# Ultrafast data mining of molecular assemblies in multiplexed high-density super-resolution images

Bioinformatics

### Simulation

The simulations in this work were performed as following (unless specifically stated otherwise): We randomly positioned and orientated the designed triangular configurations onto the canvas, and assigned the vertexes as the positions of the “molecules”. Around each of these “molecules”, we simulated the SMLM data by generating multiple localization coordinates that subject to a 2D-Gaussian distribution centering at each of the “molecules” and broadening with the experimental localization precision as the standard deviation (σ) of the Gaussian profile.

### Sample preparation

U2OS cells (ATCC HTB-96) were passaged onto glass coverslips and grown in DMEM (ThermoFisher 11965092) with 10% FBS (Gemini Bio 100-106) and 100 U/mL Penicillin-Streptomycin (ThermoFisher 15140) for 24–48 h until established. Cells were then synchronized to S-phase, via 72 h Serum withdrawal followed by 17 h incubation in full media. A concentration of 20 μM Hydroxyurea and EdU was introduced 2 h and 15 min, respectively, prior to the end of the 17 h incubation for experiments in Fig. 3 and Supplementary Figure 3; Aphidicolin was introduced 1 h prior to the end of the 17 h incubation for experiments in Fig. 4 and Supplementary Figure 4. U2OS cells were then permeabilized with 0.5% Triton in CSK buffer (10 mM Hepes, 300 mM Sucrose, 100 mM NaCl, and 3 mM MgCl2, pH = 7.4) for 10 min, and fixed with paraformaldehyde (4%) for 30 min. The cells were then rinsed with PBS and incubated in blocking buffer (2% glycine, 2% BSA, 0.2% geltin, and 50 mM NH4Cl in PBS) overnight at 4C. EdU was tagged with Alexa Fluor 647 picolyl azide through click reaction kit (ThermoFisher, C10640). RPA was stained by either Rabbit anti-RPA antibody (Abcam, ab79398) for 1 h at 1:1000 dilution at room temperature, followed by Alexa Fluor 750-conjugated anti-Rabbit antibody (ThermoFisher, A-21039) for 0.5 h at 1:10,000 dilution at room temperature (for experiments in Supplementary Figure 3), or Alexa Fluor 647 conjugated anti Rabbit antibody (Abcam, ab199240) for 1 h at 1:1000 dilution at room temperature (for experiments in Fig. 4 and Supplementary Figure 4). PCNA was immunostained by Alexa 488 conjugated anti-PCNA antibody (Abcam, ab201672) and MCM was immunostained by Alexa 568 conjugated anti-MCM antibody (Abcam, ab211916). Both antibodies were incubated for 1 h at 1:1000 dilution at room temperature. The fixed U2OS cells were then mounted onto microscope glass for single-molecule localization imaging in freshly mixed imaging buffer (1 mg/mL glucose oxidase, 0.02 mg/mL catalase, 10% glucose, and 100 mM cycteanube (MEA)).

### Optical setup and image acquisition

The single-molecule localization imaging was performed on a customized Leica DMI 300 inverse microscope. A 750 nm laser (UltraLaser, MDL-III-750-500), 639 nm laser (UltraLaser, MRL-FN-639-800), 561 nm laser (UltraLaser, MGL-FN-561-200), and 488 nm Laser (OBIS) were aligned and reflected into an HCX PL APO 63X NA = 1.47 OIL CORR TIRF Objective (Zeiss) by a penta-edged dichroic beam splitter (FF408/504/581/667/762-Di01-22 × 29). The 488, 561, 639, and 750 laser lines were adjusted to ~0.8, 1.0, 1.5, and 0.4 kW/cm2. A 405 nm Laser line (MDL-III-405-150, CNI) was also equipped to reactivate Alexa Fluor 647 fluorophores. The cell samples were sequentially illuminated, and their emitted fluorescence was also sequentially collected with single-band fluorescence filter switched in a filter wheel accordingly. In brief, the emitted fluorescence was collected by the same objective and further magnified by a 2X lens tube (Diagnostic Instruments). The fluorescence was then filtered by a single-band filter (Semrock FF01-531/40, FF01-607/36, and FF01-676/37 for Alexa Fluor 488, Alexa Fluor 568, and Alexa Fluor 647, respectively) and a chromatic aberration correction lens (AC254-300-A, Thorlabs), and collected by a sCMOS camera (Photometrics, Prime95B) at 33 Hz. 2000 frames were recorded for each color in each image stack. In particular, considering the patterned sCMOS camera, the readout noise of each pixel camera was pre-calibrated, and characterized by a Gaussian distribution. The expectation, variation, and the analog-to-digital conversion factor of such calibrations of each pixel was used in single-molecule localization as described in the Single-Molecule Localization section.

### Alignment of images from different colors

Aligning images from different colors was performed by separately mapping blue (488), green (568), and dark red (750) onto the red (639) channel, using a 2nd polynomial mapping algorithm. In brief, broad-spectrum fluorescent beads (Diameter ~ 100 nm, TetraSpec, Thermofisher, note that the 750-channel mapping was accomplished by illuminating such beads using the 561 nm laser to collect sufficient signal-to-noise ratio of the bead images) were imaged on all the four-color channels. The mass centers of the same bead were recorded as vectors (left{ {x_i^{{mathrm{CHX}}},y_i^{{mathrm{CHX}}}} right}), where i denotes the i-th bead and CHX denotes the X-th channel, and submitted for 2nd polynomial optimization of the transform coefficient (left{ {K_j^{left( x right)}} right}) and (left{ {K_j^{left( y right)}} right}).

$$x_i^{{mathrm{CHR}}} = mathop {sum }limits_{j = 0}^8 K_j^{left( x right)}left( {x_i^{{mathrm{CHX}}}} right)^lleft( {y_i^{{mathrm{CHX}}}} right)^m$$$$y_i^{{mathrm{CHR}}} = mathop {sum }limits_{j = 0}^8 K_j^{left( y right)}left( {x_i^{{mathrm{CHX}}}} right)^lleft( {y_i^{{mathrm{CHX}}}} right)^m,$$

where (l = leftlfloor {j/3} rightrfloor) is the maximum integer smaller than j/3 and (m = j – 3leftlfloor {j/3} rightrfloor) is the modulo of j/3; CHX denotes the channels other than the Red (reference) channel.

The optimized coefficient of the polynomial function was then applied to align the Blue, Green, and Dark Red real sample images to the Red channel. We note that higher-order polynomial regression might result in better optimization, depending on the optical alignment and chromatic aberration of the experimental microscope setup. Higher than 2nd order regression in this study could cause overfitting. We also note that this polynomial regression sufficiently reduced the chromatic aberration in our measurements (Supplementary Figure 6).

### Single-molecule localization

Each frame from an image stack was first box-filtered with the box size of 4 times of the FWHM of a 2D Gaussian PSF. We note that each pixel was weighted by the inverse of its variation during such box-filtering. The low-pass filtered image was then extracted from the raw image, followed by recognition of local maximums. The local maximums from all the frames of the image stack were then submitted for 2D-Gaussian single-PSF fitting.

The 2D-Gaussian single-PSF fitting were performed in GPU (Nvidia GTX 1060, CUDA 8.0) using the Maximum Likelihood Estimation (MLE) algorithm. In brief, the likelihood function at each pixel was built by convolving the Poisson distribution of the shot noise governed by the photons emitted from fluorophores nearby, and the gaussian distribution of the readout noise that characterized by the expectation, variation, and the analog-to-digital conversion factor that pre-calibrated as mentioned above. The fitting accuracy was estimated by Cramér-Rao lower bound (CRLB).

### Code availability

Codes for the dTC and dPC algorithms, as well as a testing demo (with simulation codes) are available at https://github.com/yiny02/direct-Triple-Correlation-Algorithm. The code is for Research and Educational Purposes for Non-Profit Academic and/or Research Institutions.

### Reporting Summary

Further information on experimental design is available in the Nature Research Reporting Summary linked to this article.