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4polar-STORM polarized super-resolution imaging of actin filament organization in cells.

Rimoli Caio Vaz, Valades-Cruz Cesar Augusto, Curcio Valentina, Mavrakis Manos, Brasselet Sophie

📰 Nature communications 📅 2022 📊 81 citations

Abstract

Abstract Single-molecule localization microscopy provides insights into the nanometer-scale spatial organization of proteins in cells, however it does not provide information on their conformation and orientation, which are key functional signatures. Detecting single molecules’ orientation in addition to their localization in cells is still a challenging task, in particular in dense cell samples. Here, we present a polarization-splitting scheme which combines Stochastic Optical Reconstruction Microscopy (STORM) with single molecule 2D orientation and wobbling measurements, without requiring a strong deformation of the imaged point spread function. This method called 4polar-STORM allows, thanks to a control of its detection numerical aperture, to determine both single molecules’ localization and orientation in 2D and to infer their 3D orientation. 4polar-STORM is compatible with relatively high densities of diffraction-limited spots in an image, and is thus ideally placed for the investigation of dense protein assemblies in cells. We demonstrate the potential of this method in dense actin filament organizations driving cell adhesion and motility.

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📋 Methods

✔ Verified methods section 2,598 words Read on PMC ↗

4polar-STORM optical setup

Measurements are carried out on a custom total internal reflection (TIRF) fluorescence microscope, whose detection path is adapted to retrieve four-polarization states of the single-molecule fluorescence images. The excitation light source is a continuous laser emitting at 488 nm (Sapphire 488LP-200, Coherent), whose beam is expanded by a telescope and polarized by a quarter waveplate (AQWP10M-580, Thorlabs) oriented such as to obtain close-to isotropic excitation in the sample plane. A set of mirrors reflect the beam towards the microscope, followed by a large focal length lens ( f = 400 mm) to focus the beam in the back focal plane of the objective, to provide an illumination field of view with a diameter of about 100 μm. After the reflection on a dichroic mirror (DI02-R488, Semrock Rochester NY), the excitation light is focused onto the sample by an oil immersion objective lens (Plan Apo ×100, NA = 1.45, Nikon). The emitted fluorescence is collected back by the same objective lens, passes through the dichroic mirror and a band pass emission filter (FF01-525/40, Semrock Rochester NY). At the microscope exit a non-polarizing beam splitter separates the beam into two paths, each of them being built up with a 1x relay imaging telescope that uses two (f 150 mm) lenses. In the first path, a Wollaston prism (separation angle 5°, CVI Laser Optics) is placed at the back focal intermediate image plane, aligned for 0–90° polarization split. In the second path, a similar Wollaston prism is placed just after an achromatic half-wave plate (AHWP05M-600, Thorlabs), to provide 45–135° polarized images. The two beams are recombined by a mirror reflection of the first path, and refocused on the EMCCD camera detection plane (iXon Ultra 888, Andor, 13 μm pixel size), such as to fill the CCD chip with four polarized images. The size of the images is set by a diaphragm placed in the first image plane at the exit of the microscope (typical image field of view, 40 μm × 40 μm). In addition, two diaphragms are placed in intermediate planes conjugated to the back focal plane of the objective in order to reduce the detection numerical aperture to NA det = 1.2. The imaging lens provides a total magnification of ×100, corresponding to a pixel size of 130 nm on the EMCCD. The stability of the focus throughout the measurement is ensured by a commercial system (Perfect Focus System, Nikon). For initial positionning, the sample is mounted on a XYZ piezo stage (Physik Instrumente). The acquisition parameters are controlled by a commercial imaging software (AndorSolis, Andor). For STORM imaging, a first fluorescence image is recorded with low intensity (~500 W/cm 2 , below STORM blinking conditions), ensuring the identification of relevant parts of the sample. The intensity is then raised to 5–8 kW/cm 2 , which is a typical level to provide a good compromise between signal level and blinking rate. The images are acquired at a rate of 100 ms/image, camera gain 300, with a total of about 30,000 images depending on the molecular density. The polarized path of the 4polar-STORM setup was calibrated as detailed in Supplementary Note 2 . We ensured that all directions in the sample plane could be detected with identical efficiency and precision by rotating a polarizer at the back focal plane of the collection objective, analyzing the emission from isolated nanobeads (100 nm size yellow-green Carboxylate-Modified FluoSpheres, ThermoFisher Scientific F8803, immobilized on the surface of a poly-L-lysine coated coverslip and covered with a mounting medium Fluoromount, Sigma F4680). On average, ρ values were pointed with a few degrees precision with respect to the expected polarizer direction, and δ values range from 20° to 33°. Cell culture 4polar-STORM measurements were made in U2OS osteosarcoma cells (Figs. 1 – 4 ) and B16-F1 mouse melanoma cells (Fig. 5 ). Naive U2OS cells (gift from Flavio Maina, IBDM, France) were used for assessing the effect of blebbistatin. U2OS CA-MLCK cells (gift from Sanjay Kumar, UC Berkeley, USA) cultured in 0 ng/mL doxycycline were used for all other experiments. U2OS cells were originally from ATCC (HBT-96). U2OS cells were maintained in McCoy’s 5 A medium (ThermoFisher Scientific, 26600-080) supplemented with 10% fetal bovine serum (Biowest, S181H), 100 U/mL penicillin and 100 μg/mL streptomycin (Sigma, P4333) in a humidified incubator at 37 °C and 5% CO2. B16-F1 cells (gift from Klemens Rottner, Technische Universität Braunschweig, Germany) were cultured in DMEM (ThermoFisher Scientific, 41966-029) supplemented with 10% fetal bovine serum (PAA Laboratories, A15-102), 100 U/mL penicillin and 100 μg/mL streptomycin (Sigma, P4333) in a humidified incubator at 37 °C and 5% CO2. B16-F1 cells were originally from ATCC (CRL-6323). Cell preparation for 4polar-STORM. U2OS cells 24 mm-diameter high-precision (170 μm ± 5 μm) glass coverslips (Marienfeld, 0117640) were cleaned with base piranha (Milli-Q water, 30% ammonium hydroxide, 35% hydrogen peroxide at a 5:1:1 volume ratio) for 15 min, rinsed with Milli-Q water for 2 × 5 min in a bath sonicator, sonicated in 70% ethanol for 5 min, and air-dried before coating with fibronectin (SIGMA F1141) for 2 h at room temperature (RT) and at a final fibronectin concentration of 20 μg/mL in PBS. For experiments with micropatterned substrates, medium-size (1100 μm 2 ) H-shaped patterns from CYTOO (10-900-00-18) were similarly coated with 20 μg/mL fibronectin. U2OS cells were seeded onto fibronectin-coated coverslips and allowed to spread for 5 h on micropatterned substrates or overnight on nonpatterned ones. Cells were fixed for 15 min with 4% formaldehyde (Electron Microscopy Sciences 15714) in cytoskeleton buffer (10 mM MES pH 6.1, 150 mM NaCl, 5 mM EGTA, 5 mM MgCl 2 , 5 mM glucose), washed for 2 × 5 min in PBS, then permeabilized and blocked in phosphate-buffered saline (PBS) containing 0.1% saponin and 10% bovine serum albumin (BSA) for 1 h at RT. Cells were incubated successively with primary rabbit anti-phospho-FAK antibodies at 1:200 (ThermoFisher Scientific 44-624G) and secondary donkey anti-rabbit Alexa Fluor 647-conjugated IgG secondary antibodies at 1:1000 (ThermoFisher Scientific A-31573) each for 1 h at RT and with three 10-min washes in-between antibody incubations. After five 6-min washes, cells were incubated with 0.5 μM Alexa Fluor 488 (AF488)-phalloidin (ThermoFisher Scientific A12379) in 0.1% saponin/10% BSA/PBS overnight at 4 °C in a humidified chamber. For 4polar-STORM measurements, coverslips with stained cells were mounted in an Attofluor cell chamber (ThermoFisher Scientific A7816) with freshly prepared STORM imaging buffer (see composition below) and the chamber covered with a glass coverslip to minimize contact with oxygen. To visualize focal adhesions in order to define the types of stress fibers measured, AF488-phalloidin and phospho-FAK-co-stained cells were imaged before each STORM acquisition on an optical setup employing a confocal spinning-disk unit (CSU-X1-M1 from Yokogawa) connected to the side-port of an inverted microscope (Eclipse Ti-U from Nikon Instruments), using a Nikon Plan Apo ×100/1.45 NA oil immersion objective lens, 488- and 641-nm laser lines (Coherent) and an iXon Ultra 888 EMCCD camera (1024 × 1024 pixels, 13 × 13 μm pixel size, Andor, Oxford Instruments). z-stacks were acquired with a Δz interval of 0.5 μm. B16-F1 cells 24 mm-diameter high-precision (170 μm ± 5 μm) glass coverslips (Marienfeld, 0117640) were sonicated in 70% ethanol for 5 min and air-dried before coating with mouse laminin (SIGMA L2020) for 1 h at RT and at a final laminin concentration of 25 μg/mL in coating buffer (50 mM Tris-HCl pH 8, 150 mM NaCl). B16-F1 cells were seeded onto laminin-coated coverslips and allowed to spread overnight. To stimulate lamellipodia formation, cells were treated with aluminum fluoride for 15 min by adding AlCl 3 and NaF to final concentrations of 50 μM and 30 mM, respectively, in prewarmed, full growth medium. Cells were fixed for 20 min with a mixture of prewarmed (37 °C) 0.25% glutaraldehyde (Electron Microscopy Sciences 16220) and 4% formaldehyde (Electron Microscopy Sciences 15714) in cytoskeleton buffer, and treated with fresh sodium borohydride (1 mg/mL) in PBS for 2 × 5 min to reduce background fluorescence. Cells were washed in PBS for 3 × 5 min before an overnight incubation with 0.5 μM AF488-phalloidin in 0.1% saponin/10% BSA/PBS at 4 °C in a humidified chamber. For 4polar-STORM measurements, coverslips were mounted as for U2OS cells.

Show full methods section

4polar-STORM optical setup

Measurements are carried out on a custom total internal reflection (TIRF) fluorescence microscope, whose detection path is adapted to retrieve four-polarization states of the single-molecule fluorescence images. The excitation light source is a continuous laser emitting at 488 nm (Sapphire 488LP-200, Coherent), whose beam is expanded by a telescope and polarized by a quarter waveplate (AQWP10M-580, Thorlabs) oriented such as to obtain close-to isotropic excitation in the sample plane. A set of mirrors reflect the beam towards the microscope, followed by a large focal length lens ( f = 400 mm) to focus the beam in the back focal plane of the objective, to provide an illumination field of view with a diameter of about 100 μm. After the reflection on a dichroic mirror (DI02-R488, Semrock Rochester NY), the excitation light is focused onto the sample by an oil immersion objective lens (Plan Apo ×100, NA = 1.45, Nikon). The emitted fluorescence is collected back by the same objective lens, passes through the dichroic mirror and a band pass emission filter (FF01-525/40, Semrock Rochester NY). At the microscope exit a non-polarizing beam splitter separates the beam into two paths, each of them being built up with a 1x relay imaging telescope that uses two (f 150 mm) lenses. In the first path, a Wollaston prism (separation angle 5°, CVI Laser Optics) is placed at the back focal intermediate image plane, aligned for 0–90° polarization split. In the second path, a similar Wollaston prism is placed just after an achromatic half-wave plate (AHWP05M-600, Thorlabs), to provide 45–135° polarized images. The two beams are recombined by a mirror reflection of the first path, and refocused on the EMCCD camera detection plane (iXon Ultra 888, Andor, 13 μm pixel size), such as to fill the CCD chip with four polarized images. The size of the images is set by a diaphragm placed in the first image plane at the exit of the microscope (typical image field of view, 40 μm × 40 μm). In addition, two diaphragms are placed in intermediate planes conjugated to the back focal plane of the objective in order to reduce the detection numerical aperture to NA det = 1.2. The imaging lens provides a total magnification of ×100, corresponding to a pixel size of 130 nm on the EMCCD. The stability of the focus throughout the measurement is ensured by a commercial system (Perfect Focus System, Nikon). For initial positionning, the sample is mounted on a XYZ piezo stage (Physik Instrumente). The acquisition parameters are controlled by a commercial imaging software (AndorSolis, Andor). For STORM imaging, a first fluorescence image is recorded with low intensity (~500 W/cm 2 , below STORM blinking conditions), ensuring the identification of relevant parts of the sample. The intensity is then raised to 5–8 kW/cm 2 , which is a typical level to provide a good compromise between signal level and blinking rate. The images are acquired at a rate of 100 ms/image, camera gain 300, with a total of about 30,000 images depending on the molecular density. The polarized path of the 4polar-STORM setup was calibrated as detailed in Supplementary Note 2 . We ensured that all directions in the sample plane could be detected with identical efficiency and precision by rotating a polarizer at the back focal plane of the collection objective, analyzing the emission from isolated nanobeads (100 nm size yellow-green Carboxylate-Modified FluoSpheres, ThermoFisher Scientific F8803, immobilized on the surface of a poly-L-lysine coated coverslip and covered with a mounting medium Fluoromount, Sigma F4680). On average, ρ values were pointed with a few degrees precision with respect to the expected polarizer direction, and δ values range from 20° to 33°. Cell culture 4polar-STORM measurements were made in U2OS osteosarcoma cells (Figs. 1 – 4 ) and B16-F1 mouse melanoma cells (Fig. 5 ). Naive U2OS cells (gift from Flavio Maina, IBDM, France) were used for assessing the effect of blebbistatin. U2OS CA-MLCK cells (gift from Sanjay Kumar, UC Berkeley, USA) cultured in 0 ng/mL doxycycline were used for all other experiments. U2OS cells were originally from ATCC (HBT-96). U2OS cells were maintained in McCoy’s 5 A medium (ThermoFisher Scientific, 26600-080) supplemented with 10% fetal bovine serum (Biowest, S181H), 100 U/mL penicillin and 100 μg/mL streptomycin (Sigma, P4333) in a humidified incubator at 37 °C and 5% CO2. B16-F1 cells (gift from Klemens Rottner, Technische Universität Braunschweig, Germany) were cultured in DMEM (ThermoFisher Scientific, 41966-029) supplemented with 10% fetal bovine serum (PAA Laboratories, A15-102), 100 U/mL penicillin and 100 μg/mL streptomycin (Sigma, P4333) in a humidified incubator at 37 °C and 5% CO2. B16-F1 cells were originally from ATCC (CRL-6323). Cell preparation for 4polar-STORM. U2OS cells 24 mm-diameter high-precision (170 μm ± 5 μm) glass coverslips (Marienfeld, 0117640) were cleaned with base piranha (Milli-Q water, 30% ammonium hydroxide, 35% hydrogen peroxide at a 5:1:1 volume ratio) for 15 min, rinsed with Milli-Q water for 2 × 5 min in a bath sonicator, sonicated in 70% ethanol for 5 min, and air-dried before coating with fibronectin (SIGMA F1141) for 2 h at room temperature (RT) and at a final fibronectin concentration of 20 μg/mL in PBS. For experiments with micropatterned substrates, medium-size (1100 μm 2 ) H-shaped patterns from CYTOO (10-900-00-18) were similarly coated with 20 μg/mL fibronectin. U2OS cells were seeded onto fibronectin-coated coverslips and allowed to spread for 5 h on micropatterned substrates or overnight on nonpatterned ones. Cells were fixed for 15 min with 4% formaldehyde (Electron Microscopy Sciences 15714) in cytoskeleton buffer (10 mM MES pH 6.1, 150 mM NaCl, 5 mM EGTA, 5 mM MgCl 2 , 5 mM glucose), washed for 2 × 5 min in PBS, then permeabilized and blocked in phosphate-buffered saline (PBS) containing 0.1% saponin and 10% bovine serum albumin (BSA) for 1 h at RT. Cells were incubated successively with primary rabbit anti-phospho-FAK antibodies at 1:200 (ThermoFisher Scientific 44-624G) and secondary donkey anti-rabbit Alexa Fluor 647-conjugated IgG secondary antibodies at 1:1000 (ThermoFisher Scientific A-31573) each for 1 h at RT and with three 10-min washes in-between antibody incubations. After five 6-min washes, cells were incubated with 0.5 μM Alexa Fluor 488 (AF488)-phalloidin (ThermoFisher Scientific A12379) in 0.1% saponin/10% BSA/PBS overnight at 4 °C in a humidified chamber. For 4polar-STORM measurements, coverslips with stained cells were mounted in an Attofluor cell chamber (ThermoFisher Scientific A7816) with freshly prepared STORM imaging buffer (see composition below) and the chamber covered with a glass coverslip to minimize contact with oxygen. To visualize focal adhesions in order to define the types of stress fibers measured, AF488-phalloidin and phospho-FAK-co-stained cells were imaged before each STORM acquisition on an optical setup employing a confocal spinning-disk unit (CSU-X1-M1 from Yokogawa) connected to the side-port of an inverted microscope (Eclipse Ti-U from Nikon Instruments), using a Nikon Plan Apo ×100/1.45 NA oil immersion objective lens, 488- and 641-nm laser lines (Coherent) and an iXon Ultra 888 EMCCD camera (1024 × 1024 pixels, 13 × 13 μm pixel size, Andor, Oxford Instruments). z-stacks were acquired with a Δz interval of 0.5 μm. B16-F1 cells 24 mm-diameter high-precision (170 μm ± 5 μm) glass coverslips (Marienfeld, 0117640) were sonicated in 70% ethanol for 5 min and air-dried before coating with mouse laminin (SIGMA L2020) for 1 h at RT and at a final laminin concentration of 25 μg/mL in coating buffer (50 mM Tris-HCl pH 8, 150 mM NaCl). B16-F1 cells were seeded onto laminin-coated coverslips and allowed to spread overnight. To stimulate lamellipodia formation, cells were treated with aluminum fluoride for 15 min by adding AlCl 3 and NaF to final concentrations of 50 μM and 30 mM, respectively, in prewarmed, full growth medium. Cells were fixed for 20 min with a mixture of prewarmed (37 °C) 0.25% glutaraldehyde (Electron Microscopy Sciences 16220) and 4% formaldehyde (Electron Microscopy Sciences 15714) in cytoskeleton buffer, and treated with fresh sodium borohydride (1 mg/mL) in PBS for 2 × 5 min to reduce background fluorescence. Cells were washed in PBS for 3 × 5 min before an overnight incubation with 0.5 μM AF488-phalloidin in 0.1% saponin/10% BSA/PBS at 4 °C in a humidified chamber. For 4polar-STORM measurements, coverslips were mounted as for U2OS cells.

Blebbistatin treatment

Blebbistatin from Sigma (B0560) was prepared at 10 mM in DMSO. U2OS cells were seeded onto fibronectin-coated medium-size H-shaped patterns from CYTOO and allowed to spread for 5 h, as detailed above. Cells were incubated for 15 min with 50 μM blebbistatin (i.e. in medium also containing 0.5% DMSO due to the blebbistatin stock dilution), or with medium containing 0.5% DMSO (control cells). Cells were fixed with 4% formaldehyde in cytoskeleton buffer for 15 min, and washed in PBS for 2 × 5 min before an overnight incubation with 0.5 μM AF488-phalloidin in 0.1% saponin/10% BSA/PBS at 4 °C in a humidified chamber. Cells were mounted for 4polar-STORM measurements as detailed above. Reconstitution of single actin filaments for 4polar-STORM Lyophilized rabbit skeletal muscle G-actin (Cytoskeleton, Inc. AKL99) was resuspended to 5 mg/mL (119 μM) in G-buffer (5 mM Tris-HCl pH 8, 0.2 mM Na 2 ATP, 0.1 mM CaCl 2 , 1 mM DTT), aliquots snap-frozen in liquid nitrogen and stored at −80 °C. Frozen aliquots were thawed and centrifuged for 30 min at 120,000 g in a benchtop Beckman air-driven ultracentrifuge (Beckman Coulter Airfuge, 340401) to clear the solution from aggregates. Clarified G-actin was kept at 4 °C and used within 3–4 weeks. For reconstitution experiments, G-actin was polymerized at 5 μM final concentration in actin polymerization buffer (5 mM Tris-HCl pH 8, 50 mM KCl, 1 mM MgCl 2 , 0.2 mM Na 2 ATP, 1 mM DTT) in the presence of 5 μM AF488-phalloidin for at least 2 h at RT. Flow cells for measurements on reconstituted actin filaments were prepared as follows. Microscope glass slides and coverslips were cleaned for 15 min in base-piranha solution, rinsed twice, 5 min each, with Milli-Q water in a bath sonicator, and stored in ethanol up to one month. To assemble flow cells, slides and coverslips were dried with synthetic air, and ~10 μL channels were assembled by sandwiching ~2-mm wide and ~2.5-cm-long strips of Parafilm between a cleaned glass slide and coverslip and melting on a hot plate at 120 °C. The chambers were incubated for 45 min with 1 M KOH, rinsed with actin polymerization buffer, incubated for another 15 min with 1 mg/mL poly-L-lysine (PLL; Sigma P8920), and rinsed with actin polymerization buffer. Reconstituted AF488-phalloidin-labeled actin filaments were diluted to 0.1–0.2 μM, loaded into the PLL-coated flow channels and left for 15 min to immobilize actin filaments. Actin polymerization buffer was then exchanged with STORM imaging buffer (see composition below), and flow channels sealed with VALAP (1:1:1 vasoline:lanoline:paraffin). The typical experimental conditions were TIRF illumination, laser power 150 mW, camera gain 300 and 200-ms integration time. A stack of 5000 images was used for 4polar-STORM imaging. The materials and chemicals for glass cleaning were as follows. Glass slides (26 × 76 mm) from Thermo Scientific (AA00000102E01FST20). Glass coverslips (24 × 60 mm) from Thermo Scientific (BB02400600A113FST0). Ammonium hydroxide solution from SIGMA (221228). Hydrogen peroxide solution from SIGMA (95299).

STORM imaging buffer preparation

The final composition of the buffer for 4polar-STORM measurements was 100 mM Tris-HCl pH 8, 10% w/v glucose, 5 U/mL pyranose oxidase (POD), 400 U/mL catalase, 50 mM β-mercaptoethylamine (β-MEA), 1 mM ascorbic acid, 1 mM methyl viologen, and 2 mM cyclooctatetraene (COT). D-(+)-glucose was from Fisher Chemical (G/0500/60). POD was from Sigma (P4234-250UN), bovine liver catalase from Calbiochem/Merck Millipore (219001-5MU), β-MEA from Sigma (30070), L-ascorbic acid from Sigma (A7506), methyl viologen from Sigma (856177), and COT from Sigma (138924). Glucose was stored as a 40% w/v solution at 4 °C. POD was dissolved in GOD buffer (24 mM PIPES pH 6.8, 4 mM MgCl 2 , 2 mM EGTA) to yield 400 U/mL, and an equal volume of glycerol was added to yield a final 200 U/mL in 1:1 glycerol:GOD buffer; aliquots were stored at −20 °C. Catalase was dissolved in GOD buffer to yield 10 mg/mL, and an equal volume of glycerol was added to yield a final 5 mg/mL (230 U/μL) of catalase in 1:1 glycerol:GOD buffer; aliquots were stored at −20 °C. β-MEA was stored as ~77 mg powder aliquots at −20 °C; right before use, an aliquot was dissolved with the appropriate amount of 360 mM HCl to yield a 1 M β-MEA solution. Ascorbic acid was always prepared right before use at 100 mM in water. Methyl viologen was stored as a 500 mM solution in water at 4 °C. COT was prepared at 200 mM in DMSO and aliquots stored at −20 °C. After mixing all components to yield the final buffer composition, the buffer was clarified by centrifugation for 2 min at 16,100 g, and the supernatant kept on ice for 15 min before use. Freshly prepared STORM buffer was typically used within a day.

Monte Carlo simulations

The single molecules’ images are generated from intensities that follow the model of Supplementary Note 1 . The starting parameters are the detection NA = 1.2, total intensity documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${I}_{T}={I}_{0}+{I}_{45}+{I}_{90}+{I}_{135}$$end{document} I T = I 0 + I 45 + I 90 + I 135 , (from 1000 to 10 000 photons), background pixel value (from 0 to 60 photons/pixel) and the angular (δ,ρ,η) parameters. This defines a set of intensities documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$({I}_{0},{I}_{45},{I}_{90},{I}_{135})$$end{document} ( I 0 , I 45 , I 90 , I 135 ) which are used for the generation of Gaussian point spread functions (PSF) to which noise is added using the model of Supplementary Fig. S4 . For each molecule centered at coordinates documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$left({i}_{n},{j}_{n}right)$$end{document} i n , j n , a 2D PSF shape is calculated as documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${I}_{{0,45,90,135}}left(i,jright)={I}_{{0,45,90,135}}left(delta ,rho ,eta right).{G}_{{ij}}left({i}_{n},{j}_{n},rright)+N({I}_{{0,45,90,135}})+b$$end{document} I 0 , 45 , 90 , 135 i , j = I 0 , 45 , 90 , 135 δ , ρ , η . G i j i n , j n , r + N ( I 0 , 45 , 90 , 135 ) + b with b the background/pixel value, and documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${G}_{{ij}}left({i}_{n},{j}_{n},r right)=1/ big(sqrt{pi }rbig).{{exp }}big(!-!{big(left(i-{i}_{n}right)}^{2}+{big(left(i-{i}_{n}right)}^{2}big)/{2r}^{2}big)$$end{document} G i j i n , j n , r = 1 / π r . exp − i − i n 2 + i − i n 2 / 2 r 2 the Gaussian 2D shape of radius r . N ( I ) is the noise added to the intensity I , which follows the experimental noise (see Supplementary Fig. S4 ). The detection parameters are identical to experimental ones (see Supplementary Note 2 ). Different settings can be used in this simulation such as total intensity, background level, PSF radius, calibration factors (see Supplementary Note 2 ), possibly PSF anisotropy along two orthogonal directions (in this case the Gaussian function is set with two different sizes r x and r y along x and y , respectively). In total, 500 to 1000 molecules with identical initial settings are typically generated, distributed in 5 to 10 molecules per images to simulate a 4polar-STORM detection process. The 4polar-STORM detection code is run on a set of 100 to 1000 images, following the procedure of Supplementary Note 3 . Reporting summary Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Supplementary information Supplementary Information Reporting Summary

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