subset as described in step 2. Here, instead of finding the relative shift between the reference set and all of the temporal subsets, we use an adaptively updated drift-corrected subset C_d from C_i+1 based on the drift estimation from the prior subset C_i to find the shift vector (Si+1→) for the next adjacent temporal subset (C_i+1). Thus, drift tracking for each subset (C_i+1) is equivalent to measuring its relative drift by referencing its prior subset (C_i). This adaptive approach has two key advantages. First, it transforms the long time interval drift into short time interval drift relative to the adjacent temporal subset that often has a small drift distance, thus substantially reducing the searching region of intersection shift-map. Second, it can largely reject the false-positive peaks of the intersection shift-map, thus enhancing the robustness of the drift estimation. The same process is repeated for the rest of the drift subsets (e.g., C₃,…C_n−1).

4) On the basis of the estimated discrete drift positions at each time interval T, the time points within each interval T can be estimated by cubic spline interpolation. Then, we can subtract the estimated drift positions at each image frame to get the drift-corrected localization dataset C_dc. The first stage drift correction is composed of steps (1 to 4). As its calculation is based on a comparison of the temporally separated subset with partial localizations (m/n), the intersection shift-map usually has a limited signal-to-noise ratio, thus reducing the precision for drift estimation.

5) To achieve an improved precision, we apply a second-stage drift correction by taking advantage of the full dataset. The entire drift-compensated dataset C_dc determined above in the first stage is updated as the new reference (C_r = C_dc) used in the second stage. We then again partition the drift-compensated localization dataset C_dc into n subsets as the drift subsets (C_dc1, C_dc2… C_dcn) at the same temporal interval T as stage 1 and repeat steps (2 to 4) as described above to precisely estimate the residual drift for the entire dataset. As the second stage uses a new reference set (roughly corrected reference set) that now contains all localizations (m), the robustness and precision for the second-stage drift estimation are much improved.

High-throughput SMLM imaging

The instrument setup for the high-throughput SMLM system is shown in fig. S8. A high-power 638-nm excitation laser (2 W) was used as the light source, coupled into a fast-vibrating multimode fiber (M97L02, Thorlabs) to generate flat-field illumination. A TIRF objective lens (UPlanApo 60×/1.50 oil HR, Olympus) was used for DNA-PAINT imaging, and an oil-immersion objective lens (UPlanXApo 60×/1.42 oil, Olympus) was used for STORM imaging experiments. The sample was mounted on a three-axis high-precision piezo motor linear stages (Agilis Piezo Motor series, Newport) with a travel distance of 12 mm for both lateral and axial movement. The fluorescence signals were collected by scientific complementary metal-oxide semiconductor cameras (Hamamatsu ORCA-Flash4.0). The pixel size corresponding to the sample plane was ~100 nm, thus providing a FOV of ~200 μm by 200 μm. In addition, an 850-nm laser (CPS850S, Thorlabs) was used as the light source coupled with the linear CCD (LC100, Thorlabs) and piezo focusing stage (Nano-F100, MadCityLabs) for focus locking (21). We used the redundant array of independent disks storage system (LaCie 12big Thunderbolt 3) for high-speed acquisition and storage of large image data. We used an illumination power intensity of ~4 kW/cm² for all DNA-PAINT and STORM imaging experiments in this study. For the DNA-PAINT imaging experiment (Fig. 3), an exposure time of 50 ms was used, and for other STORM imaging experiments of cells and tissue sections, an exposure time of 20 ms was used for each frame.

Numerical simulation

The simulated data shown in Fig. 2 were generated to mimic DNA origami structures with 25 target sites spaced 10 nm apart in the lateral dimension, distributed in three dimensions. The DNA origami structures were distributed with an axial position range from −400 to 400 nm with a random uniform distribution. The blinking events for each molecule follow a uniform random distribution with an on/off ratio of 1:120. We quantified tracking precision and computation time under different tracking frequencies for various imaging conditions including localization density, localization precision, and the magnitude of system drift. The selection of these imaging parameters is justified below.

Performance benchmarking

We benchmarked the performance of AIM by comparing it with two state-of-the-art drift correction methods including one of the most commonly used RCC (8) and the recently reported state-of-the-art DME (10). A workstation (Dell) equipped with a multicore central processing unit (CPU) (Intel Core i7-11700) and 64 GB of RAM was used for high-speed data processing. For fair comparison results, we performed different algorithms on the same computer with MATLAB R2020 using CPU devices. The drift tracking precision in this study is defined as the SD of the tracking error between the estimated drift and the ground truth value. For the high-throughput SMLM dataset with an image size of 2048 by 2048 pixels, we used 20 frames per bin for AIM, 2000 frames per bin for RCC, and 2 frames per bin for DME. The number of frames per bin for RCC was limited by the size of the memory available on the computer. RCC and DME used approximately 40GB of memory in the computation process. Our computer cannot handle a large dataset with over 30 million localizations for DME. Both the pixel size of the cross-correlation map used in RCC and the intersection distance used in AIM were set to 20 nm.

For single-molecule localization, our previously reported algorithm (20, 22, 23) was used to achieve a computation speed of ~2 million localizations/s on the same computer as described above. To calculate FRC resolution (24), we evenly split the entire localization dataset into two subsets along the temporal dimension, the two super-resolution images reconstructed using each subset were used to calculate the FRC resolution.

Design, self-assembly, and purification of DNA origami

The design of DNA origami structures was done using the design module of Picasso (25). Backbone staples, docking staples, and biotinylated staples were purchased from Integrated DNA Technologies, Inc. The DNA origami structures were self-assembled in one reaction mixture in 1× Tris-EDTA buffer supplemented with 12.5 mM MgCl₂. The components included 10 nM M13 bacteriophage single-stranded DNA scaffold p7249 (New England BioLabs, N4040S), 250 nM folding staples, 250 nM biotinylated staples, and 250 nM DNA-PAINT docking strands. The mixture was heated at 80°C for 5 min, followed by 65°C for 15 min to denature scaffold and staples strands before being subjected to a thermal gradient from 60° to 4°C (3 min 12 s/°C) using a thermocycler (Bio-Rad, T100TM Thermal Cycler) for annealing these staples strands to their complementary segments on the scaffold, resulting in folding the DNA origami into the designed shape.

The self-assembled DNA origami mixtures were ultrafiltrated using small-scale molecular weight cutoff membranes for damage-free, native purification, and enrichment of DNA origami from excess strands (26). Briefly, the reaction mixtures were added into the Amicon Ultra 0.5-ml filters with 50-kDa molecular cutoff membranes (Merck/EMD Millipore, UCF505096), spun for three times at 10,000 relative centrifugal force, 5 min each in 1× FoB5 buffer (5 mM tris base, 1 mM EDTA, 5 mM MgCl₂, and 5 mM NaCl). The purified and concentrated DNA origami were collected and stored at −20°C.

Sample preparation for imaging DNA origami structure

To prepare DNA origami for imaging, a coverslip (Thermo Fisher Scientific, no. 1.5, 22 mm by 22 mm, 12541B) as the substrate was attached to another piece of cover glass (Corning, no. 1.0, 18 mm by 18 mm, 2845-18) via double-sided tape to create a ~20-μl flow chamber. In our chamber, a 20 μl of biotinylated bovine albumin (1 mg/ml; Sigma-Aldrich, A4503) in buffer A [10 mM tris-HCl, 100 mM NaCl, and 0.05% (v/v) Tween 20 at pH 8.0] were incubated for 5 min and then washed with 100 μl of buffer A. Then, 20 μl of streptavidin (0.5 mg/ml; Thermo Fisher Scientific, S888) in buffer A flowed into the chamber and then incubated for 5 min for biotin-streptavidin interaction. After coating the coverslip with biotin-streptavidin, the chamber was washed with 100 μl of buffer A, followed by 100 μl of buffer B [5 mM tris-HCl, 10 mM MgCl₂, 1 mM EDTA, and 0.05% (v/v) Tween 20 at pH 8.0] before adding purified DNA origami structures in buffer B for 10 min of incubation. A 100 μl of buffer B was then flown into the chamber for final washing. Nanodiamond (Adámas Nano, NDNV140nmPMO) at 1/10,000 dilution in buffer B was added into the chamber and incubated for 10 min as fiducial markers for drift correction in SMLM. Last, the chamber was filled with an imaging buffer containing 5 nM ATTO647N-labeled P1 imager (IDT) in buffer B (25) and then sealed with epoxy (Gorilla Glue Epoxy, 5 min). The chamber was stored at 4°C until imaging.

Immunofluorescence staining for cultured cells and tissue section

For immunofluorescence staining, cells were fixed with 4% paraformaldehyde for 15 min and permeabilized with 0.2% Triton X-100 for 10 min. For the tissue section, the 3-μm-thick tissue sections from formalin-fixed paraffin-embedded (FFPE) tissue blocks were mounted on the poly-d-lysine–coated coverslips, deparaffinized in xylene, and rehydrated in graded ethanol and lastly in distilled water. The antigen retrieval was performed as previously described (27). The samples were incubated with primary antibodies (CTCF, #ab70303; H3K9me3, #ab5408, Abcam) diluted to optimized concentration at 4°C overnight. Alexa Fluor 647–conjugated goat anti-rabbit secondary antibody was applied to the sample at room temperature for 2 hours in the dark. The samples was washed again three times with washing buffer and once with phosphate-buffered saline (PBS) for 5 min per wash and stored in PBS before imaging. The imaging buffer was added into the sample dish right before imaging.

STORM imaging buffer

STORM imaging buffer for cultured cells contains 10% (w/v) glucose (Sigma-Aldrich), glucose oxidase (0.56 mg/ml; Sigma-Aldrich), catalase (0.17 mg/ml; Sigma-Aldrich), and 0.14 M 2-mercaptoethanol (βME, Sigma-Aldrich). For the formalin-fixed paraffin-embedded (FFPE) tissue section, to reduce the high background caused by the strong scattering of pathological tissue, an optical clearing process was conducted before imaging by immersing the sample in 60% (v/v) 2,2′-thiodiethanol (TDE) for 20 to 30 min to make the sample transparent (27). For the STORM imaging buffer of FFPE tissue section, 60% (v/v) TDE solution was used instead of water to match the tissue’s index and contains 10% (w/v) glucose (Sigma-Aldrich), glucose oxidase (0.56 mg/ml; Sigma-Aldrich), catalase (0.17 mg/ml; Sigma-Aldrich), 0.14 M βME (Sigma-Aldrich), and 0.2 mM cyclooctatetraene (Sigma-Aldrich). The imaging buffer was added to the sample dish right before imaging.

We acknowledge J. Xu for providing the imaging data used in Fig. 4.

Funding: This work was supported by National Institutes of Health grant R01CA254112, National Institutes of Health grant R01CA232593, and National Institutes of Health grant R21CA259787.

Author contributions: Conceptualization: H.M. Methodology: H.M. Investigation: H.M. Formal analysis: H.M. and M.C. Resources: P.N. Visualization: H.M. and Y.L. Project administration: Y.L. Writing—original draft: H.M. Writing—review and editing: H.M. and Y.L.

Competing interests: H.M. and Y.L. have a pending patent application (PCT International application no. PCT/US2023/078142) filed by the Office of Technology Management at the University of Pittsburgh in October 2023. The authors declare that they have no other competing interests.

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